공학석사학위 청구논문

工學碩士學位論文

Study on the Antecedent Runoff Condition in Seolma Cheon

Stream

2014년 2월

인하대학교 대학원

사회기반시스템공학부(토목공학전공)

이씨든

공학석사학위 청구논문

Study on the Antecedent Runoff Condition in Seolma Cheon

River Watershed

2014년 2월

지도교수 김 형 수

이 논문을 석사학위 논문으로 제출함

인하대학교 대학원

사회기반시스템공학부(토목공학전공)

이씨든

이 論文을 申鉉釋의

碩士學位 論文으로 認定함

2014년 2월

主番 983339

副番 983339

委員 983339

ABSTRACT

Curve number (CN) originally developed compiled by The Natural Resources Conservation

Service (NRCS)lsquo and has been widely used throughout the world However there is the

uncertainty of CN derived from the use of antecedent moisture condition (AMC)Antecedent

Runoff Condition (ARC) As in Korea where nearly 70 covered by mountainous area it is

still not sufficient handbook precedent to guide or support the estimation of AMCARC The

failure to develop formal criteria of applying AMC ARC will be a gaping profession and

results not only in uncertainty of CN estimation in particular but also in designing appropriate

structures in Korea as a whole This paper is aiming at presenting a critical review of

AMCARC and deriving a procedure to deal more realistically with event rainfall-runoff over

wider variety of initial conditions Proposed methods have been developed It is based on

modifying estimated runoff to observed runoff with coefficient of determination and then

applying different algebraic expression with the verification of AMC by antecedent rainfall

table of NEH-1964 Clearly indicated from 12 years period analysis and 2 years period of

verification normalized root mean square error RE and E are best described by the

application of algebraic expression by Arnold et al at the value of 08950 09460 and 00244

respectively for AMC condition and 13799 09642 and -00197 respectively for ARC

condition Therefore Arnold et al algebraic equation is the best representation criteria of

AMC and ARC This algebraic expression might be applied properly considering South Korea

condition

TABLE OF CONTENTS

Chapter I Introduction 1

11 Research Background 1

12 Literature Review 4

13 Outline of the Thesis 6

Chapter II Methodology 9

21 The Curve Number Method 9

211 SCS-CN based hydrological Models 12

22 Evaluation of the Curve Number Method 13

221 Procedures for determining the curve number 13

222 Asymptotic Method 15

223 Accuracy of procedures for determining the curve number 18

224 Seasonal variations of curve numbers 20

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition Review 21

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff Condition

application 23

232 ARC and AMC in continuous model (Soil Moisture Modeling) 25

24 Web-based Hydrograph Analysis Tool (WHAT) 28

241 Evaluation of the WHAT (Base flow Separation Method) 31

Chapter III Estimation of Antecedent Runoff ondition criteria for the Estimation of Curve

Number 32

31 Study basin 32

32 Analysis of hydrologic observation data 33

321 Limitation of data 33

322 Rainfall and runoff datasets used 34

3221 Base flow separation 36

33 Evaluation of curve number procedures 39

34 Reliability of Curve number method on Gauged Basins 47

35 Estimation of Thresholds for AMCARC 49

Chapter 4 Conclusions 61

REFERENCES 633

LIST OF FIGURES

Figure 1 1 Outline of the study 8

Figure 2 1 Standard Watershed response (from Hawkins 1993) 17

Figure 2 2 Violent Watershed response (from Hawkins 1993) 17

Figure 2 3 Procedure for the asymptotic determinationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

Figure 3 1 Seolma Cheon Examination Watershed 33

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

36

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011 38

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011 39

Figure 3 5 Schematic of Cure Number Estimation procedure 40

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed 44

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure 45

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

45

Figure 3 9 Coefficient of determination of each CN estimation procedures 48

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition proposed

Methodology 50

Figure 3 11 Schematic representation of AMCARC estimation criteria 51

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975) 52

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985) 54

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988) 56

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1988) 57

공학석사학위 청구논문

Study on the Antecedent Runoff Condition in Seolma Cheon

River Watershed

2014년 2월

지도교수 김 형 수

이 논문을 석사학위 논문으로 제출함

인하대학교 대학원

사회기반시스템공학부(토목공학전공)

이씨든

이 論文을 申鉉釋의

碩士學位 論文으로 認定함

2014년 2월

主番 983339

副番 983339

委員 983339

ABSTRACT

Curve number (CN) originally developed compiled by The Natural Resources Conservation

Service (NRCS)lsquo and has been widely used throughout the world However there is the

uncertainty of CN derived from the use of antecedent moisture condition (AMC)Antecedent

Runoff Condition (ARC) As in Korea where nearly 70 covered by mountainous area it is

still not sufficient handbook precedent to guide or support the estimation of AMCARC The

failure to develop formal criteria of applying AMC ARC will be a gaping profession and

results not only in uncertainty of CN estimation in particular but also in designing appropriate

structures in Korea as a whole This paper is aiming at presenting a critical review of

AMCARC and deriving a procedure to deal more realistically with event rainfall-runoff over

wider variety of initial conditions Proposed methods have been developed It is based on

modifying estimated runoff to observed runoff with coefficient of determination and then

applying different algebraic expression with the verification of AMC by antecedent rainfall

table of NEH-1964 Clearly indicated from 12 years period analysis and 2 years period of

verification normalized root mean square error RE and E are best described by the

application of algebraic expression by Arnold et al at the value of 08950 09460 and 00244

respectively for AMC condition and 13799 09642 and -00197 respectively for ARC

condition Therefore Arnold et al algebraic equation is the best representation criteria of

AMC and ARC This algebraic expression might be applied properly considering South Korea

condition

TABLE OF CONTENTS

Chapter I Introduction 1

11 Research Background 1

12 Literature Review 4

13 Outline of the Thesis 6

Chapter II Methodology 9

21 The Curve Number Method 9

211 SCS-CN based hydrological Models 12

22 Evaluation of the Curve Number Method 13

221 Procedures for determining the curve number 13

222 Asymptotic Method 15

223 Accuracy of procedures for determining the curve number 18

224 Seasonal variations of curve numbers 20

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition Review 21

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff Condition

application 23

232 ARC and AMC in continuous model (Soil Moisture Modeling) 25

24 Web-based Hydrograph Analysis Tool (WHAT) 28

241 Evaluation of the WHAT (Base flow Separation Method) 31

Chapter III Estimation of Antecedent Runoff ondition criteria for the Estimation of Curve

Number 32

31 Study basin 32

32 Analysis of hydrologic observation data 33

321 Limitation of data 33

322 Rainfall and runoff datasets used 34

3221 Base flow separation 36

33 Evaluation of curve number procedures 39

34 Reliability of Curve number method on Gauged Basins 47

35 Estimation of Thresholds for AMCARC 49

Chapter 4 Conclusions 61

REFERENCES 633

LIST OF FIGURES

Figure 1 1 Outline of the study 8

Figure 2 1 Standard Watershed response (from Hawkins 1993) 17

Figure 2 2 Violent Watershed response (from Hawkins 1993) 17

Figure 2 3 Procedure for the asymptotic determinationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

Figure 3 1 Seolma Cheon Examination Watershed 33

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

36

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011 38

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011 39

Figure 3 5 Schematic of Cure Number Estimation procedure 40

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed 44

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure 45

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

45

Figure 3 9 Coefficient of determination of each CN estimation procedures 48

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition proposed

Methodology 50

Figure 3 11 Schematic representation of AMCARC estimation criteria 51

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975) 52

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985) 54

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988) 56

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1988) 57

이 論文을 申鉉釋의

碩士學位 論文으로 認定함

2014년 2월

主番 983339

副番 983339

委員 983339

ABSTRACT

Curve number (CN) originally developed compiled by The Natural Resources Conservation

Service (NRCS)lsquo and has been widely used throughout the world However there is the

uncertainty of CN derived from the use of antecedent moisture condition (AMC)Antecedent

Runoff Condition (ARC) As in Korea where nearly 70 covered by mountainous area it is

still not sufficient handbook precedent to guide or support the estimation of AMCARC The

failure to develop formal criteria of applying AMC ARC will be a gaping profession and

results not only in uncertainty of CN estimation in particular but also in designing appropriate

structures in Korea as a whole This paper is aiming at presenting a critical review of

AMCARC and deriving a procedure to deal more realistically with event rainfall-runoff over

wider variety of initial conditions Proposed methods have been developed It is based on

modifying estimated runoff to observed runoff with coefficient of determination and then

applying different algebraic expression with the verification of AMC by antecedent rainfall

table of NEH-1964 Clearly indicated from 12 years period analysis and 2 years period of

verification normalized root mean square error RE and E are best described by the

application of algebraic expression by Arnold et al at the value of 08950 09460 and 00244

respectively for AMC condition and 13799 09642 and -00197 respectively for ARC

condition Therefore Arnold et al algebraic equation is the best representation criteria of

AMC and ARC This algebraic expression might be applied properly considering South Korea

condition

TABLE OF CONTENTS

Chapter I Introduction 1

11 Research Background 1

12 Literature Review 4

13 Outline of the Thesis 6

Chapter II Methodology 9

21 The Curve Number Method 9

211 SCS-CN based hydrological Models 12

22 Evaluation of the Curve Number Method 13

221 Procedures for determining the curve number 13

222 Asymptotic Method 15

223 Accuracy of procedures for determining the curve number 18

224 Seasonal variations of curve numbers 20

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition Review 21

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff Condition

application 23

232 ARC and AMC in continuous model (Soil Moisture Modeling) 25

24 Web-based Hydrograph Analysis Tool (WHAT) 28

241 Evaluation of the WHAT (Base flow Separation Method) 31

Chapter III Estimation of Antecedent Runoff ondition criteria for the Estimation of Curve

Number 32

31 Study basin 32

32 Analysis of hydrologic observation data 33

321 Limitation of data 33

322 Rainfall and runoff datasets used 34

3221 Base flow separation 36

33 Evaluation of curve number procedures 39

34 Reliability of Curve number method on Gauged Basins 47

35 Estimation of Thresholds for AMCARC 49

Chapter 4 Conclusions 61

REFERENCES 633

LIST OF FIGURES

Figure 1 1 Outline of the study 8

Figure 2 1 Standard Watershed response (from Hawkins 1993) 17

Figure 2 2 Violent Watershed response (from Hawkins 1993) 17

Figure 2 3 Procedure for the asymptotic determinationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

Figure 3 1 Seolma Cheon Examination Watershed 33

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

36

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011 38

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011 39

Figure 3 5 Schematic of Cure Number Estimation procedure 40

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed 44

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure 45

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

45

Figure 3 9 Coefficient of determination of each CN estimation procedures 48

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition proposed

Methodology 50

Figure 3 11 Schematic representation of AMCARC estimation criteria 51

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975) 52

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985) 54

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988) 56

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1988) 57

ABSTRACT

Curve number (CN) originally developed compiled by The Natural Resources Conservation

Service (NRCS)lsquo and has been widely used throughout the world However there is the

uncertainty of CN derived from the use of antecedent moisture condition (AMC)Antecedent

Runoff Condition (ARC) As in Korea where nearly 70 covered by mountainous area it is

still not sufficient handbook precedent to guide or support the estimation of AMCARC The

failure to develop formal criteria of applying AMC ARC will be a gaping profession and

results not only in uncertainty of CN estimation in particular but also in designing appropriate

structures in Korea as a whole This paper is aiming at presenting a critical review of

AMCARC and deriving a procedure to deal more realistically with event rainfall-runoff over

wider variety of initial conditions Proposed methods have been developed It is based on

modifying estimated runoff to observed runoff with coefficient of determination and then

applying different algebraic expression with the verification of AMC by antecedent rainfall

table of NEH-1964 Clearly indicated from 12 years period analysis and 2 years period of

verification normalized root mean square error RE and E are best described by the

application of algebraic expression by Arnold et al at the value of 08950 09460 and 00244

respectively for AMC condition and 13799 09642 and -00197 respectively for ARC

condition Therefore Arnold et al algebraic equation is the best representation criteria of

AMC and ARC This algebraic expression might be applied properly considering South Korea

condition

TABLE OF CONTENTS

Chapter I Introduction 1

11 Research Background 1

12 Literature Review 4

13 Outline of the Thesis 6

Chapter II Methodology 9

21 The Curve Number Method 9

211 SCS-CN based hydrological Models 12

22 Evaluation of the Curve Number Method 13

221 Procedures for determining the curve number 13

222 Asymptotic Method 15

223 Accuracy of procedures for determining the curve number 18

224 Seasonal variations of curve numbers 20

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition Review 21

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff Condition

application 23

232 ARC and AMC in continuous model (Soil Moisture Modeling) 25

24 Web-based Hydrograph Analysis Tool (WHAT) 28

241 Evaluation of the WHAT (Base flow Separation Method) 31

Chapter III Estimation of Antecedent Runoff ondition criteria for the Estimation of Curve

Number 32

31 Study basin 32

32 Analysis of hydrologic observation data 33

321 Limitation of data 33

322 Rainfall and runoff datasets used 34

3221 Base flow separation 36

33 Evaluation of curve number procedures 39

34 Reliability of Curve number method on Gauged Basins 47

35 Estimation of Thresholds for AMCARC 49

Chapter 4 Conclusions 61

REFERENCES 633

LIST OF FIGURES

Figure 1 1 Outline of the study 8

Figure 2 1 Standard Watershed response (from Hawkins 1993) 17

Figure 2 2 Violent Watershed response (from Hawkins 1993) 17

Figure 2 3 Procedure for the asymptotic determinationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

Figure 3 1 Seolma Cheon Examination Watershed 33

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

36

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011 38

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011 39

Figure 3 5 Schematic of Cure Number Estimation procedure 40

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed 44

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure 45

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

45

Figure 3 9 Coefficient of determination of each CN estimation procedures 48

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition proposed

Methodology 50

Figure 3 11 Schematic representation of AMCARC estimation criteria 51

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975) 52

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985) 54

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988) 56

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1988) 57

TABLE OF CONTENTS

Chapter I Introduction 1

11 Research Background 1

12 Literature Review 4

13 Outline of the Thesis 6

Chapter II Methodology 9

21 The Curve Number Method 9

211 SCS-CN based hydrological Models 12

22 Evaluation of the Curve Number Method 13

221 Procedures for determining the curve number 13

222 Asymptotic Method 15

223 Accuracy of procedures for determining the curve number 18

224 Seasonal variations of curve numbers 20

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition Review 21

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff Condition

application 23

232 ARC and AMC in continuous model (Soil Moisture Modeling) 25

24 Web-based Hydrograph Analysis Tool (WHAT) 28

241 Evaluation of the WHAT (Base flow Separation Method) 31

Chapter III Estimation of Antecedent Runoff ondition criteria for the Estimation of Curve

Number 32

31 Study basin 32

32 Analysis of hydrologic observation data 33

321 Limitation of data 33

322 Rainfall and runoff datasets used 34

3221 Base flow separation 36

33 Evaluation of curve number procedures 39

34 Reliability of Curve number method on Gauged Basins 47

35 Estimation of Thresholds for AMCARC 49

Chapter 4 Conclusions 61

REFERENCES 633

LIST OF FIGURES

Figure 1 1 Outline of the study 8

Figure 2 1 Standard Watershed response (from Hawkins 1993) 17

Figure 2 2 Violent Watershed response (from Hawkins 1993) 17

Figure 2 3 Procedure for the asymptotic determinationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

Figure 3 1 Seolma Cheon Examination Watershed 33

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

36

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011 38

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011 39

Figure 3 5 Schematic of Cure Number Estimation procedure 40

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed 44

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure 45

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

45

Figure 3 9 Coefficient of determination of each CN estimation procedures 48

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition proposed

Methodology 50

Figure 3 11 Schematic representation of AMCARC estimation criteria 51

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975) 52

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985) 54

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988) 56

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1988) 57

241 Evaluation of the WHAT (Base flow Separation Method) 31

Chapter III Estimation of Antecedent Runoff ondition criteria for the Estimation of Curve

Number 32

31 Study basin 32

32 Analysis of hydrologic observation data 33

321 Limitation of data 33

322 Rainfall and runoff datasets used 34

3221 Base flow separation 36

33 Evaluation of curve number procedures 39

34 Reliability of Curve number method on Gauged Basins 47

35 Estimation of Thresholds for AMCARC 49

Chapter 4 Conclusions 61

REFERENCES 633

LIST OF FIGURES

Figure 1 1 Outline of the study 8

Figure 2 1 Standard Watershed response (from Hawkins 1993) 17

Figure 2 2 Violent Watershed response (from Hawkins 1993) 17

Figure 2 3 Procedure for the asymptotic determinationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

Figure 3 1 Seolma Cheon Examination Watershed 33

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

36

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011 38

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011 39

Figure 3 5 Schematic of Cure Number Estimation procedure 40

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed 44

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure 45

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

45

Figure 3 9 Coefficient of determination of each CN estimation procedures 48

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition proposed

Methodology 50

Figure 3 11 Schematic representation of AMCARC estimation criteria 51

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975) 52

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985) 54

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988) 56

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1988) 57

LIST OF FIGURES

Figure 1 1 Outline of the study 8

Figure 2 1 Standard Watershed response (from Hawkins 1993) 17

Figure 2 2 Violent Watershed response (from Hawkins 1993) 17

Figure 2 3 Procedure for the asymptotic determinationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

Figure 3 1 Seolma Cheon Examination Watershed 33

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

36

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011 38

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011 39

Figure 3 5 Schematic of Cure Number Estimation procedure 40

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed 44

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure 45

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

45

Figure 3 9 Coefficient of determination of each CN estimation procedures 48

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition proposed

Methodology 50

Figure 3 11 Schematic representation of AMCARC estimation criteria 51

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975) 52

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985) 54

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988) 56

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1988) 57

LIST OF TABLES

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)helliphelliphelliphelliphelliphelliphelliphelliphellip 24

