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Evapotranspiration model selectionfor estimation of actual evaporationfrom bare soil, as required in annualpotential groundwater recharge studiesof a semi-arid foothill regionSeyed Adib Banimahda, Davar Khalilia, Ali Akbar Kamgar-Haghighia

& Shahrokh Zand-Parsaa

a Water Engineering Department, College of Agriculture, ShirazUniversity, Shiraz, Islamic Republic of IranAccepted author version posted online: 22 Jan 2015.Publishedonline: 06 Feb 2015.

To cite this article: Seyed Adib Banimahd, Davar Khalili, Ali Akbar Kamgar-Haghighi & ShahrokhZand-Parsa (2015): Evapotranspiration model selection for estimation of actual evaporation frombare soil, as required in annual potential groundwater recharge studies of a semi-arid foothillregion, Archives of Agronomy and Soil Science, DOI: 10.1080/03650340.2015.1009048

To link to this article: http://dx.doi.org/10.1080/03650340.2015.1009048

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Evapotranspiration model selection for estimation of actualevaporation from bare soil, as required in annual potentialgroundwater recharge studies of a semi-arid foothill region

Seyed Adib Banimahd, Davar Khalili*, Ali Akbar Kamgar-Haghighiand Shahrokh Zand-Parsa

Water Engineering Department, College of Agriculture, Shiraz University, Shiraz, Islamic Republicof Iran

(Received 17 August 2014; accepted 13 January 2015)

Improved evapotranspiration estimation is instrumental in annual potential recharge(Re) evaluations of semi-arid regions, in the context of the water balance approach.Complementary relationship areal evapotranspiration (CRAE) and advection–aridity(AA) and a general combination equation proposed by Granger and Gray (GG) wereevaluated for the estimation of actual evaporation (Ea) from bare soil under occurrenceof Re. Model capability was evaluated by utilizing data from lysimeter measurementsduring the hydrological years [(2011–2012) and (2012–2013)]. Measured parametersincluded soil moisture (SM), rainfall and related meteorological data and Re (lysimeteroutput). All models with original parameters performed poorly during 2011–2012 and2012–2013, underestimating annual Re values. The 2011–2012 data were used formodel calibration, considering annual Ea [criterion (I)] and cumulative Ea during theoccurrence period of Re [criterion(II)]. The calibrated CRAE model [criterion (II)]produced the best simulation for Ea (NRMSE < 30%). The 2012–2013 data were usedto validate the models, and the calibrated CRAE model produced acceptable results(NRMSE < 10%) in SM simulation (both criteria). But calibrated CRAE undercriterion (II) provided the best estimation of annual Re (ΔQ < 6%). According to theresults, CR models can produce acceptable estimation of annual Re, if initiallycalibrated utilizing criterion (II).

Keywords: actual evaporation; potential groundwater recharge; complementaryrelation; foothill; semi-arid

Introduction

Actual evaporation (Ea) describes the processes by which liquid water at or near the landsurface becomes atmospheric water vapour under natural conditions. Accurate estimationof Ea is necessary for work dealing with water resource management or environmentalstudies. Referring to potential groundwater recharge or potential recharge (Re) in brief soilwater flux below the root zone, which can reach the groundwater body and recharge it,reliable estimates of Ea greatly influences Re estimations, especially in arid and semi-aridregions. On the other hand, because of the uncertainty associated with prediction of Ea,estimation of Re by the water balance method is subject to substantial error. For instance,for quantification of Re utilizing soil water balance approach, underestimation of Ea leadsto overestimation of Re, and vice versa.

*Corresponding author. Email: dkhalili@shirazu.ac.ir

Archives of Agronomy and Soil Science, 2015http://dx.doi.org/10.1080/03650340.2015.1009048

© 2015 Taylor & Francis

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Several methods have been proposed for estimating actual evapotranspiration (ETa),for example, Monteith (1963, 1965), Penman (1948) and Allen et al. (1998), which canalso be used to estimate evaporation in the absence of plant. However, quantification of Ea

is complex and challenging, and hence, numerous equations have been derived bydifferent approaches, such as the water balance and energy balance methods (Monteith1973; Rana & Katerji 2000). Another approach is the complementary relationship (CR)between ETa (or Ea) and potential evapotranspiration (or potential evaporation) proposedby Bouchet (1963), which is gaining renewed attention since it is relatively simple tocalculate ETa or Ea (Brutsaert & Stricker 1979; Hobbins et al. 2001a, 2001b; Oudin et al.2005; Xu & Singh 2005; Pettijohn & Salvucci 2009; Crago et al. 2010; van Heerwaardenet al. 2010; Huntington et al. 2011; Jaksa et al. 2013). Estimating Ea using this method iseasy compared to the other available methods, especially for regional estimations, since itrequires only a standard set of meteorological variables. There are different models basedon the CR concept for simulation of Ea (or ETa), which include the advection–aridity(AA) model proposed by Brutsaert and Stricker (1979), the complementary relationshipareal evapotranspiration (CRAE) model derived by Morton (1978, 1983) and the CR(GG) model proposed by Granger and Gray (1989).

