Water Resour Manage (2011) 25:97–111DOI 10.1007/s11269-010-9689-6

Changes of Pan Evaporation in the West of Iran

Hossein Tabari · Safar Marofi

Received: 20 January 2010 / Accepted: 11 June 2010 /Published online: 2 July 2010© Springer Science+Business Media B.V. 2010

Abstract Evaporation is an important component of the hydrological cycle and itschange would be of great significance for water resources planning, irrigation controland agricultural production. The main purpose of this study was to investigate tem-poral variations in pan evaporation (Epan) and the associated changes in maximum(Tmax), mean (Tmean) and minimum (Tmin) air temperatures and precipitation (P)for 12 stations in Hamedan province in western Iran for the period 1982–2003.Significant trends were identified using the Mann–Kendall test, the Sen’s slopeestimator and the linear regression. Analysis of the Epan data revealed a significantincreasing trend in 67% of the stations at the 95% and 99% confidence levels.To put the changes in perspective, the trend in Epan averaged over all 12 stationswas (+)160 mm per decade. Trend analysis of the meteorological variables forexamination of causal mechanisms for Epan changes showed warming trends in Tmax,Tmean and Tmin series in almost all the stations, which were significant over half ofthe total stations. On the contrary, no significant changes in precipitation were foundapproximately at all of the stations. Furthermore, a moderate positive correlationwas observed between Epan and Tmax, Tmean and Tmin, while a inverse correlationwas found between Epan and P data. The results indicated that the study area hasbecome warmer and drier over the last 22 years, hence the evaporative demands ofthe atmosphere and thereby crop water requirements have increased.

Keywords Trend analysis · Temporal variations · Class A pan evaporation ·Air temperature · Precipitation

H. Tabari (B) · S. MarofiDepartment of Irrigation, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, Irane-mail: hosseintabari@gmail.com

98 H. Tabari, S. Marofi

1 Introduction

Evaporation (E) is an important component of the hydrological cycle and influencesthe availability of water, particularly for agriculture (Burn and Hesch 2007). Themeasurement of E is difficult, hence the measurement of potential evaporation isoften used instead (Jovanovic et al. 2008). In applications such as those in ecology,hydrology, agriculture and engineering, the potential evaporation is taken to beproportional to the rate at which water evaporates from a pan located at the surface,known as pan evaporation (Epan). Pan evaporation has traditionally been used torepresent the evaporative demand of the atmosphere when estimating crop waterrequirements (Roderick and Farquhar 2004).

Pan evaporation will increase as the average air temperature near the surfaceincreases. This expectation is based on an implicit assumption that, as the air temper-ature increases, everything else is held constant. That is, Epan would increase as theair at the surface warmed if there were no change in the vapour content of the air andwind speed were unchanged (Roderick and Farquhar 2004). The mechanisms causingthe observed trends in E are not clearly understood. Although there is widespreadagreement that global temperatures are increasing, there are many meteorologicalfactors that can result in an increase or a decrease in evaporation (Burn and Hesch2007).

The majority of the studies conducted in the United States and the former SovietUnion (Peterson et al. 1995; Lawrimore and Peterson 2000; Golubev et al. 2001;Hobbins et al. 2004), Australia and New Zealand (Roderick and Farquhar 2002,2004, 2005; Jovanovic et al. 2008) showed decline in Epan rates in the last decades.The similar decreasing Epan was also reported in Venezuela (Quintana-Gomez 1997),Canada (Burn and Hesch 2007) and Puerto Rico (Harmsen et al. 2004). In addition,the Second Assessment Report of the Intergovernmental Panel on Climate Change(IPCC 1996) described widespread decreases in Epan during the twentieth centuryusing pan measurements from the former Soviet Union and the United States. InAsia, Xu et al. (2006) studied the spatial distribution and temporal trend of referenceevapotranspiration (ETo), Epan and pan coefficient in the Changjiang catchment inChina during 1960–2000. They showed that there was a significant decreasing trendin both ETo and Epan, which was mainly caused by a significant decrease in the nettotal radiation and to a lesser extent by a significant decrease in the wind speed overthe catchment. Besides, no temporal trends were detected for the pan coefficient.Wang et al. (2007) considered changes of Epan and ETo in the Yangtze River basinin China from 1961 to 2000. They found that both Epan and ETo decreased duringthe summer months contributing most to the total annual reduction. Jhajharia etal. (2009) analyzed the temporal characteristics of Epan trends under the humidconditions for 11 sites of northeast India. They concluded decreasing Epan trendsmainly in pre-monsoon and monsoon seasons. The findings of this study suggestedthat mainly two parameters i.e. sunshine duration followed by wind speed stronglyinfluenced Epan changes at various sites from different regions in different seasons.

