Ruiheng XIE and Aihui WANG*

1School of Atmospheric Sciences, Chengdu University of Information Technology, Chengdu 610225, China

2Nansen-Zhu International Research Center, Institute of Atmospheric Physics,Chinese Academy of Sciences, Beijing 100029, China

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 proxy for EPET. In this study, EPET values computed from ten models are compared with observed ETpan data in ten Chinese river basins for the period 1961?2013. The daily observed meteorological variables at 2267 stations are used as the input to those models, and a ranking scheme is applied to rank the statistical quantities (ratio of standard deviations, correlation coefficient, and ratio of trends) between ETpan and modeled EPET in different river basins. There are large deviations between 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 mm d?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. Inter comparisons among different models in different river basins suggest that PETHam1 is the best model in the Pearl River basin, PETHam2 outperforms other models in the Huaihe River, 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 except in Southeast and Southwest China. The increasing EPET trend in Southeast China is mainly attributed to the reduced relative humidity.

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

1. Introduction

Evapotranspiration (ET) plays an important role in both energy and hydrologic cycles at the land surface, and it consists of open water evaporation, bare soil evaporation, rainfall interception evaporation, and vegetation transpiration(Zeng et al., 2018). The release of latent heat due to evaporation affects water and heat balances near the surface, and approximately two-thirds of precipitations falling over the land is from evaporated water (Wang et al., 2012a). Furthermore, ET is of great significance for agriculture, and it is a prerequisite for irrigation planning (Paparrizos et al., 2017).In the meteorological and agricultural sciences, there are usually three different ET notations, including actual evapotranspiration (AET), potential evapotranspiration (EPET), and pan evaporation (ETpan). AET denotes the actual moisture evaporating from the land surface under local climate conditions, andEPETis defined as the amount of evaporation and transpiration that would occur under certain meteorological conditions with a sufficient water supply but without advection and heating effects (Dingman, 1992; McMahon et al.,2013; Li et al., 2016).EPETis the upper limit of AET and can be used to estimate AET (Gao et al., 2006). ETpanis evap-oration from a water pan under local climatic/environmental conditions, and to a certain extent, it can represent open water evaporation.

ETpancan be measured at a meteorological station, and the measurement is obtained using an evaporation pan with enough water supplies at an open site. AET can also be measured by a lysimeter, the eddy covariance technique, or Bowen ratio method (Wang et al., 2012a). However, unlike routine meteorological observations, in-situ measurements of AET are not available in many regions worldwide. In practice, AET is usually calculated by empirical methods (Gao et al., 2007).EPETcannot be directly observed and is usually estimated by empirical methods (referred to asEPETmodels) using meteorological parameters as inputs.

According to the types of input variables,EPETmodels can be classified as temperature-based, radiation-based, and combination models in which multiple meteorological parameters are used as the model inputs (Bormann, 2011). For instance, to estimate reference crop evapotranspiration(ETref), the Penman?Monteith (PM) method recommended by the Food and Agriculture Organization (FAO) is one of the combination models and is widely used to estimateEPET. This model requires temperature, radiation and wind speed as inputs (Allen et al., 1998). Using station-observed meteorological data as inputs,EPETcomputed with the FAO56 model indicates an overall downward trend in most parts of China (Gao et al., 2006; Yin et al., 2010a).Although the PM method is regarded as the most representative formula for estimatingEPETand has been widely used in many studies (Gao et al., 2006; Zhang et al., 2007; Zuo et al., 2012), this model requires multiple surface meteorological quantities and several empirical coefficients, which are usually not easily obtainable. Therefore, otherEPETmodels that require fewer inputs have been developed and used commonly in research. For instance, Samani and Pessarakli(1986) concluded that the temperature-based Hargreaves model can reasonably estimateEPETin regions with Arizonian climatic conditions. The traditional Priestley?Taylor model uses only air temperature and net radiation as inputs to computeEPETand has been adopted in various studies(Priestley and Taylor, 1972). Ding et al. (2013) incorporated the leaf area index, soil moisture and mulching fraction into the original Priestley?Taylor model and found that the modified model improvedEPETestimates in cold and arid areas. In general, the performances of differentEPETmodels are region dependent, and a specific model may not be suitable for all regions in China. Therefore, to obtain the most representativeEPETmodel in each Chinese river basin,it is necessary to perform comprehensive evaluations of their performances.