A comparative study evaluating performances of the above three models for estima-tion of ETa over three different climate regions (i.e. cool temperate (humid); subtropical(humid) and semi-arid to arid) was accomplished by Xu and Singh (2005). They used theoriginal and locally calibrated parameter values of the models and found that locallycalibrated parameter values improved the model performance, especially for semi-aridregions. The poor performance of the AA original model was reported by Hobbins et al.(2001a). In another research, Xu and Li (2003) applied the AA and CRAE models (byoriginal parameters) to two catchments in Japan with different characteristics and scalesfor several representative years. They showed that both are effective in estimating catch-ment ETa. In a similar study, Liu et al. (2006) employed the three above-mentioned CRmodels in the Yellow River basin to estimate regional evapotranspiration (ET) during1981–2000. They found that all three models simulated reasonably well the ET over theannual timescale; however, the AA model gave the best estimation for the monthly timeperiod. In another research, evaluation of seven models (including the above three CRmodels) for the estimation of ETa and groundwater recharge in a humid region wasconducted in Germany using lysimeter data (Xu & Chen 2005). According to the results,it was concluded that the lysimeter measured water balance components; that is, ETa,groundwater recharge and soil moisture (SM) can be predicted by the GG model withgood accuracy. Recently, Jaksa et al. (2013) verified the existence of complementaritybetween ETa and potential ET utilizing the AA model over natural vegetation in semi-ariddesert ecosystems of southern Idaho using available data and simulated fluxes obtainedfrom the Noah Land Surface Model (LSM) and North American Regional Reanalysis(NARR) data. In a different research, two CR methods, that is, the AA and Venturiniet al.’s (2008) methods, were used to estimate spatially distributed monthly ETa for acomplex landscape over a 10-year period (2000–2009) for two large watersheds in north-west (NW) China (Matin & Bourque 2013).

A detailed review of literature reveals that the CR methods were widely applied forthe estimation of ETa for catchments with different climatic conditions (e.g. Hobbins et al.2001a, 2001b; Xu & Li 2003). Furthermore, comparison among the CR-based models wasaccomplished in different climate regions (e.g. Xu & Singh 2005). Similarly, comparisonamong CR methods and measured ETa were studied by using lysimeter measurements in ahumid region (e.g. Xu & Chen 2005).

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It appears that evaluation and comparison of the CR-based models in conjunction withestimation of Re in a semi-arid foothill region have not been previously studied.Therefore, the main objective of this study was to evaluate the three CR-based models(CRAE, AA and GG models) for the estimation of Ea from bare soil and subsequentestimation of annual Re, in a semi-arid foothill region utilizing lysimeter data. For thispurpose, at first, the three CR models with their original values were applied to test theirgeneral applicability. Then, model parameters were locally calibrated based on measuredlysimeter data and finally calibrated models were validated with independent data.

Materials and methods

Model description

On the basis of empirical observations and utilizing an energy balance analysis, Bouchet(1963) proposed the CR method, which assumes that there is a complementary feedbackmechanism between potential evaporation (Ep) and Ea over areas of regional scale. Heshowed that a larger value of Ep does not necessarily signify a larger value of Ea, bydemonstrating that as a surface dried from initially moist conditions, Ep increased while Ea

decreased. This is because Ea consumes both energy and water, thereby cooling andhumidifying the overpassing air and reducing Ep (Morton 1978). The CR concept statesthat as the surface dries, the decrease in Ea is accompanied by an equal, but opposite,change in Ep, which means that Ep ranges from its value at saturation (Ew) to twice thisvalue. The corresponding relationship is as follows (Bouchet 1963; Morton 1978, 1983)(Equation (1)):

Ea þ Ep ¼ 2Ew (1)

where Ew is the wet environment evaporation.A schematic representation of the CR (Equation (1)) under conditions of constant

radiant energy supply is given in Figure 1. The ordinate represents evaporation, and theabscissa represents water supply to the soil surface of the area, a quantity that is usuallyunknown. It is clear from Figure 1 that when there is no water available for arealevaporation, it follows that Ea = 0, even if the air is very hot and dry and Ep is at itsmaximum rate of 2Ew (the dry environment potential evaporation). As the water supply to

2Ew

Ew

Eva

pora

rtio

n

Soil water supply

EP–Ea

Ea Ea

Ea

Ep

Ep

Figure 1. A schematic diagram representing the complementary relation in estimated evaporationand water supply to soil surface, Ep, Ea and Ew are the potential, actual and wet environmentevaporation, respectively.