On the other hand, decreases of Epan have not been universal and increasesof Epan have been reported in many parts of the world. Analysis of evaporationmeasurements at Bet Dagan in Israel’s central coastal plain between 1964 and 1998by Cohen et al. (2002) showed a small but statistically significant increase in screenedClass A Epan, mainly in the dry, summer half of the year. Likewise, no changes were

Changes of Pan Evaporation in the West of Iran 99

found in total open water evaporation or ETo estimated with Penman’s combinedheat balance and aerodynamic equation because the decreases found in the radiationbalance term were offset by increases in the aerodynamic term. da Silva (2004)analyzed time-series of eight climatic variables to ascertain the existence of climatevariability in the northeast of Brazil. He indicated increasing trends for maximum(Tmax), mean (Tmean) and minimum (Tmin) temperatures, Epan, ETo and aridity index,and decreasing trends for relative humidity and precipitation (P). Oguntunde et al.(2006) investigated trends and variability in hydroclimatology variables of the VoltaRiver Basin in West Africa from 1901 to 2002 and found positive trends in Epan data.Stanhill and Möller (2008) analyzed evaporation measurements made at 16 sites inthe British Isles for evidence of long-term changes. Four out of eight studied IrishClass A evaporation pan series between 1963 and 2005 showed significant lineartrends, three of increasing and one of decreasing evaporation. Besides, five out ofeight studied UK sunken evaporation tank series between 1885 and 1968 indicatedstatistically significant linear trends, two of increasing and three of decreasingevaporation.

So far, several authors investigated the estimation of Epan and ETo in Iran (Tabari2010; Tabari et al. 2010; Sabziparvar et al. 2010; Sabziparvar and Tabari 2010), butno comprehensive study has been carried out on the temporal trends in Epan andETo time series. As the first attempt in Iran, the main aim of this study was toinvestigate temporal variations in annual Epan for 12 stations located in Hamedanprovince in western Iran during 1982–2003. Also, the influences of air temperatureand precipitation on the temporal trends detected in Epan were analyzed.

2 Materials and Methods

2.1 Study Area and Data

The study area is Hamedan province which is located in the west of Iran, at 47◦45′E to 49◦36′ E longitude and 33◦33′ N to 35◦38′ N latitude, covering 19,368 km2

of land area (Fig. 1). Hamedan is one of the mountainous provinces of Iran. Thehighest point in this province is the Alvand peak, 3,574 m high. The climate in thestudy region is semi-arid with mild summers and very cold winters. The mean annualrainfall is 320 mm. Winter precipitation is mainly snow, lasting some 6 to 8 months inthe mountainous areas and 1 to 2 months on the plateau. The rest of the precipitationis provided by scarce spring and fall rains. Hamedan is one of the coldest provincesof Iran and its temperature may drop below −30◦C on the coldest days. The meanmonthly temperature in the study area varies from −5◦C in January to 24◦C in July,with an annual mean of 11◦C.

Data including maximum, mean and minimum air temperatures, precipitation andpan evaporation were collected from 12 stations for the period 1982–2003 (Table 1).The basic statistics for the 22-years of data set are summarized in Table 2. Long-termEpan data are available for a few stations in Iran. Only stations that currently recordEpan and have at least 22 years of continuous Epan data were selected for this study.In order to increase the number of stations with data covering 22 years or more,

100 H. Tabari, S. Marofi

Fig. 1 Geographic location of the study region and the stations

one neighbouring station (Kangavar) was combined. The class A pan was chosenas the standard for measuring evaporation in Iran due to it being the internationalpreference. The class A pan is a circular pan made of galvanized iron, with 121 cmdiameter and 25.5 cm deep which is supported by a wood frame stand.

2.2 Trend Analysis

A large number of tests can be used for trend detection in long time seriesof meteorological and hydrological records. In the present study, three tests in-cluding Mann–Kendall, Sen’s slope estimator and linear regression have been

Changes of Pan Evaporation in the West of Iran 101

Table 1 Geographic characteristics of the stations used in the study

Station name Station type Longitude (E) Latitude (N) Elevation (m a.s.l.)