Many studies have compared or evaluatedEPETmodels over the past few decades (Jacobs et al., 2004; Lu et al.,2005; Douglas et al., 2009; Donohue et al., 2010; Bormann et al., 2011; Li et al., 2016; Paparrizos et al., 2017). The con

2.2. EPET models

clusions of these studies are quite different, and the “best”EPETmodels vary across different climate regimes. In contrast toEPET, the evaporation pan exchanges heat and moisture with the surrounding environment, which affects the water evaporation rate in the pan (ETpan) (Zuo et al., 2016).Although ETpanandEPEThave different physical meanings and are derived from different approaches, many studies still regard ETpanas a surrogate forEPET(Liu et al., 2004;Yin et al., 2010b; Han et al., 2012). In China, meteorological stations routinely measure ETpan, which has been used to evaluate, or are regarded as,EPETmodels (Zhou et al.,2006; and Weiβ and Menzel, 2008). However, most previous studies have evaluated the performances ofEPETmodels at only a few stations for a short time period (Xu et al.,2002; Li et al., 2016; Paparrizos et al., 2017), and the results may not be representative in large areas for a long time period. China has a vast land domain, and its climate condition varies regionally. It is necessary to investigate the applicability of differentEPETmodels in different climate regimes.

In the current study, ETpanobservations at 2267 stations for the period 1961?2013 are used to evaluate the performances of tenEPETmodels in ten Chinese river basins.Various statistical quantities are computed and inter-compared, and subsequently, the best-performingEPETmodel is obtained for each river basin. Finally, based on the bestEPETmodel for each river basin, sensitivity analyses are also conducted for theEPETto the input meteorological variables.

2. Data and methods

2.1. Meteorological data

High-quality daily observations at 2425 meteorological stations were obtained from the National Meteorological Information Center of the China Meteorological Administration (http://data.cma.cn/en). The variables used in this study include 20-cm micro-pan evaporation (ETpan), minimum air temperature (Tmin), maximum air temperature (Tmax), mean air temperature (Ta), wind speed at 10 m (U10), relative humidity (RH), and sunshine duration (SD) from 1961 to 2013. To ensure the long-term representation of those meteorological data stations, available records of less than 30 years are discarded, and 2267 observation stations remain in this study.

AsEPETis an important land surface hydrological element, and divisions of drainage basins are often used in hydrology 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 (252 stations), Yellow River (307 stations), Huaihe River (211 stations), Yangtze River (661 stations), Pearl River (236 stations) basins] and three other drainage basins[Southeast China (SE, 110 stations), Southwest China (SW, 92 stations) and Northwest China (NW, 166 stations)]. Below, the analyses will be performed for those basins.

Fig. 1. Distribution of ten drainage basins and the locations of 2267 meteorological stations in China. The station number in each basin is indicated in brackets.

By reviewing the literature, a set of 10 differentEPETmodels are adopted in our study (Table 1), and these models are widely used in various studies. They include four temperature-based models [Hargreaves (Hargreaves and Samani, 1985), Romanenko (Oudin et al., 2005), Hamon version1 (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 thoseEPETmodels, radiation-based models require solar radiation (Rs) and net radiation (Rn) as inputs, which are usually not available from in-situ measurements. Empirical formulae with available meteorological variables can be used to derive radiation datasets (Allen et al., 1998; Yang et al., 2006). For example, Yang et al.(2006) proposed a hybrid method in which surface radiation was a function of the sunshine duration. Then, the researchers used this method to calculateRsin China, the USA and Saudi Arabia and found that the modeledRsvalues were the most consistent with the observations when compared to those from other methods. Here, we adopted the method of Yang et al.(2006) to computeRs:

whereRsis the solar radiation;Rcis the solar radiation under clear-sky conditions, which is calculated by meteorological observations, ozone absorption and turbidity coefficients;nis the measured sunshine duration;Nis the maximum possible sunshine duration; anda0,a1anda2are regression coefficients. Equation (1) has been widely applied in many studies (Yang et al., 2010; Tang et al., 2011; Wang et al., 2012b; He et al., 2018). In addition, we also adopted the coefficients of Wang et al. (2012b), in whicha0is 0.33,a1is 0.70, anda2is ?0.02 in Eq. (1), which were derived from meteorological station variables.

