Comparison of Ten Potential Evapotranspiration Models and TheirAttribution Analyses for Ten Chinese Drainage Basins

Ruiheng XIE1, 2 and Aihui WANG*2

1School of Atmospheric Sciences, Chengdu University of Information Technology, Chengdu 610225, China2Nansen-Zhu International Research Center, Institute of Atmospheric Physics,

Chinese Academy of Sciences, Beijing 100029, China

(Received 13 April 2020; revised 1 June 2020; accepted 18 June 2020)

ABSTRACT

Potential evapotranspiration (EPET) is usually calculated by empirical methods from surface meteorological variables,such as temperature, radiation and wind speed. The in-situ measured pan evaporation (ETpan) can also be used as a proxyfor EPET. In this study, EPET values computed from ten models are compared with observed ETpan data in ten Chinese riverbasins for the period 1961−2013. The daily observed meteorological variables at 2267 stations are used as the input to thosemodels, and a ranking scheme is applied to rank the statistical quantities (ratio of standard deviations, correlationcoefficient, and ratio of trends) between ETpan and modeled EPET in different river basins. There are large deviationsbetween the modeled EPET and the ETpan in both the magnitude and the annual trend at most stations. In eight of the basins(except for Southeast and Southwest China), ETpan shows decreasing trends with magnitudes ranging between −0.01 mmd−1 yr−1 and −0.03 mm d−1 yr−1, while the decreasing trends in modeled EPET are less than −0.01 mm d−1 yr−1. Intercomparisons among different models in different river basins suggest that PETHam1 is the best model in the Pearl Riverbasin, PETHam2 outperforms other models in the Huaihe River, Yangtze River and Yellow River basins, and PETFAO is thebest model for the remaining basins. Sensitivity analyses reveal that wind speed and sunshine duration are two importantfactors for decreasing EPET in most basins except in Southeast and Southwest China. The increasing EPET trend in SoutheastChina is mainly attributed to the reduced relative humidity.

Key words: potential evapotranspiration model, pan evaporation, model comparison, sensitivity analysis, China

Citation: Xie, R. H. and A. H. Wang, 2020: Comparison of ten potential evapotranspiration models and their attributionanalyses for ten Chinese drainage basins. Adv. Atmos. Sci., 37(9), 959−974, https://doi.org/10.1007/s00376-020-2105-0.

Article Highlights:

•  In China, EPET and ETpan have big differences in both magnitude and trend, especially in arid regions.•  PETHam1 is the best model in the Pearl River basin, PETHam2 outperforms other models in the Huaihe, Yangtze River and

Yellow River basins, and PETFAO is the best model for the remaining basins.•  Sensitivity analyses reveal that wind speed and sunshine duration are two important factors for decreasing EPET in most

basins. 

  

1.    Introduction

Evapotranspiration (ET) plays an important role in bothenergy and hydrologic cycles at the land surface, and it con-sists of open water evaporation, bare soil evaporation, rain-fall interception evaporation, and vegetation transpiration(Zeng et al., 2018). The release of latent heat due to evapora-tion affects water and heat balances near the surface, andapproximately two-thirds of precipitations falling over theland is from evaporated water (Wang et al., 2012a). Further-

more, ET is of great significance for agriculture, and it is aprerequisite for irrigation planning (Paparrizos et al., 2017).In the meteorological and agricultural sciences, there are usu-ally three different ET notations, including actual evapotran-spiration (AET), potential evapotranspiration (EPET), andpan evaporation (ETpan). AET denotes the actual moistureevaporating from the land surface under local climate condi-tions, and EPET is defined as the amount of evaporation andtranspiration that would occur under certain meteorologicalconditions with a sufficient water supply but without advec-tion and heating effects (Dingman, 1992; McMahon et al.,2013; Li et al., 2016). EPET is the upper limit of AET andcan be used to estimate AET (Gao et al., 2006). ETpan is evap-

 

  * Corresponding author: Aihui WANG

Email: wangaihui@mail.iap.ac.cn 

 

ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 37, SEPTEMBER 2020, 959–974 • Original Paper •

 

© Institute of Atmospheric Physics/Chinese Academy of Sciences, and Science Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020  

oration from a water pan under local climatic/environ-mental conditions, and to a certain extent, it can representopen water evaporation.

ETpan can be measured at a meteorological station, andthe measurement is obtained using an evaporation pan withenough water supplies at an open site. AET can also be meas-ured by a lysimeter, the eddy covariance technique, orBowen ratio method (Wang et al., 2012a). However, unlikeroutine meteorological observations, in-situ measurementsof AET are not available in many regions worldwide. In prac-tice, AET is usually calculated by empirical methods (Gaoet al., 2007). EPET cannot be directly observed and is usu-ally estimated by empirical methods (referred to as EPET mod-els) using meteorological parameters as inputs.

According to the types of input variables, EPET modelscan be classified as temperature-based, radiation-based, andcombination models in which multiple meteorological para-meters are used as the model inputs (Bormann, 2011). Forinstance, to estimate reference crop evapotranspiration(ETref), the Penman−Monteith (PM) method recommendedby the Food and Agriculture Organization (FAO) is one ofthe combination models and is widely used to estimateEPET. This model requires temperature, radiation and windspeed as inputs (Allen et al., 1998). Using station-observedmeteorological data as inputs, EPET computed with theFAO56 model indicates an overall downward trend in mostparts of China (Gao et al., 2006; Yin et al., 2010a).Although the PM method is regarded as the most representat-ive formula for estimating EPET and has been widely used inmany studies (Gao et al., 2006; Zhang et al., 2007; Zuo etal., 2012), this model requires multiple surface meteorolo-gical quantities and several empirical coefficients, which areusually not easily obtainable. Therefore, other EPET modelsthat require fewer inputs have been developed and used com-monly in research. For instance, Samani and Pessarakli(1986) concluded that the temperature-based Hargreavesmodel can reasonably estimate EPET in regions with Arizo-nian climatic conditions. The traditional Priestley−Taylormodel uses only air temperature and net radiation as inputsto compute EPET and has been adopted in various studies(Priestley and Taylor, 1972). Ding et al. (2013) incorpor-ated the leaf area index, soil moisture and mulching frac-tion into the original Priestley−Taylor model and found thatthe modified model improved EPET estimates in cold andarid areas. In general, the performances of different EPET mod-els are region dependent, and a specific model may not besuitable for all regions in China. Therefore, to obtain themost representative EPET model in each Chinese river basin,it is necessary to perform comprehensive evaluations oftheir performances.

Many studies have compared or evaluated EPET modelsover the past few decades (Jacobs et al., 2004; Lu et al.,2005; Douglas et al., 2009; Donohue et al., 2010; Bormannet al., 2011; Li et al., 2016; Paparrizos et al., 2017). The con-clusions of these studies are quite different, and the “best”EPET models vary across different climate regimes. In con-

trast to EPET, the evaporation pan exchanges heat and mois-ture with the surrounding environment, which affects thewater evaporation rate in the pan (ETpan) (Zuo et al., 2016).Although ETpan and EPET have different physical meaningsand are derived from different approaches, many studiesstill regard ETpan as a surrogate for EPET (Liu et al., 2004;Yin et al., 2010b; Han et al., 2012). In China, meteorolo-gical stations routinely measure ETpan, which has been usedto evaluate, or are regarded as, EPET models (Zhou et al.,2006; and Weiβ and Menzel, 2008). However, most previ-ous studies have evaluated the performances of EPET mod-els at only a few stations for a short time period (Xu et al.,2002; Li et al., 2016; Paparrizos et al., 2017), and the res-ults may not be representative in large areas for a long timeperiod. China has a vast land domain, and its climate condi-tion varies regionally. It is necessary to investigate the applic-ability of different EPET models in different climate regimes.