1. Dargezin Climatological 49◦ 01′ 35◦ 21′ 1,8702. Ekbatan Research 48◦ 32′ 34◦ 52′ 1,7303. Ekbatan dam Evaporimeter 48◦ 36′ 34◦ 46′ 1,8804. Ghahavand Raingauge 49◦ 01′ 34◦ 51′ 1,4805. Kangavar Synoptic 47◦ 59′ 34◦ 30′ 1,4686. Kheir-Abad Evaporimeter 48◦ 32′ 34◦ 28′ 1,7407. Khomigan Evaporimeter 49◦ 02′ 35◦ 22′ 1,8108. Khosro-Abad Evaporimeter 48◦ 02′ 34◦ 38′ 1,5009. Malayer Synoptic 48◦ 49′ 34◦ 17′ 1,77610. Nahavand Synoptic 48◦ 24′ 34◦ 09′ 1,68511. Nozheh Synoptic 48◦ 41′ 35◦ 12′ 1,67912. Varayeneh Evaporimeter 48◦ 24′ 34◦ 05′ 1,800

used for detection of trends. Brief descriptions of these statistical methods are asfollows:

2.2.1 Linear Regression Model

Simple linear regression is an important and commonly used parametric method foridentifying monotonic trend in a time series. It is used to describe the relationshipbetween one variable with another or other variables of interest. It is often per-formed to obtain the slope of hydrological and meteorological variables on time.Positive slope shows increasing trend while negative slope indicates negative trend.Regression has the advantage that it provides a measure of significance based onthe hypothesis test on the slope and also gives the magnitude of the rate of change(Hirsch et al. 1991). The total change during the period under observation is obtainedby multiplying the slope with the number of years.

2.2.2 Mann–Kendall Test

The Mann–Kendall test is a non-parametric test for identifying trends in time seriesdata. The test compares the relative magnitudes of sample data rather than the data

Table 2 Mean values with standard deviation of the variables used in this study at different stationsduring 1982–2003

Station Tmax (◦C) Tmean (◦C) Tmin (◦C) P (mm) Epan (mm)

Dargezin 18.2 ± 0.8 11.0 ± 1.0 4.0 ± 0.8 325.9 ± 101.6 1,554 ± 183Ekbatan 19.1 ± 1.1 11.0 ± 1.1 2.9 ± 1.1 310.0 ± 71.4 1,550 ± 197Ekbatan dam 18.3 ± 0.8 10.7 ± 0.9 3.1 ± 1.0 337.0 ± 79.8 1,807 ± 211Ghahavand 19.7 ± 1.4 11.3 ± 1.2 2.9 ± 1.2 233.7 ± 51.4 1,585 ± 268Kangavar 21.0 ± 1.1 13.3 ± 0.9 4.7 ± 1.1 401.6 ± 101.4 1,705 ± 365Kheir-Abad 19.6 ± 1.3 12.8 ± 1.1 5.6 ± 0.9 312.2 ± 72.5 2,612 ± 313Khomigan 17.8 ± 1.0 10.6 ± 2.0 4.3 ± 1.6 273.3 ± 69.9 1,933 ± 180Khosro-Abad 21.8 ± 1.3 12.5 ± 1.1 2.7 ± 1.8 329.7 ± 84.0 2,262 ± 470Malayer 20.0 ± 1.1 14.0 ± 1.5 6.0 ± 0.8 307.8 ± 75.4 1,996 ± 238Nahavand 20.5 ± 0.9 13.5 ± 1.2 5.9 ± 1.1 421.7 ± 116.9 1,835 ± 250Nozheh 19.3 ± 1.0 10.9 ± 0.9 2.5 ± 1.0 331.5 ± 74.0 1,429 ± 189Varayeneh 19.8 ± 1.2 9.8 ± 1.8 0.1 ± 2.8 517.9 ± 142.4 1,878 ± 320

102 H. Tabari, S. Marofi

values themselves (Gilbert 1987). One advantage of this test is that the data neednot conform to any particular distribution. The second advantage of the test is itslow sensitivity to abrupt breaks due to inhomogeneous time series (Jaagus 2006).Mann (1945) originally used this test and Kendall (1975) subsequently derived thetest statistic distribution. According to this test, the null hypothesis H0 states thatthe deseasonalized data (x1,. . . ,xn) is a sample of n independent and identicallydistributed random variables. The alternative hypothesis H1 of a two-sided test isthat the distributions of xk and x j are not identical for all k, j ≤ n with k �= j. Thetest statistic S, which has mean zero and a variance computed by Eq. 3, is calculatedusing Eqs. 1 and 2, and is asymptotically normal:

S =n−1∑

k=1

n∑

j=k+1

sgn(x j − xk

)(1)

sgn(x j − xk

) =

⎧⎪⎪⎨

⎪⎪⎩

+1 i f(x j − xk

)> 0

0 i f(x j − xk

) = 0

−1 i f(x j − xk

)< 0

(2)

Var (S) =

[n (n − 1) (2n + 5) − ∑

tt (t − 1) (2t + 5)

]

18(3)

The notation t is the extent of any given tie and∑

tdenotes the summation over

all ties. In cases where the sample size n > 10, the standard normal variable Z iscomputed by using Eq. 4.