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the soil surface of the area increases, the resultant equivalent increase in Ea causes theoverpassing air to become cooler and more humid, which in turn produces an equivalentdecrease in Ep. Finally, when the supply of water to the soil surface of the area hasincreased sufficiently, the values of Ea and Ep converge to that of Ew.

Several kinds of CR equations (e.g. Morton 1978; Brutsaert & Stricker 1979; Granger& Gray 1989) have been proposed, which are different in calculating Ep and Ew. The Ea isusually calculated as a residual of Equation (1). Three types of the CR, that is, the CRAE,AA and GG models, are applied in this study, which are briefly summarized in the nextsection. For more detailed information, the reader is referred to the cited literatures.

CRAE model

One of the CRAE models was proposed by Morton (1978) that employs the modifiedPriestley–Taylor equation for estimation of Ew from the slope of saturation vapourpressure/temperature curve and net radiation (Priestley & Taylor 1972). Furthermore, inthis model, Ep is estimated by solving the energy balance and aerodynamic equations atequilibrium temperature using a modified Penman equation and replacing the windfunction with a vapour transfer coefficient. The Morton equation can be expressedmathematically in the following forms (Morton 1978) (Equations (2)–(15)):

Ea ¼ 86:4 2ψRn þM

λ� Δ

Δþ L

Rn

λþ L

Δþ LF

esa � eað Þλ

� �� �(2)

Rn ¼ 1� Albð ÞRs � Rnl (3)

Rnl ¼ εσ Ta þ 273ð Þ4 1� ρ 0:707þ ea158

� �h i(4)

ρ ¼ 1þ 0:25� 0:005 esa � eað Þ½ �C2 (5)

M ¼ aMRnl � bMRn (6)

L ¼ 4εσ Ta þ 273ð Þ3F

þ γ (7)

F ¼ 22

�; Ta � 0 (8)

� ¼ esa � eaj j6:11

� 0:12

(9)

Δ ¼ αβesa

β þ Tað Þ2 (10)

esa ¼ 6:11expαTa

β þ Ta

� ea ¼ RH � esa (11)

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ψ ¼ 1þ L

Δ

0:5þ 0:5RH þ L=Δ

� �RH þ L=Δ

24

35�1

þ 0:26 (12)

λ ¼ 2501� 2:4Tað Þ (13)

γ ¼ 6:65� 0:001� P (14)

P ¼ 1013:25293� 0:0065EL

293

� �5:26(15)

where Ea is the actual evaporation (mm day−1); ψ, the energy weighting factor; Rn, the netradiation (W m−2); Rs, the solar radiation (W m−2); Rnl, the long-wave net radiation (W m−2);M, the advection energy (W m−2); aM and bM are 0.66 and 0.44, respectively; F, the vapourtransfer coefficient (W m−2 mbar−1); Alb, the surface albedo; ε, the surface emissivity; ξ, thestability factor; σ, the Stefan–Boltzmann constant (=5.67 × 10–8 W m−2 (°C)−4); C, the cloudcover ratio (0–1); Ta, the mean air temperature (°C); ρ, the ratio of average atmosphericradiation to clear sky atmospheric radiation; ea, the actual vapour pressure (mbar); esa, thesaturation vapour pressure at air temperature (mbar); Δ, the rate of change of saturationvapour pressure with respect to air temperature [Pa (°C)−1]; γ, the psychometric constant[Pa (°C)−1]; L, the heat transfer coefficient [Pa (°C)−1]; λ, the specific latent heat ofvaporization (kJ kg−1); RH, the mean relative air humidity (%); P, the atmospheric pressure(Pa); El, the elevation above sea level (m); α and β are 17.27 and 237.3°C, respectively,when Ta > 0°C, or 21.88 and 265.5°C, respectively, when Ta < 0°C.