Table 3 1 CN of examination basin 34

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

40

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011 46

Table 3 4 Overall Watershed Curve Number by all Procedures 46

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression 53

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression 54

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression 56

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression 58

Table 3 9 Result of all coefficient of determination 59

CHAPTER I INTRODUCTION

11 Research Background

The hydrologic methods developed by the Natural Resources Conservation Service (NRCS

formerly the Soil Conservation Service (SCS) were originally developed as agency

procedures and did not undergo journal review procedures (Ponce and Hawkins 1996) The

only official source documentation is the NRCSlsquos National Engineering Handbook Section 4

(NEH-4) Unfortunately NEH-4 has gone through several revisions (1956 1964 1965 1969

1972 1985 and 1993) since first being published in 1954 The numerous revisions have

resulted in confusion by people who use the methods (Hjelmfelt 1991)

The accuracy of the Curve Number Method has not been thoroughly determined (Ponce and

Hawkins 1996 McCutcheon et al 2006) and empirical evidence suggests that with the current

NRCS (2001) curve number table hydrologic infrastructure is being over-designed by billions

of dollars annually (Schneider and McCuen 2005) Furthermore SCS-CN main weak points

are including it does not consider the impact of rainfall intensity and its temporal distribution

it does not address the effects of spatial scale it is highly sensitive to changes in values of its

sole parameter and it does not address clearly the effect of adjacent moisture condition

(Hawkins 1993 Ponce and Hawkins 1996 Michel et al 2005) In addition to that use of

the Curve Number Method to simulate runoff volume from forested watersheds would likely

result in an inaccurate estimate of runoff volume from a given volume of rainfall (Ponce and

Hawkins 1996 McCutcheon 2003 Garen and Moore 2005 Schneider and McCuen 2005

Michel et al 2005 McCutcheon et al 2006)

The methodlsquos credibility and acceptance has suffered however due to its origin as agency

methodology which effectively isolated from the rigors of peer review Other than the

information contained in NEH-4 which was not intended to be exhaustive (Rallison and

Cronshey 1979) no complete account of methodlsquos foundations is available to date despite

some recent noteworthy attempts (Rallison 1980 Chen 1982 Miller and Cronshey 1989)

In the four decade that has elapsed since the methodlsquos inception the increased availability of

computers has led to the use of complex hydrologic models many of which incorporate the

curve number method Thus the questions naturally arise what is the status of the curve

number method in a postulated hierarchy of hydrologic abstraction models (Miller and

Cronshey 1989 Rallison and Miller 1982)

In practice hydraulic engineer frequently use the curve number procedure of the US Soil

Conservation Service (SCS) to compute in these small to medium-sized ungagged basins

probably due to its apparent simplicity Runoff estimates are based upon the soil types land-

use practices within a basin and the influence of the antecedent soil moisture conditions for a

specific storm

An effective overhaul of the method would require a clearer understanding of its properties

than is currently available (Woodward 1991 Woodward and Gburek 1992)

Far too many water resource professionals have accepted the CN methods without

independently reviewing extensive real hydrologic data One example is the concept of the

Antecedent Moisture Condition (AMC) When the CN was originally developed it was well

known that soil moisture played a significant role on the infiltration capacity of a soil

Therefore instead of trying to determine or predict soil moisture the NRCS decided to

account for the soil moisture using the amount of rainfall received in the five days preceding

the storm event of interest The NRCS defined this 5-day measurement as the antecedent

moisture condition (AMC) (now called the antecedent runoff condition (ARC)) However

Hope and Schulze (1982) noted in a personal communication with N Miller that the use of a

5-day index for ARC was not based on physical reality but rather on subjective judgment

As one can observe even for these larger rainfall and runoff events the AMC exhibits a large

degree of scatter Additionally researchers have been unable to validate the NRCS 5-day

index method Nonetheless the concept still is frequently used by researchers and practitioners

However many leading researchers consider the AMC to represent the variation in runoff

volume (Q) from all sources such as model and data error intensity seasonal cover and site

moisture In this context the AMC and ARC represents nothing more than error bands

The rainfall runoff transformation is a nonlinear process The most important cause of non-

linearity represented by the effect of antecedent conditions consequently the runoff

coefficient depends on the initial conditions It is well known that soil moisture is a major

control on the catchment response antecedent moisture conditions have been used to

represent variability of the CN in the SCS method for predicting direct runoff (eg Rallison

and Miller 1981) But soil moisture measurements are usually not widely available and a lot

of point measurements are needed to get either an average or an antecedent catchment state

Antecedent moisture conditions can be simulated using models (either lumped or distributed)

provided standard climate data are available Alternatively some other easily measured

hydrological variable that are even if only approximately related to soil moisture conditions

may be considered

One of the several problems (Ponce and Hawkins 1996 King et al 1999) is that the Method

does not contain any expression for time and as a result ignores the

impact of rainfall intensity as well as antecedent runoff condition So far there is no

concrete guidebook for estimating the antecedent runoff conditions More importantly the

procedure to identify the ARC has been applied within the US soil condition and for decades

for mountainous topographical area like South Korea there will be encountered the variation

and bias Misestimating the runoff depth will lead to the failure in design structure

consequently there will dramatically damage ranging from capital loss to human loss Also

driving force of economic development will be getting down unavoidable

It is apparent that the CN-variability is primarily attributed to the antecedent moisture and it

has led to statistical and stochastic considerations of the curve number undermining the

physical basis of the SCS-CN methodology Furthermore incorporation of the antecedent

moisture in the existing SCS-CN method in the terms of the three AMC levels allows

unreasonable sudden jumps in the CN variation Therefore the determination of the

antecedent moisture condition plays an important role in selecting the appropriate CN value

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

This objective of this paper is to present a critical review of antecedent runoff condition ARC

and derive a procedure to deal more realistically with event rainfall-runoff over wider variety

of initial conditions

12 Literature Review

It is well known that soil moisture is a major control on catchment response antecedent soil

moisture conditions have been used to represent variability of the CN in the SCS method for

predicting direct runoff (eg Rallison and Miller 1981) But soil moisture measurements are

usually not widely available and a lot of point measurements are needed to get either an

average or an antecedent catchment state Antecedent soil moisture conditions can be

simulated using models (either lumped or distributed) provided standard climate data are

available

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

The NRCS (2001) Curve Number Method is widely used for estimating watershed runoff

from rainfall in engineering design (Jacobs et al 2003) The extensive use of the curve

number technique follows from the simplicity that lumps the complexity of runoff generation

into a single watershed parameter the maximum potential retention S that is easily converted

mathematically to a curve number CN (Nachabe and Morel-Seytoux 2005) However the

simplicity of a single lumped parameter introduces great uncertainty to estimates of runoff

Ponce and Hawkins (1996) attribute the ambiguity of the Method to several characteristics

including (Jacobs et al 2003) Use of arbitrarily limited measures of watershed

characteristics lumped into the single parameter the maximum potential retention S Lack of

peer reviewed justification and explanation of the simplified procedures necessary to

consistently determine runoff for engineering design and significant agency support

manifested as publication in the National Engineering Handbook (NRCS 2001)

Despite the limitations the NRCS (2001) Curve Number Method is used to (1) estimate

runoff from ungaged watersheds (2) evaluate the effect of changes in land use and treatment

on direct runoff and (3) parameterize rainfall-runoff relationships in watershed simulation

models

Proper CN estimates are needed to accurately evaluate water availability and close the water

budget of agriculture fields Careful measurements of runoff volume are needed to

systematically evaluate the role of key variables such as rainfall intensity soil moisture

condition tillage practice and land cover on CN values (SUDAS 2004)

13 Outline of the Thesis

This thesis consists of 4 chapters

Chapter 1 it will present the general introduction and significance of study briefly but

concisely about the antecedent runoff conditions which is practically applied in South Korea

as a case of study

Chapter 2 present an overview of previous work related to the study topic that serve as the

necessity of background for the purpose of this research Relevant and previous literature

reviews prevail the SCS curve number and general assumptions Also present the

methodology and some practical tactics to determine AMC and its critical thinking of this

application and figure out effective practice for further usage in South Korea in particular

Chapter 3 demonstrate the results and discuss the finding

Chapter 4 Conclusion

The figure 11 indicates the process of research Firstly direct runoff is necessary to be

separated from total runoff By applying base flow separation known as Web Based

Hydrograph Tools (WHAT) the base flow and direct runoff can be separated The data are

derived from the examinational rainfall station After identifying direct runoff from total

runoff curve number estimation can be calculated from equation 7 by knowing daily rainfall

and matched direct runoff However further consideration is necessary to take into account

That is to test the accuracy of curve number To test the accuracy of curve number

determination curve numbers are computed depending upon four different procedures

including arithmetic mean median geometric mean and asymptotic fit Except for the

asymptotic method unranked paired rainfall and runoff volumes from the maximum peal flow

event each year of record were used to compute the calibrated curve number After the curve

number is estimated the next step is to simulate antecedent moisture condition by applying all

the proposed algebraic expression of NEH4 with the consideration of 5 day prior to rainfall

(definition of AMC using antecedent rainfall table) Next is to validate and calibrate among

the proposed procedure to figure out the estimator of antecedent moisture condition criteria

Check evaluation of curve

number procedures

(NRMSE RE R2 NSE)

1st Proposed Method 2nd Proposed Method

Algebraic expression of NEH4

( developed Sobhani (1975) Chow

et al (1988) Hawkins et al (1985)

Arnold et al (1988)

Making AMCARC Estimation

Criteria

Data collection (Rainfall and

Runoff data)

Derive direct runoff ( by Web

Based Hydrograph Tools

WHAT)

Curve Number Estimation

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Definition of AMCARC

(NEH-4 1964)

Average conditions (NEH-4

1964)

Median curve number

(NEH-4 1964)

Antecedent rainfall table

(NEH-4 1964)

Comparison within

definitions

Determination of

AMCARC estimation

criteria

Comparison of AMCARC

Result of AMCARC

estimation criteria

Figure 1 1 Outline of the study

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

CHAPTER I INTRODUCTION

11 Research Background

The hydrologic methods developed by the Natural Resources Conservation Service (NRCS

formerly the Soil Conservation Service (SCS) were originally developed as agency

procedures and did not undergo journal review procedures (Ponce and Hawkins 1996) The

only official source documentation is the NRCSlsquos National Engineering Handbook Section 4

(NEH-4) Unfortunately NEH-4 has gone through several revisions (1956 1964 1965 1969

1972 1985 and 1993) since first being published in 1954 The numerous revisions have

resulted in confusion by people who use the methods (Hjelmfelt 1991)

The accuracy of the Curve Number Method has not been thoroughly determined (Ponce and

Hawkins 1996 McCutcheon et al 2006) and empirical evidence suggests that with the current

NRCS (2001) curve number table hydrologic infrastructure is being over-designed by billions

of dollars annually (Schneider and McCuen 2005) Furthermore SCS-CN main weak points

are including it does not consider the impact of rainfall intensity and its temporal distribution

it does not address the effects of spatial scale it is highly sensitive to changes in values of its

sole parameter and it does not address clearly the effect of adjacent moisture condition

(Hawkins 1993 Ponce and Hawkins 1996 Michel et al 2005) In addition to that use of

the Curve Number Method to simulate runoff volume from forested watersheds would likely

result in an inaccurate estimate of runoff volume from a given volume of rainfall (Ponce and

Hawkins 1996 McCutcheon 2003 Garen and Moore 2005 Schneider and McCuen 2005

Michel et al 2005 McCutcheon et al 2006)

The methodlsquos credibility and acceptance has suffered however due to its origin as agency

methodology which effectively isolated from the rigors of peer review Other than the

information contained in NEH-4 which was not intended to be exhaustive (Rallison and

Cronshey 1979) no complete account of methodlsquos foundations is available to date despite

some recent noteworthy attempts (Rallison 1980 Chen 1982 Miller and Cronshey 1989)

In the four decade that has elapsed since the methodlsquos inception the increased availability of

computers has led to the use of complex hydrologic models many of which incorporate the

curve number method Thus the questions naturally arise what is the status of the curve

number method in a postulated hierarchy of hydrologic abstraction models (Miller and

Cronshey 1989 Rallison and Miller 1982)

In practice hydraulic engineer frequently use the curve number procedure of the US Soil

Conservation Service (SCS) to compute in these small to medium-sized ungagged basins

probably due to its apparent simplicity Runoff estimates are based upon the soil types land-

use practices within a basin and the influence of the antecedent soil moisture conditions for a

specific storm

An effective overhaul of the method would require a clearer understanding of its properties

than is currently available (Woodward 1991 Woodward and Gburek 1992)

Far too many water resource professionals have accepted the CN methods without

independently reviewing extensive real hydrologic data One example is the concept of the

Antecedent Moisture Condition (AMC) When the CN was originally developed it was well

known that soil moisture played a significant role on the infiltration capacity of a soil

Therefore instead of trying to determine or predict soil moisture the NRCS decided to

account for the soil moisture using the amount of rainfall received in the five days preceding

the storm event of interest The NRCS defined this 5-day measurement as the antecedent

moisture condition (AMC) (now called the antecedent runoff condition (ARC)) However

Hope and Schulze (1982) noted in a personal communication with N Miller that the use of a

5-day index for ARC was not based on physical reality but rather on subjective judgment

As one can observe even for these larger rainfall and runoff events the AMC exhibits a large

degree of scatter Additionally researchers have been unable to validate the NRCS 5-day

index method Nonetheless the concept still is frequently used by researchers and practitioners

However many leading researchers consider the AMC to represent the variation in runoff

volume (Q) from all sources such as model and data error intensity seasonal cover and site

moisture In this context the AMC and ARC represents nothing more than error bands

The rainfall runoff transformation is a nonlinear process The most important cause of non-

linearity represented by the effect of antecedent conditions consequently the runoff

coefficient depends on the initial conditions It is well known that soil moisture is a major

control on the catchment response antecedent moisture conditions have been used to

represent variability of the CN in the SCS method for predicting direct runoff (eg Rallison

and Miller 1981) But soil moisture measurements are usually not widely available and a lot

of point measurements are needed to get either an average or an antecedent catchment state

Antecedent moisture conditions can be simulated using models (either lumped or distributed)

provided standard climate data are available Alternatively some other easily measured

hydrological variable that are even if only approximately related to soil moisture conditions

may be considered

One of the several problems (Ponce and Hawkins 1996 King et al 1999) is that the Method

does not contain any expression for time and as a result ignores the

impact of rainfall intensity as well as antecedent runoff condition So far there is no

concrete guidebook for estimating the antecedent runoff conditions More importantly the

procedure to identify the ARC has been applied within the US soil condition and for decades

for mountainous topographical area like South Korea there will be encountered the variation

and bias Misestimating the runoff depth will lead to the failure in design structure

consequently there will dramatically damage ranging from capital loss to human loss Also

driving force of economic development will be getting down unavoidable

It is apparent that the CN-variability is primarily attributed to the antecedent moisture and it

has led to statistical and stochastic considerations of the curve number undermining the

physical basis of the SCS-CN methodology Furthermore incorporation of the antecedent

moisture in the existing SCS-CN method in the terms of the three AMC levels allows

unreasonable sudden jumps in the CN variation Therefore the determination of the

antecedent moisture condition plays an important role in selecting the appropriate CN value

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

This objective of this paper is to present a critical review of antecedent runoff condition ARC

and derive a procedure to deal more realistically with event rainfall-runoff over wider variety

of initial conditions

12 Literature Review

It is well known that soil moisture is a major control on catchment response antecedent soil

moisture conditions have been used to represent variability of the CN in the SCS method for

predicting direct runoff (eg Rallison and Miller 1981) But soil moisture measurements are

usually not widely available and a lot of point measurements are needed to get either an

average or an antecedent catchment state Antecedent soil moisture conditions can be

simulated using models (either lumped or distributed) provided standard climate data are

available

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

The NRCS (2001) Curve Number Method is widely used for estimating watershed runoff

from rainfall in engineering design (Jacobs et al 2003) The extensive use of the curve

number technique follows from the simplicity that lumps the complexity of runoff generation

into a single watershed parameter the maximum potential retention S that is easily converted

mathematically to a curve number CN (Nachabe and Morel-Seytoux 2005) However the

simplicity of a single lumped parameter introduces great uncertainty to estimates of runoff

Ponce and Hawkins (1996) attribute the ambiguity of the Method to several characteristics

including (Jacobs et al 2003) Use of arbitrarily limited measures of watershed

characteristics lumped into the single parameter the maximum potential retention S Lack of

peer reviewed justification and explanation of the simplified procedures necessary to

consistently determine runoff for engineering design and significant agency support

manifested as publication in the National Engineering Handbook (NRCS 2001)

Despite the limitations the NRCS (2001) Curve Number Method is used to (1) estimate

runoff from ungaged watersheds (2) evaluate the effect of changes in land use and treatment

on direct runoff and (3) parameterize rainfall-runoff relationships in watershed simulation

models

Proper CN estimates are needed to accurately evaluate water availability and close the water

budget of agriculture fields Careful measurements of runoff volume are needed to

systematically evaluate the role of key variables such as rainfall intensity soil moisture

condition tillage practice and land cover on CN values (SUDAS 2004)

13 Outline of the Thesis

This thesis consists of 4 chapters

Chapter 1 it will present the general introduction and significance of study briefly but

concisely about the antecedent runoff conditions which is practically applied in South Korea

as a case of study

Chapter 2 present an overview of previous work related to the study topic that serve as the

necessity of background for the purpose of this research Relevant and previous literature

reviews prevail the SCS curve number and general assumptions Also present the

methodology and some practical tactics to determine AMC and its critical thinking of this

application and figure out effective practice for further usage in South Korea in particular

Chapter 3 demonstrate the results and discuss the finding

Chapter 4 Conclusion

The figure 11 indicates the process of research Firstly direct runoff is necessary to be

separated from total runoff By applying base flow separation known as Web Based

Hydrograph Tools (WHAT) the base flow and direct runoff can be separated The data are

derived from the examinational rainfall station After identifying direct runoff from total

runoff curve number estimation can be calculated from equation 7 by knowing daily rainfall

and matched direct runoff However further consideration is necessary to take into account

