Journal of Hydrology 555 (2017) 298–313 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol Research papers Projecting the potential evapotranspiration by coupling different formulations and input data reliabilities: The possible uncertainty source for climate change impacts on hydrological regime Weiguang Wang a,b,⇑, Changni Li a,b, Wanqiu Xing a,c, Jianyu Fu a,b a b c State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China School of Earth Sciences and Engineering, Hohai University, Nanjing 211100, China a r t i c l e i n f o Article history: Received 13 September 2017 Received in revised form 8 October 2017 Accepted 9 October 2017 Available online 14 October 2017 This manuscript was handled by G. Syme, Editor-in-Chief Keywords: Potential evapotranspiration Statistical downscaling model abcd model Runoff changes Uncertainty a b s t r a c t Representing atmospheric evaporating capability for a hypothetical reference surface, potential evapotranspiration (PET) determines the upper limit of actual evapotranspiration and is an important input to hydrological models. Due that present climate models do not give direct estimates of PET when simulating the hydrological response to future climate change, the PET must be estimated first and is subject to the uncertainty on account of many existing formulae and different input data reliabilities. Using four different PET estimation approaches, i.e., the more physically Penman (PN) equation with less reliable input variables, more empirical radiation-based Priestley-Taylor (PT) equation with relatively dependable downscaled data, the most simply temperature-based Hamon (HM) equation with the most reliable downscaled variable, and downscaling PET directly by the statistical downscaling model, this paper investigated the differences of runoff projection caused by the alternative PET methods by a well calibrated abcd monthly hydrological model. Three catchments, i.e., the Luanhe River Basin, the Source Region of the Yellow River and the Ganjiang River Basin, representing a large climatic diversity were chosen as examples to illustrate this issue. The results indicated that although similar monthly patterns of PET over the period 2021–2050 for each catchment were provided by the four methods, the magnitudes of PET were still slightly different, especially for spring and summer months in the Luanhe River Basin and the Source Region of the Yellow River with relatively dry climate feature. The apparent discrepancy in magnitude of change in future runoff and even the diverse change direction for summer months in the Luanhe River Basin and spring months in the Source Region of the Yellow River indicated that the PET method related uncertainty occurred, especially in the Luanhe River Basin and the Source Region of the Yellow River with smaller aridity index. Moreover, the possible reason of discrepancies in uncertainty between three catchments was quantitatively discussed by the contribution analysis based on climatic elasticity method. This study can provide beneficial reference to comprehensively understand the impacts of climate change on hydrological regime and thus improve the regional strategy for future water resource management. Ó 2017 Elsevier B.V. All rights reserved. 1. Introduction Evapotranspiration not only is an essential element of energy budget in the earth-atmosphere system, but also plays an important role in water resources (Wang et al., 2012b). Among different terms to describe the evapotranspiration, potential evapotranspiration (PET) was first introduced by Thornthwaite (1948) and for⇑ Corresponding author at: State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China. E-mail address: firstname.lastname@example.org (W. Wang). https://doi.org/10.1016/j.jhydrol.2017.10.023 0022-1694/Ó 2017 Elsevier B.V. All rights reserved. mally defined by Penman (1956) as ‘‘the amount of water transpired in a given time by a short green crop, completely shading the ground, of uniform height and with adequate water status in the soil profile.’’ As the indicator of evaporative power of atmosphere, PET determines the maximum possible water consumption from the land surface, and thus is the most excellent indicator for the changing behavior of climatic and hydrological regime. Due that PET is the important input for hydrological modelling, reliable estimation of PET constitutes the basis of evaluating climatic effect on hydrological processes, especially for future PET projection in W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 the background that climate change become more pronounced (Bates et al., 2008]. More than 50 different methods with various complexities existed for the estimation of PET (Lu et al., 2005). Generally, in terms of the required inputs of meteorological variables, these methods can be roughly classified into three categories, i.e., temperature-based methods, radiation-based methods, and aerodynamic-and radiation-based methods. Among them, the Penman (PN) method, the aerodynamic-and radiation-based one, is always considered to the most reliable method for all climatic conditions due to its physically based characteristic, and is thus recommended as the single standard method for determining the PET by the Food and Agricultural Organization of the United Nations (FAO) (Xu et al., 2006). In many regions, however, the use of PN method is always prevented by the insufficient input data. The application of temperature-based methods and radiation-based methods requiring less meteorological data were thus compelled. For example, with only requiring air temperature as input, temperature-based methods were widely used in hydrological models (Bai et al., 2016), such as the early version of the Soil and Water Assessment Tool model (SWAT, Arnold et al., 1998) and the Hydro-Informatic Modeling System model (HIMS, Liu et al., 2008). Some works on intercomparisons of PET method suggested that less data-intensive methods can also give reliable approximation of PET in certain climatological condition if the simplified methods were sufficiently calibrated (e.g., Federer et al., 1996; Vorosmarty et al., 1998; Lu et al., 2005). However, for the estimation of PET in global change study, the abilities of less data-intensive methods, particularly the temperature-based methods, to describe PET temporal variability have recently been questioned in the context of climate change. For example, compared with the more physically based one, the temperature-based version of the Palmer Drought Severity Index (PDSI) overestimated the recent trend of the global drought (Sheffield et al., 2012). Generally, physically based methods, e.g., PN method, are considered more competent in historical climate change assessment than temperature based ones (Roderick et al., 2009) due that changes in other