AA model

In the AA model, Ep is calculated by combining the energy budget and water vapourtransfer following adaptation of an equation originally derived by Penman (1948)(Equation (16)):

EP ¼ ΔΔþ γ

Rn

λþ γΔþ γ

EDa

� �(16)

where EDa (m s−1) is the drying power of the air which in general can be written as(Equation (17)):

EDa ¼ f Uzð Þ esa � eað Þ (17)

where f(Uz) is some function of the mean wind speed (U) at a reference level above theground surface, and other parameters are defined earlier. Penman (1948) originallysuggested an empirical linear approximation for f(Uz) at 2.0 m reference height, whichwas then used by Brutsaert and Stricker (1979) in the AA model, which is given asfollows (Equation (18)):

f Uzð Þ ¼ f U2ð Þ ¼ 0:0026 1þ 0:54U2ð Þ (18)

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Ew is calculated in the AA model using the Priestley and Taylor (1972) partial equilibriumevapotranspiration equation as (Brutsaert & Stricker 1979) (Equation (19)):

EwW ¼ α1Δ

Δþ γRn

λ(19)

where α1 is 1.26. Substituting Equations (19), (18), (17) and (16) in Equation (1), the finalequation for calculation of the Ea in the AA model is as:

Ea ¼ 86:4 2α1 � 1ð Þ ΔΔþ γ

Rn

λ� γΔþ γ

f U2ð Þ esa � eað Þ (20)

GG model

A similar general combination equation to Penman (1948) was proposed by Granger(1989) based on the CR concept. Following this development, Granger and Gray (1989)derived a modified form of Penman’s equation for estimating ETa from different non-saturated land covers (Equation (21)):

Ea ¼ 86:4ΔG

ΔGþ γRn

λ

� � γGΔGþ γ

EDa (21)

where G is a dimensionless relative parameter. Ea/Ep and other parameters have the samemeaning which was defined earlier. Granger and Gray (1989) showed that G is a uniqueparameter for each set of atmospheric and surface conditions. Based on the daily esti-mated values of actual evapotranspiration from water balance, Granger and Gray (1989)showed that there exists a unique relationship between G and a parameter which theycalled the relative drying power (D). Later, a modified equation of G was proposed byGranger (1998) as follows (Equations (22) and (23)):

D ¼ EDa

EDa þ Rn(22)

G ¼ 1

aG þ bGe4:902Dþ 0:006D (23)

where, aG and bG are 0.793 and 0.20, respectively.

Study area and data

This study was carried out for the two consecutive hydrological years during the periodfrom 2011 to 2013 by the lysimeter station at ‘Kuy Asatid’ Experimental Foothill Station.The station is located at the College of Agriculture of Shiraz University, Shiraz, Iran. Itsgeographical coordinates are latitude 29° 44ʹ 24.68ʹʹ (north), longitude 52° 35ʹ 45.5ʹʹ (east)and altitude of 1830 m above sea level. According to De Martonne aridity index (12.19),the study region is characterized as semi-arid region. Figure 2 shows the data related totemperature and precipitation during the two studied hydrological years. Mean monthlytemperature decreased in winter and increased in summer for both studied years.

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According to Figure 2, temporal variability in precipitation is quite noticeable during thetwo consecutive hydrological years. Annual precipitation values of the two studiedhydrological years are 363 and 456.5 mm year−1, which are, respectively, below andabove the long-term mean annual precipitation of 386 mm year−1.

The station has a cylindrical volume drainage lysimeter (2 m in diameter and 2 m depth),installed during December 2010 in the foothill region with a 17% slope, which makes itchallenging to estimate meteorological data (such as Ea) and Re. The lysimeter is repre-sentative of the evaporation in the surrounding area, confirming validation of the CRevaporation methods. A schematic of the lysimeter is illustrated in Figure 3. The lysimeterhas no vegetation, and the soil inside the lysimeter is filled in increments of 0.15 m by lightcompaction. A coarse sand layer (0.15 m) is placed at the bottom of the lysimeter tofacilitate drainage. The lysimeter has sandy loam soil down to 0.3 m depth and loam soilfor the 0.3–2.0 m depth with an average soil bulk density of 1.65 g cm−3 and is classified as‘Kuy Asatid’ series. An observation manhole was drilled next to the lysimeter to read thedaily Re from the depth of 2.0 meter. Re (drainage from 2.0 m depth) is routed through apipe to a tank located in the manhole. A run-off tank is attached to the lysimeter to collect thesurface run-off. The discharge from the surface run-off tank is routed through a pipe to arun-off sump (0.3 m diameter) located next to the lysimeter.