In the current study, ETpan observations at 2267 sta-tions for the period 1961−2013 are used to evaluate the per-formances of ten EPET models in ten Chinese river basins.Various statistical quantities are computed and inter-com-pared, and subsequently, the best-performing EPET model isobtained for each river basin. Finally, based on the bestEPET model for each river basin, sensitivity analyses are alsoconducted for the EPET to the input meteorological vari-ables.

2.    Data and methods

2.1.    Meteorological data

High-quality daily observations at 2425 meteorologicalstations were obtained from the National MeteorologicalInformation Center of the China Meteorological Administra-tion (http://data.cma.cn/en). The variables used in this studyinclude 20-cm micro-pan evaporation (ETpan), minimum airtemperature (Tmin), maximum air temperature (Tmax), meanair temperature (Ta), wind speed at 10 m (U10), relative humid-ity (RH), and sunshine duration (SD) from 1961 to 2013. Toensure the long-term representation of those meteorologicaldata stations, available records of less than 30 years are dis-carded, and 2267 observation stations remain in this study.

As EPET is an important land surface hydrological ele-ment, and divisions of drainage basins are often used in hydro-logy research, China is divided into ten drainage basins(Fig. 1), including seven river basins [the Songhua River(143 stations), Liaohe River (89 stations), Haihe River (252stations), Yellow River (307 stations), Huaihe River (211 sta-tions), Yangtze River (661 stations), Pearl River (236 sta-tions) basins] and three other drainage basins[SoutheastChina (SE, 110 stations), Southwest China (SW, 92 sta-tions) and Northwest China (NW, 166 stations)]. Below, theanalyses will be performed for those basins.

2.2.    EPET models

By reviewing the literature, a set of 10 different EPET

models are adopted in our study (Table 1), and these mod-

960 EVALUATING EPET FORMULA BASED ON PAN EVAPORATION VOLUME 37

 

  

els are widely used in various studies. They include four tem-perature-based models [Hargreaves (Hargreaves andSamani, 1985), Romanenko (Oudin et al., 2005), Hamon ver-sion1 (Lu et al., 2005) and Hamon version2 (Oudin et al.,2005)], four radiation-based models [Priestley−Taylor(Priestley and Taylor, 1972), Abtew (Oudin et al., 2005),Jensen−Haise (Jensen and Haise, 1963) and Makkink(Makkin, 1957)], and two combination models [Penman(Oudin et al., 2005) and FAO56 (Allen et al., 1998)].Among those EPET models, radiation-based models requiresolar radiation (Rs) and net radiation (Rn) as inputs, whichare usually not available from in-situ measurements. Empir-

ical formulae with available meteorological variables can beused to derive radiation datasets (Allen et al., 1998; Yang etal., 2006). For example, Yang et al.(2006) proposed ahybrid method in which surface radiation was a function ofthe sunshine duration. Then, the researchers used thismethod to calculate Rs in China, the USA and Saudi Arabiaand found that the modeled Rs values were the most consist-ent with the observations when compared to those fromother methods. Here, we adopted the method of Yang et al.(2006) to compute Rs: 

Rs

Rc= a0+a1

( nN

)+a2

( nN

)2, (1)

where Rs is the solar radiation; Rc is the solar radiationunder clear-sky conditions, which is calculated by meteorolo-gical observations, ozone absorption and turbidity coeffi-cients; n is the measured sunshine duration; N is the max-imum possible sunshine duration; and a0, a1 and a2 are regres-sion coefficients. Equation (1) has been widely applied inmany studies (Yang et al., 2010; Tang et al., 2011; Wang etal., 2012b; He et al., 2018). In addition, we also adopted thecoefficients of Wang et al. (2012b), in which a0 is 0.33, a1

is 0.70, and a2 is −0.02 in Eq. (1), which were derived frommeteorological station variables.

According to the principle of the conservation ofenergy, Rn is the difference between incoming net short-wave radiation (Rns) and the outgoing net longwave radi-ation[Rnl, Eq. (2)]. The FAO has also provided equations tocalculate these variables (Allen et al., 1998). Moreover, Yinet al.(2008) used radiation measurements in China to calib-

 

Fig. 1. Distribution of ten drainage basins and the locations of2267 meteorological stations in China. The station number ineach basin is indicated in brackets.

Table 1.   The EPET models used in the study. The input variables of these formulae include: Ta = mean air temperature (°C), Tmax =maximum temperature (°C), Tmin = minimum temperature (°C), SD = sunshine duration (h), γ = psychrometric constant (kPa °C−1), Δ =slope of the vapor pressure curve (kPa °C−1), λ= latent heat of vaporization (MJ kg−1), α = surface albedo, es = saturation vapor pressure(kPa), ea = actual vapor pressure (kPa), U2 = wind speed at 2 m height (m s−1), Rs = global solar radiation (MJ m−2), Ra = extraterrestrialradiation (MJ m−2), and Rn = net radiation (MJ m−2).

EPET models References

PETHar = 0.0023Ra(Tmax −Tmin)0.5(Ta +17.8) (Hargraves et al., 1985)

PETRom = 4.5(1+

Ta

25

)2 (1− ea

es

)(Oudin et al., 2005)

PETHam1 = 0.1651× SD12× 216.7×6.108e

17.26939Ta

Ta +237.3

Ta +273.3×1.2

(Lu et al., 2005)

PETHam2 =

(SD12

)2

e( Ta

16

)(Oudin et al., 2005)

PETPT = α∆

∆+γ

Rn

λ(Priestley and Taylor, 1972)

PETAbt = 0.53Rs

λ(1−α) (Oudin et al., 2005)

PETJen = 0.408[0.014(1.8T a +32)−0.37]Rs (Jensen and Haise, 1963)

PETmak = 0.61(∆

∆+γ

)Rs

λ−0.12 (Makkink, 1957)

PETPenman =∆Rn +2.6γ (es − ea) (1+0.536U2)

λρ(∆+γ) (Oudin et al., 2005)

PETFAO56 =

0.408∆Rn +γ900

T+273U2 (es − ea)

∆+γ(1+0.34U2)(Allen et al., 1998)

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rate the Rnl models and found that the Penman method(1948), in Eq. (4), was more accurate than the FAO24 andFAO56-PM models: 

Rn = Rns−Rnl ; (2) 

Rns = (1−α)Rs ; (3) 

Rnl = σ

T 4x,k +T 4

n,k

2

(0.56−0.25√

ea

) (0.1+0.9

nN

); (4)

σwhere α= 0.23 is the albedo for the reference crop, is theStefan−Boltzmann constant (4.903×10−9 MJ K−4 m−2 d−1),Tx,k (Tn,k) is the maximum (minimum) absolute temperaturefor 24 h (K), and ea is the actual vapor pressure (kPa).

In the Penman and FAO models, the 2-m wind speed isneeded (Table 1). Thus, we converted the 10-m wind speedto 2-m wind speed using the wind profile formula (Allen etal., 1998): 

U2 = Uz4.87

ln(67.8z−5.42), (5)

where U2 is the wind speed at 2 m above the ground sur-face (m s−1) and Uz is the measured wind speed at z m abovethe ground surface (m s−1), which is 10 m in this study.