That is to test the accuracy of curve number To test the accuracy of curve number

determination curve numbers are computed depending upon four different procedures

including arithmetic mean median geometric mean and asymptotic fit Except for the

asymptotic method unranked paired rainfall and runoff volumes from the maximum peal flow

event each year of record were used to compute the calibrated curve number After the curve

number is estimated the next step is to simulate antecedent moisture condition by applying all

the proposed algebraic expression of NEH4 with the consideration of 5 day prior to rainfall

(definition of AMC using antecedent rainfall table) Next is to validate and calibrate among

the proposed procedure to figure out the estimator of antecedent moisture condition criteria

Check evaluation of curve

number procedures

(NRMSE RE R2 NSE)

1st Proposed Method 2nd Proposed Method

Algebraic expression of NEH4

( developed Sobhani (1975) Chow

et al (1988) Hawkins et al (1985)

Arnold et al (1988)

Making AMCARC Estimation

Criteria

Data collection (Rainfall and

Runoff data)

Derive direct runoff ( by Web

Based Hydrograph Tools

WHAT)

Curve Number Estimation

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Definition of AMCARC

(NEH-4 1964)

Average conditions (NEH-4

1964)

Median curve number

(NEH-4 1964)

Antecedent rainfall table

(NEH-4 1964)

Comparison within

definitions

Determination of

AMCARC estimation

criteria

Comparison of AMCARC

Result of AMCARC

estimation criteria

Figure 1 1 Outline of the study

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

Cronshey 1979) no complete account of methodlsquos foundations is available to date despite

some recent noteworthy attempts (Rallison 1980 Chen 1982 Miller and Cronshey 1989)

In the four decade that has elapsed since the methodlsquos inception the increased availability of

computers has led to the use of complex hydrologic models many of which incorporate the

curve number method Thus the questions naturally arise what is the status of the curve

number method in a postulated hierarchy of hydrologic abstraction models (Miller and

Cronshey 1989 Rallison and Miller 1982)

In practice hydraulic engineer frequently use the curve number procedure of the US Soil

Conservation Service (SCS) to compute in these small to medium-sized ungagged basins

probably due to its apparent simplicity Runoff estimates are based upon the soil types land-

use practices within a basin and the influence of the antecedent soil moisture conditions for a

specific storm

An effective overhaul of the method would require a clearer understanding of its properties

than is currently available (Woodward 1991 Woodward and Gburek 1992)

Far too many water resource professionals have accepted the CN methods without

independently reviewing extensive real hydrologic data One example is the concept of the

Antecedent Moisture Condition (AMC) When the CN was originally developed it was well

known that soil moisture played a significant role on the infiltration capacity of a soil

Therefore instead of trying to determine or predict soil moisture the NRCS decided to

account for the soil moisture using the amount of rainfall received in the five days preceding

the storm event of interest The NRCS defined this 5-day measurement as the antecedent

moisture condition (AMC) (now called the antecedent runoff condition (ARC)) However

Hope and Schulze (1982) noted in a personal communication with N Miller that the use of a

5-day index for ARC was not based on physical reality but rather on subjective judgment

As one can observe even for these larger rainfall and runoff events the AMC exhibits a large

degree of scatter Additionally researchers have been unable to validate the NRCS 5-day

index method Nonetheless the concept still is frequently used by researchers and practitioners

However many leading researchers consider the AMC to represent the variation in runoff

volume (Q) from all sources such as model and data error intensity seasonal cover and site

moisture In this context the AMC and ARC represents nothing more than error bands

The rainfall runoff transformation is a nonlinear process The most important cause of non-

linearity represented by the effect of antecedent conditions consequently the runoff

coefficient depends on the initial conditions It is well known that soil moisture is a major

control on the catchment response antecedent moisture conditions have been used to

represent variability of the CN in the SCS method for predicting direct runoff (eg Rallison

and Miller 1981) But soil moisture measurements are usually not widely available and a lot

of point measurements are needed to get either an average or an antecedent catchment state

Antecedent moisture conditions can be simulated using models (either lumped or distributed)

provided standard climate data are available Alternatively some other easily measured

hydrological variable that are even if only approximately related to soil moisture conditions

may be considered

One of the several problems (Ponce and Hawkins 1996 King et al 1999) is that the Method

does not contain any expression for time and as a result ignores the

impact of rainfall intensity as well as antecedent runoff condition So far there is no

concrete guidebook for estimating the antecedent runoff conditions More importantly the

procedure to identify the ARC has been applied within the US soil condition and for decades

for mountainous topographical area like South Korea there will be encountered the variation

and bias Misestimating the runoff depth will lead to the failure in design structure

consequently there will dramatically damage ranging from capital loss to human loss Also

driving force of economic development will be getting down unavoidable

It is apparent that the CN-variability is primarily attributed to the antecedent moisture and it

has led to statistical and stochastic considerations of the curve number undermining the

physical basis of the SCS-CN methodology Furthermore incorporation of the antecedent

moisture in the existing SCS-CN method in the terms of the three AMC levels allows

unreasonable sudden jumps in the CN variation Therefore the determination of the

antecedent moisture condition plays an important role in selecting the appropriate CN value

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

This objective of this paper is to present a critical review of antecedent runoff condition ARC

and derive a procedure to deal more realistically with event rainfall-runoff over wider variety

of initial conditions

12 Literature Review

It is well known that soil moisture is a major control on catchment response antecedent soil

moisture conditions have been used to represent variability of the CN in the SCS method for

predicting direct runoff (eg Rallison and Miller 1981) But soil moisture measurements are

usually not widely available and a lot of point measurements are needed to get either an

average or an antecedent catchment state Antecedent soil moisture conditions can be

simulated using models (either lumped or distributed) provided standard climate data are

available

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

The NRCS (2001) Curve Number Method is widely used for estimating watershed runoff

from rainfall in engineering design (Jacobs et al 2003) The extensive use of the curve

number technique follows from the simplicity that lumps the complexity of runoff generation

into a single watershed parameter the maximum potential retention S that is easily converted

mathematically to a curve number CN (Nachabe and Morel-Seytoux 2005) However the

simplicity of a single lumped parameter introduces great uncertainty to estimates of runoff

Ponce and Hawkins (1996) attribute the ambiguity of the Method to several characteristics

including (Jacobs et al 2003) Use of arbitrarily limited measures of watershed

characteristics lumped into the single parameter the maximum potential retention S Lack of

peer reviewed justification and explanation of the simplified procedures necessary to

consistently determine runoff for engineering design and significant agency support

manifested as publication in the National Engineering Handbook (NRCS 2001)

Despite the limitations the NRCS (2001) Curve Number Method is used to (1) estimate

runoff from ungaged watersheds (2) evaluate the effect of changes in land use and treatment

on direct runoff and (3) parameterize rainfall-runoff relationships in watershed simulation

models

Proper CN estimates are needed to accurately evaluate water availability and close the water

budget of agriculture fields Careful measurements of runoff volume are needed to

systematically evaluate the role of key variables such as rainfall intensity soil moisture

condition tillage practice and land cover on CN values (SUDAS 2004)

13 Outline of the Thesis

This thesis consists of 4 chapters

Chapter 1 it will present the general introduction and significance of study briefly but

concisely about the antecedent runoff conditions which is practically applied in South Korea

as a case of study

Chapter 2 present an overview of previous work related to the study topic that serve as the

necessity of background for the purpose of this research Relevant and previous literature

reviews prevail the SCS curve number and general assumptions Also present the

methodology and some practical tactics to determine AMC and its critical thinking of this

application and figure out effective practice for further usage in South Korea in particular

Chapter 3 demonstrate the results and discuss the finding

Chapter 4 Conclusion

The figure 11 indicates the process of research Firstly direct runoff is necessary to be

separated from total runoff By applying base flow separation known as Web Based

Hydrograph Tools (WHAT) the base flow and direct runoff can be separated The data are

derived from the examinational rainfall station After identifying direct runoff from total

runoff curve number estimation can be calculated from equation 7 by knowing daily rainfall

and matched direct runoff However further consideration is necessary to take into account

That is to test the accuracy of curve number To test the accuracy of curve number

determination curve numbers are computed depending upon four different procedures

including arithmetic mean median geometric mean and asymptotic fit Except for the

asymptotic method unranked paired rainfall and runoff volumes from the maximum peal flow

event each year of record were used to compute the calibrated curve number After the curve

number is estimated the next step is to simulate antecedent moisture condition by applying all

the proposed algebraic expression of NEH4 with the consideration of 5 day prior to rainfall

(definition of AMC using antecedent rainfall table) Next is to validate and calibrate among

the proposed procedure to figure out the estimator of antecedent moisture condition criteria

Check evaluation of curve

number procedures

(NRMSE RE R2 NSE)

1st Proposed Method 2nd Proposed Method

Algebraic expression of NEH4

( developed Sobhani (1975) Chow

et al (1988) Hawkins et al (1985)

Arnold et al (1988)

Making AMCARC Estimation

Criteria

Data collection (Rainfall and

Runoff data)

Derive direct runoff ( by Web

Based Hydrograph Tools

WHAT)

Curve Number Estimation

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Definition of AMCARC

(NEH-4 1964)

Average conditions (NEH-4

1964)

Median curve number

(NEH-4 1964)

Antecedent rainfall table

(NEH-4 1964)

Comparison within

definitions

Determination of

AMCARC estimation

criteria

Comparison of AMCARC

Result of AMCARC

estimation criteria

Figure 1 1 Outline of the study

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

As one can observe even for these larger rainfall and runoff events the AMC exhibits a large

degree of scatter Additionally researchers have been unable to validate the NRCS 5-day

index method Nonetheless the concept still is frequently used by researchers and practitioners

However many leading researchers consider the AMC to represent the variation in runoff

volume (Q) from all sources such as model and data error intensity seasonal cover and site

moisture In this context the AMC and ARC represents nothing more than error bands

The rainfall runoff transformation is a nonlinear process The most important cause of non-

linearity represented by the effect of antecedent conditions consequently the runoff

coefficient depends on the initial conditions It is well known that soil moisture is a major

control on the catchment response antecedent moisture conditions have been used to

represent variability of the CN in the SCS method for predicting direct runoff (eg Rallison

and Miller 1981) But soil moisture measurements are usually not widely available and a lot

of point measurements are needed to get either an average or an antecedent catchment state

Antecedent moisture conditions can be simulated using models (either lumped or distributed)

provided standard climate data are available Alternatively some other easily measured

hydrological variable that are even if only approximately related to soil moisture conditions

may be considered

One of the several problems (Ponce and Hawkins 1996 King et al 1999) is that the Method

does not contain any expression for time and as a result ignores the

impact of rainfall intensity as well as antecedent runoff condition So far there is no

concrete guidebook for estimating the antecedent runoff conditions More importantly the

procedure to identify the ARC has been applied within the US soil condition and for decades

for mountainous topographical area like South Korea there will be encountered the variation

and bias Misestimating the runoff depth will lead to the failure in design structure

consequently there will dramatically damage ranging from capital loss to human loss Also

driving force of economic development will be getting down unavoidable

It is apparent that the CN-variability is primarily attributed to the antecedent moisture and it

has led to statistical and stochastic considerations of the curve number undermining the

physical basis of the SCS-CN methodology Furthermore incorporation of the antecedent

moisture in the existing SCS-CN method in the terms of the three AMC levels allows

unreasonable sudden jumps in the CN variation Therefore the determination of the

antecedent moisture condition plays an important role in selecting the appropriate CN value

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

This objective of this paper is to present a critical review of antecedent runoff condition ARC

and derive a procedure to deal more realistically with event rainfall-runoff over wider variety

of initial conditions

12 Literature Review

It is well known that soil moisture is a major control on catchment response antecedent soil

moisture conditions have been used to represent variability of the CN in the SCS method for

predicting direct runoff (eg Rallison and Miller 1981) But soil moisture measurements are

usually not widely available and a lot of point measurements are needed to get either an

average or an antecedent catchment state Antecedent soil moisture conditions can be

simulated using models (either lumped or distributed) provided standard climate data are

available

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

The NRCS (2001) Curve Number Method is widely used for estimating watershed runoff

from rainfall in engineering design (Jacobs et al 2003) The extensive use of the curve

number technique follows from the simplicity that lumps the complexity of runoff generation

into a single watershed parameter the maximum potential retention S that is easily converted

mathematically to a curve number CN (Nachabe and Morel-Seytoux 2005) However the

simplicity of a single lumped parameter introduces great uncertainty to estimates of runoff

Ponce and Hawkins (1996) attribute the ambiguity of the Method to several characteristics

including (Jacobs et al 2003) Use of arbitrarily limited measures of watershed

characteristics lumped into the single parameter the maximum potential retention S Lack of

peer reviewed justification and explanation of the simplified procedures necessary to

consistently determine runoff for engineering design and significant agency support

manifested as publication in the National Engineering Handbook (NRCS 2001)

Despite the limitations the NRCS (2001) Curve Number Method is used to (1) estimate

runoff from ungaged watersheds (2) evaluate the effect of changes in land use and treatment

on direct runoff and (3) parameterize rainfall-runoff relationships in watershed simulation

models

Proper CN estimates are needed to accurately evaluate water availability and close the water

budget of agriculture fields Careful measurements of runoff volume are needed to

systematically evaluate the role of key variables such as rainfall intensity soil moisture

condition tillage practice and land cover on CN values (SUDAS 2004)

13 Outline of the Thesis

This thesis consists of 4 chapters

Chapter 1 it will present the general introduction and significance of study briefly but

concisely about the antecedent runoff conditions which is practically applied in South Korea

as a case of study

Chapter 2 present an overview of previous work related to the study topic that serve as the

necessity of background for the purpose of this research Relevant and previous literature

reviews prevail the SCS curve number and general assumptions Also present the

methodology and some practical tactics to determine AMC and its critical thinking of this

application and figure out effective practice for further usage in South Korea in particular

Chapter 3 demonstrate the results and discuss the finding

Chapter 4 Conclusion

The figure 11 indicates the process of research Firstly direct runoff is necessary to be

separated from total runoff By applying base flow separation known as Web Based

Hydrograph Tools (WHAT) the base flow and direct runoff can be separated The data are

derived from the examinational rainfall station After identifying direct runoff from total

runoff curve number estimation can be calculated from equation 7 by knowing daily rainfall

and matched direct runoff However further consideration is necessary to take into account

That is to test the accuracy of curve number To test the accuracy of curve number

determination curve numbers are computed depending upon four different procedures

including arithmetic mean median geometric mean and asymptotic fit Except for the

asymptotic method unranked paired rainfall and runoff volumes from the maximum peal flow

event each year of record were used to compute the calibrated curve number After the curve

number is estimated the next step is to simulate antecedent moisture condition by applying all

the proposed algebraic expression of NEH4 with the consideration of 5 day prior to rainfall

(definition of AMC using antecedent rainfall table) Next is to validate and calibrate among

the proposed procedure to figure out the estimator of antecedent moisture condition criteria

Check evaluation of curve

number procedures

(NRMSE RE R2 NSE)

1st Proposed Method 2nd Proposed Method

Algebraic expression of NEH4

( developed Sobhani (1975) Chow

et al (1988) Hawkins et al (1985)

Arnold et al (1988)

Making AMCARC Estimation

Criteria

Data collection (Rainfall and

Runoff data)

Derive direct runoff ( by Web

Based Hydrograph Tools

WHAT)

Curve Number Estimation

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Definition of AMCARC

(NEH-4 1964)

Average conditions (NEH-4

1964)

Median curve number

(NEH-4 1964)

Antecedent rainfall table

(NEH-4 1964)

Comparison within

definitions

Determination of

AMCARC estimation

criteria

Comparison of AMCARC

Result of AMCARC

estimation criteria

Figure 1 1 Outline of the study

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

consequently there will dramatically damage ranging from capital loss to human loss Also

driving force of economic development will be getting down unavoidable

It is apparent that the CN-variability is primarily attributed to the antecedent moisture and it

has led to statistical and stochastic considerations of the curve number undermining the

physical basis of the SCS-CN methodology Furthermore incorporation of the antecedent

moisture in the existing SCS-CN method in the terms of the three AMC levels allows

unreasonable sudden jumps in the CN variation Therefore the determination of the

antecedent moisture condition plays an important role in selecting the appropriate CN value

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

This objective of this paper is to present a critical review of antecedent runoff condition ARC

and derive a procedure to deal more realistically with event rainfall-runoff over wider variety

of initial conditions

12 Literature Review

It is well known that soil moisture is a major control on catchment response antecedent soil

moisture conditions have been used to represent variability of the CN in the SCS method for

predicting direct runoff (eg Rallison and Miller 1981) But soil moisture measurements are

usually not widely available and a lot of point measurements are needed to get either an

average or an antecedent catchment state Antecedent soil moisture conditions can be

simulated using models (either lumped or distributed) provided standard climate data are

available

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

The NRCS (2001) Curve Number Method is widely used for estimating watershed runoff

from rainfall in engineering design (Jacobs et al 2003) The extensive use of the curve

number technique follows from the simplicity that lumps the complexity of runoff generation

into a single watershed parameter the maximum potential retention S that is easily converted

mathematically to a curve number CN (Nachabe and Morel-Seytoux 2005) However the

simplicity of a single lumped parameter introduces great uncertainty to estimates of runoff

Ponce and Hawkins (1996) attribute the ambiguity of the Method to several characteristics

including (Jacobs et al 2003) Use of arbitrarily limited measures of watershed

characteristics lumped into the single parameter the maximum potential retention S Lack of

peer reviewed justification and explanation of the simplified procedures necessary to

consistently determine runoff for engineering design and significant agency support

manifested as publication in the National Engineering Handbook (NRCS 2001)

Despite the limitations the NRCS (2001) Curve Number Method is used to (1) estimate

runoff from ungaged watersheds (2) evaluate the effect of changes in land use and treatment

on direct runoff and (3) parameterize rainfall-runoff relationships in watershed simulation

models

Proper CN estimates are needed to accurately evaluate water availability and close the water

budget of agriculture fields Careful measurements of runoff volume are needed to

systematically evaluate the role of key variables such as rainfall intensity soil moisture

condition tillage practice and land cover on CN values (SUDAS 2004)