atmospheric variables (e.g., wind speed and relative humidity) other than temperature are proved to have dominant effect on overall change in PET (e.g., Xu et al., 2006; McVicar et al., 2012; Wang et al., 2012b). However, as for future projection study, the issues become more complicated. Although PN method is more reliable compared with temperature-based or radiation-based one, more confidences are always found in downscaling GCMs-derived temperature and radiation data than that of relative humidity and wind speed data (Randall et al., 2007; Wang et al., 2015), which are the indispensable input data of the PN method. This thus leaves us in a dilemma in practice with respect to future PET projection: should we use more reliable methods (e.g., PN method) with uncertain data quality, or more empirical methods (e.g., temperature-based methods) with more reliable input data (Kingston et al., 2009). Recently, Wang et al. (2015) investigated the performance of different project approaches for future reference evapotranspiration (RET), a more narrowly defined term of PET with clearer vegetation type definition, by combination between RET estimating method and input data reliabilities and found uncertainties still lied in estimating how much the RET changed. Apart from the most excellent indicator for the activity of climate change, PET is still the important input data to hydrological models of water balance study, especially under changing climate conditions (Hobbins et al., 2001; Xu and Singh, 2005). However, evidence from many studies suggested that the PET estimation is not critical for the performance of hydrological model in runoff simulation (Bai et al., 2016). For example, using 27 different PET estimation methods, Oudin et al. (2005) compared the perfor- 299 mance of four conceptual rainfall-runoff models for 308 catchments and found simplistic (e.g., temperature-based methods) performed similarly (even better sometimes) compared with complex PET estimation methods. Similarly, Kannan et al. (2007) concluded that the temperature-based Hargreaves method appears to be at least as good as the more complex Penman-Montieth method in SWAT distributed hydrological model run for a small catchment in Southeastern regions of the United Kingdom. More recently, Bai et al. (2016) investigated the sensitivities of monthly hydrological models to different PET across 37 catchments in China under different climatic conditions and found different PET inputs can produce similar runoff in both non-humid and humid regions. However, for the studies on the impact climate change on water availability though hydrological models, the issue may not be that simple, especially in the context of more pronounced climatic effect in the future (Bates et al., 2008; Wang et al., 2013a, 2015; Yang et al., 2015). The choice of PET method for the hydrological modelling should be restricted by more factors. On the one hand, PET changes are proved to more sensitive to changes in relative humidity and wind speed than air temperature, which is particularly true in China (Xing et al., 2017). On the other hand, data availability may have important influence for climate change impact assessments since less confidence is proved in GCM-derived vapor pressure, cloud cover, wind speed and net radiation compared with temperature (Randall et al., 2007; Haddeland et al., 2011). The choice of PET method used in the hydrological model may thus be a specific source of uncertainty in future projection of runoff. However, systematic investigation on the impact of applying different PET estimation approaches in hydrological model on prediction of future runoff is scare. Moreover, the influences of PET on AET and hydrological modeling are considered to be different in energy-limited region and water-limited regions (Donohue et al., 2007; Roderick et al., 2009; Wang et al., 2012b, 2016a). The diverse PET estimation approaches may thus give rise to different uncertainty of runoff projections between various climatic regions. Therefore, to address these research gap, this paper further extends our previous study of Wang et al. (2015) by comprehensively investigating PET methods dependence for future runoff projections for three catchments in China representing a large geographic and climatic diversity. Four different PET projection approaches include more physically based Penman (PN) equation with relatively uncertain downscaled data, more empirical radiation-based Priestley-Taylor (PT) equation with more reliable downscaled data, the simplest and temperature-based Hamon (HM) equation with the most reliable downscaled temperature data, and statistical downscaling method with directly selecting PET as predictand. The abcd model was used to achieve the uncertainty analysis. 2. Study areas and data descriptions This study was conducted for the three catchments, i.e., the Luanhe River Basin, the Source Region of the Yellow River and the Ganjiang River Basin, representing a large climatic diversity. The locations and the aridity index from geo-spatial datasets (UNEP, 1997) of the three catchments are shown in Fig. 1a. The Luanhe River Basin, located in the northeastern part of the Haihe River Basin with a drainage area of 44,900 km2, is characterized by the temperate continental monsoon climate type (Fig. 1b). The average temperature is between 0.3 and 11 °C, gradually decreasing from the lower basin to the upper basin. With strong interannual and intra-annual variability, precipitation of the Luanhe River Basin has the multi-year average value of 560 mm, which mostly occurs in summer, especially in July and August. Located in 95.5–103.5°E and 32–36.5°N, the Source Region of the Yellow 300 W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 Fig. 1. Locations and the aridity index from geo-spatial datasets of the three catchments (a), meteorological stations, hydrological station, elevation, the mean annual precipitation (P), potential evapotranspiration (PET) and runoff (R) in the Luanhe River Basin (b), the Source Region of the Yellow River (c) and the Ganjiang River Basin (d). River has a drainage area of 121,972 km2 with the Tangnaihai hydrological station as the control outlet of the basin (Fig. 1c). Characterized by a wet and warm summer and a cold and dry winter, the region belongs to the Tibetan Plateau climate system with annual average temperature and precipitation of 0.5 °C and 495 mm, respectively. The Source Region of the Yellow River has a great elevation varying from 2670 m in the east to 6253 m in the west, and most of the regions are covered by alpine meadows and steppes. With a controlling area of 81,158 km2, the Ganjiang River Basin is the seventh largest branch of the Yangtze River (Fig. 1d). As one of the typical rainstorm regions in China, the Ganjiang River Basin, belongs