Z =

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

S − 1√Var (S)

i f S > 0

0 i f S = 0

S + 1√Var (S)

i f S < 0

(4)

Positive values of Z indicate increasing trends while negative values of Z showdecreasing trends. When testing either increasing or decreasing monotonic trendsat a α significance level, the null hypothesis was rejected for absolute value of Zgreater than Z1−α/2, obtained from the standard normal cumulative distributiontables (Partal and Kahya 2006; Modarres and da Silva 2007). In this research,significance levels of α = 0.01 and 0.05 were applied.

2.2.3 Sen’s Slope Estimator

If a linear trend is present in a time series, then the true slope (change per unittime) can be estimated by using a simple non-parametric procedure developed bySen (1968). The slope estimates of N pairs of data are first computed by

Qi = x j − xk

j − kf or i = 1, ..., N (5)

Changes of Pan Evaporation in the West of Iran 103

where x j and xk are data values at times j and k( j > k), respectively. The median ofthese N values of Qi is Sen’s estimator of slope. If N is odd, then Sen’s estimator iscomputed by

Qmed = Q[(n+1)/2] (6)

If N is even, then Sen’s estimator is computed by

Qmed = 12

(Q[N/2] + Q[(N+2)/2]

)(7)

Finally, Qmed is tested by a two-sided test at the 100(1 − α)% confidence intervaland the true slope may be obtained by the non-parametric test (Partal and Kahya2006).

In this work, the confidence interval was computed at two different confidencelevels (α = 0.01 and α = 0.05) as follows:

Cα = Z1−α/2

√Var (S) (8)

where Var(S) has been defined in Eq. 3, and Z1−α/2 is obtained from the standardnormal distribution.

Then, M1 = (N − Cα)/2 and M2 = (N + Cα)/2 are computed. The lower andupper limits of the confidence interval, Qmin and Qmax, are the Mth

1 largest and the(M1 + 1)th largest of the Nordered slope estimates Qi. If M1 is not a whole number,the lower limit is interpolated. Correspondingly, if M2 is not a whole number, theupper limit is interpolated (Salmi et al. 2002).

3 Results and Discussion

3.1 Trends in Epan

Annual trends of Epan and their magnitude (in mm year−1) obtained by the Mann–Kendall test, the Sen’s slope estimator and the linear regression are given in Table 3.As shown, both positive and negative trends were observed in Epan series, whichwere mostly positive. Ten of the 12 stations showed increasing trends. Amongthe increasing trends, eight significant trends were detected at the 95% and 99%

Table 3 Values of slope b ofthe linear regression analysis,values of statistics Z of theMann–Kendall test and valuesof statistics Qmed of the Sen’sslope estimator for annualEpan (1982–2003)

aTrends statistically significantat the 99% confidence levelbTrends statistically significantat the 95% confidence level

Station Z Qmed b (mm year−1)

Dargezin 3.30a 21.78a 20.109a

Ekbatan 2.68a 17.07a 18.158a

Ekbatan dam −1.72 −11.80 −11.914Ghahavand −0.99 −9.69 −9.572Kangavar 2.09b 26.60b 25.255b

Kheir-Abad 2.09b 21.71b 26.286a

Khomigan 2.14b 12.01b 13.204b

Khosro-Abad 1.72 32.60 29.335Malayer 1.13 11.74 7.0553Nahavand 2.37b 16.29b 16.577b

Nozheh 2.96a 19.76a 19.217a

Varayeneh 3.81a 41.80a 39.300a

104 H. Tabari, S. Marofi

confidence levels. The observed increase in Epan, which is largely determined byavailable energy, could be caused by increases in temperature and/or net radiationover the last century. A change in temperature may be due to climate change,whereas a change in net radiation associated with a change in surface albedomay be due to historical land use change (Oguntunde et al. 2006). The significantincreasing trends varied between (+)132 mm per decade in the Khomigan station and(+)393 mm per decade in the Varayeneh station. When averaged over all 12 stations,the trend in annual Epan rate for the period 1982–2003 was (+)160 mm per decade orto 9% of climatological mean, that is 1,845.7 mm. The positive trends of Epan seriesfound in this study are in good agreement with results obtained for other territoriesin Brazil (da Silva 2004), Israel (Cohen et al. 2002) and West Africa (Oguntundeet al. 2006), but are different from Epan changes reported in China (Xu et al. 2006;Wang et al. 2007), India (Jhajharia et al. 2009), Australia (Roderick and Farquhar2004; Jovanovic et al. 2008) and New Zealand (Roderick and Farquhar 2005) wheredecreasing trends have been identified.