An access tube was installed in the centre of the lysimeter and readings by the neutronprobe (NP) below the soil surface were taken in 0.3-m increments to the deepest readingat 1.5 m depth. Standard counts (readings) were taken on each day that readings weretaken. Lysimeter NP data are not reported here because of the large volume of thecollected data. The NP (Model 503 Hydroprobe, CPN Corporation, Pacheco, CA, USA)was field-calibrated for volumetric soil water content using measured samples of thevolumetric soil water content. SM content values were integrated through the lysimeterdepth to calculate a water storage value in mm for each reading time, and differencesbetween water stored at the beginning and end of each time period were considered equal

Prec

ipita

tion

(mm

)

400

350

300

250

200

150

100

50

0

Month

P (2011–2012) P (2012–2013) T (2012–2013)T (2011–2012)

25.0

20.0

15.0

10.0

5.0

0.0

November

December

January

FebruaryMarc

hApril May June

JulyAugust

October

September

P (2011–2012) 0 103 0 61 154 45 0 0 0 0 0 0

01003993.516.537.526.598

4.1

5.2 4.6 6.3

3.8 4.1 8.0

10.5 12.1

13.3 19.3

16.3 22.8

22.7 25.3

26.4 24.4

23.9 20.8

21.5

13014.5

15.2 9.2

9.515.6

P (2012–2013)

T (2011–2012)

T (2012–2013)

Tem

prat

ure

(°C

)

Figure 2. Monthly precipitation and average monthly temperature for the two studied hydrologicalyears.

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to change in the SM (ΔS) for that time period. The ΔS data for the lysimeter withmeasured precipitation and daily Re data were used to compute field Ea from bare soilat that time period using soil water balance approach.

The measured lysimeter data, that is, Ea from bare soil, Re, SM together with rainfalland meteorological data were used to evaluate and calibrate the three models, CRAE, AAand GG. For this purpose, the three above-mentioned CR models by original and locallycalibrated parameter values were applied to simulate Ea. The calculation was made on adaily basis, and comparison was made on an annual basis and also during occurrenceperiod of Re.

The annual Re values (drainage from 2.0 m depth) for the first and second studyhydrological years were measured as: 74.5 mm [day of year (DOY) 35–143], 27.3 mm(DOY 28–135), respectively. It is noted that rather different patterns of temporal distribu-tions were associated with individual precipitation events of the first and second hydro-logical years. The individual events of the first year were generally of lower intensities (e.g.February 2012), thus contributing to infiltration and nonzero measured value of Re, and as aresult, the amounts of produced run-off measured were negligible. However, events of thesecond hydrological year were of high intensity nature, which produced major run-offevents with smaller portions going to annual Re.

The standard meteorological daily values, that is, precipitation, minimum andmaximumair temperature, relative humidity, sunshine duration and wind velocity at 2.0 m elevation,were obtained from the Meteorological Station at College of Agriculture, Shiraz University,near the study area. Daily solar radiation values were estimated using the Angstrom–Prescott equation with modified parameters for the study region (Zand-Parsa et al. 2011).

In calibrating the parameters of the CR model, two factors were considered to beimportant related to the estimation for Re; that is, they should be able to produce theannual total values of Ea from bare soil reasonably well and they should produce totalvalues for occurrence period of Re as close as possible. Therefore, two criteria were used

Manhole

Run-offsump

RO

Re

Potential recharge conveyance pipe

LysimeterGravel

P Ea

2.0 m

200 cm34 cm

Accesstube

Run-offtank

Potential rechargecollecting tank

Figure 3. A schematic of the lysimeter, RO: the run-off, P: the precipitation, Ea: the actualevaporation from bare soil, Re: the potential recharge.

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in calibrating the parameter values: first, the measured annual Ea from bare soil for thefirst hydrological year (2011–2012) was used to calibrate the parameters of the CRmethod. Second, Ea calculated from the daily water balance model for the first studyhydrological year (2011–2012) was applied to calibrate the parameters for occurrenceperiod of Re. In this respect, calibration was made based on the best estimation of annualEa [criterion (I)] and the best estimation of cumulative Ea during occurrence period of Re[criterion (II)]. Third, the independent data (including Re) related to the second hydro-logical year (2012–2013) were applied for the validation of the calibrated models.

In this research, the Newton–Raphson’s optimization algorithm was used to calibratethe CR evaporation model, by comparing the simulated cumulative Ea values from baresoil with the calculated Ea values by lysimeter data. In this case, minimization of anobjective function (OF) is intended, which is calculated as (Equation (24)):

OF ¼ CEam � CEap �2

(24)

where CEam and CEap are the calculated and simulated cumulative Ea values from baresoil during the annual period [criterion (I)] or occurrence period of Re [criterion (II)].

The water balance equation was used to test the CR-based models (Equation (25)):

P ¼ Reþ Ea þ ΔS � RO (25)

where P and RO are precipitation and run-off, respectively, and other parameters aredefined earlier.

Two alternatives were used to test the CR models with original and locally calibratedparameters using the water balance approach. First, the simulated Ea values from bare soil,the measured SM values and precipitation were applied in the water balance Equation (25)to simulate Re for both criteria. Second, the simulated Ea values from bare soil, themeasured Re values and precipitation were used to simulate SM for both criteria byEquation (25).