to the subtropical moist monsoon climate zone with moderate climate and sufficient rainfall. The multi-year mean annual precipitation of the Ganjiang River Basin are 1640 mm, with over 70% of the annual precipitation occurring from March to June (Yang et al., 2003; Li et al., 2017). Daily meteorological data from 1961 to 2000 of 28 observation stations (see Fig. 1b–d) including precipitation, temperature, wind speed, relative humidity and sunshine duration were provided by the National Climatic Centre (NCC) of the China Meteorological Administration (CMA). Monthly runoff observations of the three catchments (1961–2000) were collected from the Hydrological Bureau. In addition, twenty-six large-scale atmospheric variables during the period of 1961–2000 obtained from the NCEP (National Centers for Environmental prediction) reanalysis dataset, such as mean sea level pressure, total precipitation, mean temperature at 2 m, specific near surface humidity, wind speed at 1000 hPa, etc., were used to calibrate and validate the statistical downscaling W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 model. The future climate projections were obtained from the second generation of Canadian Earth System Model (CanESM2), participating in the CMIP5 experiment (Taylor et al., 2012). CanESM2 was selected since it can fully meet the data requirement to force the PET estimation model and hydrological model used in this study. More importantly, CanESM2 was identified as one of the five most suitable climate models for China based on specific evaluation on 20 climate models (Chen and Frauenfeld, 2014) and ranked in top two in simulating temperature in high altitude area (Su et al., 2013). In practice, CanESM2 were broadly used in climate impact studies with favorable feasibility in China (e.g., Wen et al., 2013; Das and Umamahesh, 2016; Zhang et al., 2016). The past observed atmospheric variables from NCEP reanalysis dataset processed at the same spatial resolution with CanESM2 (2.8125° 2.8125°), which is required by the statistical downscaling model. Daily climate model variables under a stabilization scenario (RCP4.5) including long-term and global emissions of greenhouse gases, short-lived species and land-use-land-cover (Clarke et al., 2007; Moss et al., 2010) over the period of 2006–2100 were used to generate future climatic variables series. The dataset of NCEP reanalysis and CanESM2 were downloaded from the internet site (http://www.cccsn.ec.gc.ca). 3. Methodology In order to investigate the uncertainty of future runoff response to climate change due to different future PET estimation approaches, the projected future PETs from physically-based formulation, radiation-based formulation, temperature-based formulation and direct downscaling output from GCM were used as inputs to drive the calibrated hydrological model. The differences of projected future runoff were then investigated. The schematic illustration of the computation processes is shown in Fig. 2. The detailed descriptions of downscaling method, PET estimation methods and hydrological model are given below. 301 3.1. Statistical downscaling model (SDSM) As a hybrid of the stochastic weather generator and regression methods, the statistical downscaling model (SDSM) developed by Wilby et al. (2002) was used to project future variables including precipitation, mean daily air temperature (Tmean), daily maximum air temperature (Tmax), daily minimum air temperature (Tmin), net radiation (Rn), relative humidity (RHmean) and wind speed (U). The major work of the SDSM is to establish quantitative relationship between large-scale circulation patterns and local-scale observed variables. Due to low-cost and rapid assessments, statistical downscaling methodologies represents the more promising option than dynamical downscaling approaches (Wilby and Dawson, 2007; Tatsumi et al., 2015), and have thus been widely applied to assessments on meteorological, hydrological and environmental responses to climatic change (e.g., Pervez and Henebry, 2014; Mahmood and Babel, 2014; Gulacha and Mulungu, 2016). The main procedure for downscaling large-scale climatic variables consists of the following steps. First, determining appropriate atmospheric variables for predictors by the screening operation in SDSM version 4.2. Second, constructing the multiple regression model between the predictors (the screened largescale climatic variables from NCEP reanalysis) and predictands (atmospheric variables in meteorological stations) during the period of 1961–1990. Third, calibrating and validating the regression model in the sub-periods of 1961–1990 and 1991–2000, respectively. Finally, the future climate data provided by CanESM2 under RCP4.5 scenario over the period of 2006–2100 were inputted into the multiple regression models to generate the future daily climatic series of each meteorological station. Besides, four statistics, i.e., the correlation coefficient (r), the ratio of simulated to observed standard deviation (RS), the coefficient of efficiency (Ens) and the model biases (Bias) were selected to assess the performance of SDSM. The formulas of the four statistics are shown in Table 1. Generally, the closer the values of r, RS and Ens to 1 and the value of Bias to 0, the better the model performed. Fig. 2. Schematic illustration of this study. 302 W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 Table 1 Formulas of the four assessment criteria (Qs,i, simulated value; Qo,i, observed value; s , mean simulated value; Q o , mean observed value). Q Assessment criteria Formula r Pn s ÞðQ Q oÞ ðQ s;i Q o;i i¼1 qP ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ r ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ P n i¼1 sÞ ðQ s;i Q n 2 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ P RS i¼1 oÞ ðQ o;i Q 2 s Þ2 ðQ s;i Q i¼1 1 n n 1 n n RS ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ P Ens Ens Bias i¼1 oÞ ðQ o;i Q 2 Pn ðQ o;i Q s;i Þ2 ¼ 1 Pi¼1 n 2 Bias ¼ 1n n P i¼1 ðQ o;i Q o Þ ðQ s;i Q o;i Þ i¼1 3.2. Potential evapotranspiration estimation methods Three typical equations reflecting various data requirements and usually used within hydrological models, i.e., Penman (PN) (Penman, 1948), Priestley-Taylor (PT) (Priestley and Taylor, 1972) and Hamon (HM) (Hamon, 1961), were employed to estimate PET in this study. Among them, Penman (PN) is the most reliable physically-based one with explicitly incorporating both physiological and aerodynamic parameters (Xu et al., 2006). However, it requires multiple meteorological variables, including Tmean, Tmax, Tmin, RHmean, U and sunshine duration (n), and not all the variables can be ensured with great accuracy and reliability, especially in future conditions. Priestley-Taylor (PT) is radiation-based method that requires Tmean and Rn as inputs. The aerodynamic