In the Hargreaves and Jensen−Haise models, the EPET

is a function of Ta and Rs. From these models (Table 1),when Ta is lower than −17.8°C for the Hargreaves modeland −3.1°C for the Jensen−Haise model, the EPET would benegative. These are not correct in reality. Similarly, thePriestley−Taylor method requires Ta and Rn as inputs.However, Rs occurs only in the daytime, but the Rnl is avail-able for both daytime and nighttime. During the cold sea-son in high latitudinal regions, the relatively short daytimeSD would also reduce the Rs, leading to Rnl values greaterthan Rns. Under the above two circumstances, Rn will be lessthan zero, and then, the EPET from the Priestley−Taylormodel would also be negative. As an important factor of agri-culture, EPET is more prominent during the crop growing sea-sons than in other seasons, and EPET should be very small oreven negligible in the cold seasons. To avoid appearance ofa negative EPET value due to the meteorological inputs insome EPET models, our analyses are confined to the grow-ing season of March to October during each year. After theabove procedure, EPET is set as the missing value if it is stillless than zero.

2.3.    Sensitivity analysis

To estimate the effects of changes in various meteorolo-gical factors on modeled EPET, sensitivity analyses are alsoconducted for each EPET model. Because different EPET mod-els have different structures and input requirements andthese input variables have diverse magnitude ranges, it is diffi-cult to directly conduct the EPET sensitivity analysis with dif-ferent input variables (Gong et al., 2006). In this study, we

adopt a dimensionless relative sensitivity coefficient (SC),which has been widely used in ET studies (McCuen, 1974;Gong et al., 2006; Yin et al., 2010a; Zuo et al., 2012): 

SC =∂EPET

∂X|X|

EPET≈ ∆EPET

∆X|X|

EPET, (6)

where SC is the sensitivity coefficient, and X is one of themodel input variables. SC represents the relative change inEPET induced by the relative change in the meteorologicalfactor X. In other words, the relative change in X multipliedby SC equals the relative change in EPET. For example,SC=0.1 indicates that 10% of X change would cause 1% ofEPET change. A positive (negative) SC represents thatchanges in EPET are consistent (inconsistent) with those inX. The higher SC is, the stronger the X effect imposed onEPET will be. However, SC cannot fully reflect the impact ofeach meteorological factor on the EPET changes. A literat-ure review of previous studies revealed that EPET was themost sensitive to RH in the Yangtze River basin (Gong etal., 2006) and the Weihe River basin (Zuo et al., 2012) inChina. However, Yin et al. (2010b) reported that RH wasonly a highly sensitive but not a dominant factor of EPET,and its insignificant trend during 1971−2008 could onlyinduce a small change in EPET. To further address this issue,we combined the relative change (RC) in each input vari-able and its SC for EPET attribution analysis. The RC (units:%) is described as follows (Yin et al., 2010a): 

RC =53TX

|X| , (7)

where TX is the linear trend in the annual time series for anyvariable X, and |X| is its absolute mean during the past 53years. RC represents the mean percentage change in the vari-able X during the study period. Based on Eqs. (6) and (7),we also conducted attribution analyses below. At each sta-tion, we recalculated the EPET with individual input meteorolo-gical variables changing from −10% to 10% by assumingthat other factors remained unchanged (Yin et al., 2010b).Then, we calculated SC using Eq. (6) and RC using Eq. (7).The product of SC and RC denotes the relative contribution(RCT) of the target meteorological variable to the EPET

change. Inter comparisons of RCTs for different meteorolo-gical factors can represent the relative importance of each met-rological variable for the EPET change.

2.4.    Ranking scheme

To quantify the differences between modeled EPET andETpan, we compute three statistical quantities, including theratio of EPET standard deviations to that of ETpan, the correla-tion coefficient, and the ratio of EPET trends to ETpan trends.Moreover, to evaluate the performance of EPET models interms of those statistical quantities in each basin, a rankingscheme is utilized. Wang et al. (2012c) applied this app-roach to rank four statistical quantities between reanalysisproducts and observations in the Tibetan Plateau to evalu-ate the performances of each reanalysis product. In the

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present study, based on each statistical quantity, the meanranking scores from 1 to 10 are given to each EPET model.The ranking score is computed as follows: Among all 10EPET models, the highest correlation coefficient is given aranking score of 1, and the lowest one is given a score of10. Regarding the ratio of standard deviations and the ratioof trends, 1 is given to the model with the ratio closest to 1,and 10 indicates the ratio farthest away from 1. Then, we aver-age all ranking scores of three quantities in each basin, andthe mean magnitude from the lowest to the highest repres-ents the closest to the least close relationships between EPET

models and ETpan.

3.    Results

3.1.    Spatial distribution and magnitude of the modeledEPET

Figure 2 shows the spatial distribution of the multiplegrowing seasonal mean EPET and ETpan from 1961 to 2013.This figure shows the apparent spatial variations in EPET. Atthe majority of stations, the mean ETpan is above 4 mm d−1.The stations with relatively low ETpan are mainly located inthe Yangtze River basin and Liaohe River basin, while largevalues appear in the Yellow River basin and NorthwestChina, where the magnitude of ETpan is generally larger than8 mm d−1 at most stations. In terms of magnitudes, PETRom

is more consistent with ETpan than other models, with amean EPET above 3 mm d−1 at 85% of stations in China andeven larger than 8 mm d−1 in Northwest China. For the distri-bution pattern, PETRom is also the closest to ETpan, and the

spatial correlation coefficient is up to 0.86. PETFAO andPETAbt also correlate well with ETpan, while the spatial correl-ation coefficients are 0.72 and 0.74, respectively. Com-pared to other models and ETpan, the EPET values from bothPETHam1 and PETHam2 are relatively low, especially forPETHam2, with values of less than 2 mm d−1 at 93% of sta-tions. In addition, for the radiation-based models, the PETJen

produces the largest value with a magnitude larger than 4mm d−1 in eastern China.

Figure 3 shows the ranges of ETpan and EPET from differ-ent models from three basins: the Yangtze River basin(Fig. 3a), Yellow River basin (Fig. 3b), and NorthwestChina (Fig. 3c). The three basins represent the humid, semi-arid and arid regions in China, respectively. By comparison,the modeled EPET is relatively close to ETpan in the humidYangtze River basin; however, in arid Northwest China,they show obvious differences. This finding implies thatETpan and EPET are closer to each other in the humid regionthan in the arid region. This may be caused by the largernon-uniformity of climate conditions between the waterbody in the pan and the surrounding environment in the aridregions, and the non-uniformity is related to differences in sur-face temperature, moisture and albedo, which are also lar-ger in arid regions (Zuo et al., 2016). Furthermore, in allthree basins, no model can capture the peak values of ETpan,and the modeled EPET amplitudes are smaller than those ofETpan, and the biases of their maximum values are particu-larly large. Except for PETJen, the radiation-based modelsshow relatively small differences between the upper andlower quartile than those of the temperature-based models,which somehow indicates that the temporal and spatial variab-

 

 

Fig. 2. Spatial distribution of the annual meangrowth season (Mar−Oct) pan evaporation and EPET calculated by differentmodels: (a) Hargreaves, (b) Romanenko, (c) Hamon version 1, (d) Hamon version 2, (e) Priestley and Taylor, (f) Abtew,(g) Jensen and Haise, (h) Makkink, (i) Penman, (j) FAO56 and (k) ETpan.

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ilities in the radiation-based models (PETPT, PETAbt, andPETMak) should also be smaller than those of the temperat-ure-based models (PETRom, PETHam1, PETHam2). Addition-ally, PETFAO is closer in magnitude to ETpan than PETPM.Although both PETFAO and PETPM have similar structuresand input requirements, PETPM displays a narrower mag-nitude range than that from PETFAO due to its lower max-imum value.