The results of the simulated values of cumulative Ea from bare soil, annual Re andaverage simulated SMs were compared by ΔQ (Equation (26)). Furthermore, normalizedroot mean square error (NRMSE) was used for term-by-term comparison of the dailymeasured and simulated results of Ea from bare soil and SM (Equation (27)):

ΔQ ¼ 100

Pni¼1

ðyiÞ �Pni¼1

ðxiÞ����

����Pni¼1

ðxiÞ(26)

NRMSE ¼ 100

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

Pni¼1

ðxi � yiÞ2� s

�X(27)

where xi and yi are the ith daily measured and simulated values, respectively, X are themean measured values, and n is the number of observations. The NRMSE gives informa-tion on the short-term performances of the associated models by allowing a term-by-term

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comparison of the actual deviation between the simulated and measured values. Thesimulated values are acceptable when the NRMSE < 30% (Jamieson et al. 1991).

Results and discussion

Results obtained using original parameters

Simulated values and statistical test (ΔQ and NRMSE) results are given in Table 1,indicating that all three models with original parameters highly overestimated the Ea

values from bare soil for both studied hydrological years. The largest values of Ea weresimulated by the AA model for both studied years. As the statistical test results ofsimulation Ea show, the CRAE model had the minimum, but unacceptable values of ΔQ(213.2%, 127.4%) and NRMSE (122.6%, 112.6%), respectively, for the first and secondhydrological years. Xu and Singh (2005) showed that all three above-mentioned modelsoverestimated the ETa values of a catchment located in north-western Cyprus (a semi-aridregion) for the period of 1989–1993. For illustration purposes, Figure 4a, b and c showsregression graphs (at 95% significance level) of the lysimeter data and simulation resultsfor the CRAE, AA and GG models with original parameters during the second hydro-logical year. According to Figure 4a, b and c, in spite of rather high values of determina-tion coefficients (R2) in all cases (all values above 0.887), results of simulated Ea frombare soil with original parameters were not acceptable since simulated results andlysimeter data do not correspond to the 1:1 line.

The impact of poorly estimated Ea values on annual Re and SM evaluation was furtherinvestigated. Table 2 shows the results on estimation of annual Re and SM simulation.According to Table 2, all three models underestimated the annual Re for both thehydrological years. The high values of ΔQ corresponding to simulated values of Reshowed that all models performed poorly for both the hydrological years with differenttemporal variability of precipitation. Furthermore, as shown in Table 2, the unacceptableand very high values of NRMSE (all cases above 93%) and ΔQ (all cases above 113.6%)were obtained for simulated SM values in the first and second hydrological years by usingall three evaporation original models and water balance approach. Simulated results of the

Table 1. The annual observed and simulated actual evaporation (Ea) from bare soil by using theCRAE, AA and GG models with original parameters and related statistical test results for the firstand second study hydrological years (October–September).

Hydrological year Model

Annual

Ea (mm) ΔQ (%) NRMSE (%)

First (2011–2012) CRAE 953.0 213.2 122.6AA 1783.6 486.3 252.4GG 1284.0 322.1 152.0Observed 304.2

Second (2012–2013) CRAE 1091.4 127.4 112.6AA 2031.5 323.3 266.0GG 1431.4 198.3 152.0Observed 479.9

Notes: CRAE, complementary relationship areal evapotranspiration; AA, advection–aridity, GG, Granger andGray (1989); Q ¼ simulated value�observed value

observed value ; NRMSE, normalized root mean square error.

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Figure 4. Comparison between the Ea values observed in the lysimeter and those simulated bythree CR models with original parameters for the second hydrological year (October–September)under potential recharge condition, (a): complementary relationship areal evapotranspiration(CRAE), (b): advection–aridity (AA) and (c): Granger and Gray (1989) (GG).

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Ea values, annual Re and SM values indicate that it would be necessary to locally calibratethe models.

Results obtained using locally calibrated parameters

The first hydrological year data (October 2011–September 2012) were used to calibratethe parameters of the CR-based evaporation models for both criteria. Then, the secondhydrological year data (October 2012–September 2013) were used for the validation ofthe models. Accordingly, criterion (I) and criterion (II) were used to evaluate the cali-brated models for both the years. The parameter α1 is the only calibrating parameter forthe AA model, but in the present research, this model was not calibrated because the valueof 1.26 for α1 has largely been accepted by many researchers (e.g. Priestley & Taylor1972; Davies & Allen 1973; Stewart & Rouse 1977; Pereira 2004; Suleiman &Hoogenboom 2007; Rahimikhoob et al. 2012; among many others), for different climaticconditions. As a result in the present research, only parameters aM and bM (CRAE model)and aG and bG (GG model) were calibrated. The original and calibrated parameter valuesusing the two criteria are given in Table 3 for the CRAE and GG models. The calibratedparameters of the GG model were in agreement with Xu and Singh (2005) in which theyshowed that for a semi-arid region (north-western Cyprus) parameters aG and bG for GGmodel were replaced by larger calibrated values. Xu and Singh (2005) also showed that it

Table 2. Statistical test results and soil moisture and of annual potential recharge simulationutilizing evaporation models with original parameters and water balance approach for the first andsecond hydrological years (October–September).