term in PT equation was replaced by a coefficient (a). Considering that the temperature observations are obtained more easily than other meteorological variables, a number of alternative PET estimation methods only requiring temperature had been developed. Wherein, Hamon (HM) is a popular one and was employed in this study, which only requires Tmean as an input. The detailed information of the three methods is shown in Table 2. Previous study revealed that not all the future variables obtained by SDSM have high confidence (Wang et al., 2014). The built SDSM in constructing temperature variables (Tmean, Tmax, Tmin) and Rn always perform better than in constructing other meteorological variables (e.g., U, RHmean) (Wang et al., 2015). In order to investigate the impact of different methods and data in different reliability on future PET, the following four approaches were selected: (1) PN (physically-based method) with six downscaled variables (including Tmean, Tmax, Tmin, Rn, U and RHmean) based on SDSM (for the brevity, we call it SD-PN method after here), (2) PT (radiation-based method) with relatively reliable downscaled inputs (Rn, Tmean) based on SDSM (SD-PT method), (3) HM (temperature-based method) with the most reliable downscaled variable (Tmean) based on SDSM (SD-HM method), (4) downscaling with directly selecting PET calculated by PN equation as predictand (PN-SD method). 3.3. The abcd model The abcd model is a widely used monthly hydrological model worldwide. It has been successfully applied in many basins in China with different climatic features (e.g., Bai et al., 2016; Du et al., 2016; Wang and Zhou, 2016) and was thus used in this study to simulate the hydrological processes of three catchments with a large climatic diversity. Taking precipitation and PET as inputs (Alley, 1984; Vandewiele et al., 1992; Sankarasubramanian and Vogel, 2002), the abcd model proposed by Thomas, 1981, is a conceptual monthly water balance model with four parameters (a, b, c, and d). The catchment-averaged monthly precipitation and PET were obtained by Thiessen polygon method (Thiessen, 1911) based on the stations observations. The structure of abcd model consists of two parts: soil moisture storage in the upper layer and groundwater storage in the lower layer. In general, the actual evapotranspiration is a function of precipitation and soil water storage in abcd model. There are two state variables, i.e., the water availability (W) and the evapotranspiration opportunity (Y) Thomas (1981). The water availability is derived by W i ¼ Si1 þ Pi ð1Þ where W i is the water availability at the end of the i th month; Si1 is the soil moisture storage at the beginning of the i th month; Pi is the monthly precipitation. While the other state variable (Y) is determined by Y i ¼ Ei þ Si ð2Þ where Y i and Ei are the monthly evapotranspiration opportunity and actual evapotranspiration, respectively. Besides, a nonlinear relationship between Y i and W i was assumed in the abcd model, as follows: Wi þ b Yi ¼ 2a sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 Wi þ b W ib 2a a ð3Þ the parameter a (0 < a 6 1) represents the propensity of runoff to occur before the soil is fully saturated (Thomas et al., 1983), b is the upper limit on the sum of Ei and Si . Thomas (1981) assumed that after a rainfall the loss rate of soil moisture by actual evapotranspiration was proportionate to PET for the month, PET i Si ¼ Y i exp b ð4Þ where PET i is the monthly potential evapotranspiration. Combining Eqs. (2) and (4), actual evapotranspiration can be estimated as PET i Ei ¼ Y i 1 exp : b ð5Þ At the part of groundwater storage, runoff is divided into direct and indirect parts, as follows: Table 2 Methods used to estimate potential evapotranspiration. Tmean, mean daily air temperature (°C), which is defined as the mean of the Tmax and Tmin; Tmax, daily maximum air temperature (°C); Tmin, daily minimum air temperature (°C); RHmean, mean relative humidity; U2, wind speed at 2 m (m/s); n, sunshine duration (h); Rn, net radiation (MJ/ m2day), which is calculated by the measured meteorological data (e.g. Tmax, Tmin, RHmean, n et al.); D, slope of vapor pressure curve (kPa/°C); c, psychrometric constant (kPa/°C); k, latent heat of vaporization (MJ/kg); es, saturation vapor pressure (kPa); e*(Tmean), saturation vapor pressure at the mean temperature; N, daylight hours (h); the above unobservable variables are calculated based on the Allen et al. (1998). Besides, a and k are the empirical coefficients, which are calibrated by the PN equation in this study. Method Formula Data needed Reference Penman (PN) 2 Þð1RH mean Þes PET ¼ DRn þ6:43cð1þ0:536U ðDþcÞk Tmean, Tmax, Tmin, RHmean, U2 and n Penman (1948) Priestley-Taylor (PT) PET ¼ a ðDDþRcnÞk Tmean and Rn Priestley and Taylor (1972) Hamon (HM) N e ðT mean Þ PET ¼ k 12 T mean þ273:2 Tmean Hamon (1961) W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 Rsi ¼ ð1 cÞðW i Y i Þ ð6Þ Gi1 þ cðW i Y i Þ 1þd ð7Þ Gi ¼ Rg i ¼ dGi ð8Þ Ri ¼ Rsi þ Rg i ð9Þ where Rsi , Rg i and Ri are the monthly direct runoff, groundwater discharge and total runoff, respectively. Gi and Gi1 are the groundwater storages at the end and beginning of the i th month, respectively. Parameter c is a groundwater recharge coefficient which controls the water input to the aquifers. Parameter d is the groundwater runoff recession constant. In this study, the 40 years observed data was divided into two periods. The data in the first sub-period (1961–1990) and second sub-period (1991–2000) were used for model calibration and validation, respectively. The widely used genetic algorithm (Wang, 1991) was selected to optimize the parameter values of the abcd model. Meanwhile, the coefficient of efficiency (Ens) and correlation coefficient (r) (see Table 1) were used to assess the performance of the abcd model. 