According to the principle of the conservation of energy,Rnis the difference between incoming net shortwave radiation (Rns) and the outgoing net longwave radiation[Rnl, Eq. (2)]. The FAO has also provided equations to calculate these variables (Allen et al., 1998). Moreover, Yin et al.(2008) used radiation measurements in China to calib-rate theRnlmodels and found that the Penman method(1948), in Eq. (4), was more accurate than the FAO24 and FAO56-PM models:

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 = extraterrestrial radiation (MJ m?2), and Rn = net radiation (MJ m?2).

whereα= 0.23 is the albedo for the reference crop,is the Stefan?Boltzmann constant (4.903×10?9MJ K?4m?2d?1),Tx,k(Tn,k) is the maximum (minimum) absolute temperature for 24 h (K), andeais the actual vapor pressure (kPa).

In the Penman and FAO models, the 2-m wind speed is needed (Table 1). Thus, we converted the 10-m wind speed to 2-m wind speed using the wind profile formula (Allen et al., 1998):

whereU2is the wind speed at 2 m above the ground surface (m s?1) andUzis the measured wind speed atzm above the ground surface (m s?1), which is 10 m in this study.

In the Hargreaves and Jensen?Haise models, theEPETis a function ofTaandRs. From these models (Table 1),whenTais lower than ?17.8°C for the Hargreaves model and ?3.1°C for the Jensen?Haise model, theEPETwould be negative. These are not correct in reality. Similarly, the Priestley?Taylor method requiresTaandRnas inputs.However,Rsoccurs only in the daytime, but theRnlis available for both daytime and nighttime. During the cold season in high latitudinal regions, the relatively short daytime SD would also reduce theRs, leading toRnlvalues greater thanRns. Under the above two circumstances,Rnwill be less than zero, and then, theEPETfrom the Priestley?Taylor model would also be negative. As an important factor of agriculture,EPETis more prominent during the crop growing seasons than in other seasons, andEPETshould be very small or even negligible in the cold seasons. To avoid appearance of a negativeEPETvalue due to the meteorological inputs in someEPETmodels, our analyses are confined to the growing season of March to October during each year. After the above procedure,EPETis set as the missing value if it is still less than zero.

2.3. Sensitivity analysis

To estimate the effects of changes in various meteorological factors on modeledEPET, sensitivity analyses are also conducted for eachEPETmodel. Because differentEPETmodels have different structures and input requirements and these input variables have diverse magnitude ranges, it is difficult to directly conduct theEPETsensitivity analysis with different 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):

where SC is the sensitivity coefficient, andXis one of the model input variables. SC represents the relative change inEPETinduced by the relative change in the meteorological factorX. In other words, the relative change inXmultiplied by SC equals the relative change inEPET. For example,SC=0.1 indicates that 10% ofXchange would cause 1% ofEPETchange. A positive (negative) SC represents that changes inEPETare consistent (inconsistent) with those inX. The higher SC is, the stronger theXeffect imposed onEPETwill be. However, SC cannot fully reflect the impact of each meteorological factor on theEPETchanges. A literature review of previous studies revealed thatEPETwas the most sensitive to RH in the Yangtze River basin (Gong et al., 2006) and the Weihe River basin (Zuo et al., 2012) in China. However, Yin et al. (2010b) reported that RH was only a highly sensitive but not a dominant factor ofEPET,and its insignificant trend during 1971?2008 could only induce a small change inEPET. To further address this issue,we combined the relative change (RC) in each input variable and its SC forEPETattribution analysis. The RC (units:%) is described as follows (Yin et al., 2010a):

whereTXis the linear trend in the annual time series for any variableX, and |X| is its absolute mean during the past 53 years. RC represents the mean percentage change in the variableXduring the study period. Based on Eqs. (6) and (7),we also conducted attribution analyses below. At each station, we recalculated theEPETwith individual input meteorological variables changing from ?10% to 10% by assuming that 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 theEPETchange. Inter comparisons of RCTs for different meteorological factors can represent the relative importance of each metrological variable for theEPETchange.