3.2.    Trends and variability

Figure 4 shows the linear trends in the EPET models andETpan during 1961−2013. There are apparent differences,and opposing trend signs occur in some cases. ETpan has anupward trend in Southeast and Southwest China, while ithas a downward trend in other basins. The downward trendin ETpan ranges from −0.01 mm d−1 yr−1 to −0.03 mm d−1 yr−1,while the decreasing EPET trends are always less than −0.01mm d−1 yr−1. In the Songhua River and Liaohe River basin,and Southeast and Northwest China, the trends in PETFAO

and ETpan are the most similar, and in Northwest China, PET-FAO is the only model that can successfully capture thedecreasing ETpan trend. In Southwest China, the trend in PET-Mak is consistent with that of ETpan, and PETHam2 can best cap-ture the trend in ETpan in the remaining basins. In addition,PETRom is proportional to Ta (Table 1) and its temporal variab-ilities are consistent with that of Ta, showing an increasingtrend in all basins.

We further assess the inter annual variability in themodeled EPET and ETpan. Figure 5 shows the growing sea-sonal mean anomalies of EPET and ETpan from 1961 to 2013in three different drainage basins, and the correspondinganomalies of Ta and SD are also exhibited. In the YangtzeRiver basin (Fig. 5b), Ta shows an apparently upward trendsince the 1990s, and SD shows an abrupt decline around theearly 1980s. ETpan also displays a significant downwardtrend, and its anomalies change from positive to negative in1981. For most models except for PETRom, the inter annualvariability is relatively small, and their standard deviationsare no more than 0.2 mm d−1. In terms of the temperature-based equations, PETRom is the most consistent with Ta andhas been significantly increasing since the 1990s (Fig. 5a).Although the trend of Rs in the Yellow River basin and North-west China is not obvious (Figs. 5d and f), the warmingtrend since the 1990s is still significant (p=99%). The ETpan

shows obviously decreasing trends in the Yellow Riverbasin and Northwest China (Figs. 5c and e), and the down-ward trend is dramatic in Northwest China (T=−0.034 mmd−1 yr−1). Additionally, except for PETRom, the inter annualvariability in the EPET models is still small, and the stand-ard deviations are also less than 0.2 mm d−1 in these twobasins.

Because both ETpan and EPET have obvious seasonal vari-ations, so seasonality changes of modeled EPET are also invest-igated. Figure 6 exhibits the monthly trends in the EPET mod-els and ETpan. ETpan shows a decreasing trend during allmonths in the three basins, and the largest declining ratesoccur in May and June. In contrast, PETRom has an appar-

 

Fig. 3. Boxplots of annual mean growth season (Mar−Oct)ETpan and EPET calculated from different models in threeselected basins: (a) Yangtze River basin, (b) Yellow Riverbasin, and (c) Northwest China.

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ent upward trend in all months due to its highly consistentvariability with that of temperature. Except for PETRom, thePET trends in all EPET models in all months are synchron-ous in the Yangtze River basin and show downward trendsfrom June to September (Fig.6a). Among them, the trend inPETHam2 is the closest to that of ETpan. Additionally, themonthly trend of PETHam2 is closer to that of ETpan thanother models in the Yellow River basin (Fig.6b). However,in Northwest China (Fig.6c), the monthly trends in all mod-els are greatly different from ETpan. Although the decliningtrend in PETFAO is consistent with that of ETpan, the trendmagnitudes of the two are very different. This is likely dueto the differences in the physical processes of EPET andETpan in this region, and we will discuss this further in sec-tion 4. Overall, compared to humid regions, the differences

between the ETpan and EPET monthly trends are muchgreater in arid regions.

3.3.    Ranking scores

The ranking scores of the three statistical quantities areshown in Fig. 7. For the ratio of standard deviations (Fig. 7a),PETRom has the best performance, maintaining a value of 1in all basins, followed by PETJen. The ranking scores ofPETJen are less than 3 in most basins except for SouthwestChina, but the other radiation-based models do not performwell. In addition, PETPM also has relatively high rankingscores in all basins. The above results indicate that the variab-ilities in ETpan and modeled EPET are quite different. Interms of the correlation coefficient, the PETRom has highscores in the Haihe River, Huaihe River, Yangtze River and

 

 

Fig. 4. Trends in annual growing season mean ETpan and EPET from 1961 to 2013 in (a) Songhua River basin, (b) LiaoheRiver basin, (c) Haihe River basin, (d) Yellow River basin, (e) Huaihe River basin, (f) Yangtze River basin, (g)Southeast China, (h) Pearl River basin, (i) Southwest China, and (j) Northwest China. The EPET model with the closesttrend to that in ETpan is marked with a star (*).

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Pearl River basins (Fig. 7b), and PETPT also has poor scoresin all basins. PETFAO shows good performance in mostbasins except for the Yangtze River and Pearl River basins,where PETHam1 has the lowest score. There are nine basinswith correlation coefficients greater than 0.5 between ETpan

and PETFAO, except for the Pearl River basin, and betweenETpan and PETHam1/PETHam2, except for Northwest China.Notably, in Northwest China, several modeled EPET are negat-ively correlated with ETpan, except for PETFAO (0.65),PETPM (0.21) and PETHar (0.27). This further illustrates thatEPET is very different from ETpan, especially in the aridregion. Regarding the ratio of trends (Fig. 7c), PETRom haspositive trends and the worst scores in most basins whereETpan shows negative trends. In summary, PETHam2 and PET-

FAO show the best performances based on the ranking scoresin all basins. In Northwest China, the ratios of trends aregreater than zero only in PETFAO and PETPM, which are theonly models that produce a negative trend as in ETpan.Finally, we average the ranking scores of all three statist-ical quantities in each basin, and the model with the lowestscore is selected and regarded as the best model for this

basin (Fig. 8). For example, PETHam2 performs best in the Yel-low River, Huaihe River and Yangtze River basins, whilePETHam1 is outperformed in the Pearl River basin. For theremainder of the basins, PETFAO is the best model.

3.4.    Sensitivity analyses

Among the selected best models in each basin, PETFAO

considers temperature, relative humidity, wind speed andnet radiation, and it is also the most commonly used EPET

model in climate research (Gao et al., 2006; Gong et al.,2006; Yin et al., 2010a; Zuo et al., 2012). Both PETHam1

and PETHam2 belong to a temperature-based model and arederived from air temperature and sunshine duration. All thebest models that were selected are affected by multiple met-eorological factors. To determine the RCT of each meteorolo-gical variable to EPET changes, we apply a sensitivity ana-lysis to the best-performing model in each basin. Becausethe best-performing EPET models are not troubled by a negat-ive value, the sensitivity analyses are conducted for thewhole year instead of only the growing seasons as in the previ-ous sections.

 

 

Fig. 5. Mean EPET anomaly in (a) the Yangtze River basin, (c) the Yellow River basin, and (e) Northwest China, and theanomalies in temperature and sunshine duration (b, d, f) averaged over the growing seasons (Mar−Oct) from 1961 to2013. The red curve indicates the temperature anomaly (left axis), and the blue curve is the sunshine duration anomaly(right axis).