The rate of increasing trend in annual Epan obtained in this study is much smallerthan that reported by da Silva (2004) when he analyzed climatic changes in thenortheast of Brazil and detected a trend of 41.6% per decade. On the contrary,the magnitude found in this research is greater than those reported by Cohen et al.(2002) and Oguntunde et al. (2006) who investigated trends of Epan in Israel andWest Africa, respectively. Cohen et al. (2002) defined an increasing trend of 2.17%per decade, while Oguntunde et al. (2006) detected a positive trend of 2 mm perdecade for the period 1901–1969 and 18 mm per decade during 1970–2002.

The comparison between the results of the parametric and non-parametricmethods shows that the methods were greatly coincident. All of significant positivetrends detected by the non-parametric tests were confirmed by the parametricmethod.

3.2 Meteorological Relations

It is important to understand the causes of changes in Epan in order to make morerobust predictions about future changes in the hydrological cycle. Pan evaporation ismainly a function of temperature, radiation, wind speed, humidity and precipitation.In this section, possible causes of the increase in Epan are discussed in view ofthe trends of the meteorological variables available in the study area includingmaximum, mean and minimum temperatures and precipitation.

Correlations In order to identify the dominant variables associated with the changesin Epan in the study area, they are correlated with all the meteorological variablesincluding maximum, mean and minimum temperatures and precipitation (Table 4).As shown, positive correlations between Epan and Tmax were found in almost all thestations. The positive correlations were significant at Dargezin, Ekbatan, Khomigan,Nahavand and Varayeneh stations. Likewise, Epan positively correlated with Tmean

in most of the stations, which were significant at Dargezin, Ekbatan, Khomigan,Nahavand and Nozheh stations. Furthermore, there were positive correlations be-tween Epan and Tmin in the majority of the stations. The positive correlations weresignificant at Ekbatan, Khosro-Abad and Nozheh stations. Nevertheless, only onesignificant negative correlation was observed at Kangavar station. In general, pan

Changes of Pan Evaporation in the West of Iran 105

Tab

le4

Res

ults

ofP

ears

on’s

corr

elat

ion

betw

een

pan

evap

orat

ion

and

the

met

eoro

logi

calv

aria

bles

Stat

ion

Tm

axT

mea

nT

min

Pr

Equ

atio

nr

Equ

atio

nr

Equ

atio

nr

Equ

atio

n

Dar

gezi

n0.

465a

Epa

n=

99.1

12T

max

0.50

6aE

pan

=98

.587

Tm

ean

0.34

5E

pan

=75

.048

Tm

in0.

085

Epa

n=

0.15

37P

−25

0.25

+46

8.24

+12

52.7

+15

03.5

Ekb

atan

0.58

1aE

pan

=10

3.27

Tm

ax0.

516a

Epa

n=

98.2

93T

mea

n0.

498a

Epa

n=

83.8

33T

min

−0.2

43E

pan

=−0

.668

7P

−42

3.3

+46

6.58

+13

09.5

+17

56.9

Ekb

atan

dam

0.02

5E

pan

=6.

2192

Tm

ax−0

.171

Epa

n=

−40.

685T

mea

n−0

.320

Epa

n=

−66.

45T

min

−0.3

11E

pan

=−0

.821

P+

1693

.3+

2242

.5+

2201

4.5

+20

84G

haha

vand

−0.0

26E

pan

=−4

.932

1Tm

ax−0

.139

Epa

n=

−30.

352T

mea

n−0

.185

Epa

n=

−41.

6Tm

in−0

.117

Epa

n=

−0.6

086

P+

1682

+19

29.3

+17

05.8

+17

27.1

Kan

gava

r0.

209

Epa

n=

66.3

46T

max

0.23

9E

pan

=10

2.23

Tm

ean

−0.7

36a

Epa

n=

−248

.78T

min

−0.1

20E

pan

=−0

.431

8P

+31

4.34

+34

7.26

+28

73.6

+18

78.9

Khe

ir-A

bad

0.40

6E

pan

=10

1.43

Tm

ax0.

150

Epa

n=

42.4

07T

mea

n0.

217

Epa

n=

75.1

12T

min

−0.3

15E

pan

=−0

.608

7P

+62

5.33

+20

68.1

+21

95.2

+17

16.9

Kho

mig

an0.

474a

Epa

n=

84.9

16T

max

0.41

6aE

pan

=38

.133

Tm

ean

0.38

7E

pan

=41

.496

Tm

in−0

.577

aE

pan

=−1

.483

6P

+42

4.86

+15

27.5

+17

55.4

+23

39.1

Kho

sro-

Aba

d0.

116

Epa

n=

40.9

06T

max

−0.0

74E

pan

=−3

1.41

6Tm

ean

0.54

1aE

pan

=13

6.82

Tm

in−0

.381

Epa

n=

−2.1

302

P+

1372

.1+

2655

.5+

1892

.5+

2964

.8M

alay

er0.

273

Epa

n=

57.7

89T

max

0.00

5E

pan

=0.