13 Outline of the Thesis

This thesis consists of 4 chapters

Chapter 1 it will present the general introduction and significance of study briefly but

concisely about the antecedent runoff conditions which is practically applied in South Korea

as a case of study

Chapter 2 present an overview of previous work related to the study topic that serve as the

necessity of background for the purpose of this research Relevant and previous literature

reviews prevail the SCS curve number and general assumptions Also present the

methodology and some practical tactics to determine AMC and its critical thinking of this

application and figure out effective practice for further usage in South Korea in particular

Chapter 3 demonstrate the results and discuss the finding

Chapter 4 Conclusion

The figure 11 indicates the process of research Firstly direct runoff is necessary to be

separated from total runoff By applying base flow separation known as Web Based

Hydrograph Tools (WHAT) the base flow and direct runoff can be separated The data are

derived from the examinational rainfall station After identifying direct runoff from total

runoff curve number estimation can be calculated from equation 7 by knowing daily rainfall

and matched direct runoff However further consideration is necessary to take into account

That is to test the accuracy of curve number To test the accuracy of curve number

determination curve numbers are computed depending upon four different procedures

including arithmetic mean median geometric mean and asymptotic fit Except for the

asymptotic method unranked paired rainfall and runoff volumes from the maximum peal flow

event each year of record were used to compute the calibrated curve number After the curve

number is estimated the next step is to simulate antecedent moisture condition by applying all

the proposed algebraic expression of NEH4 with the consideration of 5 day prior to rainfall

(definition of AMC using antecedent rainfall table) Next is to validate and calibrate among

the proposed procedure to figure out the estimator of antecedent moisture condition criteria

Check evaluation of curve

number procedures

(NRMSE RE R2 NSE)

1st Proposed Method 2nd Proposed Method

Algebraic expression of NEH4

( developed Sobhani (1975) Chow

et al (1988) Hawkins et al (1985)

Arnold et al (1988)

Making AMCARC Estimation

Criteria

Data collection (Rainfall and

Runoff data)

Derive direct runoff ( by Web

Based Hydrograph Tools

WHAT)

Curve Number Estimation

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Definition of AMCARC

(NEH-4 1964)

Average conditions (NEH-4

1964)

Median curve number

(NEH-4 1964)

Antecedent rainfall table

(NEH-4 1964)

Comparison within

definitions

Determination of

AMCARC estimation

criteria

Comparison of AMCARC

Result of AMCARC

estimation criteria

Figure 1 1 Outline of the study

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

It is well known that soil moisture is a major control on catchment response antecedent soil

moisture conditions have been used to represent variability of the CN in the SCS method for

predicting direct runoff (eg Rallison and Miller 1981) But soil moisture measurements are

usually not widely available and a lot of point measurements are needed to get either an

average or an antecedent catchment state Antecedent soil moisture conditions can be

simulated using models (either lumped or distributed) provided standard climate data are

available

The practical application of this procedure should be simple and direct It replies on the

determination curve numbers which are widely documented in the literature for various land

uses and soil types (NEH-4 1964 Chow et al 1988 Pigrim amp Cordery 1993) Nevertheless

in spite of its apparent simplicity the application of the curve number procedure lead to

diversity of the interpretation and confusion due to ignorance about limitations because the

existing documentation of how it was developed is severely limited (Hawkins 1979 Boznay

1989 Hjelmfelt 1991 Pilgrim amp Cordery 1993) Difficulties in its application are mainly

related to the classification of soils outside the USA into the four hydrological soil group A B

C D and the determination of antecedent moisture condition (AMC) which is an index of

basin wetness Care is required in its application and verification against measured of flood

data in each region where the method is applied is necessary

The NRCS (2001) Curve Number Method is widely used for estimating watershed runoff

from rainfall in engineering design (Jacobs et al 2003) The extensive use of the curve

number technique follows from the simplicity that lumps the complexity of runoff generation

into a single watershed parameter the maximum potential retention S that is easily converted

mathematically to a curve number CN (Nachabe and Morel-Seytoux 2005) However the

simplicity of a single lumped parameter introduces great uncertainty to estimates of runoff

Ponce and Hawkins (1996) attribute the ambiguity of the Method to several characteristics

including (Jacobs et al 2003) Use of arbitrarily limited measures of watershed

characteristics lumped into the single parameter the maximum potential retention S Lack of

peer reviewed justification and explanation of the simplified procedures necessary to

consistently determine runoff for engineering design and significant agency support

manifested as publication in the National Engineering Handbook (NRCS 2001)

Despite the limitations the NRCS (2001) Curve Number Method is used to (1) estimate

runoff from ungaged watersheds (2) evaluate the effect of changes in land use and treatment

on direct runoff and (3) parameterize rainfall-runoff relationships in watershed simulation

models

Proper CN estimates are needed to accurately evaluate water availability and close the water

budget of agriculture fields Careful measurements of runoff volume are needed to

systematically evaluate the role of key variables such as rainfall intensity soil moisture

condition tillage practice and land cover on CN values (SUDAS 2004)

13 Outline of the Thesis

This thesis consists of 4 chapters

Chapter 1 it will present the general introduction and significance of study briefly but

concisely about the antecedent runoff conditions which is practically applied in South Korea

as a case of study

Chapter 2 present an overview of previous work related to the study topic that serve as the

necessity of background for the purpose of this research Relevant and previous literature

reviews prevail the SCS curve number and general assumptions Also present the

methodology and some practical tactics to determine AMC and its critical thinking of this

application and figure out effective practice for further usage in South Korea in particular

Chapter 3 demonstrate the results and discuss the finding

Chapter 4 Conclusion

The figure 11 indicates the process of research Firstly direct runoff is necessary to be

separated from total runoff By applying base flow separation known as Web Based

Hydrograph Tools (WHAT) the base flow and direct runoff can be separated The data are

derived from the examinational rainfall station After identifying direct runoff from total

runoff curve number estimation can be calculated from equation 7 by knowing daily rainfall

and matched direct runoff However further consideration is necessary to take into account

That is to test the accuracy of curve number To test the accuracy of curve number

determination curve numbers are computed depending upon four different procedures

including arithmetic mean median geometric mean and asymptotic fit Except for the

asymptotic method unranked paired rainfall and runoff volumes from the maximum peal flow

event each year of record were used to compute the calibrated curve number After the curve

number is estimated the next step is to simulate antecedent moisture condition by applying all

the proposed algebraic expression of NEH4 with the consideration of 5 day prior to rainfall

(definition of AMC using antecedent rainfall table) Next is to validate and calibrate among

the proposed procedure to figure out the estimator of antecedent moisture condition criteria

Check evaluation of curve

number procedures

(NRMSE RE R2 NSE)

1st Proposed Method 2nd Proposed Method

Algebraic expression of NEH4

( developed Sobhani (1975) Chow

et al (1988) Hawkins et al (1985)

Arnold et al (1988)

Making AMCARC Estimation

Criteria

Data collection (Rainfall and

Runoff data)

Derive direct runoff ( by Web

Based Hydrograph Tools

WHAT)

Curve Number Estimation

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Definition of AMCARC

(NEH-4 1964)

Average conditions (NEH-4

1964)

Median curve number

(NEH-4 1964)

Antecedent rainfall table

(NEH-4 1964)

Comparison within

definitions

Determination of

AMCARC estimation

criteria

Comparison of AMCARC

Result of AMCARC

estimation criteria

Figure 1 1 Outline of the study

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

Ponce and Hawkins (1996) attribute the ambiguity of the Method to several characteristics

including (Jacobs et al 2003) Use of arbitrarily limited measures of watershed

characteristics lumped into the single parameter the maximum potential retention S Lack of

peer reviewed justification and explanation of the simplified procedures necessary to

consistently determine runoff for engineering design and significant agency support

manifested as publication in the National Engineering Handbook (NRCS 2001)

Despite the limitations the NRCS (2001) Curve Number Method is used to (1) estimate

runoff from ungaged watersheds (2) evaluate the effect of changes in land use and treatment

on direct runoff and (3) parameterize rainfall-runoff relationships in watershed simulation

models

Proper CN estimates are needed to accurately evaluate water availability and close the water

budget of agriculture fields Careful measurements of runoff volume are needed to

systematically evaluate the role of key variables such as rainfall intensity soil moisture

condition tillage practice and land cover on CN values (SUDAS 2004)

13 Outline of the Thesis

This thesis consists of 4 chapters

Chapter 1 it will present the general introduction and significance of study briefly but

concisely about the antecedent runoff conditions which is practically applied in South Korea

as a case of study

Chapter 2 present an overview of previous work related to the study topic that serve as the

necessity of background for the purpose of this research Relevant and previous literature

reviews prevail the SCS curve number and general assumptions Also present the

methodology and some practical tactics to determine AMC and its critical thinking of this

application and figure out effective practice for further usage in South Korea in particular

Chapter 3 demonstrate the results and discuss the finding

Chapter 4 Conclusion

The figure 11 indicates the process of research Firstly direct runoff is necessary to be

separated from total runoff By applying base flow separation known as Web Based

Hydrograph Tools (WHAT) the base flow and direct runoff can be separated The data are

derived from the examinational rainfall station After identifying direct runoff from total

runoff curve number estimation can be calculated from equation 7 by knowing daily rainfall

and matched direct runoff However further consideration is necessary to take into account

That is to test the accuracy of curve number To test the accuracy of curve number

determination curve numbers are computed depending upon four different procedures

including arithmetic mean median geometric mean and asymptotic fit Except for the

asymptotic method unranked paired rainfall and runoff volumes from the maximum peal flow

event each year of record were used to compute the calibrated curve number After the curve

number is estimated the next step is to simulate antecedent moisture condition by applying all

the proposed algebraic expression of NEH4 with the consideration of 5 day prior to rainfall

(definition of AMC using antecedent rainfall table) Next is to validate and calibrate among

the proposed procedure to figure out the estimator of antecedent moisture condition criteria

Check evaluation of curve

number procedures

(NRMSE RE R2 NSE)

1st Proposed Method 2nd Proposed Method

Algebraic expression of NEH4

( developed Sobhani (1975) Chow

et al (1988) Hawkins et al (1985)

Arnold et al (1988)

Making AMCARC Estimation

Criteria

Data collection (Rainfall and

Runoff data)

Derive direct runoff ( by Web

Based Hydrograph Tools

WHAT)

Curve Number Estimation

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Definition of AMCARC

(NEH-4 1964)

Average conditions (NEH-4

1964)

Median curve number

(NEH-4 1964)

Antecedent rainfall table

(NEH-4 1964)

Comparison within

definitions

Determination of

AMCARC estimation

criteria

Comparison of AMCARC

Result of AMCARC

estimation criteria

Figure 1 1 Outline of the study

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

application and figure out effective practice for further usage in South Korea in particular

Chapter 3 demonstrate the results and discuss the finding

Chapter 4 Conclusion

The figure 11 indicates the process of research Firstly direct runoff is necessary to be

separated from total runoff By applying base flow separation known as Web Based

Hydrograph Tools (WHAT) the base flow and direct runoff can be separated The data are

derived from the examinational rainfall station After identifying direct runoff from total

runoff curve number estimation can be calculated from equation 7 by knowing daily rainfall

and matched direct runoff However further consideration is necessary to take into account

That is to test the accuracy of curve number To test the accuracy of curve number

determination curve numbers are computed depending upon four different procedures

including arithmetic mean median geometric mean and asymptotic fit Except for the

asymptotic method unranked paired rainfall and runoff volumes from the maximum peal flow

event each year of record were used to compute the calibrated curve number After the curve

number is estimated the next step is to simulate antecedent moisture condition by applying all

the proposed algebraic expression of NEH4 with the consideration of 5 day prior to rainfall

(definition of AMC using antecedent rainfall table) Next is to validate and calibrate among

the proposed procedure to figure out the estimator of antecedent moisture condition criteria

Check evaluation of curve

number procedures

(NRMSE RE R2 NSE)

1st Proposed Method 2nd Proposed Method

Algebraic expression of NEH4

( developed Sobhani (1975) Chow

et al (1988) Hawkins et al (1985)

Arnold et al (1988)

Making AMCARC Estimation

Criteria

Data collection (Rainfall and

Runoff data)

Derive direct runoff ( by Web

Based Hydrograph Tools

WHAT)

Curve Number Estimation

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Definition of AMCARC

(NEH-4 1964)

Average conditions (NEH-4

1964)

Median curve number

(NEH-4 1964)

Antecedent rainfall table

(NEH-4 1964)

Comparison within

definitions

Determination of

AMCARC estimation

criteria

Comparison of AMCARC

Result of AMCARC

estimation criteria

Figure 1 1 Outline of the study

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

Check evaluation of curve

number procedures

(NRMSE RE R2 NSE)

1st Proposed Method 2nd Proposed Method

Algebraic expression of NEH4

( developed Sobhani (1975) Chow

et al (1988) Hawkins et al (1985)

Arnold et al (1988)

Making AMCARC Estimation

Criteria

Data collection (Rainfall and

Runoff data)

Derive direct runoff ( by Web

Based Hydrograph Tools

WHAT)

Curve Number Estimation

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Definition of AMCARC

(NEH-4 1964)

Average conditions (NEH-4

1964)

Median curve number

(NEH-4 1964)

Antecedent rainfall table

(NEH-4 1964)

Comparison within

definitions

Determination of

AMCARC estimation

criteria

Comparison of AMCARC

Result of AMCARC

estimation criteria

Figure 1 1 Outline of the study

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

CHAPTER II METHODOLOGY

In this chapter we are going to cover the review of literature regarding to Curve number

hydrology methodology critical thinking on antecedent runoff condition and applicable

methodology to define antecedent runoff condition Base flow separation technique known as

Web based Hydrograph Analysis Tools (WHAT) and further discussion how it integrates base

flow separation to define standard of antecedent conditions

21 The Curve Number Method

The curve number procedure of US the soil Conservation Service is a widely used method for

estimating runoff depth direct runoff from the rainfall on small to medium-sized ungagged

basin The basic reference is the National Engineering Handbook Section 4 Hydrology

(1964) hereafter referred to as ―NEH-4

The SCS-CN (original) method is a procedure for estimating the depth of runoff from depth of

precipitation in given soil textural classification land useland cover and an estimate of

watershed wetness The method combines the watershed parameters and climatic factors in

one entity called the curve number which varies with cumulative rainfall soil cover land use

and initial water content

Originally this technique was originally derived from the examination of annual flood event

data Implicit in the reasoning of Mockus (1949) and Andrews (1954) the curve number

runoff equation can be derived from a watershed water balance for a storm event written as

(1)aP I F Q

where P is the storm event rainfall Ia is the initial abstraction (includes interception

depression storage and infiltration losses prior to ponding and the commencement of

overland flow) F is the cumulative watershed retention of water and Q is the total runoff

from the rain event

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

Victor Mockus (Ponce 1996) hypothesized that the ratio of actual runoff to the maximum

potential runoff (expressed as rainfall P minus initial abstraction Ia added later by the SCS

over the objections of Mockus) is equal to the ratio of the actual retention of water during a

rainstorm to maximum potential retention S in a catchment (Ponce and Hawkins 1996) or

runoff

2a

Q F

P I S

To reduce the number of unknown parameters (3) in Equations (1) and (2) the SCS

hypothesized that

3aI S

Where λ is the initial abstraction ratio or coefficient a relation between the initial abstraction

Ia and maximum potential retention S has not been defined theoretically or conceptually

As the Method is currently practiced runoff can be computed using the tabulated curve

numbers based on the land use and condition hydrologic soil group and the rainfall depth

from combining Equations (1) and (2) as

2

4a

a

P IQ

P I S

Equation (4) is valid for precipitation P gt Ia For P lt Ia Q = 0 such that no runoff occurs

when the rainfall depth is less than or equal to the initial abstraction Ia With initial

abstraction included in Equation (4) the actual retention F= P ndash Q asymptotically approaches

a constant value of S + Ia as the rainfall increases

Using the value of λ = 02 Equation (4) becomes

202

0208

0 02 5

P SQ for P S

P S

Q for P S

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

Equation (5) contains only one parameter (maximum potential retention S) which varies

conceptually between 0 and infin For convenience in practical applications maximum potential

retention S is defined in terms of a dimensionless parameter CN (curve number) that varies

over the more restricted range of 0 lt CN lt 100

1000 1000

10 610

S CN aCN S

25400 25400

254 6254

S CN bCN S

The CN ranges from 0 to 100 and is a transformation of S which varies between 0 S A

value of S can be calculated from P and Q if 02 (Hawkins 1993)

2

2

5 2 4 5 254 ( )

5 2 4 5 10 ( ) 7

S P Q Q PQ metricunits or

S P Q Q PQ inchunits

The numbers 1000 and 10 (in inches) as expressed in Equation (6a) or 25400 and 254 (in

millimeters) as expressed in Equation (6b) are arbitrarily chosen constants having the same

units as the maximum potential retention S

Watershed curve numbers are estimated by cross referencing land use hydrologic condition

and hydrologic soil group for ungagged watersheds in standard tables (NRCS 2001) or

calculated for gaged watersheds by algebraic rearrangement of Equations (5) (6) and (7) as

2

10008

5 2 4 5 10CN a

P Q Q PQ

2

254008

5 2 4 5 254CN b

P Q Q PQ

Measured pairs of rainfall volume P and runoff volume Q from an individual storm event are

or

or

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

used with Equation (7) to determine the watershed curve number CN The measured rainfall

and runoff are expressed in inches or millimeters for Equations (8a) and (8b) respectively

The CN value for representative land uses soil types and hydrological conditions along with

a conversion table AMC for three AMC conditions AMC I (dry) AMC II (normal) AMC III

( wet) which statistically correspond to 90 50 and 10 cumulative probability of exceedance

of runoff depth for a given rainfall respectively [42] are given in NEH-4 table [1] The higher

the antecedent moisture or rainfall amount the higher is the CN and therefore the high

runoff potential of the watershed and vice versa

If the watershed includes segments with several types of soil and soil cover complex

appreciate CNs are assigned to each segment and a weighted CN can be estimated for the

entire watershed using the equation

1 1 2 2 9n n

W

CN A CN A CN ACN

A

Where nCN and nA are the CN and area respectively for the thn watershed n is the total

number of segments in the watershed and A is the total area of the watershed

211 SCS-CN based hydrological Models

This paper provides a recent documentation on the subject with their limitations and

advantages and computer models developed over the year The empirical methods are

Williams and LaSeur Hawkins Pandit and Gopalakrishnan Mishra et al Mishra and Singh

