Sensitivity analysis of potential evapotranspiration to key climatic factors in the Shiyang River Basin

This paper focuses on determining the spatial and temporal characteristics of the sensitivity coefficients (SCs) between potential evapotranspiration (ET0) and key climatic factors across the Shiyang River Basin (SYRB) from 1981 to 2015. Penman–Monteith equation and a sensitivity analysis were used to calculate ET0 and the SCs for key climatic factors. Sen’s slope was used to analyze the observed series. According to the results, the sensitivity significances were in the order of relative humidity (RH)> net solar radiation (NSR)>wind speed (WS)>maximum air temperature (Tmax)>minimum air temperature (Tmin). The SCs for the RH and NSR were larger in the upper mountainous region, while the other three coefficients were larger in the middle and lower reaches. All five climatic factors for the ET0 SCs showed increasing trends in the mountainous region, and the Tmax, WS and RH SCs increased in the middle and lower reaches. Over the past 35 years, the change in ET0 was dominated by the air temperature (T ), RH and NSR, and the increase in ET0 during the studied period was mainly due to the increases in T and NSR.


GRAPHICAL ABSTRACT INTRODUCTION
Potential evapotranspiration (ET 0 ) refers to the actual evapotranspiration (AET) under full water supply conditions and is an important indicator of regional evaporation potential (Guo et al. ). As an important part of the hydrological cycle (Horváth et al. ), ET 0 is related not only to the water balance and water conversion (Darshana et al. ) but also to the surface energy balance, and it plays a crucial role in the global climate system (Aouissi et al. ). In the current calculation methods for ET 0 (Lhomme ), the Penman-Monteith (P-M) equation recommended by the Food and Agriculture Organization (FAO) is based on the energy balance and diffusion principles for water vapor turbulence; it considers the influences of the aerodynamics and solar radiation terms (Li et al. ) and is widely used in the field of hydrometeorology (Penman ; Hao et al. ).
Climate change has profoundly affected the ecohydrology models of basins and has caused a series of problems about water resources (Xu et al. ). In arid and semiarid areas, small changes in climate factors have had significant impacts on hydrological processes (Ti et al. ). As a key parameter of the hydrological cycle, analyzing the sensitivity of ET 0 to climate variables is an important research topic that has attracted attention in the hydrological field in recent years (Bormann ). Zhao et al. () showed that the wind speed (WS) has the greatest impact on ET 0 on the Qinghai-Tibet Plateau. Zhao et al. () believed that the influence of relative humidity (RH) on ET 0 is most significant in the Heihe River Basin. Research by Yang et al. () on the Huang-Huai-Hai Plain showed that ET 0 is most sensitive to net solar radiation (NSR) in the eastern part of the plain and to T in the southwestern region. Yang et al. () believed that NSR is the most sensitive meteorological factor to ET 0 in the Tao River Basin. Studies by Lian & Huang () in an oasis-desert region during a growing season showed that selecting extreme pixels or edges can achieve reasonable estimates of ET 0 and that validation of remote sensing models is necessary. Zheng & Wang () used a global sensitivity analysis method to study the sensitivities of ET 0 to climate variables in China; the results showed that the spatial variation in the sensitivity varied seasonally and that stations at low latitudes were more sensitive to the NSR and less sensitive to T than those at high latitudes.
Studies by Gao et al. () in the West Liao River Basin indicated that the T increased significantly, while WS, NSR and RH decreased remarkably. ET 0 is most sensitive to NSR and RH and is least sensitive to the average temperature. Liu et al. () selected Beijing as a study area to investigate the effects of climate change on ET 0 . The results showed that the T was the most key factor for ET 0 change, followed by RH and WS, and the T min and T max were less sensitive factors.
The hydro-geomorphological pattern of the mountain-

STUDY AREA
The SYRB is located to the east of the Hexi Corridor in Gansu Province, has a total area of 41,600 km 2 and is geo-