7264

Tm

ean

0.20

8E

pan

=57

.924

Tm

in−0

.211

Epa

n=

−0.6

64P

+83

7.92

+19

86.2

+16

47.2

+22

00.7

Nah

avan

d0.

451a

Epa

n=

119.

33T

max

0.62

8aE

pan

=12

7.64

Tm

ean

0.35

1E

pan

=78

.928

Tm

in−0

.284

Epa

n=

−0.6

088

P−

616.

49+

113.

26+

1368

.6+

2091

.4N

ozhe

h0.

217

Epa

n=

40.1

09T

max

0.42

3aE

pan

=88

.693

Tm

ean

0.51

5aE

pan

=91

.927

Tm

in−0

.324

Epa

n=

−0.8

287

P+

653.

45+

462.

79+

1202

.2+

1704

.3V

aray

eneh

0.58

1aE

pan

=15

0.64

Tm

ax0.

281

Epa

n=

50.9

66T

mea

n0.

353

Epa

n=

101.

46T

min

−0.5

46a

Epa

n=

−1.2

256

P−

1112

.4+

1378

.5+

1279

.4+

2513

.2

Ave

rage

0.31

4–

0.23

2–

0.18

1–

−0.2

22–

Epa

nan

dP

are

in(m

m/y

ear)

;Tm

ax,T

mea

nan

dT

min

are

in(◦

C)

a Pea

rson

’sco

rrel

atio

nst

atis

tica

llysi

gnif

ican

tatt

he95

%co

nfid

ence

leve

l

106 H. Tabari, S. Marofi

evaporation had significant positive correlations with maximum, mean and minimumtemperatures in the majority of the stations. This reveals dependence of temperatureand Epan in the study area. Besides, there is evidence of a week inverse relationshipbetween Epan and precipitation in ten stations, but the correlation coefficient wasnot significantly different from zero in the majority of the stations. When averagedover all 12 stations, negative regression coefficient of −0.22 was obtained betweenEpan and precipitation. Jovanovic et al. (2008) found a very strong inverse correlationbetween Epan and P (correlation coefficient of −0.81) in Australia.

Overall, the strongest correlation was found between Epan and Tmax (averagecorrelation coefficient of 0.31) in this study. Jovanovic et al. (2008) also reportedcorrelation coefficient of 0.53 between Epan and temperature. Mean temperatureappears to be the second most dominant variable influencing Epan over all sta-tions (average correlation coefficient of 0.23), although there are no meaningfuldifferences between average correlation coefficients obtained for the meteorologicalvariables. In addition, a correlation coefficient of 0.18 was found between Tmin andEpan when averaged over all 12 stations. Figure 2 also shows time series of themeteorological variables and their relationships with Epan series in the study area.It is clear that the pattern of recent rapid warming is reflected in the Epan changes.

Combined influences of the meteorological variables on Epan were also investi-gated in this study. The average values of the Epan and meteorological variables werecalculated for each year (from 1982 to 2003) over the 12 stations. Then, multiplelinear regression (MLR) was applied for evaluating the relationship between Epan

and all of the meteorological variables. In the MLR method, the Epan variablewas defined as the dependent one and Tmax, Tmean, Tmin and P were consideredas independent. The results showed that there was a strong correlation (r = 0.65,p value = 0.041) between these variables and Epan indicating that the combinedinfluences of the meteorological variables on Epan are much more than the influencesof each variable separately.

Trends Results of the three statistical tests on Tmax, Tmean, Tmin and P series aregiven in Tables 5, 6, 7 and 8. As shown in Table 5, all trend signals in annual Tmax werepositive indicating a warming climate. The non-parametric tests (Mann–Kendall andSen’s slope estimator) detected significant trends at Ekbatan, Kangavar, Kheir-Abadand Varayeneh stations, while the parametric method (linear regression) identifiedsix significant trends. Significant increasing trend rates in Tmax lay in the range of(+)0.631◦C per decade in the Nahavand station to (+)1.295◦C per decade in theKheir-Abad station.

Analysis of Tmean series indicated positive trends in almost all the stations(Table 6). The Mann–Kendall test, the Sen’s slope estimator and the linear regressionmethod detected four, three and six significant increasing trends, respectively. Thesignificant increasing trends ranged between (+)0.715◦C per decade in the Nozhehstation and (+)1.426◦C per decade in the Khomigan station. Hasanean (2001) alsofound a significant positive trend in Tmean at the 99% confidence level for Jerusalemand Tripoli stations when investigated trends in Tmean series at eight meteorologicalstations in the East Mediterranean.