2.4. Ranking scheme

To quantify the differences between modeledEPETand ETpan, we compute three statistical quantities, including the ratio ofEPETstandard deviations to that of ETpan, the correlation coefficient, and the ratio ofEPETtrends to ETpantrends.Moreover, to evaluate the performance ofEPETmodels in terms of those statistical quantities in each basin, a ranking scheme is utilized. Wang et al. (2012c) applied this approach to rank four statistical quantities between reanalysis products and observations in the Tibetan Plateau to evaluate the performances of each reanalysis product. In the present study, based on each statistical quantity, the mean ranking scores from 1 to 10 are given to eachEPETmodel.The ranking score is computed as follows: Among all 10EPETmodels, the highest correlation coefficient is given a ranking score of 1, and the lowest one is given a score of 10. Regarding the ratio of standard deviations and the ratio of trends, 1 is given to the model with the ratio closest to 1,and 10 indicates the ratio farthest away from 1. Then, we average all ranking scores of three quantities in each basin, and the mean magnitude from the lowest to the highest represents the closest to the least close relationships betweenEPETmodels and ETpan.

3. Results

3.1. Spatial distribution and magnitude of the modeled EPET

Figure 2 shows the spatial distribution of the multiple growing seasonal meanEPETand ETpanfrom 1961 to 2013.This figure shows the apparent spatial variations inEPET. At the majority of stations, the mean ETpanis above 4 mm d?1.The stations with relatively low ETpanare mainly located in the Yangtze River basin and Liaohe River basin, while large values appear in the Yellow River basin and Northwest China, where the magnitude of ETpanis generally larger than 8 mm d?1at most stations. In terms of magnitudes, PETRomis more consistent with ETpanthan other models, with a meanEPETabove 3 mm d?1at 85% of stations in China and even larger than 8 mm d?1in Northwest China. For the distribution pattern, PETRomis also the closest to ETpan, and the spatial correlation coefficient is up to 0.86. PETFAOand PETAbtalso correlate well with ETpan, while the spatial correlation coefficients are 0.72 and 0.74, respectively. Compared to other models and ETpan, theEPETvalues from both PETHam1and PETHam2are relatively low, especially for PETHam2, with values of less than 2 mm d?1at 93% of stations. In addition, for the radiation-based models, the PETJenproduces the largest value with a magnitude larger than 4 mm d?1in eastern China.

Figure 3 shows the ranges of ETpanandEPETfrom different models from three basins: the Yangtze River basin(Fig. 3a), Yellow River basin (Fig. 3b), and Northwest China (Fig. 3c). The three basins represent the humid, semiarid and arid regions in China, respectively. By comparison,the modeledEPETis relatively close to ETpanin the humid Yangtze River basin; however, in arid Northwest China,they show obvious differences. This finding implies that ETpanandEPETare closer to each other in the humid region than in the arid region. This may be caused by the larger non-uniformity of climate conditions between the water body in the pan and the surrounding environment in the arid regions, and the non-uniformity is related to differences in surface temperature, moisture and albedo, which are also larger in arid regions (Zuo et al., 2016). Furthermore, in all three basins, no model can capture the peak values of ETpan,and the modeledEPETamplitudes are smaller than those of ETpan, and the biases of their maximum values are particularly large. Except for PETJen, the radiation-based models show relatively small differences between the upper and lower quartile than those of the temperature-based models,which somehow indicates that the temporal and spatial variab-ilities in the radiation-based models (PETPT, PETAbt, and PETMak) should also be smaller than those of the temperature-based models (PETRom, PETHam1, PETHam2). Additionally, PETFAOis closer in magnitude to ETpanthan PETPM.Although both PETFAOand PETPMhave similar structures and input requirements, PETPMdisplays a narrower magnitude range than that from PETFAOdue to its lower maximum value.

Fig. 2. Spatial distribution of the annual meangrowth season (Mar?Oct) pan evaporation and EPET calculated by different models: (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.

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

3.2. Trends and variability

Figure 4 shows the linear trends in theEPETmodels and ETpanduring 1961?2013. There are apparent differences,and opposing trend signs occur in some cases. ETpanhas an upward trend in Southeast and Southwest China, while it has a downward trend in other basins. The downward trend in ETpanranges from ?0.01 mm d?1yr?1to ?0.03 mm d?1yr?1,while the decreasingEPETtrends are always less than ?0.01 mm d?1yr?1. In the Songhua River and Liaohe River basin,and Southeast and Northwest China, the trends in PETFAOand ETpanare the most similar, and in Northwest China, PETFAOis the only model that can successfully capture the decreasing ETpantrend. In Southwest China, the trend in PETMakis consistent with that of ETpan, and PETHam2can best capture the trend in ETpanin the remaining basins. In addition,PETRomis proportional toTa(Table 1) and its temporal variabilities are consistent with that ofTa, showing an increasing trend in all basins.