4. Results 303 (Tmean, Tmax, Tmin, Rn, RHmean and U) at each meteorological station. The statistic assessment of calibration and validation results for Duolun station are summarized in Table 4, from which it can be seen that simulated meteorological variables were generally consistent with observations. It is especially true for Tmean, Tmax, Tmin and Rn. For these variables, r, RS and Ens between simulated and observed ones exceeded 0.90 in calibration and validation. During the calibration period, the values of Bias for Tmean, Tmax, Tmin and Rn were 0.00, while during the validation period, the related values were 0.22 °C/day, 0.15 °C/day, 0.31 °C/day and 0.51 MJ/m2day, respectively. However, the simulations of U and RHmean were less satisfactory than that of Tmean, Tmax, Tmin and Rn with the r and Ens values of about 0.81. Meanwhile, the comparisons of daily meteorological variables simulated by SDSM and observed data during the validation period (1991–2000) are displayed in Fig. 4, showing similar conclusions with the above analysis. Concurrently, Fig. 5 compares the observed and downscaled mean monthly precipitation in the validation period. The simulated precipitation was closely consistent with observations, although the values of downscaled precipitation were slightly overestimated in some months. Generally, the statistical relationships built by SDSM are capable of reproducing daily meteorological variables and can be used to project the future climate scenarios over the three catchments. Moreover, the performance of the built downscaling model in constructing Tmean, Tmax, Tmin and Rn are better than that in constructing RHmean and U. 4.1. Performance assessment of SDSM in constructing various predictands 4.1.1. Performance assessment of SDSM in constructing meteorological variables The selection of the predictor is a critical step for constructing the downscaling model (Wilby et al., 2002). Similar with what is adopted in previous studies (e.g., Khan et al., 2006; Wang et al., 2013c), the predictor selection was performed by the screening of the most relevant predictors set based on the correlation and partial correlation analysis in the individual predictors and predictand (Huang et al., 2011; Wang et al., 2013c). Taking the mean temperature in Duolun station (42.18 °N, 116.47 °E) as an example, Fig. 3 demonstrates the partial correlation coefficient (p-corr) and the correlation (corr) between daily mean temperature and 26 atmospheric variables. 10 predictor variables can be selected due to high correlation. Under the same selection criterion with mean temperature, the predictors identified for other local variables in Duolun station are summarized in Table 3. Four assessment criteria, i.e., r, RS, Ens and Bias, were used to evaluate the performance of SDSM in constructing six meteorological predictands 4.1.2. Performance assessment of four approaches in estimating potential evapotranspiration For offering intuitionistic information in evaluating the performance of four PET methods, Fig. 6 displays the statistic results of inter-comparison of model skills during the validation period with a Taylor diagram, a polar-style graph. It can be seen that the SD-PN and PN-SD methods agreed with observations that lied closest the point marked by ‘‘observed”, and the statistic results for SD-PN and PN-SD were almost identical in all catchments. For the PET estimated by SD-PN and PN-SD methods in three catchments, the correlation between simulated and observed ones exceeded or equaled to 0.9. The normalized standard deviation ranged from 1.2 to 2.0, and the values of RMSE were lower than 0.8. Compared with the SD-PN and PN-SD methods, the SD-PT and SD-HM methods showed weaker capability of matching local climatic information with larger RMSE and lower correlation. In addition, the spatial distributions of the statistic points in the Ganjiang River Basin with bigger aridity index were closer compared with that in the other catchments, indicating that the PET was less affected Fig. 3. The absolute values of correlation coefficient (corr) and partial correlation coefficient (p = corr) between the mean daily air temperature (Tmean) and 26 NCEP atmospheric variables for Duolun station. 304 W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 Table 3 Selected predictor variables for all predictands including mean temperature (Tmean), maximum temperature (Tmax), minimum temperature (Tmin), net radiation (Rn), wind speed (U), relative humidity (RHmean), precipitation (P) and potential evapotranspiration (PET) at Duolun station. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Variable mslpgl p1_fgl p1_ugl p1_vgl p1_zgl p1thgl p1zhgl p5_fgl p5_ugl p5_vgl p5_zgl p500gl p5thgl p5zhgl p8_fgl p8_ugl p8_vgl p8_zgl p850gl p8thgl p8zhgl prcpgl s500gl s850gl shumgl tempgl Description Predictands Tmean p Mean sea level pressure 1000 hPa Wind Speed 1000 hPa Zonal Velocity 1000 hPa Meridional Velocity 1000 hPa Vorticity 1000 hPa Wind Direction 1000 hPa Divergence 500 hPa Wind Speed 500 hPa Zonal Velocity 500 hPa Meridional Velocity 500 hPa Velocity 500 hPa Geopotential 500 hPa Wind Direction 500 hPa Divergence 850 hPa Wind Speed 850 hPa Zonal Velocity 850 hPa Meridional Velocity 850 hPa Velocity 850 hPa Geopotential 850 hPa Wind Direction 850 hPa Divergence Total precipitation Specific humidity at 500 hPa Specific humidity at 850 hPa Specific Near Surface Humidity Mean Temperature at 2 m p p Tmax p p Tmin p p p Rn p p U p p p p RHmean p P p PET p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p Table 4 Performance of SDSM in constructing meteorological variables over the Duolun station. The left and right sides of the line represent the statistics in calibration and validation periods, respectively. Variables r RS Ens Bias Tmean Tmax Tmin Rn U RHmean 0.98/0.98 0.98/0.98 0.97/0.97 0.96/0.95 0.79/0.80 0.76/0.76 0.99/1.02 0.99/1.00 0.97/1.02 0.97/1.03 0.80/0.96 0.81/0.81 0.97/0.96 0.96/0.96 0.94/0.94 0.93/0.91 0.62/0.59 0.58/0.56 0.00/-0.22 0.00/-0.15 0.00/-0.31 0.00/0.51 0.00/0.26 -0.01/-2.28 by the estimating methods over humid areas. Generally, all methods are generally acceptable of estimating the PET over the three catchments. Meanwhile, the SD-PN and PN-SD methods have better performance than the other two methods. 4.2. Calibration and validation of the abcd model The PET estimated by PN method and observed monthly precipitation were used to drive the abcd model in the three catchments. Fig. 7 displays the abcd-simulated and observed monthly runoff series during the calibration and validation periods. It can be seen that both simulated monthly runoff amount and hydrograph shape were consistent with observed values except some peak runoff. The parameter values of the abcd model optimized by genetic algorithm and the assessment criteria are presented in Table 5. The correlation in the three catchments ranged from 0.83 to 0.90 in the calibration and validation. The values of Ens over calibration and validation periods exceeded 0.70 and 0.64, respectively. Although the performance of the abcd model in validation period is not as good as that in calibration period over the Source Region of the Yellow River and Ganjiang River Basin, the model results shown in Fig. 7 and Table 5 are overall acceptable, indicating that the calibrated abcd model is applicable to project the future runoff. p p p p p p p p p p p p p 4.3. Impact of different potential evapotranspiration inputs on runoff projection With the future climate variables during the period of 2021– 2050 constructed based on SDSM as inputs, the calibrated abcd model was driven to simulate hydrological processes under RCP4.5 scenario output in three catchments. Wherein, the future daily PET was projected by coupling different formulations and input data