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Table 2 shows the SC for RH is always less than zero,implying opposing variations in RH and EPET. RH is afactor that is highly sensitive to EPET, and the minimum ofSC can reach −1.32. However, due to the insignificant trendin RH during the study period, the RC of RH is less than8% in the basins where the best model is PETFAO. Thus, RHis not a determining factor of EPET changes, and the corres-ponding RCTs of RH to EPET changes are less than 2%,except for Southeast China. However, in Southeast China,RH decreases by 7.32%, which induces EPET increases of5.73%, and RH is the primary contributor to increasing EPET

in this basin (Table 3). In other basins where PETFAO is selec-ted, the wind speed at 2 m (U2) is the most responsiblefactor for EPET reductions, although it is not the most sensit-ive factor. The SC is greater than 0.5 in the Songhua River,Liaohe River and Haihe River basins and Northwest China.Furthermore, the reduction in U2 in these basins is morethan 40%, which leads to a more than 20% reduction inEPET. In Southwest China, the RC of U2 is −27.25%, whichdrives EPET reduction by 5.35%, and the RCT of U2 to EPET

change is far less than that in other basins. Thus, the changein EPET is affected by multiple factors in this basin, with theoverall RCT of the meteorological variables to an EPET

change of 2.86% and the actual relative change in EPET of0.71%. The two values are very close, which further illus-

 

Fig. 6. Annual trends in ETpan and EPET during each month inthree selected basins: (a) Yangtze River basin, (b) YellowRiver basin, and (c) Northwest China.

 

Fig. 7. Ranking scores of (a) the ratio of standard deviations,(b) the correlation coefficient, and (c) the ratio of trends, indifferent basins. The label of 1 (10) represents the best (worst)score of a modeled EPET compared to ETpan.

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trates that sensitivity analyses can be used to attribute thechanges in EPET in Southwest China (Yin et al., 2010b).Tmax has little effect on EPET, which would lead to a 6.77%enhancement in EPET in Northwest China and less than 4%in other regions. For Tmin, low sensitivity appears in nearlyall basins; the lowest SC (−0.01) appears in NorthwestChina, and the highest SC (0.21) is in Southeast China.However, it has great RC in some basins, especially in theSonghua River and Liaohe River basin, where the RCreaches 608.27% and 277.55%. This is due to the averageTmin being close to zero in these basins, where a slight

change in absolute value would cause a large percentagechange in Tmin. The RCTs of Tmin to EPET are quite differentin different basins, and the value is 24.16% and 14.85% inthe Songhua River and Liaohe River basin, respectively, butless than 4% in other basins. Therefore, Tmin is a vitallyimportant variable for EPET changes in the Songhua andLiao River basins. For basins with PETFAO as the selectedbest model, the SC of EPET to SD ranges from −0.26(Songhua River basin) to 0.14 (Southwest China), with negat-ive values in the Songhua River, Liaohe River and HaiheRiver basins and Northwest China and positive values in

 

 

Fig. 8. Average ranking scores of three statistical quantities in (a) Songhua River basin, (b) Liaohe River basin, (c) HaiheRiver basin, (d) Yellow River basin, (e) Huaihe River basin, (f) Yangtze River basin, (g) Southeast China, (h) Pearl Riverbasin, (i) Southwest China, and (j) Northwest China. The lowest (highest) value indicates the best (worst) performance of theEPET models,and the best model is marked with a star (*).

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other basins, while the RCTs of SD to EPET change are lessthan 5% in all basins. This result indicates that SD is not theprimary factor for EPET change in these basins.

For the basins with PETHam1 and PETHam2 as the bestmodels, both Ta and SD are the inputs of the models. Interms of PETHam2, SD is more sensitive than Ta, and the SCfor SD is 2 in those basins. For PETHam1, the SC for Ta

(1.25) is higher than that of SD (1). In addition, the min-imum RC for SD can reach −21.01% in the Huaihe Riverbasin. As a result, SD is the primary contributor to EPET

change in those basins. The RCTs to EPET change rangefrom −12.91% (Pearl River basin) to −42.02% (HuaiheRiver basin). Although the percentage changes in EPET arelarge, the actual EPET trend does not exceed −0.01 mm d−1 yr−1.This is because the EPET magnitudes calculated by PETHam1

and PETHam2 are too small (Fig. 2). In general, the summa-tion of RCT from individual meteorological variables is aclose approximation to the actual EPET changes in eightbasins (except for Southeast and Northwest China), wherethe differences are less than 5%. In both Southeast and North-west China, the large differences in RCTs and actual EPET

change may be due to the other variables in the radiation cal-culation formulas, such as ozone absorption and turbiditycoefficients.

3.5.    Relationship between ETpan and EPET

ETpan and EPET can be linked by regression equations,i.e., EPET = KpanETpan, where Kpan is the regression coeffi-cient (Chiew and McMahon, 1992; Linacre, 1994; McMa-hon et al., 2013). Linacre (1994) provided a Kpan with avalue of 0.7 by analyzing the data from a dozen placesaround the world, and this value was adopted in some stud-ies (Weiβ and Menzel, 2008). However, many studies havereported that Kpan is dependent on the local climate condi-tions and should not be globally unified (McVicar et al.,2007; Zheng et al., 2009). To further understand the relation-ship between ETpan and EPET, we also calculated Kpan basedon our selected EPET model in each basin (Fig. 9). TheYangtze River basin (Fig. 9f) has the largest Kpan, with avalue of 0.38, and the minimum value of Kpan (0.13) appearsin Northwest China (Fig. 9j). Moreover, the determinationcoefficient (R2) is below 0.5 in Northwest China, further indic-ating that ETpan may not be used as a EPET proxy in the aridregion.

4.    Discussion

In the current study, ETpan and EPET calculated by anempirical method show differences in magnitudes, inter

Table 2.   Sensitivity coefficient (SC) of the best-performing EPET models in each basin during 1961−2013. The abbreviation of eachvariable name is shown in Table 1. The SC is computed from Eq. (6) in the text.

Basin Model Ta Tmax Tmin RH U2 SD

Songhua River FAO − 0.08 0.04 −1.32 0.57 −0.26Liaohe River FAO − 0.23 0.05 −1 0.54 −0.21Haihe River FAO − 0.51 0.08 −0.83 0.5 −0.17

Yellow River Ham2 0.61 − − − − 2Huaihe River Ham2 0.93 − − − − 2Yangtze River Ham2 1.11 − − − − 2

SE FAO − 0.54 0.21 −0.77 0.15 0.12Pearl River Ham1 1.25 − − − − 1

SW FAO − 0.45 0.12 −0.30 0.15 0.14NW FAO − 0.47 −0.01 −0.68 0.54 −0.24

Table 3.   The relative contributions (RCT = SC × RC) of each meteorological variable to EPET changed in ten drainage basins. Themeteorological variables are the required inputs of the best-performing model in each basin. The abbreviation of each variable name isshown in Table 1. SC and RC are derived from Eqs. (6) and (7), respectively.

RCT (%) Ta Tmax Tmin RH U2 SD

Songhua River − 0.43 24.16 0.51 −26.43 2.03Liaohe River − 0.75 14.85 −2.1 −22.65 1.68Haihe River − 2.93 3.05 1.87 −24.53 3.09

Yellow River 9.8 − − − − −17.55Huaihe River 7.51 − − − − −42.02Yangtze River 6.57 − − − − −21.51

SE − 3.12 1.92 5.73 −4.69 −1.39Pearl River 4.78 − − − − −12.91

SW − 3.15 3.57 1.33 −5.35 0.16NW − 6.77 −2.63 0.37 −22.12 0.6

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annual variability and trends. Some of the reasons stemfrom the differences in their definitions. The definition ofEPET assumes no advection and no heating effects, whichmeans no water-advected energy and no heat storage effects(McMahon et al., 2013), while the evaporation pan has

strong heat storage. In fact, the wall and bottom of the evapor-ation pan can receive and reflect radiation, which will influ-ence the evaporation rate. Moreover, according to Zuo et al.(2016), the size of the evaporation pan will also affect theevaporation rate; for instance, the smaller the water body is,

 

 

Fig. 9. Relationship between annual ETpan and EPET calculated by the best-performing model for each basin:(a)Songhua River basin, (b) Liaohe River basin, (c) Haihe River basin, (d) Yellow River basin, (e) Huaihe River basin,(f) Yangtze River basin, (g) Southeast China, (h) Pearl River basin, (i) Southwest China, and (j) Northwest China.The slope (Kpan, EPET = KpanETpan) and determinant coefficients (R2) are also indicated.