We further assess the inter annual variability in the modeledEPETand ETpan. Figure 5 shows the growing seasonal mean anomalies ofEPETand ETpanfrom 1961 to 2013 in three different drainage basins, and the corresponding anomalies ofTaand SD are also exhibited. In the Yangtze River basin (Fig. 5b),Tashows an apparently upward trend since the 1990s, and SD shows an abrupt decline around the early 1980s. ETpanalso displays a significant downward trend, and its anomalies change from positive to negative in 1981. For most models except for PETRom, the inter annual variability is relatively small, and their standard deviations are no more than 0.2 mm d?1. In terms of the temperaturebased equations, PETRomis the most consistent withTaand has been significantly increasing since the 1990s (Fig. 5a).Although the trend ofRsin the Yellow River basin and Northwest China is not obvious (Figs. 5d and f), the warming trend since the 1990s is still significant (p=99%). The ETpanshows obviously decreasing trends in the Yellow River basin and Northwest China (Figs. 5c and e), and the downward trend is dramatic in Northwest China (T=?0.034 mm d?1yr?1). Additionally, except for PETRom, the inter annual variability in theEPETmodels is still small, and the standard deviations are also less than 0.2 mm d?1in these two basins.

Fig. 4. Trends in annual growing season mean ETpan and EPET from 1961 to 2013 in (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 EPET model with the closest trend to that in ETpan is marked with a star (*).

Because both ETpanandEPEThave obvious seasonal variations, so seasonality changes of modeledEPETare also investigated. Figure 6 exhibits the monthly trends in theEPETmodels and ETpan. ETpanshows a decreasing trend during all months in the three basins, and the largest declining rates occur in May and June. In contrast, PETRomhas an apparent upward trend in all months due to its highly consistent variability with that of temperature. Except for PETRom, the PET trends in allEPETmodels in all months are synchronous in the Yangtze River basin and show downward trends from June to September (Fig.6a). Among them, the trend in PETHam2is the closest to that of ETpan. Additionally, the monthly trend of PETHam2is closer to that of ETpanthan other models in the Yellow River basin (Fig.6b). However,in Northwest China (Fig.6c), the monthly trends in all models are greatly different from ETpan. Although the declining trend in PETFAOis consistent with that of ETpan, the trend magnitudes of the two are very different. This is likely due to the differences in the physical processes ofEPETand ETpanin this region, and we will discuss this further in section 4. Overall, compared to humid regions, the differences between the ETpanandEPETmonthly trends are much greater in arid regions.

3.3. Ranking scores

Fig. 5. Mean EPET anomaly in (a) the Yangtze River basin, (c) the Yellow River basin, and (e) Northwest China, and the anomalies in temperature and sunshine duration (b, d, f) averaged over the growing seasons (Mar?Oct) from 1961 to 2013. The red curve indicates the temperature anomaly (left axis), and the blue curve is the sunshine duration anomaly(right axis).

The ranking scores of the three statistical quantities are shown in Fig. 7. For the ratio of standard deviations (Fig. 7a),PETRomhas the best performance, maintaining a value of 1 in all basins, followed by PETJen. The ranking scores of PETJenare less than 3 in most basins except for Southwest China, but the other radiation-based models do not perform well. In addition, PETPMalso has relatively high ranking scores in all basins. The above results indicate that the variabilities in ETpanand modeledEPETare quite different. In terms of the correlation coefficient, the PETRomhas high scores in the Haihe River, Huaihe River, Yangtze River and Pearl River basins (Fig. 7b), and PETPTalso has poor scores in all basins. PETFAOshows good performance in most basins except for the Yangtze River and Pearl River basins,where PETHam1has the lowest score. There are nine basins with correlation coefficients greater than 0.5 between ETpanand PETFAO, except for the Pearl River basin, and between ETpanand PETHam1/PETHam2, except for Northwest China.Notably, in Northwest China, several modeledEPETare negatively correlated with ETpan, except for PETFAO(0.65),PETPM(0.21) and PETHar(0.27). This further illustrates thatEPETis very different from ETpan, especially in the arid region. Regarding the ratio of trends (Fig. 7c), PETRomhas positive trends and the worst scores in most basins where ETpanshows negative trends. In summary, PETHam2and PETFAOshow the best performances based on the ranking scores in all basins. In Northwest China, the ratios of trends are greater than zero only in PETFAOand PETPM, which are the only models that produce a negative trend as in ETpan.Finally, we average the ranking scores of all three statistical quantities in each basin, and the model with the lowest score is selected and regarded as the best model for this basin (Fig. 8). For example, PETHam2performs best in the Yellow River, Huaihe River and Yangtze River basins, while PETHam1is outperformed in the Pearl River basin. For the remainder of the basins, PETFAOis the best model.