Similar to the Tmean series, 11 warming trends were found in Tmin data(Table 7). Among the warming trends, seven significant trends were identified by

Changes of Pan Evaporation in the West of Iran 107

Fig. 2 Time series plots of themeteorological variables andtheir relationships with Epanseries in Hamedan province

1500

1700

1900

2100

2300

1982 1986 1990 1994 1998 2002E

pan

(m

m)

17

18.25

19.5

20.75

22

Tm

ax (

oC

)

Pan evaporation

Maximum temperature

1500

1700

1900

2100

2300

1982 1986 1990 1994 1998 2002

Ep

an (

mm

)

9

10.25

11.5

12.75

14

Tm

ean (

oC

)

Pan evaporation

Mean temperature

1500

1700

1900

2100

2300

1982 1986 1990 1994 1998 2002

Ep

an (

mm

)

1.5

2.75

4

5.25

6.5

Tm

in (

oC

)

Pan evaporation

Minimum temperature

1500

1700

1900

2100

2300

1982 1986 1990 1994 1998 2002

Ep

an (

mm

)

200

300

400

500

600

P (

mm

)

Pan evaporation

Precipitation

108 H. Tabari, S. Marofi

Table 5 Values of slope b ofthe linear regression analysis,values of statistics Z of theMann–Kendall test and valuesof statistics Qmed of the Sen’sslope estimator for annualmean of Tmax (1982–2003)

aTrends statistically significantat the 95% confidence levelbTrends statistically significantat the 99% confidence level

Station Z Qmed b (◦C year−1)

Dargezin 1.16 0.046 0.0445Ekbatan 2.55a 0.087a 0.1006b

Ekbatan dam 0.71 0.021 0.0244Ghahavand 1.41 0.045 0.0782Kangavar 2.68b 0.116a 0.1101b

Kheir-Abad 3.17b 0.118b 0.1295b

Khomigan 0.76 0.020 0.0333Khosro-Abad 1.27 0.055 0.0675Malayer 1.64 0.057 0.0746a

Nahavand 1.58 0.057 0.0631a

Nozheh 0.59 0.025 0.0405Varayeneh 3.11b 0.114b 0.1185b

the statistical tests. The magnitude of significant positive trends in annual Tmin variedfrom (+)1.086◦C per decade in the Nozheh station to (+)1.360◦C per decade inthe Ekbatan station. The minimum, mean and maximum temperatures show, ingeneral, a similar warming pattern, although the magnitude of the increasing trendsin Tmin data was higher than that in Tmax. This is coincident with results of Salingerand Griffiths (2001) that investigated trends in New Zealand daily temperature andrainfall extremes. The positive trends of Tmax and Tmin series found in this researchmatch the findings of Turkes and Sumer (2004) and Smadi (2006) for Turkey andJordan, respectively. The rate of increasing trends in annual Tmax, Tmean and Tmin

obtained in this study is greater than that reported by da Silva (2004) that investigatedclimatic variability in the northeast of Brazil.

As shown in Table 8, the majority of the stations exhibited decreasing trends in Ptime series. Only one significant trend of (+)44.837 mm per decade was observed inthe Ghahavand station (99% confidence level). Roderick and Farquhar (2004) alsopointed out that the trend in precipitation of Australia for 1970–2002 when averagedover all sites was not statistically significant. Besides, the other study carried out byRoderick and Farquhar (2005) in New Zealand indicated that there were very fewstations showing statistically significant changes in precipitation. Furthermore, nosignificant changes in precipitation were found by Cohen et al. (2002) in Israel. The

Table 6 Values of slope b ofthe linear regression analysis,values of statistics Z of theMann–Kendall test and valuesof statistics Qmed of the Sen’sslope estimator for annualmean of Tmean (1982–2003)

aTrends statistically significantat the 99% confidence levelbTrends statistically significantat the 95% confidence level

Station Z Qmed b (◦C year−1)

Dargezin 1.64 0.064 0.0725Ekbatan 3.53a 0.106a 0.1232a

Ekbatan dam 2.46b 0.073b 0.0789a

Ghahavand 2.89a 0.107a 0.1177a

Kangavar 0.82 0.027 0.0135Kheir-Abad 0.68 0.020 0.0200Khomigan 1.69 0.087 0.1426b

Khosro-Abad −0.08 0.000 0.0049Malayer 0.20 0.013 −0.0282Nahavand 1.47 0.047 0.0824b

Nozheh 2.15b 0.055 0.0715b

Varayeneh 0.31 0.025 0.0056

Changes of Pan Evaporation in the West of Iran 109

Table 7 Values of slope b ofthe linear regression analysis,values of statistics Z of theMann–Kendall test and valuesof statistics Qmed of the Sen’sslope estimator for annualmean of Tmin (1982–2003)

aTrends statistically significantat the 99% confidence levelbTrends statistically significantat the 95% confidence level