Evapotranspiration (ET 0 )
The P-M equation is extensively used to determine ET 0 due to its accurate representation of the regional energy balance and aerodynamic influence on terrestrial ET (Li et al. ).
It is described as follows: where Δ represents the saturation vapor pressure-temperature relationship slope (kPa/ C); G represents the soil heat flux (MJ/m 2 /d); R n represents the net radiation (MJ/m 2 /d); ρ a represents the air density (kg/m 3 ); c p represents the constant pressure ratio; e s and e α represent the saturated and actual vapor pressures, respectively (kPa); r α and r s represent the aerodynamic and stomatal resistance, respectively (s/m); γ represents the psychrometric constant (kPa/ C); and λ represents the latent heat of vaporization, 2.45 MJ/kg.

Sensitivity coefficient
The sensitivity coefficient (SC) is described as follows: where Se vi represents the SC of the ith meteorological factor, and G vi represents the contribution rate of the ith factor to the change in ET 0 . The SC for a meteorological element is positive or negative, indicating that ET 0 increases or decreases as the element increases, respectively (Huo et al. ). The greater the SC is, the greater the effect of ET 0 due to the meteorological factor is (Yang

Sen's slope
Sen's slope (SS) (Sen ) is widely used in trend and magnitude analysis by using the median value of the slope series to evaluate the trend. The formula is where Sen represents the value of SS; x i and x j represent the values at moments i and j, respectively, 1 i < j n; and n is the length of the sequence.

Annual variation in SCs
The absolute values of the SCs indicate the degree of sensitivity of ET 0 to each meteorological factor, therefore, the analysis of the degrees of sensitivity is based on the absolute value of each sensitivity factor. Figure 3 T min was the least sensitive in the spring and summer, and T max was the least sensitive in the autumn and winter. The SCs for T max and T min were negative in some months, which is mainly because the actual values of T max and  T min were negative during these months. Therefore, ET 0 still increased as the T increased. Figure 4 shows the spatial distributions of the multiyear   show that ET 0 is more sensitive to changes in WS, NSR and RH in arid and semiarid regions of China and that ET 0 is more prone to significant fluctuations due to changes in these three climatic factors.

Interannual variation in SCs
The sensitivity statistics of the key climatic factors in the two regions based on SS are listed in Table 3. The SCs of T max , T min and WS showed increasing trends; their variation amplitudes were 0.011/10 a, 0.010/10 a and 0.008/10 a, respectively, in the upper region and 0.008/10 a, 0.001/10 a and 0.010/10 a, respectively, in the middle and lower reaches.
The RH SC showed decreasing trends with amplitudes of À0.006/10 a and À0.013/10 a in the upper and middlelower regions, respectively. The SC for the NSR in the upper mountainous reaches increased, and that decreased in the middle and lower reaches; the amplitudes of the changes in the two regions were 0.004/10 a and À0.010/10 a, respectively.
A comparison of the two regions shows that the sensitivities of ET 0 to WS, RH and NSR in the middle-lower reaches of the plain were more significant, indicating that ET 0 fluctuated more in the middle and lower reaches of the plain than in the upstream mountainous region, was more sensitive to climatic factors and responded greatly to climate change.

Contributions of meteorological factors to the changes in ET 0
The previous analysis showed that although the T min SC was negative, the change in ET 0 was positively driven and showed an increasing trend during the statistical period.
Therefore, for ease of analysis, the absolute value of the T min contribution rate was used. The contribution rates of each meteorological element to the changes in ET 0 in the two regions of the basin were calculated according to Equation (3) and are shown in Table 4. The T contributed the most to the change in ET 0 , followed by RH and NSR, and the contribution of WS was the smallest. In comparison, the contribution rates of the meteorological factors to the change in ET 0 were higher in the middle and lower plains than in the upstream mountains, which validated that ET 0 in plains is vulnerable to climate change. The contributions of RH in the two regions were opposite and positive upstream. An increase in RH inhibits ET 0 in the upper region to some extent, while the decreasing RH in the middle and lower reaches made ET 0 increase.

DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.