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

Potential evapotranspiration (ET₀) refers to the actual evapotranspiration (AET) under full water supply conditions and is an important indicator of regional evaporation potential (Guo et al. 2015). As an important part of the hydrological cycle (Horváth et al. 2010), ET₀ is related not only to the water balance and water conversion (Darshana et al. 2013) but also to the surface energy balance, and it plays a crucial role in the global climate system (Aouissi et al. 2016). In the current calculation methods for ET₀ (Lhomme 1997), 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. 2015) and is widely used in the field of hydrometeorology (Penman 1948; Hao et al. 2013).

Climate change has profoundly affected the ecohydrology models of basins and has caused a series of problems about water resources (Xu et al. 2013). In arid and semiarid areas, small changes in climate factors have had significant impacts on hydrological processes (Ti et al. 2018). As a key parameter of the hydrological cycle, analyzing the sensitivity of ET₀ to climate variables is an important research topic that has attracted attention in the hydrological field in recent years (Bormann 2010).

Zhao et al. (2014) showed that the wind speed (WS) has the greatest impact on ET₀ on the Qinghai-Tibet Plateau. Zhao et al. (2015) believed that the influence of relative humidity (RH) on ET₀ is most significant in the Heihe River Basin. Research by Yang et al. (2013) on the Huang-Huai-Hai Plain showed that ET₀ 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. (2014) believed that NSR is the most sensitive meteorological factor to ET₀ in the Tao River Basin. Studies by Lian & Huang (2016) in an oasis-desert region during a growing season showed that selecting extreme pixels or edges can achieve reasonable estimates of ET₀ and that validation of remote sensing models is necessary. Zheng & Wang (2015) used a global sensitivity analysis method to study the sensitivities of ET₀ 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. (2015) in the West Liao River Basin indicated that the T increased significantly, while WS, NSR and RH decreased remarkably. ET₀ is most sensitive to NSR and RH and is least sensitive to the average temperature. Liu et al. (2014) selected Beijing as a study area to investigate the effects of climate change on ET₀. The results showed that the T was the most key factor for ET₀ change, followed by RH and WS, and the T_min and T_max were less sensitive factors.

The hydro-geomorphological pattern of the mountain-basin system in the Shiyang River Basin (SYRB) is unique, and the hydro-geomorphological and geo-ecological patterns are quite different. The SYRB is representative of the inland river basins in China. Over the past half century, the hydrological processes of the SYRB have changed dramatically, resulting in several hydrological and ecological problems (Wang et al. 2012) that seriously threaten the sustainable development of the ecosystems in the basin. It is urgent and important to analyze the sensitivity of evapotranspiration (ET) to climatic factors under the background of climate change, qualitatively and quantitatively study the mechanism and extent of climate change affecting ET₀, and determine the causes of ET₀ changes and the characteristics of its response to climate change in the SYRB.

Few studies have performed sensitivity analyses of climatic factors and ET₀ in the SYRB, and few time series are available. Based on the hydrometeorological observation series in the SYRB and neighboring stations, the P-M model was used to evaluate ET₀ and combined the results with the Beven (Beven 1979) sensitivity method to perform an analysis of the sensitivities of ET₀ to key climatic factors, including T_max,T_min, WS, RH and NSR. Based on the spatial and temporal distributions of the sensitivity coefficients (SCs) and the change characteristics, the relationships between ET₀ and key climate elements determined the causes of ET₀ changes and their responses to climate change in the SYRB during 1981–2015 were explored. This research is of great importance both in theory and practice for thorough comprehension for climate change impacting on the hydrological cycle and providing scientific support for the planning and efficient use of water resources, ecological environment protection and sustainable development.

The SYRB is located to the east of the Hexi Corridor in Gansu Province, has a total area of 41,600 km² and is geographically located from 101°22′ to 104°14′ E and from 36°57′ to 39°27′ N (Figure 1). The topography is high in the south and low in the north. The Yellow River Basin and Heihe River Basin are located to the southeast and southwest of the SYRB, respectively, while the Tengger Desert lies to the northwest, and the Badan Jaran Desert lies to the northeast. The elevation in the SYRB decreases from upstream to downstream from 5,130 to 1,263 m. The total annual precipitation (P) in the area ranges from 110 to 530 mm, and the annual average temperature ranges from 0 to 9 °C. The northern Qilian Mountains in the upper reaches have a semiarid climate in a cold temperate zone and include the catchment areas of eight major tributaries. The middle and lower reaches of the plain, which mainly include the Wuwei Basin and Yongchang Basin in the middle reaches and the Minqin Basin in the lower reaches, have a warm temperate arid climate, and the terrain is relatively flat.

The hydrometeorological observation sequences from five reference meteorological stations (Minqin, Jinchang, Wuwei, Gulang and Yongchang) in the SYRB from 1981 to 2015 were collected and assembled. The data are from the China Meteorological Data Service Center (http://data.cma.cn/).