Hydrological year Model

Soil moisture Potential recharge

ΔQ (%) NRMSE (%) Annual value (mm) ΔQ (%)

First (2011–2012) CRAE 113.6 95 22.20 70.2AA 202.2 163 11.74 84.2GG 138.6 109 18.92 74.6Measured 74.47

Second (2012–2013) CRAE 131.1 101 15.05 44.9AA 218.0 206 7.11 73.9GG 134.1 122 7.79 71.5Measured 27.29

Note: For abbreviations see Table 1.

Table 3. Original and calibrated parameter values of CRAE and GG models (criteria (I) and (II)).

CRAE GG

Model Parameter aM bM aG bG

Original 0.660 0.440 0.793 0.200Calibrated for criterion (I) 0.5237 0.7461 7.893 3.883Calibrated for criterion (II) 0.5275 0.7393 4.644 3.918

Notes: Criterion (I): annual period; criterion (II): occurrence period of potential recharge (Re), CRAE, comple-mentary relationship areal evapotranspiration model; GG, Granger and Gray (1989) model.

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was necessary to modify the constant terms of the CRAE model for proper application intheir study area.

Figure 5a and b illustrates the relationships between the cumulative values of the Ea

values observed from the lysimeter data and the two CR methods (CRAE and GG) withlocally calibrated parameters based on criterion (II). It is notable that all of the linearregression relationships in this figure are statistically significant at 95% confidence level(P-values computed were much more than 0.05). It is obvious from Figure 5a and b thatthe results obtained from the calibrated CRAE evaporation model for criterion (II) weremore closely correlated to the observed values (R2 of 0.991) than those simulated usingthe GG (R2 of 0.835) model. This result is in agreement with Xu and Singh (2005) inwhich they reported the best correlation between the CRAE and water balance models forthree different climatic conditions.

Results of the observed and simulated Ea values from bare soil by criteria (I and II)using the two CR evaporation models (CRAE and GG) with locally calibrated

Figure 5. Comparison between the actual evaporation (Ea) values observed in the lysimeter andthose simulated by two CR models with locally calibrated parameters for the second hydrologicalyear (October–September) of criterion (II) under recharge condition, (a): complementary relation-ship areal evapotranspiration (CRAE), (b): Granger and Gray (1989) (GG).

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parameters are shown in Table 4. Compared to the obtained results of Ea with originalparameters (Table 1), relatively major improvements were found for the GG model forboth criteria; that is, the 1431.4 mm value was changed to 343.6 mm [for criterion (I)]and to 442.6 mm [for criterion (II)] by the GG model for the validation in thehydrological year. The results confirmed the findings of Xu and Singh (2005).According to the results, for the case of criterion (I), the two calibrated models(CRAE and GG) were able to produce good estimations for the annual values of Ea,for the calibration period, as expected. Furthermore, the CRAE model provided the bestsimulation of Ea during the occurrence of Re and annual periods for both the first(calibration) and second (validation) hydrological years with acceptable NRMSE values(less than 30%). Similarly, the results for criterion (II) for both applied models (CRAEand GG) produced reasonable values for cumulative Ea values from bare soil during theRe period for the calibration hydrological year, as expected. However, the calibrationand validation of daily results of the GG calibrated models during the occurrence of Reand also the annual period were not acceptable with NRMSE > 30%. Additionally, theCRAE model was able to acceptably simulate the annual Ea values from bare soil forboth calibration and validation periods with NRMSE values of 6% and 14%, respec-tively. Also as the results indicate, the CRAE method provided the best estimation of Ea

from bare soil for the Re period with NRMSE values of 4% and 3%, respectively, forthe calibration and validation periods.

As shown in Table 5, annual Re values resulting from utilization of the two calibratedevaporation models (CRAE and GG) in the water balance Equation (25) were estimatedwith high accuracy (ΔQ < 10%), for both criteria during the calibration year. However, theresults of the validation period only confirmed the good performance of the CRAE

Table 4. The observed and simulated actual evaporation (Ea) from bare soil by using the CRAEand GG complementary models with locally calibrated parameters for both criteria and relatedstatistical test results for the first (calibration) and second (validation) study hydrological years(October–September).