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the greater the evaporation rate will be. When the waterbody in the pan is sufficiently wide, the ETpan would becloser to the water surface evaporation. After adjusting forthe energy exchange of the pan, ETpan can be consideredopen-water evaporation (Dingman, 1992; McMahon et al.,2013). However, the empirical EPET models were designedto underlie various surface and climate conditions, and theymay not only represent water evaporation. For example, PET-FAO calculated the EPET in the reference surface with anassumed crop height of 0.12 m, a fixed surface resistance of70 s m−1 and an albedo of 0.23 (Allen et al., 1998). PETMak

was used to estimate grass ET under cool conditions(Makkink, 1957). In summary, there are big differences inmagnitude between ETpan and EPET, particularly in the northw-est arid region. Despite the difference in magnitude, thetrend in ETpan agrees with that of modeled EPET in mostregions (Gao et al., 2006; Zhang et al., 2007; Zheng et al.,2009; Yang and Yang, 2012). In Northwest China, there isnot only a large difference in magnitude but also in thetrend (Figs. 3c and 5c), and only PETFAO can capture the neg-ative ETpan trend well. This is because the significantlydecreasing trend in ETpan is mainly caused by the signific-ant downward trend in wind speed in this region (Shen etal., 2009; Yang and Yang, 2012; Wang et al., 2017), andonly PETPM and PETFAO use wind speed as inputs.Moreover, all the EPET models required air temperature,which exhibits a significant upward trend during the studyperiod (Shen et al., 2009), inducing an increasing trend inEPET in Northwest China. For PETFAO, U2 is the majorfactor of EPET changes in this region, the SC of U2 is 0.55,and the RC of U2 reaches −41.62%; therefore, PETFAO cancapture the negative trend in EPET in Northwest China.Since most EPET models perform poorly in NorthwestChina, the applicability of EPET models in arid regionsremains to be explored (Steiner et al., 1991; Li et al., 2016).

It should be noted that Rs is greatly impacted by aero-sol and it usually reduces the solar irradiance arriving at thesurface (Hu et al., 2017). In recent years, air pollution inChina has become a serious issue, which also brings largeamounts of aerosol. Current research does not consider theabove effects, and thus the computed Rs based on sunshineduration only might be overestimated and affect the accur-acy of EPET results. The weight setting of the ranking scoresis also worthy of further attention. We put equal weight foreach of the three statistical metrics in this research. As wementioned previously, the trend in ETpan agrees with that ofmodeled EPET in most regions, and thus it might be reason-able to give larger weight to the ratio of trends in theseregions. However, it is difficult to determine weight valuesfor each metric at the current stage. It is necessary toexplore this in future research by using different weights inranking schemes.

Despite the magnitude differences between ETpan andEPET in some basins, there is also a close relationshipbetween them. Previous studies have revealed that the mag-nitude of ETpan is generally greater than ETref (Jensen et al.,

1990; Weiβ and Menzel, 2008 ), while ETpan and EPET (orETref) are usually linked by the regression coefficient Kpan

(Fig.9). In addition, there are different types of evaporationpan in practice. For instance, Class-A pans are used in mostcountries, such as the USA and Australia, while 20-cmmicro-pans are popular in China. With different types ofpans, the magnitudes of Kpan are also different. The pan coeffi-cients for the Class-A pan are higher than the Chinesemicro-pan coefficients, but the seasonal ranges of Kpan val-ues for the two different pans are similar (McVicar et al.,2007; McMahon et al., 2013).

Although we characterize EPET changes through sensitiv-ity analyses, and conclude that wind speed and sunshine dura-tion are the major factors affecting EPET changes, EPET isnot affected by only these two factors. For total ET, transpira-tion is a very important component that is controlled by theleaf area index (LAI), surface roughness, and vegetationroot distributions (Arora, 2002). Furthermore, because ofthe increasing CO2 fertilization effects, climate change, andland use-land cover change, global-scale LAI shows a signific-ant upward trend (Zhu et al., 2016), which would causechanges in transpiration. According to Zeng et al.(2018), agreening Earth would induce a significant increase in ter-restrial ET. Therefore, similar to ET, EPET is also affectedby the CO2, vegetation and land use-land cover change.ETpan is the evaporation of the open water surface withoutconsidering the effects of transpiration or interception.

5.    Conclusion

Based on meteorological observations, we calculatedthe EPET of ten Chinese drainage basins using 10 differentEPET models. Then, we compared the ETpan and EPET toobtain the best-performing model for each basin. By compar-ison, large disparities exist between modeled EPET andETpan. The daily ETpan is over 4 mm d−1 at the majority of sta-tions, while the EPET calculated by most models is less than3 mm d−1. In eight basins (except for Southeast and Southw-est China), the downward annual ETpan trends range from−0.01 mm d−1 yr−1 to −0.03 mm d−1 yr−1, while the decreas-ing EPET trends are less than −0.01 mm d−1 yr−1. Addition-ally, the differences are larger in arid regions than in humidregions, and the largest disparities appear in NorthwestChina, where only PETFAO can successfully capture the negat-ive trend in ETpan.

Then, a scheme was applied to rank the three statisticalquantities of ETpan and EPET in different basins, includingthe ratio of standard deviations, the correlation coefficient,and the ratio of trends. The results show that PETHam1 is thebest model for the Pearl River basin, while PETHam2 is outper-formed in the Huaihe River, Yangtze River and YellowRiver basins. In terms of the remaining basins, PETFAO isthe best-performing model. The sensitivity analyses of thebest-performing EPET model in each basin reveal that U2

and SD are the two factors contributing to the overalldecrease in EPET. The contributions of SD to EPET change

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are always greater than 10% in the basins with selectedPETHam1/PETHam2, and the contributions of U2 are largerthan 20% in the Haihe River, Songhua River and LiaoheRiver basins and Northwest China. In addition, in theSonghua River and Liaohe River basins, Tmin also contrib-utes considerably to the EPET changes, and the RCT canreach 24.16% and 14.85% respectively. In Southeast China,the upward trend in EPET is primarily controlled by thedecreasing RH. Furthermore, the Kpan varies from 0.13 (North-west China) to 0.38 (Yangtze River basin), and is larger inthe humid regions than in the arid regions.

Understanding the characteristics of EPET and its impact-ing factors can help us to gain insight into the hydrologicalprocess and, in particular, water resource management in anarid region. Through the current study, we have identifiedthe best-performing EPET models in each Chinese basin andderived long-term, high-quality daily EPET datasets inChina, which can be used as a benchmark for EPET researchin the future. Moreover, the selected model in each basinalso reduces the input requirements, which is particularly prac-tical in regions with limited availability of meteorologicalvariables.