Developed in 1976 by Williams and LaSeur is a continuous simulation model by relating the

SCS-CN parameter (S) with the soil moisture (M) for computation of direct surface runoff

They accounted antecedent moisture (M) which depleted continuously between storms by

evapotranspiration and deep storage M is assumed to vary with the lake evaporation as given

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

2

0

a

a

a

a

P IQ if P I

P I S

Q I S

absM S S and

1

10

1t T

c tt

MM

b M E

Where absS absolute potential maximum retention equal to 20 t-time

cb -depletion

coefficient M-soil moisture index at the beginning of the first storm t

M -soil moisture

index at any time t t

E -average monthly lake evaporation for day t and T-number of days

between storms

The advantages of this model are that it eliminates sudden quantum jumps in the CN values

when changing from one AMC level to other However the downside is that it utilizes an

arbitrarily assigned value of 20 inches for absolute potential maximum retention and assumes

physically unrealizable decay of soil moisture with Lake Evapotranspiration which is false

assumption

Mishra and Singh (1998) proposed used a linear regression approach similar to the unit

hydrograph scheme to transform rainfall excess into direct runoff They described the AMC

based on the NEH-4 table and varied CN with time t using the following equation

22 Evaluation of the Curve Number Method

221 Procedures for determining the curve number

Measured rainfall and runoff volumes for the event with annual peak flow were used to

determine a curve number for each year of record on watersheds Representative watershed

curve numbers for gaged watersheds were selected from a set of curve numbers determined

using the (1) arithmetic mean (2) median (3) geometric mean (4) asymptotic value and (5) a

nonlinear least squares fit procedures To access the accuracy of NRCS (2001) Curve Number

Method these calibrated values were compared to the NRCS (2001) tabulated curve numbers

for the specific hydrologic soil group (Group A B C or D) cover-complex (land use

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

treatment or practice) and hydrologic condition (poor fair or good) on each gaged

watershed The detailed procedures for each technique follow

Arithmetic curve number The curve number for each year of record for a particular

watershed is averaged to determine the representative curve number

Median curve number The median was originally determined for the NRCS (2001) curve

number tables using the Graphical Method The direct runoff was plotted versus the rainfall

volume to determine the curve that divides the plotted points into two equal groups The curve

number for that curve is the median curve number

Geometric mean curve number The NRCS (2001) Statistical Method determines the

geometric mean curve number (Yuan 1939) from a lognormal distribution of annual

watershed curve numbers about the median (Hjelmfelt et al 1982 Hauser and Jones 1991

Hjelmfelt 1991) The procedure is

The maximum potential retention S is computed from each pair of annual runoff

volume Q and rainfall volume P as Equation (8)

The mean micro and standard deviation δ of the logarithms of the annual maximum

potential retention S was determined as

log

2

log

log

log13

log14

1

S

S

S

S

N

S

N

where N is the number of years in the watershed rainfall-runoff record The mean of the

transformed values the mean (log S) is the median of the series of the maximum potential

retention if the distribution is lognormal

The geometric mean (GM) of the maximum potential retention S is the antilogarithm

of the mean (log S) in base 10 logarithms

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

log10 15S

GMS

Finally the geometric mean curve number for rainfall and runoff volumes expressed in

inches is

1000 25400

( ) 1610 254

GM GM

GM GM

CN inch units CN metricunitsS S

Nonlinear Least Squares Fit For a record of N observed rainfall P and observed runoff Qo

the optimal value of the maximum potential retention S for the watershed is that which

minimizes the objective function

2

1

17N

oi pi

i

f Obj Q Q

where Qp is the runoff computed from the NRCS (2001) runoff Equation (5) The square root

of the minimum objective function divided by N (number of observations) is the standard

error The measure of variance reduction R2 is similar to the correlation coefficient r2

2

2 1 18

o

e

Q

SR

S

where oQS is the standard deviation of the observed runoff values and se is the standard error

222 Asymptotic Method

Handbook table values of CN give guidance in the absence of better information but

incorporate only limited land uses and conditions and are often untested With increasing user

sophistication coupled with the awareness that the runoff Calculation is more sensitive to CN

than to rainfall interest in determining local CNs from local rainfall-runoff data has grown

Three methods of analyzing local event rainfall and runoff for CN are outlined here

In this method the Hawkinslsquos method CN calculated using Equation (6) and (7) are plotted

against the respective P values and the asymptotic value at high rainfalls is taken as the final

CN The analysis can be done on ordered or unordered data and we have plotted ordered data

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

to increase the clarity of the figure The actual analysis used unordered data as this should

give more accurate result (Hawkins et al 2009) In some cases however the CN does not

reach an asymptotic value but keeps declining and the CN cannot be calculated (Figure 2b)

This is called complacent behavior (Hawkins 1993) and is possibly due to insufficient data in

the series The opposite is violent behavior in which the CN values suddenly increase after an

initial decline Hawkins 1993) We again used nonlinear least squares (nls) in R (R

Development Core Team 2010) to calculate the asymptotic S1 related to CN1 values by

inserting Equation (6) into the suggested empirical equations (Hawkins 1993) to fit standard

behavior

25400 25400

100 exp 11254 254

CN P kPS S

Or violent behavior depending on the data

25400

1 exp 12254

CN P kPS

In these equations k is a fitting constant that describes the slope of the log (CN)-log (P)

relationship The non-least square function maximizes the log-Likelihood therefore

separation between standard and violent behavior was based on which Equation ((11) or (12))

gave the highest log-likelihood Additionally if the asymptotic S value was greater than the

maximum calculated S value based on Equation (6) we assumed complacent behavior

(Hawkins 1993)

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

Figure 2 1 Standard Watershed response (from Hawkins 1993)

Figure 2 2 Violent Watershed response (from Hawkins 1993)

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

The procedure for the asymptotic determination of observed watershed curve

1 Rank the rainfall and mnoff depths independently

2 Calculate curve numbers for each ordered pair

3 Plot the resulting curve numbers with respect to the

conesponding precipitations

4 Define the curve number from the asymptofic behavior as

standard violent or complacent

Figure 2 3 Procedure for the asymptotic determination

223 Accuracy of procedures for determining the curve number

The relative accuracy of the four methods for determining the watershed curve

number from the series of measured runoff depth and the rainfall depth has not

been fully explored and defined Therefore the accuracy of all four procedures for

calibrating curve numbers to estimate runoff volumes was assessed by using coefficient of

determination R square Relative Error (RE) Nash-Sutcliffe efficiency E and error statistic

based on the Normalized root mean square error NRMSE The coefficient of determination is

expressed as following

R square (2R )

2

( ) ( )2 1

22

( ) ( )

1 1

19

n

obs i obs est i est

i

n n

obs i obs est i est

i i

Q Q Q Q

R

Q Q Q Q

Relative Error

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

( ) ( ) ( ) 100 20est i obs i obs iRE Q Q Q

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

Normal Root Mean Square Error

2

1

1

22

N

obs comp ii

obs

N Q Q

NRMSEQ

where i is the number of each event from 1 to N (the total number of rainfall-runoff events)

Qest is the computed runoff volume Qobs is the observed event runoff volume and est obsQ Q

are the mean of the estimated and observed runoff volumes respectively

R square (2R ) can be also be expressed as the squared ratio between the covariance and the

multiplied standard deviations of the observed and predicted values Therefore it estimates

the combined dispersion against the single dispersion of the observed and predicted values

The range of 2R lies between 0 and 1 which describes how much of the observed of the

observed dispersion is explained by the prediction A value of zero means that the dispersion

of the prediction is equal to that of the observation The fact that only the dispersion is

quantified is one of the major drawbacks of 2R if it is considered alone A model which

systematically over or under predict all the time will still result in good 2R values close to 10

even if all prediction were wrong

Relative Error Relative error gives an indication of how good a measurement is relative to

the size of the thing being measured

Nash and Sutcliffe Efficiency (E) The efficiency of E is proposed by Nash and Sutcliffe

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

(1970) The normalization of the variance of the observation series results in relatively higher

value of E in catchments with higher dynamics and lower values of E in catchments with

lower dynamics To obtain comparable values of E in a catchment with lower dynamics and

prediction has to be better than in a basin high dynamics The range of E lies between 10

(perfect fit) and infinity An efficiency of E lower than zero indicates that the mean value of

observed time series would have been a better predictor than the model

The normalized root-mean-square deviation or error (NRMSE) is a frequently used

measure of the differences between values predicted by a model or an estimator and the

values actually observed NRMSE is a good measure of accuracy but only to compare

forecasting errors of different models for a particular variable and not between variables as it

is scale-dependent The larger the NRMSE the poorer is the estimated curve number and

vice-a-versa

224 Seasonal variations of curve numbers

Jacobs and Srinivasan (2005) and Paik et al (2005) showed that the watershed curve number

seems to vary from season to season And this seasonality of curve numbers seems to occur

for some North Georgia forested watersheds However a physical justification for these

variations has not been developed (Tedela et al 2007) For this report the working hypothesis

is that seasonal differences in recharge and evapotranspiration may affect watershed

maximum potential retention by raising or lowering water tables and by adding or depleting

soil moisture Furthermore the dropping of and seasonal regrowth of deciduous leaves may

affect the initial abstraction

To investigate the seasonal variation of curve numbers the observed rainfall and runoff

volume data were divided according to the two seasons and analyzed separately The

watershed curve number for each season was computed using measured rainfall and runoff

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

volumes in Equation (8) Tedela et al (2007) discovered that inclusion of storm events during

the transitions between seasons obscured some of the observed differences in curve numbers

determined for the growing and dormant seasons Transitional hydrologic conditions are

evidently affected by a combination of tree growth and dormancy Therefore the rainfall and

runoff volumes from the months of October and November and March and April were not

included in computing the record of seasonal curve numbers To test the arbitrary exclusion of

what seems to be transition months this study investigated the effect of seasonal variation

with or without the transitions

23 Antecedent Moisture Condition (AMC) and Antecedent Runoff Condition

Review

The original NEH4 exposition of the CN contained the AMC motion in two forms both

seemingly independent First as a climatic definition presented in the since discontinued

NEH4 Table 42 or based on discontinued NEH4 Table 42 indicating AMC status (III and

III) based on 5-day prior rainfall depths and season Second as an undocumented table (Table

101 in NEH4) that gave the I II and III equivalents This was linked to explaining that

observed variation in direct runoff between events

Prior 5-day rainfall depths The cumulative 5-day rainfall depth is a characterizing climatic

description of a site A number of subsequent papers (Including Gray et al 1982 Hawkins

1983) examined this and found that for most stations ndashand using the Table 42 criteria ndashthe

apparent dominant rainfall-defined status was in AMC I This invited local interpretations and

selection of AMC I CN from soils and cover data with consequent reduction in design peaks

and volumes From this realization in 1993 the SCS dropped the Table 42 definitions from

update NEH4 (Shaw 1993) Furthermore CN at AMC II status was defined as the reference

CN as that occurring with the annual floods and as the basis find continued application

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

usually in continuous daily time-step models a topic covered elsewhere in this report

AMC conversion values The correspondence between CN at three AMC status levels was

stated in NEH4 Table 101 without explanatory background or hydrologic reference the

original data sources and the deviation technique have not been located However in attempts

to formulate the relationships the table offerings have been re-expressed algebraically as

shown in Table 15 The first three of these equations are essentially identical Reduces very

nearly to 49 and 50 upon simplification Equation 23 and 24 are known to arise from simple

linear fits on the storage term ―S of the CNs offered in NEH4 Table 101 Specifically 23a

and 23b are fit to 45 points from CN = 50 to CN = 95 giving (Hawkins et al 1985)

2

2

( ) 2281 ( ) 0999 0206

( ) 0427 ( ) 0994 0088

S I S II r Se in

S II S II r Se in

It should be note that the coefficient in the above are very nearly reciprocals or

0427 1 2281

Sobhani

(1975)

( ) ( ) [2334 001334 ( )] 24

( ) ( ) [04036 00059 ( ) 24

CN I CN II CN II a

CN III CN II CN II b

Hawkins

et al

(1985)

( ) ( ) [2281 001381 ( )] 25

( ) ( ) [0427 000573 ( ) 25

CN I CN II CN II a

CN III CN II CN II b

Chow et

al (1988)

( ) 42 ( ) 10 0058 ( ) 26

( ) 23 ( ) 23 ( ) 10 013 ( ) 26

CN I CN II CN II a

CN III CN III CN II CN II b

Arnold et

al (1988)

( ) ( ) ( ( )) 27

( ) ( )exp[000673(100 ( )] 27

CN I CN II F CN II a

CN III CN II CN II b

( ( ) 20(100 ( ) [100 ( ) exp(2533 00636(100 ( )]F CN II CN II CN II CN II

(23a)

(23b)

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

Double

Normal

1

1

( ) 100( ( 100) 051 28

( ) 100( ( 100) 051 28

II

II

CN I F CN a

CN III F CN b

Table 21 Algebraic expression of NEH4 Table 101 (Source NEH4 Table 101)

Double normal plotting the ultimate practical fitting of the Table 101 AMC relations can be

found by plotting CN I II and III on the Y-axis on double normal-probability paper against

CNII (X -axis) with the CNs shown as ―probability in percent This pragmatic exercise

leads to three equally spaced and tightly-fitting parallel straight lines This is consistent with

the reciprocal coefficients mentioned above and suggests a smoothing procedure on limited

data to create the original relationship Fit to the ―data in NEH4630 Table 101 the

expressions are shown as Equation 28 below

1

1

100( ( 100) 051) 027

100( ( 100) 051) 028

I II

II II

CN F CN Se CN

CN F CN Se CN

Where F Normal probability integral and 1F inverse of F

AMC and ARC as ―error band The ―AMC concept was converted to an ―error bands

concept via findings by Hjemfelt et al (1982) of error probabilities associated with the table

value of AMC I and AMC III AMC III was shown to approximate the direct runoff for a

given rainfall for which 90 percent of runoffs were less while AMC I approximated the direct

runoff for the same rainfall for which 10 percent of the runoff were less Further research by

Grabau et al (2008) further affirms with concept but refines AMC I and III probabilities as

about 12 and 88 percent respectively leading to about 75 percent of the runoff event falling

between ARC I and ARC III

23 1 Antecedent Moisture Condition (AMC)Antecedent Runoff

Condition application

However determination of antecedent moisture condition content and classification into the

antecedent moisture classes AMC I AMC II and AMC III representing dry average and wet

(28)

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

conditions is an essential matter for the application of the SCS curve number procedure that

is without a clear answer yet The definition of antecedent moisture condition AMC II is the

basis from which adjustments to the corresponding curve numbers for dry soils (AMC I) and

wet soils (AMC III) are made Nevertheless Hjelmfelt (1991) noted that the SCS gives three

definitions for AMC II

Average conditions (NEH-4 1964) The SCS defines the antecedent moisture

condition as an index of basin wetness In particular AMC II is defined as ―the average

condition However Hjelmfelt (1991) pointed out that it is not clear if this is to be

quantitative or qualitative definition and if quantitative

Median curve number (NEH-4 1964) The curve number that divides the plotting of

the relationship between direct runoff and the corresponding rainstorm into two equal

numbers of points (the median) is associated with AMC II AMC I and AMC II are

defined by envelope curve

Antecedent rainfall table (NEH-4 1964) The appropriate moisture group AMC I

AMC II AMC III is based on a five-day antecedent rainfall amount and season

category (dormant and growing seasons)

Table 2 1 Seasonal rainfall limits for AMC (Source NEH-4 1964)

Common practice makes the method dependent on the antecedent precipitation index a

simple indicator derived from rainfall depth which can be used to determine antecedent

moisture condition of the soil

Furthermore Morel-Seytoux amp Verdin (1981) noted that examination of the SCS curve

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

number procedure also shows that the infiltration rate implied in the SCS procedure fluctuates

with the rainfall intensity which disagree with field and laboratory measurements and

physical infiltration theory The SCS infiltration rate only produces a monotonic decreasing

infiltration curve for constant rainfall intensity Morel-Seytoux amp Verdin (1981) extended the

SCS curve number procedure using infiltration theory and established a table relating the

curve number (CN) to the hydraulic conductivity of the soil under conditions of natural

saturation (K) and the storage suction factor (Sf) This table allows the use of infiltration

equations to estimate rainfall excess for any ungagged basin assuming that the curve number

can be determined from knowledge of soil types and land use

232 ARC and AMC in continuous model (Soil Moisture Modeling)

The curve number event runoff equation and the ARC-CN relationships offered in NEH4

Table 101 have found application as a hydrologic interpretation of soil profile and site

characteristics in ecologic models Insofar as this is a major extension of the method not

covered in the original formulation in NEH4 there is a lack of hand book authority or

precedent to guide or support it

Continuous models with the CN method as a soil moisture manager are sometimes used to

determine watershed yield it is also popular as the hydrology underpinning for upland water

quality models Such approaches also find wide application in continuous hydrologic

simulation usually in planning agricultural or wild land management This application is

widespread but only defining and cursory coverage is given here A full critical review is

needed but is well beyond the scope of this report

Abbreviated and selected listing of such continuous model include SWAT (Arnold et al

1994) SWRRB (Arnold et al 1990 Williams et al 1985) EPIC (Williams et al 1984)

GLEAMS (Leonard et al 1987) CREAMS (Knisel 1980 ) NLEAP (Shaffer et al 1991)

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

AGNPS (Young et al 1989) Cronshey and Theurer 1998) ARDBSN (Stone et al 1986)

SPUR (Carlson et al 1995) PRZM (Carsel et al 1984) ACRU(Schulze 1992) RUSLE2

(Foster et al 2003) SPAW (Saxton 1993) and TVAHYSIM (Betson et al 1980)

Essentially all of the current works are technical descendent of the pioneering paper by