Period

Hydrological year Model

Annual Recharge period

Ea (mm)ΔQ(%)

NRMSE(%) Ea (mm) ΔQ (%)

NRMSE(%)

Criterion (I)First (2011–2012)

calibrationCRAE 305.6 0.5 7 94.9 4.4 6GG 304.5 0.1 24 90.8 8.6 36Observed 304.2 99.3

Second(2012–2013)validation

CRAE 428.1 10.8 18 143.3 17.6 27GG 343.6 28.4 58 92.50 46.8 43Observed 479.9 173.9

Criterion (II)First (2011–2012)

calibrationCRAE 307.0 0.9 6 99.3 2 × 10–2 4GG 392.2 28.9 39 99.3 2.2 × 10–13 40Observed 304.2 99.3

Second(2012–2013)validation

CRAE 446.8 6.9 14 143.3 17.5 3GG 442.6 7.8 48 99.8 42.6 50Observed 479.9 173.9

Note: For abbreviations see Tables 1 and 3.

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evaporation model of criterion (II) with ΔQ < 6%. Accordingly, the CRAE model was ableto produce the best estimated value of annual Re as shown by the ΔQ statistical values.

Furthermore, according to NRMSE values of Table 5, the SM content was simulatedwith reasonable accuracy by applying two calibrated evaporation models for both criteriaduring the first hydrological year. However, during the validation process of both criteria,only the CRAE (NRMSE < 10%) model produced acceptable results. For illustrativepurposes, Figure 6 shows daily variation of the observed and simulated SM values duringthe validation period (the second hydrological year) of criterion (II). As shown inFigure 6, the values of simulated SM using the CRAE evaporation method (water balanceapproach) were closer to the observed values than those simulated when the GG evapora-tion models were applied in the water balance method. Furthermore, as illustrated inFigure 6, the simulated SM using the CRAE model was in good correspondence to theobserved values during the recharge period of the second hydrological year (DOY of 28–136), which led to the best estimation of annual Re by the CRAE method.

Conclusions

The CRAE, AA and GG complementary relation models were used to simulate Ea from baresoil in a foothill region of a semi-arid environment. Simulated Ea values were evaluated inthe light of available data from lysimeter measurements. Acceptable Ea values are essentialin the estimation of annual Re. Initially, the three CR models with their original values wereutilized to test their general applicability. Due to poorly obtained results, the CRAE and GGmodels were locally calibrated based on observed Ea from bare soil of the first hydrologicalyear and were validated with independent data of the second hydrological year. The AAmodel was not calibrated since several previous studies had already agreed upon a constant

Table 5. Statistical test results of annual potential recharge and also soil moisture simulationutilizing CRAE and GG models with locally calibrated parameters for both criteria and waterbalance approach for the first (calibration) and second (validation) study hydrological years(October–September).

Hydrological year Model

Soil moisture Potential recharge

ΔQ (%)NRMSE(%)

Annual value(mm)

ΔQ(%)

Criterion (I)First (2011–2012)

calibrationCRAE 24.4 9 70.75 5.0GG 5.2 13 81.47 9.4Measured 74.47

Second (2012–2013)validation

CRAE 6.1 10 31.43 15.2GG 28.1 35 44.7 63.8Measured 27.29

Criterion (II)First (2011–2012)

calibrationCRAE 12.6 8 70.39 5.5GG 26.5 20 81.92 10.0Measured 74.47

Second (2012–2013)validation

CRAE 8.6 10 26.93 1.3GG 15.0 25 43.1 57.9Measured 27.29

Note: For abbreviations see Tables 1 and 3.

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parameter value. Calibration was made based on the best estimation of annual Ea [criterion(I)] and the best estimation of cumulative Ea during the occurrence of Re [criterion(II)].

According to results, both ΔQ and NRMSE revealed very poor performances of thethree CR models with original parameters for simulating Ea, annual Re and SM underrecharge occurrence condition. Accordingly, the CRAE model with locally calibratedparameters of criterion (II) made the best simulation of Ea during the occurrence of Reand annual periods for both the first (calibration) and second (validation) hydrologicalyears with acceptable NRMSE value (less than 30%). Additionally, the validation resultsshowed good performance of the CRAE calibrated model of criterion (II) for estimatingannual Re with ΔQ < 6%. Furthermore, acceptable results of SM simulation in valida-tion period of both criteria were achieved utilizing the CRAE calibrated method, withNRMSE < 10%. According to the results of this research, it is necessary to calibrate thethree studied CR models during the occurrence of Re [criterion (II)] in order to havegood estimation of Re.

Disclosure StatementNo potential conflict of interest was reported by the authors.

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