Acknowledgments.    This paper was financially supported bythe National Natural Science Foundation of China (GrantNo. 41875106) and the National Key R&D Program of China(Grant No. 2016YFA0602401). We also thank the two anonym-ous reviewers for their constructive comments.

REFERENCES 

Allen, R. G., L. S. Pereira, D. Raes, and M. Smith, 1998: Cropevapotranspiration—Guidelines for computing crop waterrequirements. FAO irrigation and drainage paper No.56,Food and Agriculture Organization (FAO), Rome.

 

Arora, V., 2002: Modeling vegetation as a dynamic component insoil-vegetation-atmosphere transfer schemes and hydrolo-gical models. Reviews of Geophysics, 40, 1006,https://doi.org/10.1029/2001RG000103.

 

Bormann, H., 2011: Sensitivity analysis of 18 different potentialevapotranspiration models to observed climatic change at Ger-man climate stations. Climatic Change, 104(3-4), 729−753,https://doi.org/10.1007/s10584-010-9869-7.

 

Chiew, F. H. S., and T. A. Mcmahon, 1992: An Australian compar-ison of penman’s potential evapotranspiration estimates andclass A evaporation pan data. Australian Journal of SoilResearch, 30, 101−12, https://doi.org/10.1071/SR9920101.

 

Ding, R. S., S. Z. Kang, F. S. Li, Y. Q. Zhang, and L. Tong,2013: Evapotranspiration measurement and estimation usingmodified Priestley-Taylor model in an irrigated maize fieldwith mulching. Agricultural and Forest Meteorology, 168,140−148, https://doi.org/10.1016/j.agrformet.2012.08.003.

 

Dingman, S. L., 1992: Physical Hydrology. Prentice Hall, UpperSavage, 575 pp.

 

Donohue, R. J., T. R. McVicar, and M. L. Roderick, 2010: Assess-ing the ability of potential evaporation formulations to cap-ture the dynamics in evaporative demand within a changingclimate. Journal of Hydrology, 386(1−4), 186−197,

https://doi.org/10.1016/j.jhydrol.2010.03.020. 

Douglas, E. M., J. M. Jacobs, D. M. Sumner, and R. L. Ray,2009: A comparison of models for estimating potential evapo-transpiration for Florida land cover types. Journal of Hydro-logy, 373(3-4), 366−376, https://doi.org/10.1016/j.jhydrol.2009.04.029. 

Gao, G., D. L. Chen, G. Y. Ren, Y. Chen, and Y. M. Liao, 2006:Spatial and temporal variations and controlling factors ofpotential evapotranspiration in China: 1956−2000. Journalof Geographical Sciences, 16(1), 3−12, https://doi.org/10.1007/s11442-006-0101-7. 

Gao, G., D. L. Chen, C. Y. Xu, and E. Simelton, 2007: Trend ofestimated actual evapotranspiration over China during 1960−2002. Journal of Geophysical Research., 112, D11120,https://doi.org/10.1029/2006JD008010. 

Gong, L. B., C. Y. Xu, D. L. Chen, S. Halldin, and Y. D. Chen,2006: Sensitivity of the Penman-Monteith reference evapotran-spiration to key climatic variables in the Changjiang(Yangtze River) basin. Journal of Hydrology, 329, 620−629,https://doi.org/10.1016/j.jhydrol.2006.03.027. 

Han, S. J., D. Xu, and S. L. Wang, 2012: Decreasing potential evap-oration trends in china from 1956 to 2005: Accelerated inregions with significant agricultural influence? Agriculturaland Forest Meteorology, 154−155, 44−56, https://doi.org/10.1016/j.agrformet.2011.10.009. 

Hargreaves, G. H., and Z. A. Samani, 1985: Reference crop evapo-transpiration from temperature. Applied Engineering in Agri-culture, 1(2), 96−99, https://doi.org/10.13031/2013.26773. 

He, Y. Y., K. C. Wang, C. L. Zhou, and M. Wild, 2018: A revisitof global dimming and brightening based on the sunshine dura-tion. Geophysical Research Letters., 45, 4281−4289,https://doi.org/10.1029/2018GL077424. 

Hu, B., and Coauthors, 2017: Quantification of the impact of aero-sol on broadband solar radiation in North China. ScientificReports, 7, 44851, https://doi.org/10.1038/srep44851. 

Jacobs, J. M., M. C. Anderson, L. C. Friess, and G. R. Diak,2004: Solar radiation, longwave radiation and emergent wet-land evapotranspiration estimates from satellite data in Flor-ida, USA. Hydrological Sciences Journal, 49(3), 476,https://doi.org/10.1623/hysj.49.3.461.54352.

 

Jensen, M. E., and H. R. Haise, 1963: Estimating evapotranspira-tion from solar radiation. Proceedings of the American Soci-ety of Civil Engineers, Journal of the Irrigation and Drain-age Division, 89, 15−41.

 

Jensen, M. E., R. D. Burman, and R. G. Allen, 1990: Evapotran-spiration and Irrigation Water Requirements. American Soci-ety of Civil Engineers.

 

Li, S. E., S. Z. Kang, L. Zhang, J. H. Zhang, T. S. Du, L. Tong,and R. S. Ding, 2016: Evaluation of six potential evapotran-spiration models for estimating crop potential and actualevapotranspiration in arid regions. Journal of Hydrology,543, 450−461, https://doi.org/10.1016/j.jhydrol.2016.10.022. 

Linacre, E. T., 1994: Estimating U.S. class a pan evaporationfrom few climate data. Water International, 19, 5−14,https://doi.org/10.1080/02508069408686189. 

Liu, B. H., M. Xu, M. Henderson, and W. G. Gong, 2004: A spa-tial analysis of pan evaporation trends in China: 1955−2004.Journal of Geophysical Research, 109, D15102,https://doi.org/10.1029/2004JD004511. 

Lu, J. B., G. Sun, S. G. McNulty, and D. M. Amatya, 2005: A com-

972 EVALUATING EPET FORMULA BASED ON PAN EVAPORATION VOLUME 37

 

  

parison of six potential evapotranspiration methods forregional use in the southeastern United States. Journal of theAmerican Water Resources Association, 41(3), 621−633,https://doi.org/10.1111/j.1752-1688.2005.tb03759.x. 

Makkink, G. F., 1957: Testing the Penman formula by means oflysimeters. Journal of the Institution of Water Engineers, 11,277−288. 

McCuen, R. H., 1974: A sensitivity and error analysis CF proced-ures used for estimating evaporation. Journal of the Amer-ican Water Resources, 10, 486−497, https://doi.org/10.1111/j.1752-1688.1974.tb00590.x. 

McMahon, T. A., M. C. Peel, L. Lowe, R. Srikanthan, and T. R.McVicar, 2013: Estimating actual, potential, reference cropand pan evaporation using standard meteorological data: Apragmatic synthesis. Hydrology and Earth System Sciences,17(4), 1331−1363, https://doi.org/10.5194/hess-17-1331-2013. 

McVicar, T. R., T. G. VanNiel, L. T. Li, M. F. Hutchinson, X. M.Mu, and Z. H. Liu, 2007: Spatially distributing monthly refer-ence evapotranspiration and pan evaporation considering topo-graphic influences. Journal of Hydrology, 338(3−4),196−220, https://doi.org/10.1016/j.jhydrol.2007.02.018. 

Oudin, L., F. Hervieu, C. Michel, C. Perrin, V. Andréassian, F.Anctil, and C. Loumagne, 2005: Which potential evapotran-spiration input for a lumped rainfall-runoff model? Part 2—Towards a simple and efficient potential evapotranspirationmodel for rainfall-runoff modelling Journal of Hydrology,303, 290−306, https://doi.org/10.1016/j.jhydrol.2004.08.026. 