Figure 2 shows the variations of T_max, T_min, WS, RH, NSR and ET₀ during 1981–2015. The results show that the values of T_max, T_min, NSR and ET₀ in the middle and lower reaches were higher than that in the upper mountainous reaches; T_max and T_min fluctuated significantly in the middle and lower reaches; the oasis areas are greatly affected by human activities, with low vegetation coverage and more sensitive to climate change. Therefore, the fluctuation of temperature is relatively significant. The multiyear average values of T_max in mountainous and oasis areas are 0.16 and 9.95 °C, respectively, while the average values of T_min are −0.08 and 0.52 °C, respectively. WS fluctuated more significantly in the upper mountainous with the multiyear average value of 4.86 m/s. Temperature may be related to the complex terrain, the diversity of vegetation and the great difference of the vertical zone of the underlying surface of the upper mountain area. NSR and ET₀ fluctuated largely in both two regions. The multiyear average values of ET₀ in the mountainous and oasis areas are 684.46 and 894.71 mm, respectively. Since 2003, the ET₀ in the middle and lower reaches of the river has been rising significantly. The increase of T and WS is the possible reason. In addition, the vegetation state has also improved with the implementation of the regulation plan of Shiyang River, and the enhancement of vegetation dynamics promotes the increase of ET, thus leading to a certain increase in ET.

The analysis of change magnitude and trend based on SS for ET₀ and the five key climatic factors in the mountainous area and the oasis plains are shown in Table 1. The increasing trends in ET₀ were significant in both regions, with increases of 5.61 and 28.01 mm/10 a in the mountain and plains, respectively. In contrast to the decrease in RH in the middle and lower reaches, all of the other factors showed increasing trends. The increase in NSR in the upper reaches was 3.30 (MJ/m²/d)/10 a, followed by RH with an increase of 0.33/10 a; T_max, T_min and WS had small variations of 0.01 °C/10 a, 0.01 °C/10 a and 0.01 (m/s)/10 a, respectively. The NSR in the middle and lower plains increased at a rate of 11.48 (MJ/m²/d)/10 a, RH decreased at a rate of 0.91/10 a, and T_max, T_min and WS increased at rates of 0.29 °C/10 a, 0.45 °C/10 a and 0.01 (m/s)/10 a, respectively. Overall, the variabilities in ET₀ and the meteorological elements were higher in the middle and lower plains, and lower in the upstream area. The climate conditions in the oasis plains had higher variabilities than those in the upstream mountains, and the impacts on ET₀ were also more significant.

Huo et al. (2013) showed that T, P and RH increased, while WS decreased in arid areas of China. The research of Yang et al. (2013) on the Huang-Huai-Hai Plain showed that T has increased, but NSR, RH and WS have decreased. These results are different from the conclusion of this study. In comparison, all of the regions show increasing T, which is consistent with global changes. Other factors have different variation characteristics, which are mainly related to the different climatic zones, underlying surface conditions, elevations, research periods and statistical methods used.

The absolute values of the SCs indicate the degree of sensitivity of ET₀ to each meteorological factor, therefore, the analysis of the degrees of sensitivity is based on the absolute value of each sensitivity factor. Figure 3(a) and 3(b) shows the annual distributions of the monthly SCs in the mountainous regions and the middle-lower plains in the SYRB. The statistical results of the seasonal SCs of ET₀ to the climate elements are shown in Table 2. The results show that the SCs of ET₀ to WS and NSR were positive for the entire year, and the SC for RH was negative, indicating that ET₀ increased with increases in WS and NSR and decreased with an increase in RH. The SCs of ET₀ to T_max, T_min and NSR showed increasing trends first and then decreasing trends, where the maximum occurred in July and August, and the minimum occurred in December and January. The SC for WS first decreased and then increased; the values were the highest in December and the smallest in July and August. The maximum values of RH in the mountainous area and the plains occurred in January and April, respectively, and the minimum values occurred in September and January, respectively. On a seasonal scale, the effects of NSR and RH on ET₀ were dominant throughout the year; 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, ET₀ still increased as the T increased.

Figure 4 shows the spatial distributions of the multiyear averaged SCs of ET₀ to each climate factor. The spatial distributions show that the SCs had obvious zonal characteristics. The SCs for T_max and WS increased from the upstream to the downstream regions, with the value of T_max range from 0.11 to 0.36 and WS range from 0.19 to 0.38 in the study area. The SC for T_min was relatively small, and the range was between −0.09 and −0.01. The RH SC ranged from −1.50 to −0.49; the highest absolute values were located in the southeastern mountainous areas, and the lowest values were distributed across the Wuwei Basin in the middle reaches. The SCs for the NSR ranged from 0.32 to 0.63, with the higher values in the upper reaches and the lower values in the northern part of the Minqin Basin. Based on the values of the five SCs, there was a significant difference in the sensitivity of ET₀ to each meteorological factor. The order of the absolute values of the SCs was as follows: RH > NSR > WS > T_max > T_min.