Williams and LaSeur (1976) Later addition by Arnold et al (1990) provided the essentials

found in many contemporary versions The most popular module appears to be the one

incorporated in SWAT (Nietsch et al 2002) A more recent procedure along similar lines with

successful application is given by Mishra and Singh (2004) An alternative with some

enhancements was given shortly following the Williams and LaSeur (1976) paper by Hawkins

(1977 1978) It was applied to the continuous daily model ACRU (Schulze 1982 1992) in

South Africa (which uses IaS = 010 however)

A critique of both of these approaches ndash based on mass conservation consideration ndashis given

by Mishra and Singh (2004) who suggest the corrected and improved method Their approach

incorporated in a river basin model applied to condition in India Michel et al (2005)

present a criteria review of these procedure and highlight several inconsistencies when used in

continuous models and derive a procedure to deal more realistically with event rainfall-runoff

over a wider variety of method is as follow

The soil water balance modeling strategy spring from the notion that CNndashand thus S (or 12S)

ndashis a continuous function of soil moisture with time Thus it gives physical meaning to S as

the maximum possible post ndashIa different between rainfall and runoff and is a time-variable

measure for site water storage potential While variation in details abound a basic

representation of the general method is as follows

1 CN values ndash assumed to be condition II ndashare selected from handbook tables or charts

from handbook tables or charts for the soil and land use conditions under study

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

2 From this conditions I and III are established using the handbook relationships in

NEH4 Table 101 In some versions the storage indices (S) corresponding to ARC I

and ARC III may be taken to be site wilting point and fieldslsquo capacity respectively

3 Direct runoff (Q) is generated from the daily rainfall P and the daily CN the latter

defined by allocating the soil moisture with condition I and III as the limiting cases

4 Total losses of runoff (P-Q) are counted as additions to moisture Site moisture losses

from evapotranspiration and drainagepercolation are calculated by various sub

process models

5 The CN for the next day is calculated from the residual soil moisture content

following the above accounting limited by the wilting point (or ARC I) and by a

special case under very wet conditions in excess of field capacity

Within this general structure the CN status may be either continuous (a range of soil water

contents between AMC I and III) or discrete (I II and III) Variants also exist in time step

selection parameter identification association processes GIS application and accounting

intervals

While these models use the CN runoff equation as a central core much of the subsequent

model operation and logic are beyond the scope of this report In some cases the primary role

of the CN logic is in managing soil moisture coupled with other processes such as snowmelt

and very little (or no) direct surface runoff is generated (See Ahl etal 2006 Ahl and Woods

2006)

It is worth nothing that the curve number relationships that began as humble annual peak flow

data plots are now interpreted as measures of soil physics Condition I and III originally seen

as extremes of rainfall-runoff response are asserted to be the profilelsquos wilting point and field

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

capacity

Soil moisture effects on direct runoff The above begs the question of actual effects of prior

rain or start-of-storm soil on event runoff either in the P-Q or CN context Hawkins and Cate

(1998) were able to how consistent positive effect of prior 5-day rainfall in only 11 of 25

cases for small rain-fed agricultural watershed and very mixed effects from intensity and

storm distribution factors A later study (Hawkins and Verweire 2005) with a larger sample

(43watersheds) reaffirms the above general findings and point out the complex role of storm

intensity which seems to be less important than prior rainfall

CN and direct runoff variation the above leads naturally into the independent quantification

of natural observed variation of Q given P Such would promote the opportunity of natural

observed variation of Q given P Such would promote the opportunity to generate large

samples of random data and evaluate the probability of extreme natural event Insofar as

variation in Q is variation in CN this problem directs attention to CN scatter around CN (II)

24 Web-based Hydrograph Analysis Tool (WHAT)

For accurate model calibration and validation the direct runoff and base flow components

from stream flow have to be first separated

The process of separating the base flow component from the varying stream flow hydrograph

is called ―hydrograph analysis The shape of the hydrograph varies depending on physical

and meteorological conditions in a watershed (Bendient and Huber 2002) thereby

complicating hydrograph analysis There are numerous methods called hydrograph analysis

or ―base flow separation available to separate base flow from measured stream flow

hydrographs The traditional hydrograph analysis methods are not very efficient because these

subjective techniques do not provide consistent results Thus the US Geological Survey

(USGS) has developed and distributed an automated hydrograph analysis program called

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

HYSEP (Sloto and Crouse 1996) Digital filtering methods have also been used in base flow

separation because they are easy to use and provide consistent results (Lyne and Hollick

1979 Chapman 1987 Nathan and McMahon 1990 Arnold et al 1995 Arnold and Allen

1999 Eckhardt 2005) The BFLOW (Lyne and Hollick 1979 Arnold and Allen 1999) and

the Eckhardt (Eckhardt 2005) digital filters are widely used for hydrograph analysis

Although a new parameter was introduced in the Eckhardt digital filter to reflect local

hydrogeological situations (BFImax) and representative values were proposed for various

aquifers the use of a BFImax value specific to local conditions is strongly recommended

instead of using the proposed representative BFImax values

Lim et al (2005) developed the Web GIS-based Hydrograph Analysis Tool (WHAT)

(httpsengineeringpurdueedu~what) to provide fully automated functions for base flow

separation Lim et al (2005) compared the filtered base flow for 50 gaging stations in Indiana

USA using the Eckhardt filter with a default BFImax value of 080 and the BFLOW filter The

Nash-Sutcliffe coefficient values were 091 for 50 Indiana gaging stations However the use

of the default BFImax value of 080 for 50 Indiana gaging stations is not recommended

because the filtered base flow data were compared with the results from the BFLOW digital

filter which did not reflect the physical characteristics in the aquifer and watershed

The Web Based Hydrograph Analysis Tool (WHAT) (httpsengineergpurdueedu~what) wa

s developed (Lim et al 2005) to provide a Web GIS interface for the 48 continental states in

the USA for base flow separation using a local minimum method the BFLOW digital filter

method and the Eckhardt filter method The Web Geographic Information System (GIS)

version of the WHAT system accesses and uses US Geological Survey (USGS) daily stream

flow data from the USGS web server To evaluate WHAT performance the filtered results

using the Eckhardt digital filter with default BFImax value of 080 were compared with the

results from the BFLOW filter method that was previously validated (Lim et al 2005) The

Nash-Sutcliffe coefficient values were 091 and the R2 values were over 098 for 50 Indiana

gaging stations However the use of the default BFImax value of 080 for 50 Indiana gaging

stations is not recommended because the filtered base flow data were compared with the

results from the BFLOW digital filter which did not reflect physical characteristics in the

aquifer and watershed Although the WHAT system cannot consider server release and

snowmelt that can affect stream hydrographs the fully automated WHAT system can play an

important role for sustainable ground water and surface water exploitation

The digital filter method has been used in signal analysis and processing to separate high

frequency signal from low frequency signal (Lyne and Hollick 1979) This method has been

used in base flow separation because high frequency waves can be associated with the direct

runoff and low frequency waves can be associated with the base flow (Eckhardt 2005) Thus

filtering direct runoff from base flow is similar to signal analysis and processing (Eckhardt

2005) Equation shows the digital filter used for base flow separation (Lyne and Hollick

1979 Nathan and McMahon 1990 Arnold and Allen 1999 Arnold et al 2000)

For validation of hydrology components of models direct runoff and base flow components

of the stream flow hydrograph typically need to be separated because direct runoff and base

flow are usually simulated separately in the computer models

Equation below shows the digital filter used for base flow separation (Lyne and Hollick

1979 Nathan and McMahon 1990 Arnold and Allen 1999 Arnold et al 2000)

1 1

129

2t t t tq q Q Q

where tq is the filtered direct runoff at the t time step (m3s) 1tq is the filtered direct

runoff at the t-1 time step (m3s) α is the filter parameter tQ is the total stream flow at the t

time step (m3s) and 1tQ is the total stream flow at the t-1 time step (m

3s)

The Eckhardt filter separates the base flow from stream flow with Equation as shown below

1 1

1

3 1 130

3 3

131

2 2

t t t t

t t t

b b Q Q

b b Q

where tb is the filtered base flow at the t time step 1tb is the filtered base flow at the t-1

time step α is the filter parameter tQ is the total stream flow at the t time step (m3s) and

1tQ is the total stream flow at the t-1 time step (m

3s)

max 1 max

max

1 132

1

t t

t

BFI b BFI Qb

BFI

Where tb is the filtered base flow at the t time step 1tb is the filtered base flow at the t-1

time step BFImax is the maximum value of long-term ratio of base flow to total stream flow

α is the filter parameter and Qt is the total stream flow at the t time step

241 Evaluation of the WHAT (Base flow Separation Method)

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

The range of E lies between 10 (perfect fit) and infinity An efficiency of E lower than zero

indicates that the mean value of observed time series would have been a better predictor than

the model

CHAPTER III ESTIMATION OF ANTECEDENT RUNOFF ONDITION

CRITERIA FOR THE ESTIMATION OF CURVE NUMBER

31 Study basin

The Seolma Cheon River Watershed is selected for this study The watershed were

selected because it is a test delta managed by a South Korean construction technology

researcher fellow who is situated at the Kyonggido Paju city Juksungmyun which is about

46km upstream from the Imjin river estuary Seolma River is arborization form to the

Imjin Riverlsquos first tributary and has a river channel length of 113km and basin area of

185km2 Rainfall-runoff data of the Seolma river basin elected as the examination basin

was selected as the recorded data of that operation of the examination basin in 2001 and

hydrologic characteristics were investigated

The topography characteristics of the basin were investigated by each sub watershed at the

inundation level observatory It is better to use a large scale map for various topography

factors of the basin because the whole basin area is only 850km2 The calculated

topography factors are sub watershed area channel length basin average range shape

factor and basins center etc

Figure 3 1 Seolma Cheon Examination Watershed

32 Analysis of hydrologic observation data

321 Limitation of data

There are some limitations to the data as most of the detailed management records related to

these studies are difficult to access In our study rainfall (P) data was explicitly matched to

the runoff (Q) data Unreasonable and clearly wrongly recorded data were removed manually

such as Q data with missing P data In addition the daily Q data was manually matched to

runoff generating storms in the P data To account for possible differences in season the data

was split in summer season and dry season data to represent different land uses

322 Rainfall and runoff datasets used

The one watershed records of rainfall and runoff volumes used for this study were obtained

from the daily record at the experiment area to get precisely and accurate measured result

(Appendix A) The number of select rainfall-runoff data is 12 records year and 10 second

interval time then convert to daily rainfall-runoff record A number of estimated runoff

volumes were generated for using the curve number procedure

Table 3 1 CN of examination basin

According to Dinaple (1965) the direct runoff was computed by separating the base flow

from the total flow by using Web based Hydrograph Tools (WHAT)

For comparison to measured values runoff volumes Q are computed using

2000 2001

2002 2003

2005 2004

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

3221 Base flow separation

Firstly direct runoff is necessary to be separated from total runoff By applying base flow

separation known as Web Based Hydrograph Tools (WHAT) the base flow and direct runoff

2006 2007

2008 2009

2010 2011

can be separated The data are derived from the Juksungmyun examinational rainfall station

from 2000 to 2011 By applying base flow separation known as Web Based Hydrograph Tools

(WHAT) the base flow and direct runoff can be derived from the analysis The data is derived

from the Juksungmyun experimental rainfall station from 2000 to 2011

2000 2001

2002 2003

2004 2005

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011

(Where Direct Runoffs are derived from Web based Hydrograph Tools WHAT)

2006 2007

2008 2009

2010 2011

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

The Eckhardt filter separates the base flow from stream flow with Equation as shown below

1 1

1

3 1 130

3 3

131

2 2

t t t t

t t t

b b Q Q

b b Q

where tb is the filtered base flow at the t time step 1tb is the filtered base flow at the t-1

time step α is the filter parameter tQ is the total stream flow at the t time step (m3s) and

1tQ is the total stream flow at the t-1 time step (m

3s)

max 1 max

max

1 132

1

t t

t

BFI b BFI Qb

BFI

Where tb is the filtered base flow at the t time step 1tb is the filtered base flow at the t-1

time step BFImax is the maximum value of long-term ratio of base flow to total stream flow

α is the filter parameter and Qt is the total stream flow at the t time step

241 Evaluation of the WHAT (Base flow Separation Method)

Nash-Sutcliffe efficiency

2 2

1 1

2

1

12 21

n n

obs obs obs est

i i

n

obs obs

i

Q Q Q Q

E i n

Q Q

The range of E lies between 10 (perfect fit) and infinity An efficiency of E lower than zero

indicates that the mean value of observed time series would have been a better predictor than

the model

CHAPTER III ESTIMATION OF ANTECEDENT RUNOFF ONDITION

CRITERIA FOR THE ESTIMATION OF CURVE NUMBER

31 Study basin

The Seolma Cheon River Watershed is selected for this study The watershed were

selected because it is a test delta managed by a South Korean construction technology

researcher fellow who is situated at the Kyonggido Paju city Juksungmyun which is about

46km upstream from the Imjin river estuary Seolma River is arborization form to the

Imjin Riverlsquos first tributary and has a river channel length of 113km and basin area of

185km2 Rainfall-runoff data of the Seolma river basin elected as the examination basin

was selected as the recorded data of that operation of the examination basin in 2001 and

hydrologic characteristics were investigated

The topography characteristics of the basin were investigated by each sub watershed at the

inundation level observatory It is better to use a large scale map for various topography

factors of the basin because the whole basin area is only 850km2 The calculated

topography factors are sub watershed area channel length basin average range shape

factor and basins center etc

Figure 3 1 Seolma Cheon Examination Watershed

32 Analysis of hydrologic observation data

321 Limitation of data

There are some limitations to the data as most of the detailed management records related to

these studies are difficult to access In our study rainfall (P) data was explicitly matched to

the runoff (Q) data Unreasonable and clearly wrongly recorded data were removed manually

such as Q data with missing P data In addition the daily Q data was manually matched to

runoff generating storms in the P data To account for possible differences in season the data

was split in summer season and dry season data to represent different land uses

322 Rainfall and runoff datasets used

The one watershed records of rainfall and runoff volumes used for this study were obtained

from the daily record at the experiment area to get precisely and accurate measured result

(Appendix A) The number of select rainfall-runoff data is 12 records year and 10 second

interval time then convert to daily rainfall-runoff record A number of estimated runoff

volumes were generated for using the curve number procedure

Table 3 1 CN of examination basin

According to Dinaple (1965) the direct runoff was computed by separating the base flow

from the total flow by using Web based Hydrograph Tools (WHAT)

For comparison to measured values runoff volumes Q are computed using

2000 2001

2002 2003

2005 2004

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

3221 Base flow separation

Firstly direct runoff is necessary to be separated from total runoff By applying base flow

separation known as Web Based Hydrograph Tools (WHAT) the base flow and direct runoff

2006 2007

2008 2009

2010 2011

can be separated The data are derived from the Juksungmyun examinational rainfall station

from 2000 to 2011 By applying base flow separation known as Web Based Hydrograph Tools

(WHAT) the base flow and direct runoff can be derived from the analysis The data is derived

from the Juksungmyun experimental rainfall station from 2000 to 2011

2000 2001

2002 2003

2004 2005

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011

(Where Direct Runoffs are derived from Web based Hydrograph Tools WHAT)

2006 2007

2008 2009

2010 2011

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

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Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

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Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

CHAPTER III ESTIMATION OF ANTECEDENT RUNOFF ONDITION

CRITERIA FOR THE ESTIMATION OF CURVE NUMBER

31 Study basin

The Seolma Cheon River Watershed is selected for this study The watershed were

selected because it is a test delta managed by a South Korean construction technology

researcher fellow who is situated at the Kyonggido Paju city Juksungmyun which is about

46km upstream from the Imjin river estuary Seolma River is arborization form to the

Imjin Riverlsquos first tributary and has a river channel length of 113km and basin area of

185km2 Rainfall-runoff data of the Seolma river basin elected as the examination basin

was selected as the recorded data of that operation of the examination basin in 2001 and

hydrologic characteristics were investigated

The topography characteristics of the basin were investigated by each sub watershed at the

inundation level observatory It is better to use a large scale map for various topography

factors of the basin because the whole basin area is only 850km2 The calculated

topography factors are sub watershed area channel length basin average range shape

factor and basins center etc

Figure 3 1 Seolma Cheon Examination Watershed

32 Analysis of hydrologic observation data

321 Limitation of data

There are some limitations to the data as most of the detailed management records related to

these studies are difficult to access In our study rainfall (P) data was explicitly matched to

the runoff (Q) data Unreasonable and clearly wrongly recorded data were removed manually

such as Q data with missing P data In addition the daily Q data was manually matched to

runoff generating storms in the P data To account for possible differences in season the data

was split in summer season and dry season data to represent different land uses

322 Rainfall and runoff datasets used

The one watershed records of rainfall and runoff volumes used for this study were obtained

from the daily record at the experiment area to get precisely and accurate measured result

(Appendix A) The number of select rainfall-runoff data is 12 records year and 10 second

interval time then convert to daily rainfall-runoff record A number of estimated runoff

volumes were generated for using the curve number procedure

Table 3 1 CN of examination basin

According to Dinaple (1965) the direct runoff was computed by separating the base flow

from the total flow by using Web based Hydrograph Tools (WHAT)

For comparison to measured values runoff volumes Q are computed using

2000 2001

2002 2003

2005 2004

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

3221 Base flow separation

Firstly direct runoff is necessary to be separated from total runoff By applying base flow

separation known as Web Based Hydrograph Tools (WHAT) the base flow and direct runoff

2006 2007

2008 2009

2010 2011

can be separated The data are derived from the Juksungmyun examinational rainfall station

from 2000 to 2011 By applying base flow separation known as Web Based Hydrograph Tools

(WHAT) the base flow and direct runoff can be derived from the analysis The data is derived

from the Juksungmyun experimental rainfall station from 2000 to 2011

2000 2001

2002 2003

2004 2005

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011

(Where Direct Runoffs are derived from Web based Hydrograph Tools WHAT)

2006 2007

2008 2009

2010 2011

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Figure 3 1 Seolma Cheon Examination Watershed