reliabilities (i.e., SD-PN, SD-PT, SD-HM and PN-SD methods). The distributions of the monthly PET values are presented in the box-and-whisker plots (see Fig. 8a–c). Of the four PET projection approaches used in this study, SD-HM provided larger PET values in summer months and smaller ones in the other months, especially for the Luanhe River Basin. Compared with the PET series in the Luanhe River Basin and the Source Region of the Yellow River, a better agreement for four monthly PET series was presented in the Ganjiang River Basin no matter for the quartile, the maximum/minimum values or the mean values. In addition, the PET in January, November and December over the period of 2021–2050 showed smaller ranges than that in the other months. Generally, the obvious differences in PET magnitude still exist in all catchments, especially for spring and summer months in the Luanhe River Basin and the Source Region of the Yellow River with relatively dry climate feature, although the monthly patterns of PET projected by four approaches are similar. Besides, the PET projected by SD-PN and PN-SD approaches were closer to each other for each catchment, demonstrating that the simulation of PET using SDSM by establishing the ‘‘black box’’ relationship between large-scale climatic data and PET was also an alternative. As the other extremely important input variable of the hydrological model, the mean monthly precipitation over the three catchments are displayed in Fig. 8d. The monthly distribution for future precipitation was generally consistent with the observed pattern in baseline period, suggesting that downscaled precipitation under RCP4.5 scenario can locally reflect the historical climate conditions. W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 305 Fig. 4. Observed and downscaled daily Tmean (a), Tmax (b), Tmin (c), Rn (d), U (e) and RHmean (f) in the Duolun station during the validation period (1991–2000). Fig. 9 demonstrates the results of simulated monthly runoff for the period of 2021–2050. The overall impression of Fig. 9 is that the ranges of four runoff series were larger than that of the corresponding monthly PET, indicating that the runoff for the same month varies greatly in different years. Concurrently, there were apparent differences in runoff over the three catchments reflected by obvious discrepancy in magnitude of the quartile, maximum/ minimum values and mean values. The differences between four runoff series for a given catchment were therefore due to the diverse PET values. Furthermore, it is worth noting that the differences of runoff series in the Luanhe River Basin and the Source Region of the Yellow River with relatively dry climate feature were more obvious than that in the Ganjiang River Basin with humid climate condition. 4.4. Discrepancy of runoff changes caused by different potential evapotranspiration inputs By taking the period of 1961–2000 as a reference period, the changes in seasonal and annual mean runoff across the three catchments in the future period (2021–2050) under the RCP4.5 scenario are shown in Fig. 10. The results suggested that the PET projected by coupling different formulations and input data reliabilities can cause the obvious distinctions in the runoff changes, 306 W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 Fig. 5. Observed and downscaled mean monthly precipitation (P) in the validation period (1991–2000) over the Luanhe River Basin (a), the Source Region of the Yellow River (b) and the Ganjiang River Basin (c). which may be quite significant in some situations. For example, for the spring months (MAM) in the Source Region of the Yellow River the runoff changes using two PET types (SD-PN and PN-SD) had the opposite sign to that based on the other two PET types (Fig. 10a). A similar phenomenon can be seen in the Luanhe River Basin, but for the summer months (JJA). There can also be obvious differences in the impact of different PET methods on runoff projection even where the four PET types resulted in the same sign of runoff change. For instance, for the changes in annual mean runoff over the Luanhe River Basin, the runoff reductions in the period of 2041–2050 using SD-HM PET was approximately double of that using the other PET types (Fig. 10b). On the contrary, the runoff increments in the Luanhe River Basin over the period of 2031– 2040 using SD-HM PET was less than one-fifth of that using the other PET types. Generally, there are noticeable discrepancy in the magnitude of change in runoff and even the adverse change direction over the three catchments. Meanwhile, the more apparent discrepancies can be found in the Luanhe River Basin and the Source Region of the Yellow River compared with that in the Ganjiang River Basin. 5. Discussion 5.1. Uncertainty in potential evapotranspiration through different approaches The results in this study demonstrated that although the monthly patterns of PET projected by four approaches during the period of 2021–2050 for each catchment were similar, the noticeable differences in PET magnitude still existed in all catchments, suggesting there were uncertainties existing. Similar findings were also made in some previous studies (e.g., McAfee, 2013; Wang et al., 2015). In other studies (e.g., Kingston et al., 2009; Kay and Davies, 2008), the different methods used to estimate PET was even found to cause differences in the direction of projected changes in PET. The uncertainty in PET during the history periods derive primarily from the variables used. For instance, temperature is the only climatic variable used in the HM method. Thus, the impact of other variables (e.g., radiation, wind speed and humidity) on PET cannot be reflected directly. Increasing air temperature can lead to the increase of PET when using temperature-based methods, and the influence of increasing temperature on PET may be tempered or even counteracted by the impact of changes in radiation, humidity and wind speed (McAfee, 2013; Xing et al., 2017). Thompson et al. (2014) found that the PET estimated by temperature-based methods (Linacre, Blaney-Criddle, and Hamon methods) are larger than that estimated by the other methods during the period of 1961–1990 over the four representative subcatchments located in the Mekong River Basin. While the radiation is the relatively major factor to affect the PET when using empirical radiation-based methods (e.g., Priestley-Taylor, Turc and Abtew methods). In practical applications, the simpler models with less data requirements (e.g., temperature-based and radiation-based methods) were recommended by Oudin et al. (2005), especially in the situations where data were scarce. Moreover, the aerodynamic-and radiation-based PN method, the data-intensive one with six input climatic variables, can adequately reflect the meteorological