3.4. Sensitivity analyses

Among the selected best models in each basin, PETFAOconsiders temperature, relative humidity, wind speed and net radiation, and it is also the most commonly usedEPETmodel in climate research (Gao et al., 2006; Gong et al.,2006; Yin et al., 2010a; Zuo et al., 2012). Both PETHam1and PETHam2belong to a temperature-based model and are derived from air temperature and sunshine duration. All the best models that were selected are affected by multiple meteorological factors. To determine the RCT of each meteorological variable toEPETchanges, we apply a sensitivity analysis to the best-performing model in each basin. Because the best-performingEPETmodels are not troubled by a negative value, the sensitivity analyses are conducted for the whole year instead of only the growing seasons as in the previous sections.

Table 2 shows the SC for RH is always less than zero,implying opposing variations in RH andEPET. RH is a factor that is highly sensitive toEPET, and the minimum of SC can reach ?1.32. However, due to the insignificant trend in RH during the study period, the RC of RH is less than 8% in the basins where the best model is PETFAO. Thus, RH is not a determining factor ofEPETchanges, and the corresponding RCTs of RH toEPETchanges are less than 2%,except for Southeast China. However, in Southeast China,RH decreases by 7.32%, which inducesEPETincreases of 5.73%, and RH is the primary contributor to increasingEPETin this basin (Table 3). In other basins where PETFAOis selected, the wind speed at 2 m (U2) is the most responsible factor forEPETreductions, although it is not the most sensitive factor. The SC is greater than 0.5 in the Songhua River,Liaohe River and Haihe River basins and Northwest China.Furthermore, the reduction inU2in these basins is more than 40%, which leads to a more than 20% reduction inEPET. In Southwest China, the RC ofU2is ?27.25%, which drivesEPETreduction by 5.35%, and the RCT ofU2toEPETchange is far less than that in other basins. Thus, the change inEPETis affected by multiple factors in this basin, with the overall RCT of the meteorological variables to anEPETchange of 2.86% and the actual relative change inEPETof 0.71%. The two values are very close, which further illus-trates that sensitivity analyses can be used to attribute the changes inEPETin Southwest China (Yin et al., 2010b).Tmaxhas little effect onEPET, which would lead to a 6.77%enhancement inEPETin Northwest China and less than 4%in other regions. ForTmin, low sensitivity appears in nearly all basins; the lowest SC (?0.01) appears in Northwest China, and the highest SC (0.21) is in Southeast China.However, it has great RC in some basins, especially in the Songhua River and Liaohe River basin, where the RC reaches 608.27% and 277.55%. This is due to the averageTminbeing close to zero in these basins, where a slight change in absolute value would cause a large percentage change inTmin. The RCTs ofTmintoEPETare quite different in different basins, and the value is 24.16% and 14.85% in the Songhua River and Liaohe River basin, respectively, but less than 4% in other basins. Therefore,Tminis a vitally important variable forEPETchanges in the Songhua and Liao River basins. For basins with PETFAOas the selected best model, the SC ofEPETto SD ranges from ?0.26(Songhua River basin) to 0.14 (Southwest China), with negative values in the Songhua River, Liaohe River and Haihe River basins and Northwest China and positive values in other basins, while the RCTs of SD toEPETchange are less than 5% in all basins. This result indicates that SD is not the primary factor forEPETchange in these basins.

Fig. 6. Annual trends in ETpan and EPET during each month in three selected basins: (a) Yangtze River basin, (b) Yellow River 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, in different basins. The label of 1 (10) represents the best (worst)score of a modeled EPET compared to ETpan.

Fig. 8. Average ranking scores of three statistical quantities in (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 lowest (highest) value indicates the best (worst) performance of the EPET models,and the best model is marked with a star (*).