The SCs of the meteorological elements in the upper mountainous regions and the middle-lower plains of the basin were determined separately. The SCs of WS, T_max and T_min were all higher in the plains than in the mountains, indicating that the sensitivity of ET₀ to those three factors was lower in the upper mountains. These differences may be related to the latitudes, elevations and the underlying surface conditions of the two regions.

The research of Zhao et al. (2014) in the Loess Plateau showed that ET₀ was most sensitive to WS, followed by NSR. Huo et al. (2013) concluded that ET₀ is more sensitive to WS and RH in arid areas of China. The analysis of ET₀ and various climatic factors in the Heihe River Basin by Zhao et al. (2015) showed that ET₀ has the highest SC to RH, followed by WS, and the spatial differences in the degree of sensitivity are significant. The climate factors with the highest ET₀ SCs in the SYRB are WS, NSR and RH, which is consistent with previous results. These results show that ET₀ is more sensitive to changes in WS, NSR and RH in arid and semiarid regions of China and that ET₀ is more prone to significant fluctuations due to changes in these three climatic factors.

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 −0.006/10 a and −0.013/10 a in the upper and middle-lower 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 −0.010/10 a, respectively.

A comparison of the two regions shows that the sensitivities of ET₀ to WS, RH and NSR in the middle-lower reaches of the plain were more significant, indicating that ET₀ 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.

The previous analysis showed that although the T_min SC was negative, the change in ET₀ 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 ET₀ 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 ET₀, 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 ET₀ were higher in the middle and lower plains than in the upstream mountains, which validated that ET₀ 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 ET₀ in the upper region to some extent, while the decreasing RH in the middle and lower reaches made ET₀ increase.

In general, the increases in T and NSR were the main reasons for the increase in ET₀ in the SYRB. The increase in RH in the upper reaches weakened the increase in ET₀, while it accelerated the increase in ET₀ in the middle and lower reaches.

Yang et al. (2014) believed that NSR and T together resulted in the increase of ET₀ in the Taohe River Basin and that T contributed more than NSR. The increase of ET₀ in the SYRB is mainly attributed to T, RH and NSR, and the increase of T is the main reason. This phenomenon suggests that ET₀ in the two basins is greatly affected by climate warming. The contribution of RH to ET₀ in the SYRB is higher than that in the Taohe River Basin, mainly because of the high SC of ET₀ to RH and the larger range of RH in the SYRB. The change in ET₀ is affected not only by the SCs of the climatic factors but is also closely related to the change of each factor itself. This also indicates that ET₀ in arid regions is more susceptible to the restriction of air humidity conditions.

P is scarce in the middle and lower reaches of the arid inland river basin, and it is difficult to form surface runoff to effectively recharge groundwater. The water system in the upstream mountainous area is well developed, groundwater is discharged, and the surface water is collected near the outlet, which constitutes the total available water resources of the mountain-basin system. Currently, the exploitation and utilization of water resources in oasis areas is high, the circulation and transformation patterns of the surface water and groundwater have changed, and the natural hydrological process has been changed significantly by artificial systems. The current hydrological processes in the SYRB have been affected by human activities. This paper only discussed the impact of climate factors on ET₀ without considering human activities. However, the planting structure, irrigation methods, water conservancy projects and comprehensive management measures in river basins all have impacts on the various elements of the hydrological cycle. The relationship between ET₀ and human activities needs to be explored in future studies.

ET₀ in the SYRB was estimated by the P-M equation in this paper. The SCs of ET₀ to T_max, T_min, WS, RH and NSR were calculated based on the Beven sensitivity calculation method. SS was used to analyze the amplitude and spatial–temporal characteristics of the SC for each element in the SYRB during 1981–2015. The following conclusions were obtained:

On the annual scale, the sensitivities of ET₀ to each meteorological factor were in the following order: RH > NSR > WS > T_max > T_min. The effects of NSR and RH on ET₀ were dominant throughout the year on the seasonal scale. T_min was the least sensitive in the spring and summer, and T_max was the lowest in the autumn and winter.

The SCs of T_max and WS increased from upstream to downstream; the highest value of the RH SC was located in the mountainous areas southeast of the basin, and the lowest value was distributed in the Wuwei Basin in the middle reaches. The SC of the NSR in the mountainous region had the highest value, while that in the northern part of the lower Minqin Basin was smaller. In general, the SCs of ET₀ to each climatic factor in the upper mountains showed increasing trends, while those of T_max, T_min, WS and RH in the middle and lower plains increased and NSR decreased.

ET₀ had an increasing trend during the study period. The contributions of T, RH and NSR to the change in ET₀ were dominant. The increases in T and NSR were the main reasons for the increase in ET₀.

This work was supported by the National Key Research and Development Program of China (2017YFC0404701), National Key Research and Development Program during the 13th Five-Year Plan, Ministry of Science and Technology, PRC (2016YFA0601500) and Innovation Project of Guangxi Graduate Education (YCBZ2018023).

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