information. The PN method was suggested as the preferable one for determining the PET, even though the use of this method was always prevented by the insufficient input data in some regions (Donohue et al., 2010; McAfee, 2013). However, the uncertainty in future projection of PET is caused not only by the used formulas, but also by the accuracy of the required meteorological variables. The biases in any of the input variables could impact the magnitude of PET. As indicated by Yin et al. (2015), the uncertainty in variables mainly arises from GCMs. W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 307 Fig. 6. Taylor diagrams for estimated four potential evapotranspiration types (SD-PN, SD-PT, SD-HM and PN-SD) evaluated against observed ones in the Luanhe River Basin (a), the Source Region of the Yellow River (b) and the Ganjiang River Basin (c) during the validation period (1991–2000). Three metrics of the correlation (curved axis), the ratio of the standard deviations (x and y axes) and the RMSE (dashed line) are presented in it. Furthermore, more confidences are always found in downscaling GCM-derived temperature and radiation than that of the other meteorological variables (Randall et al., 2007; Wang et al., 2015). This is also supported by the results of the current study (see Fig. 4 and Table 4). In fact, it is difficult to establish perfect multiple regression equation for variables with conditional behavior (Gulacha and Mulungu, 2016). Taking the precipitation as an example, the amounts depend on wet/dry day occurrence, and thus lies on regional scale predictors, e.g., atmospheric pressure. The intermediate processes exist between regional forcing and some local meteorological factors in the conditional model (Wilby and Dawson, 2004). Therefore, not all of meteorological variables required in evapotranspiration and hydrological model can be perfectly modeled (Goncu and Albek, 2016). Generally, there are appreciable uncertainties in PET projected by coupling different formulations and input data reliabilities (i.e., SD-PN, SD-PT, SDHM and PN-SD approaches) in all catchments, especially for spring and summer months in the Luanhe River Basin and the Source Region of the Yellow River with relatively smaller aridity index (Fig. 8a–c). 5.2. Uncertainty in runoff projection caused by the alternative potential evapotranspiration methods As the appropriate indicator for the activity of climate change and hydrological regime, PET is also considered as the important input for hydrological model, and thus PET method can determine the direction of projections of future water resources (Hobbins et al., 2001; Xu and Singh, 2005; Kingston et al., 2009; Wang et al., 2012b). The different PET magnitudes were given by the four projection methods when applied to climate model data under the RCP4.5 emissions scenario over the period of 2021–2050, and this can have an obvious impact on the subsequent hydrological simulation in all catchments of this study (see Fig. 9). Although many studies have indicated that the runoff simulations were insensitive to the different PET inputs in historical period (e.g., Andreassian, et al., 2004; Oudin et al., 2005; Bai et al., 2016), the future PET projection method can further add substantial uncertainty to the existing uncertainty associated with the climate change signal between GCMs (Kingston et al., 2009; Yin et al., 2015). Moreover, as indicated by Bai et al. (2016), the reasons for the insensitivities of runoff simulations to PET inputs are attributed to model parameter calibration using all PET types. It is worth noting that the set of parameters in abcd model was only calibrated by using observed precipitation, runoff and one PET type (calculated by PN equation) rather than using four PET types in this study. This can ensure that the differences of projection future runoff come from the selection of different PET projection methods. Despite that the PET methodrelated uncertainty is less than the GCM/RCM-related uncertainty as for future runoff projection (Kay and Davies, 2008; Wang et al., 2012a; Thompson et al., 2014), the apparent uncertainties in runoff projection caused by the PET projected by coupling differ- 308 W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 Fig. 7. Comparison between abcd-simulated and observed monthly runoff for calibration (1961–1990) and validation (1991–2000) periods in the Luanhe River Basin (a), the Source Region of the Yellow River (b) and the Ganjiang River Basin (c). Table 5 Model parameter and the performance assessment of the abcd model during calibration and validation periods over the three catchments. Catchment Luanhe River Basin Source Region of the Yellow River Ganjiang River Basin Parameter values Calibration Validation a b c d Ens r Ens r 0.981 0.744 0.951 290 421 457 0.446 0.125 0.372 0.089 0.060 0.258 0.700 0.753 0.810 0.838 0.869 0.900 0.715 0.654 0.646 0.870 0.832 0.873 W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 309 Fig. 8. Box-and-whisker plots for the monthly potential evapotranspiration values projected by four approaches (SD-PN, SD-PT, SD-HM and PN-SD) ((a), (b) and (c)) and monthly mean precipitation (d) for the period of 2021–2050 under RCP4.5 over the three catchments. In the box-and-whisker plots, the outer edges of the boxes and the horizontal lines within the boxes represent the 25th, 75th, and 50th percentiles of potential evapotranspiration values. The whiskers represent the minimum and maximum potential evapotranspiration values. The filled circles within the boxes represent the average potential evapotranspiration. 310 W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 Fig. 9. Box-and-whisker plots for the monthly runoff values for the different PET methods in the period of 2021–2050 under RCP4.5 over the Luanhe River Basin (a), the Source Region of the Yellow River (b) and the Ganjiang River Basin (c). The explanations of the box-and-whisker plots can be found in Fig. 8. ent formulations and input data reliabilities still exist in the three catchments, especially for summer months in the Luanhe River Basin and spring months in the Source Region of the Yellow River (see Figs. 9 and 10). 