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

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

For the basins with PETHam1and PETHam2as the best models, bothTaand SD are the inputs of the models. In terms of PETHam2, SD is more sensitive thanTa, and the SC for SD is 2 in those basins. For PETHam1, the SC forTa(1.25) is higher than that of SD (1). In addition, the minimum RC for SD can reach ?21.01% in the Huaihe River basin. As a result, SD is the primary contributor toEPETchange in those basins. The RCTs toEPETchange range from ?12.91% (Pearl River basin) to ?42.02% (Huaihe River basin). Although the percentage changes inEPETare large, the actualEPETtrend does not exceed ?0.01 mm d?1yr?1.This is because theEPETmagnitudes calculated by PETHam1and PETHam2are too small (Fig. 2). In general, the summation of RCT from individual meteorological variables is a close approximation to the actualEPETchanges in eight basins (except for Southeast and Northwest China), where the differences are less than 5%. In both Southeast and Northwest China, the large differences in RCTs and actualEPETchange may be due to the other variables in the radiation calculation formulas, such as ozone absorption and turbidity coefficients.

3.5. Relationship between ETpan and EPET

ETpanandEPETcan be linked by regression equations,i.e.,EPET=KpanETpan, whereKpanis the regression coefficient (Chiew and McMahon, 1992; Linacre, 1994; McMahon et al., 2013). Linacre (1994) provided aKpanwith a value of 0.7 by analyzing the data from a dozen places around the world, and this value was adopted in some studies (Weiβ and Menzel, 2008). However, many studies have reported thatKpanis dependent on the local climate conditions and should not be globally unified (McVicar et al.,2007; Zheng et al., 2009). To further understand the relationship between ETpanandEPET, we also calculatedKpanbased on our selectedEPETmodel in each basin (Fig. 9). The Yangtze River basin (Fig. 9f) has the largestKpan, with a value of 0.38, and the minimum value ofKpan(0.13) appears in Northwest China (Fig. 9j). Moreover, the determination coefficient (R2) is below 0.5 in Northwest China, further indicating that ETpanmay not be used as aEPETproxy in the arid region.

4. Discussion

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.

In the current study, ETpanandEPETcalculated by an empirical method show differences in magnitudes, inter annual variability and trends. Some of the reasons stem from the differences in their definitions. The definition ofEPETassumes no advection and no heating effects, which means 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 evaporation pan can receive and reflect radiation, which will influence the evaporation rate. Moreover, according to Zuo et al.(2016), the size of the evaporation pan will also affect the evaporation rate; for instance, the smaller the water body is,the greater the evaporation rate will be. When the water body in the pan is sufficiently wide, the ETpanwould be closer to the water surface evaporation. After adjusting for the energy exchange of the pan, ETpancan be considered open-water evaporation (Dingman, 1992; McMahon et al.,2013). However, the empiricalEPETmodels were designed to underlie various surface and climate conditions, and they may not only represent water evaporation. For example, PETFAOcalculated theEPETin the reference surface with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s m?1and an albedo of 0.23 (Allen et al., 1998). PETMakwas used to estimate grass ET under cool conditions(Makkink, 1957). In summary, there are big differences in magnitude between ETpanandEPET, particularly in the northwest arid region. Despite the difference in magnitude, the trend in ETpanagrees with that of modeledEPETin most regions (Gao et al., 2006; Zhang et al., 2007; Zheng et al.,2009; Yang and Yang, 2012). In Northwest China, there is not only a large difference in magnitude but also in the trend (Figs. 3c and 5c), and only PETFAOcan capture the negative ETpantrend well. This is because the significantly decreasing trend in ETpanis mainly caused by the significant downward trend in wind speed in this region (Shen et al., 2009; Yang and Yang, 2012; Wang et al., 2017), and only PETPMand PETFAOuse wind speed as inputs.Moreover, all theEPETmodels required air temperature,which exhibits a significant upward trend during the study period (Shen et al., 2009), inducing an increasing trend inEPETin Northwest China. For PETFAO,U2is the major factor ofEPETchanges in this region, the SC ofU2is 0.55,and the RC ofU2reaches ?41.62%; therefore, PETFAOcan capture the negative trend inEPETin Northwest China.Since mostEPETmodels perform poorly in Northwest China, the applicability ofEPETmodels in arid regions remains to be explored (Steiner et al., 1991; Li et al., 2016).