32 Analysis of hydrologic observation data

321 Limitation of data

There are some limitations to the data as most of the detailed management records related to

these studies are difficult to access In our study rainfall (P) data was explicitly matched to

the runoff (Q) data Unreasonable and clearly wrongly recorded data were removed manually

such as Q data with missing P data In addition the daily Q data was manually matched to

runoff generating storms in the P data To account for possible differences in season the data

was split in summer season and dry season data to represent different land uses

322 Rainfall and runoff datasets used

The one watershed records of rainfall and runoff volumes used for this study were obtained

from the daily record at the experiment area to get precisely and accurate measured result

(Appendix A) The number of select rainfall-runoff data is 12 records year and 10 second

interval time then convert to daily rainfall-runoff record A number of estimated runoff

volumes were generated for using the curve number procedure

Table 3 1 CN of examination basin

According to Dinaple (1965) the direct runoff was computed by separating the base flow

from the total flow by using Web based Hydrograph Tools (WHAT)

For comparison to measured values runoff volumes Q are computed using

2000 2001

2002 2003

2005 2004

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

3221 Base flow separation

Firstly direct runoff is necessary to be separated from total runoff By applying base flow

separation known as Web Based Hydrograph Tools (WHAT) the base flow and direct runoff

2006 2007

2008 2009

2010 2011

can be separated The data are derived from the Juksungmyun examinational rainfall station

from 2000 to 2011 By applying base flow separation known as Web Based Hydrograph Tools

(WHAT) the base flow and direct runoff can be derived from the analysis The data is derived

from the Juksungmyun experimental rainfall station from 2000 to 2011

2000 2001

2002 2003

2004 2005

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011

(Where Direct Runoffs are derived from Web based Hydrograph Tools WHAT)

2006 2007

2008 2009

2010 2011

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

the runoff (Q) data Unreasonable and clearly wrongly recorded data were removed manually

such as Q data with missing P data In addition the daily Q data was manually matched to

runoff generating storms in the P data To account for possible differences in season the data

was split in summer season and dry season data to represent different land uses

322 Rainfall and runoff datasets used

The one watershed records of rainfall and runoff volumes used for this study were obtained

from the daily record at the experiment area to get precisely and accurate measured result

(Appendix A) The number of select rainfall-runoff data is 12 records year and 10 second

interval time then convert to daily rainfall-runoff record A number of estimated runoff

volumes were generated for using the curve number procedure

Table 3 1 CN of examination basin

According to Dinaple (1965) the direct runoff was computed by separating the base flow

from the total flow by using Web based Hydrograph Tools (WHAT)

For comparison to measured values runoff volumes Q are computed using

2000 2001

2002 2003

2005 2004

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

3221 Base flow separation

Firstly direct runoff is necessary to be separated from total runoff By applying base flow

separation known as Web Based Hydrograph Tools (WHAT) the base flow and direct runoff

2006 2007

2008 2009

2010 2011

can be separated The data are derived from the Juksungmyun examinational rainfall station

from 2000 to 2011 By applying base flow separation known as Web Based Hydrograph Tools

(WHAT) the base flow and direct runoff can be derived from the analysis The data is derived

from the Juksungmyun experimental rainfall station from 2000 to 2011

2000 2001

2002 2003

2004 2005

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011

(Where Direct Runoffs are derived from Web based Hydrograph Tools WHAT)

2006 2007

2008 2009

2010 2011

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

2000 2001

2002 2003

2005 2004

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

3221 Base flow separation

Firstly direct runoff is necessary to be separated from total runoff By applying base flow

separation known as Web Based Hydrograph Tools (WHAT) the base flow and direct runoff

2006 2007

2008 2009

2010 2011

can be separated The data are derived from the Juksungmyun examinational rainfall station

from 2000 to 2011 By applying base flow separation known as Web Based Hydrograph Tools

(WHAT) the base flow and direct runoff can be derived from the analysis The data is derived

from the Juksungmyun experimental rainfall station from 2000 to 2011

2000 2001

2002 2003

2004 2005

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011

(Where Direct Runoffs are derived from Web based Hydrograph Tools WHAT)

2006 2007

2008 2009

2010 2011

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Figure 3 2 Rainfall during summer from June to September Plot annually from 2000 to 2011

3221 Base flow separation

Firstly direct runoff is necessary to be separated from total runoff By applying base flow

separation known as Web Based Hydrograph Tools (WHAT) the base flow and direct runoff

2006 2007

2008 2009

2010 2011

can be separated The data are derived from the Juksungmyun examinational rainfall station

from 2000 to 2011 By applying base flow separation known as Web Based Hydrograph Tools

(WHAT) the base flow and direct runoff can be derived from the analysis The data is derived

from the Juksungmyun experimental rainfall station from 2000 to 2011

2000 2001

2002 2003

2004 2005

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011

(Where Direct Runoffs are derived from Web based Hydrograph Tools WHAT)

2006 2007

2008 2009

2010 2011

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

can be separated The data are derived from the Juksungmyun examinational rainfall station

from 2000 to 2011 By applying base flow separation known as Web Based Hydrograph Tools

(WHAT) the base flow and direct runoff can be derived from the analysis The data is derived

from the Juksungmyun experimental rainfall station from 2000 to 2011

2000 2001

2002 2003

2004 2005

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011

(Where Direct Runoffs are derived from Web based Hydrograph Tools WHAT)

2006 2007

2008 2009

2010 2011

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

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pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Figure 3 3 Rainfall versus Direct Runoff Plot annually from 2000 to 2011

(Where Direct Runoffs are derived from Web based Hydrograph Tools WHAT)

2006 2007

2008 2009

2010 2011

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Figure 3 4 Rainfall versus Direct Runoff Plot from 2000 to 2011

33 Evaluation of curve number procedures

After identifying direct runoff from total runoff curve number estimation can be calculated

from equation (7) by knowing daily rainfall and matched direct runoff However further

consideration is necessary to take into account That is to test the accuracy of curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon four different procedures including arithmetic mean median geometric mean and

asymptotic fit Except for the asymptotic method unranked paired rainfall and runoff volumes

from the maximum peal flow event each year of record were used to compute the calibrated

curve number

To test the accuracy of curve number determination curve numbers are computed depending

upon the arithmetic mean median geometric mean and asymptotic fit as shown the Table

below Except for the asymptotic method unranked paired rainfall and runoff volumes from

the maximum peal flow event each year of record were used to compute the calibrated curve

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

number

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Data Analysis and Data Management ( Rainfall and runoff datasets are being used to derive direct runoff by the application of Web Based

Hydrograph Tools)

Evaluation of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Figure 3 5 Schematic of Cure Number Estimation procedure

The table 32 indicates the curve number estimation generated from rainfall events throughout

the entire year from 2000 to 2011 during summer season (from June to September)

Table 3 2 Curve number estimation from the selected rainfall from 2000 to 2011 in summer

No P (mm) Q (m3s) S (mm) CN No P (mm) Q (m3s) S (mm) CN

1 1500 000 7500 7720 124 6700 3048 4974 8362

2 050 000 250 9903 125 1450 1404 039 9985

3 1000 047 3001 8943 126 050 000 250 9903

4 800 098 1700 9373 127 250 000 1250 9531

5 1450 096 3930 8660 128 2650 000 13250 6572

6 4150 080 15058 6278 129 1150 000 5750 8154

7 450 063 895 9660 130 150 000 750 9713

8 600 564 031 9988 131 800 000 4000 8639

9 4700 751 8703 7448 132 150 000 750 9713

10 600 258 480 9814 133 250 000 1250 9531

11 150 000 750 9713 134 050 000 250 9903

12 2750 228 6888 7867 135 050 000 250 9903

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

13 800 091 1759 9352 136 600 102 1072 9595

14 4500 041 18090 5840 137 1300 099 3359 8832

15 500 000 2500 9104 138 1400 395 1745 9357

16 7000 333 20939 5481 139 1600 1152 465 9820

17 9200 1268 18443 5793 140 100 000 500 9807

18 150 066 117 9954 141 1650 463 2067 9248

19 350 000 1750 9355 142 200 000 1000 9621

20 200 000 1000 9621 143 1250 556 957 9637

21 7650 165 27231 4826 144 1250 663 733 9720

22 050 000 250 9903 145 8050 3188 7136 7807

23 100 000 500 9807 146 4600 000 23000 5248

24 650 000 3250 8866 147 650 046 1723 9365

25 300 000 1500 9442 148 5750 4578 1139 9571

26 900 000 4500 8495 149 1800 1561 219 9914

27 150 000 750 9713 150 200 028 398 9846

28 600 044 1571 9418 151 2250 534 3222 8874

29 65 035 1878 9312 152 100 045 075 9970

30 05 009 086 9966 153 1400 214 2657 9053

31 36 058 13438 654 154 050 000 250 9903

32 35 121 36 986 155 500 065 1032 9609

33 05 0 25 9903 156 100 042 083 9968

34 30 934 3424 8812 157 2850 376 5841 8130

35 1005 9138 811 969 158 1750 490 2196 9204

36 2 0 10 9621 159 680 049 1791 9341

37 05 0 25 9903 160 080 000 400 9845

38 15 0 75 9713 161 660 000 3300 8850

39 13 0 65 7962 162 080 000 400 9845

40 05 0 25 9903 163 450 000 2250 9186

41 415 2334 2191 9206 164 450 000 2250 9186

42 15 0 75 9713 165 750 000 3750 8714

43 15 85 781 9702 166 200 140 063 9975

44 25 105 206 9919 167 1450 196 2936 8964

45 2 022 446 9827 168 050 030 023 9991

46 2200 036 8193 7561 169 1600 1330 255 9901

47 2100 009 9050 7373 170 1550 360 2255 9184

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

48 700 005 2887 8979 171 050 000 250 9903

49 500 000 2500 9104 172 050 000 250 9903

50 1750 032 6405 7986 173 3100 2587 483 9813

51 600 004 2491 9107 174 150 116 034 9987

52 5450 1274 7893 7629 175 050 000 250 9903

53 6100 349 17308 5947 176 4850 4154 645 9753

54 250 111 192 9925 177 700 048 1875 9313

55 050 038 012 9995 178 450 022 1336 9500

56 850 000 4250 8567 179 050 000 250 9903

57 600 000 3000 8944 180 3800 1976 2304 9168

58 050 000 250 9903 181 9600 000 48000 3460

59 150 131 017 9993 182 100 000 500 9807

60 5700 132 20033 5591 183 1450 000 7250 7779

61 3650 1820 2368 9147 184 600 000 3000 8944

62 4750 121 16398 6077 185 800 230 981 9628

63 23550 3490 45451 3585 186 700 067 1658 9387

64 12250 569 36879 4078 187 2420 462 4028 8631

65 650 000 3250 8866 188 040 000 200 9922

66 100 000 500 9807 189 100 000 500 9807

67 850 000 4250 8567 190 040 000 200 9922

68 750 000 3750 8714 191 2740 988 2699 9039

69 1700 000 8500 7493 192 720 483 257 9900

70 3000 000 15000 6287 193 950 000 4750 8425

71 3700 000 18500 5786 194 500 000 2500 9104

72 3400 000 17000 5991 195 050 000 250 9903

73 3550 023 14777 6322 196 100 034 105 9959

74 050 000 250 9903 197 250 000 1250 9531

75 350 000 1750 9355 198 350 140 307 9881

76 650 000 3250 8866 199 350 134 323 9875

77 450 000 2250 9186 200 17150 8010 12268 6743

78 300 000 1500 9442 201 1800 1109 789 9699

79 1250 000 6250 8025 202 250 000 1250 9531

80 600 005 2436 9125 203 800 097 1708 9370

81 400 126 452 9825 204 1450 254 2545 9089

82 300 208 098 9962 205 100 007 266 9896

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

83 550 071 1139 9571 206 050 000 250 9903

84 950 564 451 9826 207 1850 531 2272 9179

85 2300 407 4012 8636 208 600 199 644 9753

86 150 000 750 9713 209 1340 000 6700 7913

87 700 000 3500 8789 210 660 000 3300 8850

88 050 000 250 9903 211 340 000 1700 9373

89 150 000 750 9713 212 300 000 1500 9442

90 100 000 500 9807 213 640 067 1460 9456

91 100 000 500 9807 214 4280 000 21400 5427

92 350 000 1750 9355 215 020 000 100 9961

93 050 000 250 9903 216 020 000 100 9961

94 600 000 3000 8944 217 340 000 1700 9373

95 600 000 3000 8944 218 1220 377 1402 9477

96 100 000 500 9807 219 8160 3882 5683 8172

97 050 000 250 9903 220 020 000 100 9961

98 150 000 750 9713 221 280 000 1400 9478

99 150 000 750 9713 222 10080 9274 711 9728

100 350 070 565 9782 223 1300 043 4252 8566

101 050 000 250 9903 224 020 000 100 9961

102 150 000 750 9713 225 2360 000 11800 6828

103 1100 214 1809 9335 226 1220 000 6100 8063

104 800 616 183 9929 227 100 000 500 9807

105 250 127 157 9938 228 020 000 100 9961

106 500 271 282 9890 229 2540 1108 1996 9272

107 1050 000 5250 8287 230 1250 402 1383 9484

108 050 000 250 9903 231 300 189 125 9951

109 550 000 2750 9023 232 250 023 602 9769

110 100 000 500 9807 233 7650 4767 3271 8859

111 1250 000 6250 8025 234 3550 1231 3644 8745

112 100 000 500 9807 235 1750 1020 862 9672

113 3350 1894 1751 9355 236 4150 2876 1353 9494

114 950 433 703 9731 237 100 000 500 9807

115 1350 187 2699 9039 238 250 000 1250 9531

116 1350 073 3895 8670 239 400 000 2000 9270

117 3800 2147 1989 9274 240 750 597 149 9942

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

118 050 000 250 9903 241 400 000 2000 9270

119 6750 4115 3030 8934 242 2300 811 2320 9163

120 100 063 042 9984 243 050 003 140 9945

121 1450 178 3078 8919 244 300 087 365 9858

122 350 035 814 9689 245 2350 539 3451 8804

123 150 013 369 9857

Figure 3 6 Curve number versus Rainfall plot amp Asymptotic Fitting Curve plot and Residual

plot for asymptotic curve number fits for Seolma Cheon River Watershed

Based on the graphic representation on figure 36 asymptotic curve number is 7857 with

regression equation

005697857 (100 7857) pCN e

005697857 (100 7857) pCN e

Runoff estimated by Arithmetic Mean Runoff estimated by Median

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Figure 3 7 Plot of the comparison of measure runoff to the estimated runoff for each

procedure

Figure 38 Plot of the comparison of measure runoff to the estimated runoff for all procedure

From the figure 37 the geometric mean curve numbers of all year were greater than the curve

numbers based on the other calculation procedures However the geometric mean and median

curve numbers do not seem to be significantly different as expected if the watershed curve

number distribution are logarithmic In addition the arithmetic mean curve numbers generally

are close in magnitude to median curve number The mean median and geometric mean

Runoff estimated by Geometry Runoff estimated by Asymptotic CN

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

derived curve number do not seem to be significantly different

The asymptotic curve numbers were smaller than the curve number based on the other

procedures and some of them are not available due to the fitting points of rainfall and

estimated curve number by equation 7 It is remarkable that asymptotic curve numbers are

expected to be smaller because set of curve number that are not too scattered are associated

with the largest numbers rainfall volume observed or infinitely large volumes Remarkable is

that the asymptotic fit is biased to smaller curve number with very low frequencies of

occurrence

Table 3 3 Watershed Curve Number by all procedures from 2000 to 2011

Year Arithmetic Mean Median Geometric Mean Asymptotic Fit

200 9380 9773 9750 7100

2001 9385 9713 9697 8586

2002 8085 8790 8955 NA

2003 9585 9748 9729 8688

2004 9397 9713 9674 8954

2005 9225 9689 9628 7819

2006 9190 9595 9560 7107

2007 9433 9475 9719 8955

2008 9025 9564 9590 NA

2009 9380 9699 9683 6654

2010 9078 9449 9568 7931

2011 9473 9513 9654 9021

Table 3 4 Overall Watershed Curve Number by all Procedures

Arithmetic Mean Median Geometric Mean Asymptotic Fit

9314 9615 9652 7857

Also included in table 34 are the NRCS (2001) curve number derived from table The

geometric mean curve numbers of all year were greater than the curve number based on the

other calculation However the geometric mean and median curve numbers do not seem to be

significantly different as expected if the watershed curve number distributions are logarithmic

In addition the arithmetic mean curve number generally fall or are close in magnitude to one

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

of the values

The asymptotic curve numbers was smaller than the curve numbers based on the other

procedure The asymptotic curve numbers are expected to be smaller because these values are

associated with the largest rainfall volumes observed or infinitely large volume

34 Reliability of Curve number method on Gauged Basins

To assess the reliability of the handbook CN method the runoff depth were estimated from

the theoretical CN and compared with the measure runoff depth The theoretical CN was

computed as the basin mean value derived from the asymptotic method to take into account 5-

day antecedent rainfall and season differentiation To evaluate model performance two

additional indexes were computed to assess the agreement of estimated runoff and measured

runoff There are the Normal root-mean-square error (NRMSE) R2 RE and Nash and

Sutcliffe (1970) efficiency (E)

Arithmetic Mean Procedure R2 = 07233 Median Procedure R

2 = 07315

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Figure 3 9 Coefficient of determination of each CN estimation procedures

Procedure of CN

estimation CN R

2 RE NRMSE E

Arithmetic Mean 9314 07233 06274 00653 04054

Median 9615 07315 07240 00722 01864

Geometric Mean 9652 07320 07357 00733 01496

Asymptotic Fit 7857 06376 01809 00738 0601

Table 26 Reliability of Curve number method

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures are determined from coefficient of determination and goodness of fit such as

Normalized Root Mean Square Error (NRMSE) Relative Error (RE) R-Square (R2) and

Nash Sutcliffe coefficient (E)

Based on the tests shown in table 36 the asymptotic procedure is the best for curve number

estimation In addition to that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another Hence

curve number derived from asymptotic method is used for further analysis Asymptotic curve