5.3. The reasons for different uncertainty of runoff projections between various climatic regions The different impacts of PET projection approaches on future runoff between various climatic regions were found in this study (Figs. 9 and 10). On the one hand, the obvious uncertainties in runoff projection over the Luanhe River Basin and the Source Region of the Yellow River were derived from the greater differences of future PET series. On the other hand, as the other extremely important input variable of the hydrological model, precipitation plays a dominant role in runoff change (Zhang et al., 2011; Croitoru et al., 2013; Liu et al., 2013; Thompson et al., 2014; Guo et al., 2015). It is perhaps not surprising that the higher proportion of precipitation in the catchments with smaller aridity index (e.g., the Luanhe River Basin and the Source Region of the Yellow River) are consumed by evapotranspiration, giving rise to more noticeable impacts of different PET approaches on runoff projection in these catchments compared with the other catchments with bigger aridity index. Meanwhile, the impact of precipitation that might temper the influence of different PET projection approaches on runoff when the contribution of precipitation to runoff is greater than the contribution of PET to runoff. Here, the contribution analysis based on climatic elasticity method was used to further explain the different uncertainty of runoff projections between various climatic regions. As a hydroclimatic property (Xu et al., 2014), the climate elasticity of runoff is defined as the proportional change in runoff due to the proportional change in one or more climatic variables (Sankarasubramanian et al., 2001; Fu et al., 2007). Budyko hypothesis (Budyko, 1948, 1974) states that the annual water balance can 311 W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 Fig. 10. The seasonal (a) and annual (b) changes in runoff for the different PET methods over the three catchments. Table 6 The attribution analysis for the three catchments. The variables in this table are calculated based on the Wang et al. (2016b). Catchment Luanhe River Basin Source Region of the Yellow River Ganjiang River Basin Breakpoint 1979 1989 1991 Elasticity Change from period-1 to period-2 Contribution (%) eP ePET ex DR DP DPET Dx gP gPET gx gP - gPET 2.3695 1.4893 1.5723 1.3695 0.4893 0.5723 2.6844 2.2951 0.6317 39.6 26.0 130.8 38.0 22.4 229.3 37.7 24.2 88.2 0.3867 0.0452 0.3429 30.9 50.2 142.7 8.8 7.9 27.9 77.9 44.0 71.0 39.7 42.3 114.8 be expressed as a function of available water and energy. As one widely used equation in many curves of Budyko assumptions, Fu equation (Fu, 1981) was selected to quantitatively analyze the impacts of changes in the climate (precipitation and potential evapotranspiration) and catchment characteristics (x) on runoff change in this section. Table 6 shows the results of the contribution analysis for the three catchments over the period of 1961–2000. In the Luanhe River Basin, precipitation and x presented positive contributions to the runoff change with contribution rates of 30.9% and 77.9%, respectively, indicating that land use/cover was the main driving factor for the runoff decrease in the Luanhe River Basin. The value of the contribution of x to runoff decline in the Luanhe River Basin was slightly higher than that in the previous studies (Bao et al., 2012; Wang et al., 2013b). Moreover, the difference of contribution rates between precipitation and PET to runoff reduce was 39.7%. While the contributions of precipitation, PET and x to the runoff decrease in the Source Region of the Yellow River were 50.2%, 7.9% and 44.0%, respectively. In addition, the significant increase in precipitation (229.3 mm) played a dominating role in the increase of runoff with contribution rates of 142.7% in the Ganjiang River Basin with humid climate condition. It also can be seen that the largest difference of contribution rates between precipitation and PET to runoff change was occurred in the Ganjiang River Basin (114.8%), followed by the Source Region of the Yellow River (42.3%). Generally, the results of contribution analysis suggest that the more humid the area, the greater impact of precipitation on runoff change than the influence of PET on runoff change. Therefore, the more noticeable uncertainties were found in the Luanhe River Basin and the Source Region of the Yellow River with relatively dry climate feature compared with that in the Ganjiang River Basin. 6. Conclusion In this study, based on the abcd monthly hydrological model, we explored the influences of different PET inputs estimated by four different approaches on runoff projection in three catchments (i.e., the Luanhe River Basin, the Source Region of the Yellow River and the Ganjiang River Basin) representing a large climatic diversity. Generally, although the similar monthly patterns of future PET during the period of 2021–2050 were provided by using the more physically based Penman (PN) equation with less reliable input variables, more empirical radiation-based Priestley-Taylor (PT) equation with relatively dependable downscaled data, temperature-based Hamon (HM) equation with the most reliable downscaled temperature, and statistical downscaling method with directly choosing PET calculated by Penman (PN) equation as predictand, the obvious differences in PET magnitude estimated by four approaches still existed in all catchments, especially for spring and summer months in the Luanhe River Basin and the Source Region of the Yellow River with relatively dry climate feature. More importantly, there were apparent uncertainties in runoff projection in the three catchments reflected by obvious discrepancy in magnitude of change in runoff and even the diverse change direction for summer months in the Luanhe River Basin and spring months in the Source Region of the Yellow River. Meanwhile, the 312 W. Wang et al. / Journal of Hydrology 555 (2017) 298–313 more noticeable uncertainties were generally found in the Luanhe River Basin and the Source Region of the Yellow River with smaller aridity index compared with that in the Ganjiang River Basin. Apart from the relatively smaller uncertainties in more humidity Ganjiang River Basin, the fact that the runoff change was more attributed to the precipitation in Ganjiang River Basin compared with the other two basins should be the more important reason, which was revealed by the contribution analysis based on climatic elasticity method. Acknowledgments This work was jointly supported by the National Science Foundation of China (51779073, 51379057), the Fundamental Research Funds for the Central Universities (2017B21414, 2015B14114), the National ‘‘Ten Thousand Program” Youth Talent, the QingLan Project, and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). Thanks to the National Climatic Centre (NCC) of the China Meteorological Administration (CMA) for providing the valuable meteorological data and also thanks to the Canadian Climate Data and Scenarios (http://www.cccsn.ec.gc.ca) for offering the dataset of NCEP reanalysis and CanESM2. Cordial thanks are extended to the Editor in Chief, Professor Geoff Syme, and two anonymous referees for their valuable comments, which greatly improved the quality of the paper. References Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration: Guidelines for computing crop water requirements, FAO Irrig. Drain. 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