Station Z Qmed b (◦C year−1)

Dargezin 1.41 0.047 0.0427Ekbatan 4.21a 0.120a 0.1360a

Ekbatan dam 3.42a 0.115a 0.1120a

Ghahavand 3.02a 0.109a 0.1167a

Kangavar −0.93 −0.050 −0.0692Kheir-Abad 1.05 0.025 0.0445Khomigan 0.54 0.025 0.0390Khosro-Abad 2.45b 0.122b 0.1290b

Malayer 0.88 0.025 0.0395Nahavand 3.85a 0.075a 0.1125a

Nozheh 3.14a 0.120a 0.1086a

Varayeneh 3.85a 0.075a 0.1125a

absence of any major trends in precipitation is not surprising given the large year-to-year variability that is typical of precipitation records (Roderick and Farquhar 2004).

Overall, the study area has experienced a rapid warming over the 1982–2003period. One expected consequence of this warming is that the air near the surfaceshould be drier, which should result in an increase in the rate of evaporation fromterrestrial open water bodies (Roderick and Farquhar 2002). The main factorsassociated with increasing Epan are temperature variables (min, mean and max).Besides, increasing Epan was not strongly related to P changes. In other words, thechange of pan evaporation is not very sensitive to changes in precipitation.

The concurrent occurrences of significant increasing trends in Epan and significantpositive trends in Tmax, Tmean and Tmin were found at Ekbatan station. Likewise,the concurrent occurrences of significant positive trends in Epan and significantwarming trends in Tmean and Tmin were observed at Nozheh station. Furthermore, theconcurrent occurrences of significant upward trends in Epan and significant increasingtrends in Tmax and Tmin were detected at Varayeneh station. The significant increasingtemperature and pan evaporation together with decreasing precipitation can beexpected to have led to a marked increase in aridity. In other words, Hamedanprovince has become more arid over the last 22 years, not because precipitation haschanged, but rather because evaporation, and hence the atmospheric demand forwater, has increased. These results support the suggestion of Smit et al. (1988) that

Table 8 Values of slope b ofthe linear regression analysis,values of statistics Z of theMann–Kendall test and valuesof statistics Qmed of the Sen’sslope estimator for annual P(1982–2003)

aTrends statistically significantat the 99% confidence levelbTrends statistically significantat the 95% confidence level

Station Z Qmed B (mm year−1)

Dargezin −0.11 −0.850 2.8020Ekbatan −0.67 −1.775 −1.1209Ekbatan dam −0.45 −2.100 −1.2896Ghahavand 2.65a 4.300a 4.4837a

Kangavar −0.68 −1.300 −1.7198Kheir-Abad −0.37 −1.058 −1.0112Khomigan −0.48 −0.941 −0.3477Khosro-Abad −0.62 −1.169 −1.7293Malayer 0.00 −0.433 −2.1691Nahavand −0.34 −1.146 −1.4379Nozheh −1.10 −3.489 −3.3021Varayeneh −1.83 −9.292 −9.2357

110 H. Tabari, S. Marofi

mid-latitude regions such as the mid-western USA, southern Europe and Asia arebecoming warmer and drier.

4 Conclusions

In this study, we analyzed changes of observed Epan and the associated variationsin Tmax, Tmean, Tmin and P data for 12 stations in Hamedan province in westernIran from 1982 to 2003. Trend analysis was carried out by the Mann–Kendall test,the Sen’s slope estimator and the linear regression method. Significantly increasingEpan was observed in 67% of the stations at the 95% and 99% confidence levels.Likewise, the significant positive trends in Epan ranged from (+)132 mm per decadein the Khomigan station to (+)393 mm per decade in the Verayeneh station.Analysis of relations between Epan and the meteorological variables indicated thatEpan has significant positive correlations with Tmax, Tmean and Tmin. The concurrentoccurrences of significant increasing trends in Epan and significant positive trendsin Tmax, Tmean or Tmin were found at Ekbatan, Kangavar, Kheir-Abad, Nahavand,Nozheh and Varayeneh stations. In contrast, concurrent occurrence of significantpositive trends in Epan and significant decreasing trends in P were not observed.

Due to lack of wind speed, relative humidity and radiation data, their relations topan evaporation changes were not investigated in this study. It is also recommendedto evaluate the relations in other areas in Iran with similar climatic conditions,provided that the data are available. The results of this research revealed that thestudy area has become more arid in recent years. The findings of this study needto be verified in other climatic conditions of Iran especially in arid climates whereevaporation changes are crucial for estimating crop water requirements.

Acknowledgements Special thanks are due to the different people who collected the requireddata at 12 mentioned sites. The authors are grateful to the anonymous reviewers whose suggestionssignificantly contributed to improve the work.

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