Geometry Procedure R2 = 07320 Asymptotic CN Procedure R

2 = 06376

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

number is 7857 with regression equation 005697857 (100 7857) pCN e

After the curve number is estimated the next step is to simulate antecedent moisture

condition by applying all the proposed algebraic expression of NEH4 with the consideration

of 5 day prior to rainfall (definition of AMC using antecedent rainfall table) Next is to

validate and calibrate among the proposed procedure to figure out the estimator of antecedent

moisture condition criteria

35 Estimation of Thresholds for AMCARC

To reduce uncertainties in the CN method new rainfall thresholds for the definition of the

AMC class where computed The new thresholds have been evaluated for each of the basin as

the precipitation of the antecedent 5-day time span which minimizes the difference between

measured and estimated runoff The optimization procedure was based on a simple manual

trial-and-error approach The differentiation between growth and dormant seasons was not

considered in this analysis

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Figure 3 10 Antecedent Moisture Condition (AMC)Antecedent Run off Condition

proposed Methodology

Algebraic expression of

NEH4 ( developed Sobhani

(1975) Chow et al (1988)

Hawkins et al (1985)

Arnold et al (1988)

Data collection (Rainfall

and Runoff data)

Derive direct runoff ( by

Web Based Hydrograph

Tools WHAT)

Calibration amp Validation

( NRMSE RENSE R2)

Determination of AMCARC

estimation criteria

Asymptotic FitGeometric MeanMedianArithmetic

Mean

Accuracy of curve number procedures

Matlab Program is used to encode the following procedures

Coefficient of Determination and Goodness of Fit ( NRMSE RE Rsquare)

Curve Number Estimation

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

Algebraic expression of NEH4

Arnold et al

(1988)

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Once curve number has been estimated proposed algebraic equation can be used to determine

the criteria for choosing ARCAMC

Curve Number

estimation by

all procedures

Hawkins

et al (1985)

Sobhani

(1975)Chow et al

(1988)

ARCAMC criteria

determination

Algebraic expression of NEH4

Arnold et al

(1988)

Calibrated Validated by Coefficient of Determination

and Goodness of Fit ( NRMSE RE Rsquare)

Determination of AMCARC estimation criteria

Compare among Coefficient of Determination and Goodness of Fit

Figure 3 11 Schematic representation of AMCARC estimation criteria

Once algebraic expressions are computed comparison among coefficient of determination

and Goodness of fit is necessary to follow up Finally AMCARC criteria are identified

Second step of the proposed procedure is to determine AMCARC criteria estimation using

algebraic Expression developed by Sobhani (1975) Hawkins et al (1985) Chow et al 1988

and Arnold et al (1990)

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Algebraic Expression of NEH4 developed by Sobhani 1975

Figure 3 12 Verification of AMCARC condition (using algebraic expression by Sobhani

1975)

AMC R2 RE NRMSE E

2000-2011 0327801474 094605433 0896495482 0024430041

2011 0918578445 094605433 1733367342 0059823241

2010 0348851642 096495701 3596402064 -0030357167

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

2010 2011

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Table 3 5 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect Sobhanilsquos algebraic expression

Fig 312 shows about the plot of rainfall direct runoff and AMCARC versus time in

different time period That is 12 year of daily record and the below graph are the plot of daily

record in 2011 and 2010 respectively from June to September In other words they are plotted

during summer season

With the value of R-square 03278 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 0946 it is

indicated that model overestimate observed data (direct runoff) by 946 However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff with R-square equal to 09185 for

AMC condition and 09383 for ARC condition yet it model overestimate observed data by

9460 percent In 2010 it shows the value close to the estimation of 12 years period ranging

from 2000 to 2011

Algebraic Expression of NEH4 developed by Hawkins et al 1985

2010 2011

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Figure 3 13 Verification of AMCARC condition (using algebraic expression by Hawkins et

al 1985)

AMC R2 RE NRMSE E

2000-2011 0333680999 0946660232 0907297388 0023098886

2011 0928099542 0946660232 1754467056 0058310338

2010 0350696295 09660276 3714648349 -0033086936

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 6 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Hawkins et allsquos algebraic expression

Fig 313 and Table 36 present about the plot of rainfall direct runoff and AMC versus time

in different time period by the application of Hawkin et al 1985 That is 12 year of daily

record and the below graph are the plot of daily record in 2011 and 2010 respectively from

June to September in summer

With the value of R-square 03336 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed Also with RE equal to 09466 and 09461 for

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

AMC and ARC respectively it is indicated that model overestimate observed data (direct

runoff) by 9466 and 9441 in respect to AMC and ARC condition However model

performance is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly well describes the observed direct runoff yet it model overestimate observed

runoff

Overall algebraic equations by Hawkins at el seem to be more reliable than by Sobhani

Remarkable is that the two proposed equations are very close to one another in term of

reliability

Algebraic Expression of NEH4 developed by Chow et al 1988

2010 2011

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Figure 3 14 Verification of AMCARC condition (using algebraic expression by chow et al

1988)

AMC R2 RE NRMSE E

2000-2011 0330815816 0946759955 0909419272 0022190703

2011 0924871529 0946759955 1758274536 0057751809

20100350433876 0966201253 373475769 -0033653731

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 0380569445 098809233 1086921876 -0086673899

Table 3 7 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to chow et allsquos algebraic expression

Graphic representation in figure 314 indicates the rainfall direct runoff and AMC and ARC

versus time relationship different time period by the application of Chow et al 1988 That is

12 year of daily record and the below graph are the plot of daily record in 2011 and 2010

respectively in summer

With the same consideration as in previous description overall the simulated direct runoff

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

with algebraic equation represented CN I and CN III by Chow et al 1988 is closely similar to

the two other proposed equation Closely look into the coefficient of determination

simulation of direct runoff is somewhere in between the two proposed methods It is

noticeably that also overestimate the observed direct runoff by 9467 and 9641 in regard

to AMC and ARC condition

Algebraic Expression of NEH4 developed by Arnold et al 1990

Figure 3 15 Verification of AMCARC condition (using algebraic expression by Arnold et al

1990)

2010 2011

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

AMC R2 RE NRMSE E

2000-2011 0308655367 0945964916 0895016283 0024420732

2011 090537271 0945964916 1729746927 0060640334

2010 0348083522 0964796732 3576773151 -0028484523

ARC R2 RE NRMSE E

2000-2011 0369420822 096416947 1379920476 -0019679303

2011 093839593 096416947 267172036 0014620395

2010 093839593 096416947 267172036 0014620395

Table 3 8 Coefficient of determination and Goodness of fit of AMC ARC and Regression

Equation in respect to Arnold et allsquos algebraic expression

Figure 315 represents plot of rainfall direct runoff and simulated direct runoff by AMC

taking into account of algebraic equation developed by Arnold et al 1990

With the value of R-square 03086 for AMC condition and 03694 for ARC condition it is

denoted that it poorly explains the observed direct runoff Also with RE equal to 09459 for

AMC condition and 09641 for ARC condition it is indicated that model overestimate

observed data (direct runoff) by 9459 and 9641 respectively However model performance

is fairly fit among validated value across the year 2011 and 2010

Regarding to validation and calibration of the estimated model (direct runoff estimation) in

2011 it fairly describes the observed direct runoff yet it model overestimate observed data

Third step to compare among Coefficient of Determination and Goodness of Fit

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Sobhani Hawkins et al Chow et al Arnold et al

R2 03278 03337 03308 03087

RE 09461 09467 09468 09460

NRMSE 08965 09073 09094 08950

E 00244 00231 00222 00244

R2 09186 09281 09249 09054

RE 09461 09467 09468 09460

NRMSE 17334 17545 17583 17297

E 00598 00583 00578 00606

R2 03489 03507 03504 03481

RE 09650 09660 09662 09648

NRMSE 35964 37146 37348 35768

E -00304 -00331 -00337 -00285

Algebraic Expression

2000-2011

2011

2010

AMCCoefficient of

Determination

Sobhani Hawkins et al Chow et al Arnold et al

R2 03694 03694 03694 03694

RE 09642 09642 09642 09642

NRMSE 13799 13799 13799 13799

E -00197 -00197 -00197 -00197

R2 09384 09384 09384 09384

RE 09642 09642 09642 09642

NRMSE 26717 26717 26717 26717

E 00146 00146 00146 00146

R2 03806 03806 03806 09384

RE 09881 09881 09881 09642

NRMSE 108692 108692 108692 26717

E -00867 -00867 -00867 00146

2000-2011

2011

2010

Algebraic ExpressionARC

Coefficient of

Determination

Table 3 9 Result of all coefficient of determination

Table 39 present results of coefficient of determination of AMC from the four different

proposed equations

Clearly indicated in the table 39 for 12 years period analysis normalized root mean square

error RE and E are best described by the application of algebraic expression by Arnold et al

at the value of 08950 09460 and 00244 for AMC condition In addition for all the

coefficient of determination in regard to ARC condition Arnold et al algebraic equation is the

best representation criteria However overall calculated coefficients of determination

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

among proposed method are very close to each other In the other words it remarkably

indicates the least residual variance

In addition to that for all the application of algebraic equation in determining AMC and ARC

criteria it overestimates the actual runoff by over 90 However in terms of estimation

performance proposed expression by Arnold et al fairly explains the observed direct runoff

more reliable than others proposed expressions With regarding to R-square proposed method

by Hawkins et al is the most reliable for AMC condition

For the verification observed and estimated runoff data from 2010 and 2011 have been

conducted As results from the comparison of coefficient of determination Arnold et al is the

most favorable estimation of antecedent moisture condition criteria as well as antecedent

runoff condition criteria

Proposed methods are overall is very close to one and another it is implied that all the

application of proposed method can be used to describe the antecedent moisture condition

criteria and as antecedent runoff condition criteria Also the antecedent rainfall table from

NEH report

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

CHAPTER 4 CONCLUSIONS

WHAT is the acronym of Web Based Hydrograph Analysis Tool which is the useful internet

based application that allows the user to get the results of base flow from different digital

filters by just simple click and then get the preferable results In accordance to its simplicity it

might be recommended for further study to determine base flow

Application of curve number procedures and evaluation of each procedure by the coefficient

of determination

The relative accuracy and correlation of rainfall-runoff derived curve numbers based on four

procedures determined from coefficient of determination and goodness of fit show that the

asymptotic procedure is the best for curve number estimation It is found that asymptotic CN

number is the most appropriate procedure in Seolma Cheon River watershed with the value of

7857 It is noticeably that the curve number derived by the three procedures known as

arithmetic mean median and geometric mean are in general not very different these finding

only serve to highlight that one highlight that one procedure is as similar as another

Proposed methods are developed by modifying estimated runoff to observed runoff with

coefficient of determination and then applying different algebraic expression developed In

addition by choosing precipitation from antecedent moisture condition due to the 5 prior to

rainfall (NEH-1964 AMC definition) it is indicated that the overall results of estimated runoff

is nearly double to the observed runoff The reason is originated from the selection of

precipitation according antecedent rainfall table

Clearly indicated from 12 years period analysis and 2 years period of verification normalized

root mean square error RE and E are best described by the application of algebraic expression

by Arnold et al at the value of 08950 09460 and 00244 respectively for AMC condition

and 13799 09642 and -00197 respectively for ARC condition Furthermore for all the

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

coefficient of determination with the respect to ARC condition Arnold et al algebraic

equation is the best representation criteria Therefore Arnold et al is the most appropriate for

antecedent moisture condition criteria as well as for antecedent runoff condition Therefore

this algebraic expression might be used in South Korea condition properly Since calculated

coefficients of determination among proposed method are very close to each other it

remarkably indicates the least residual variance

From results and the validation of AMCARC it is implied that the determination of AMC has

some inconsistency from one to another Thus for long time period of time determination of

AMC might be accepted for further usage

For further study it is recommended to compare the Base flow Separation and CN Estimation

Method for determining ARC and AMC as well as to figure out the best practices for

identifying ARC and AMC By applying different base flow digital filter the research might

find out the better results of ARC and AMC in turn it might be useful to get better

understanding about ARC and AMC as well as the optimization value of AMC and ARC with

regards to Korea condition

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

REFERENCES

Andrews RG (1954) The use of relative infiltration indices in computing runoff in Rainfall-runoff

relationship Singh VP Water Resources Publications

Arnold JG Williams JR Nicks AD and Sammons NB (1990) SWRRB A basin scale simulation model for

soil and water resources management Texas AampM University Press pp 142

Babu PS and Mishra SK (2011) An improved SCS- CN inspired model J of Hydrological

Engineering ASCE 17(11) pp 1164-1172

Chow VT Maidment DR and Mays LW (1988) Applied Hydrology Mc-Graw-Hill New

York pp 572

Eckhardt K (2005) How to construct recursive digital filters for baseflow separation Hydrological Process

19(2) pp 337-349

Elhakeem M and Papanicolaou AN (2009) Estimation of the runoff curve number via direct rainfall

simulator measurements in the state of Iowa USA Water Resources Management 23(12) pp 2455ndash2473

Garen DC and Moore DS (2005a) Curve number hydrology in water quality modeling uses abuses and

future direction J of the American Water Resources Association 412 (April 2005) Paper 03127 pp 377-

388

Garen DC and Moore DS (2005b) Reply to discussion of curve number hydrology in water quality

modeling uses abuses and future directions by MT Walter and SB Shaw J of the American Water

Resources Association 416 (December 2005) pp 1493-1494

Grabau MR Hawkins RH VerWeire KE and Slack DC (2008 in review) Curve numbers as random

variables empirical observations and implication for design and modeling J of American Society of

Agricultural and Biological Engineering [in Review]

Hawkins RH (1993) Asymptotic determination of runoff curve numbers from data J of Irrigation and

Drainage Engineering ASCE 119(2) pp 334-345

Hawkins RH Hjelmfelt Jr AT and Zevenbergen AW (1985) Runoff probability storm depth and curve

numbers J of Irrigation and Drainage Division ASCE 111(4) pp 330-340

Hawkins RH (1996) Discussion of SCS runoff equation revisited for variable source runoff areas by TS

Steenhuis M Mitchell JRossing and MFWalter J of Irrigation and Drainage Engineering ASCE

122(5) pp 319

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

Hawkins RH Ward TJ Woodward DE and Van Mullen JA (2009) Curve number hydrology State of the

practice American Society of Civil Engineers ASCE USA

Hjelmfelt Jr AT and Kramer LA (1983) Discussion of antecedent moisture condition probability by D D

Gray et al J of Irrigation and Drainage Engineering ASCE 109 p300

Hjelmfelt Jr AT (1991) Investigation of curve number procedure J of Hydraulic Engineering Division

Amer Soc Civ Eng 117(6) pp 725-737

Jain MK Mishra SK Singh VP (2006) Evaluation of AMC dependent SCS-CN based models using

watershed characteristics J of Water Resources Management 20( 4) pp 531-552

Kim NW and Lee JW (2008) Temporally weighted average curve number method for daily runoff

simulation J of Hydrological Processes 22(25) pp 4936-4948

King KW Arnold JG and Bingner RL (1999) Comparison of Green ndashAmpt and curve number methods on

Goodwin Creek using SWAT Transaction of the American Society of Agricultural Engineers 42(4) pp

919-925

Kwak JW Kim SJ Yin SH and KIM HS (2010) direct runoff simulation using CN regression equation for

Bocheong Stream J of Korean Society on Water Quality 26(4) pp 590-597 [Korean Literature]

Michel C Vazken A and Charles P (2005) Soil conservation service curve number method

how to mend among soil moisture accounting procedure Water Resources Research 41(2)

pp 1-6

Miliani F Ravazzani G and Manicini M (2011) Adaptation of precipitation index for the estimation of

antecedent moisture condition in large mountainous basin J of Hydrological Engineering 16(3) pp 218-227

Mishra SK Jain MK and Singh VP (2004) Evaluation of SCS-CN based models incorporating antecedent

moisture J of Water Resources Management 18(6) pp 567-589

Mishra SK Jain MK Pandey RP and Singh VP (2005) Catchment area-based evaluation of the AMC-

dependent SCS-CN-based rainfall-runoff models J of Hydrological Processes 19 pp 2701ndash2718

Mishra SK Pandey RP Jain MK and Singh VP (2008) A rain duration and modified AMC dependent

SCS- CN procedure for long duration rainfall- runoff events Water Resources Management 22(7) pp

861-876

Mockus V (1949) Estimation of total (peak rates of) surface runoff for individual storms Exhibit A of

Appendix B Interim Survey Rep Grand (Neosho) River Watershed USDA Washington DC

Pandit A and Gopalakrishnan G (1996) Estimation of annual storm runoff coefficients by continuous

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

Van Mullem JA (1992) Soil moisture and runoffmdashanother look ASCE Water Forum 92 Proceedings of the

Irrigation and Drainage Session Baltimore MD

Williams JR and LaSeur V (1976) Water yield model using SCS curve numbers J of Hydraulic Engineers

102( 9) pp 1241-1253

simulation J of Irrigation and Drainage Engineers ASCE 122(4) pp 211-220

Ponce VM and Hawkins RH (1996) Runoff curve number has it reached maturity J of Hydrologic

Engineering ASCE 1(1) pp 11-19

Rallison RE (1980) Origin and evolution of the SCS runoff equationrdquo Proceedings of Symposium on

Watershed Management 1980 American Society of Civil Engineering New York pp 921-924

Rallison RE and Cronshey RG (1979) Discussion of runoff curve numbers with varying site moisture Proc

Amer Soc Civ Eng 105(IR4) pp 439-441

Sahu RK Mishra SK Eldho TI and Jain MK (2007) An advanced soil moisture accounting procedure for

SCS curve number method Hydrological Processes 21(21) pp 2827-2881

Sahu RK Mishra SK and Eldho TI (2010) An improved AMC-coupled runoff curve number model

Hydrological Processes 24(20) pp 2834-2839

Schneider LE and McCuen RH (2005) Statistical guideline for curve number generation J of Irrigation and

Drainage Engineering 131(3) 282-290

Silveira L Charbonnier F and Genta JL (2000) The antecedent soil moisture condition of the curve number

procedure J of Hydrological Sciences 45(1)

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