It should be noted thatRsis greatly impacted by aerosol and it usually reduces the solar irradiance arriving at the surface (Hu et al., 2017). In recent years, air pollution in China has become a serious issue, which also brings large amounts of aerosol. Current research does not consider the above effects, and thus the computedRsbased on sunshine duration only might be overestimated and affect the accuracy ofEPETresults. The weight setting of the ranking scores is also worthy of further attention. We put equal weight for each of the three statistical metrics in this research. As we mentioned previously, the trend in ETpanagrees with that of modeledEPETin most regions, and thus it might be reasonable to give larger weight to the ratio of trends in these regions. However, it is difficult to determine weight values for each metric at the current stage. It is necessary to explore this in future research by using different weights in ranking schemes.

Despite the magnitude differences between ETpanandEPETin some basins, there is also a close relationship between them. Previous studies have revealed that the magnitude of ETpanis generally greater than ETref(Jensen et al.,1990; Weiβ and Menzel, 2008), while ETpanandEPET(or ETref) are usually linked by the regression coefficientKpan(Fig.9). In addition, there are different types of evaporation pan in practice. For instance, Class-A pans are used in most countries, such as the USA and Australia, while 20-cm micro-pans are popular in China. With different types of pans, the magnitudes ofKpanare also different. The pan coefficients for the Class-A pan are higher than the Chinese micro-pan coefficients, but the seasonal ranges ofKpanvalues for the two different pans are similar (McVicar et al.,2007; McMahon et al., 2013).

Although we characterizeEPETchanges through sensitivity analyses, and conclude that wind speed and sunshine duration are the major factors affectingEPETchanges,EPETis not affected by only these two factors. For total ET, transpiration is a very important component that is controlled by the leaf area index (LAI), surface roughness, and vegetation root distributions (Arora, 2002). Furthermore, because of the increasing CO2fertilization effects, climate change, and land use-land cover change, global-scale LAI shows a significant upward trend (Zhu et al., 2016), which would cause changes in transpiration. According to Zeng et al.(2018), a greening Earth would induce a significant increase in terrestrial ET. Therefore, similar to ET,EPETis also affected by the CO2, vegetation and land use-land cover change.ETpanis the evaporation of the open water surface without considering the effects of transpiration or interception.

5. Conclusion

Based on meteorological observations, we calculated theEPETof ten Chinese drainage basins using 10 differentEPETmodels. Then, we compared the ETpanandEPETto obtain the best-performing model for each basin. By comparison, large disparities exist between modeledEPETand ETpan. The daily ETpanis over 4 mm d?1at the majority of stations, while theEPETcalculated by most models is less than 3 mm d?1. In eight basins (except for Southeast and Southwest China), the downward annual ETpantrends range from?0.01 mm d?1yr?1to ?0.03 mm d?1yr?1, while the decreasingEPETtrends are less than ?0.01 mm d?1yr?1. Additionally, the differences are larger in arid regions than in humid regions, and the largest disparities appear in Northwest China, where only PETFAOcan successfully capture the negative trend in ETpan.

Then, a scheme was applied to rank the three statistical quantities of ETpanandEPETin different basins, including the ratio of standard deviations, the correlation coefficient,and the ratio of trends. The results show that PETHam1is the best model for the Pearl River basin, while PETHam2is outperformed in the Huaihe River, Yangtze River and Yellow River basins. In terms of the remaining basins, PETFAOis the best-performing model. The sensitivity analyses of the best-performingEPETmodel in each basin reveal thatU2and SD are the two factors contributing to the overall decrease inEPET. The contributions of SD toEPETchange are always greater than 10% in the basins with selected PETHam1/PETHam2, and the contributions ofU2are larger than 20% in the Haihe River, Songhua River and Liaohe River basins and Northwest China. In addition, in the Songhua River and Liaohe River basins,Tminalso contributes considerably to theEPETchanges, and the RCT can reach 24.16% and 14.85% respectively. In Southeast China,the upward trend inEPETis primarily controlled by the decreasing RH. Furthermore, theKpanvaries from 0.13 (Northwest China) to 0.38 (Yangtze River basin), and is larger in the humid regions than in the arid regions.

Understanding the characteristics ofEPETand its impacting factors can help us to gain insight into the hydrological process and, in particular, water resource management in an arid region. Through the current study, we have identified the best-performingEPETmodels in each Chinese basin and derived long-term, high-quality dailyEPETdatasets in China, which can be used as a benchmark forEPETresearch in the future. Moreover, the selected model in each basin also reduces the input requirements, which is particularly practical in regions with limited availability of meteorological variables.

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