Paparrizos, S., F. Maris, and A. Matzarakis, 2017: Sensitivity ana-lysis and comparison of various potential evapotranspira-tion formulae for selected Greek areas with different cli-mate conditions. Theoretical and Applied Climatology,128(3−4), 745−759, https://doi.org/10.1007/s00704-015-1728-z. 

Penman, H. L., 1948: Natural evaporation from open water, baresoil and grass. Proceedings of the Royal Society A: Mathemat-ical, Physical and Engineering Sciences, 193, 120−145,https://doi.org/10.1098/rspa.1948.0037. 

Priestley, C. H. B., and R. J. Taylor, 1972: On the assessment ofsurface heat flux and evaporation using large-scale paramet-ers. Monthly Weather Review, 100, 81−92, https://doi.org/10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2. 

Samani, Z. A., and M. Pessarakli, 1986: Estimating potential cropevapotranspiration with minimum data in Arizona. Transac-tions of the ASAE, 29(2), 522−524, https://doi.org/10.13031/2013.30184. 

Shen, Y. J., C. M. Liu, M. Liu, Y. Zeng, and C. Y. Tian, 2009:Change in pan evaporation over the past 50 years in the aridregion of China. Hydrological Processes, 24, 225−231,https://doi.org/10.1002/hyp.7435. 

Steiner, J., T. Howell, and A. D. Schneider, 1991: Lysimetric evalu-ation of daily potential evapotranspiration models for grainsorghum. Agronomy Journal, 83, 240−247, https://doi.org/10.2134/agronj1991.00021962008300010055x. 

Tang, W. J., K. Yang, J. Qin, C. C. K. Cheng, and J. He, 2011:Solar radiation trend across China in recent decades: Arevisit with quality-controlled data. Atmospheric Chemistryand Physics, 11, 393−406, https://doi.org/10.5194/acp-11-393-2011. 

Wang, A. H., and X. B. Zeng, 2012c: Evaluation of multire ana-

lysis products with in situ observations over the Tibetan Plat-eau. Journal of Geophysical Research, 117, D05102,https://doi.org/10.1029/2011JD016553.

 

Wang, K. C., and R. E. Dickinson, 2012a: A review of global ter-restrial evapotranspiration: Observation, modeling, climato-logy, and climatic variability. Reviews of Geophysics., 50,RG2005, https://doi.org/10.1029/2011RG000373.

 

Wang, K. C., R. E. Dickinson, M. Wild, and S. Liang, 2012b:Atmospheric impacts on climatic variability of surface incid-ent solar radiation. Atmospheric Chemistry and Physics,12(20), 9581−9592, https://doi.org/10.5194/acp-12-9581-2012. 

Wang, T. T., J. Zhang, F. B. Sun, and W. B. Liu, 2017: Pan evapor-ation paradox and evaporative demand from the past to thefuture over china: A review. WIREs Water, 4(3), e1207,https://doi.org/10.1002/wat2.1207. 

Weiß, M., and L. Menzel, 2008: A global comparison of four poten-tial evapotranspiration equations and their relevance tostream flow modelling in semi-arid environments. Advancesin Geosciences, 18, 15−23, https://doi.org/10.5194/adgeo-18-15-2008.

 

Xu, C. Y., and V. P. Singh, 2002: Cross comparison of empiricalequations for calculating potential evapotranspiration withdata from Switzerland. Water Resources Management,16(3), 197−219, https://doi.org/10.1023/A:1020282515975.

 

Yang, H. B., and D. W. Yang, 2012: Climatic factors influencingchanging pan evaporation across China from 1961 to 2001.Journal of Hydrology, 414−415, 184−193, https://doi.org/10.1016/j.jhydrol.2011.10.043. 

Yang, K., J. He, W. J. Tang, J. Qin, and C. C. K. Cheng, 2010:On downward shortwave and longwave radiations over highaltitude regions: Observation and modeling in the Tibetan Plat-eau. Agricultural and Forest Meteorology, 150(1), 38−46,https://doi.org/10.1016/j.agrformet.2009.08.004.

 

Yang, K., T. Koike, and B. S. Ye, 2006: Improving estimation ofhourly, daily, and monthly solar radiation by importingglobal data sets. Agricultural and Forest Meteorology, 137,43−55, https://doi.org/10.1016/j.agrformet.2006.02.001.

 

Yin, Y. H., S. H. Wu, D. Zheng, and Q. Y. Yang, 2008: Radi-ation calibration of FAO56 Penman-Monteith model to estim-ate reference crop evapotranspiration in China. AgriculturalWater Management, 95, 77−84, https://doi.org/10.1016/j.agwat.2007.09.002.

 

Yin, Y. H., S. H. Wu, and E. F. Dai, 2010b: Determining factorsin potential evapotranspiration changes over China in theperiod 1971−2008. Chinese Science Bulletin, 55(29),3329−3337, https://doi.org/10.1007/s11434-010-3289-y.

 

Yin, Y. H., S. H. Wu, G. Chen, and E. F. Dai, 2010a: Attributionanalyses of potential evapotranspiration changes in Chinasince the 1960s. Theoretical and Applied Climatology,101(1-2), 19−28, https://doi.org/10.1007/s00704-009-0197-7.

 

Zeng, Z. Z., L. Q. Peng, and S. L. Piao, 2018: Response of terre-strial evapotranspiration to earth’s greening. Current Opin-ion in Environmental Sustainability, 33, 9−25, https://doi.org/10.1016/j.cosust.2018.03.001.

 

Zhang, Y. Q., C. M. Liu, T. N. Tang, and Y. H. Yang, 2007:Trends in pan evaporation and reference and actual evapotran-spiration across the Tibetan Plateau. J. Geophys. Res., 112,D12110, https://doi.org/10.1029/2006JD008161.

 

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Zheng, H. X., X. M. Liu, C. M. Liu, X. Q. Dai, and R. R. Zhu,2009: Assessing contributions to panevaporation trends inHaihe River Basin, China. Journal of Geophysical Research,114, D24105, https://doi.org/10.1029/2009JD012203. 

Zhou, M. C., H. Ishidaira, H. P. Hapuarachchi, J. Magome, A. S.Kiem, and K. Takeuchi, 2006: Estimating potential evapotran-spiration using Shuttleworth−Wallace model and NOAA-AVHRR NDVI data to feed a distributed hydrologicalmodel over the Mekong River basin. Journal of Hydrology,327(1), 151−173, https://doi.org/10.1016/j.jhydrol.2005.11.013. 

Zhu, Z. C., and Coauthors, 2016: Greening of the earth and itsdrivers. Nat. Clim. Change, 6, 791−795, https://doi.org/10.

1038/nclimate3004. 

Zuo, D. P., Z. X. Xu, H. Yang, and X. C. Liu, 2012: Spatiotem-poral variations and abrupt changes of potential evapotranspir-ation and its sensitivity to key meteorological variables inthe Wei River Basin, China. Hydrological Processes, 26(8),1149−1160, https://doi.org/10.1002/hyp.8206.

 

Zuo, H. C., B. L. Chen, S. X. Wang, Y. Guo, B. Zuo, L. Y. Wu,and X. Q. Gao, 2016: Observational study on complement-ary relationship between pan evaporation and actual evapotran-spiration and its variation with pan type. Agricultural andForest Meteorology, 222, 1−9, https://doi.org/10.1016/j.agrformet.2016.03.002.

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