Impacts of climate and vegetation on actual evapotranspiration in typical arid mountainous regions using a Budyko-based framework

It is important to understand how actual evapotranspiration (ETa) changes occur and what the dominant contributing factors are. This study investigated the impacts of climatic factor and vegetation coverage on the variations of ETa using a Budyko-based framework. Climatic seasonal index and vegetation coverage index were selected as indicating factors. Two reservoir watersheds, i.e. the Wangkuai Reservoir Watershed and the Xidayang Reservoir Watershed, of the Daqing River Basin were selected as case studies. Also, relationships between the ETa and climatic and vegetation factors were analyzed. Results showed that the improved vegetation conditions positively contributed to the ETa changes, leading to an increase of 42.15 and 58.56 mm of ETa in the two watersheds, while the increasing climate seasonality had a negative effect, resulting in a drop of 11.48 and 13.47 mm of ETa. Vegetation coverage was recognized as the dominant factor to the changes of ETa, compared to the climatic factor. Our research could offer supporting information for water resources management, agricultural production improvement and eco-environment construction in arid regions.


Evapotranspiration (ET) is a crucial component in hydrolo-
gical processes, which could account for up to over 60% of the precipitation on a global scale (Oki & Kanae ) and more than 90% in arid regions (Glenn et al. ). Given that the differences between precipitation and evapotranspiration (ET) have been commonly used to evaluate the water availability at catchment scale (Falkenmark et al. ), it is of vital importance to quantify the actual evapotranspiration (ET a ) and its influencing factors to assist decision making in water resources management and ecological protection.
Although it is often difficult to measure the ET a directly either at field scale or at catchment scale, several ET a quantification methods have been proposed including meteorological ( It has been widely accepted that evapotranspiration (ET) changes with climate variability (Brümmer et   This region has a semi humid continental monsoon climate.

Evapotranspiration data
In this study, MODIS satellite remote sensing data

The Budyko function
The Budyko framework can take a number of mathematical forms. In this study, Fu's function (Fu ) was used to assess the impacts of climatic and vegetation factors on ET a . This function was selected for its simple structure and clear physical meaning with few parameters applied: where P is precipitation; ET p is potential evapotranspiration calculated using the method of Priestley & Taylor (); ω is the water-heat coupling control parameter which is a parameter that represents the vegetation and topography of the river basin, and its value range is [1, þ∞]. The changes in water storage were often ignored at annual scale (Zhao et al. ).

Indices for vegetation and climatic factors
where ∅ is the dryness index, ∅ ¼ ET 0 = P. δ P and δ ET0 are the seasonal amplitudes of P and ET 0 , respectively. They represent the range of precipitation and potential evapotranspiration. S reflects the non-uniformity in the intra-annual distribution of water and energy (Ning et al. ).
According to Fu's formula, when ω → 1, ET → 0. Therefore, the values of M and S are: when ET → 0, vegetation transpiration T → 0, that is, M → 0. Or when runoff R → P, the matching between precipitation and potential evapotranspiration tends to be the worst, that is, S → ∞.
According to the relationship between ω, M and S under extreme conditions, that is, boundary conditions (Ning et al.
In order to verify the performances of the empirical formula, we tested the above formulas by estimating the annual ET of the two watersheds against the MODIS ET measurements combining with the Fu's function (Zhang et al. ).

Attribution analysis to climate and vegetation factors
In order to fully understand the contribution of climatic and vegetation variables to ET changes, contribution analysis was applied in our study. The total differential method is one of the most widely used methods in the attribution of water cycle change. Since ω is the hydrothermal coupling parameter, the contribution of M and S to ET a can be calculated by using Fu's function with the total differential method. The total differential method is actually Taylor's first-order expansion. Based on the complementary relation of elasticity coefficient (Zhou et al. ), the following equation is proposed: Based on algebraic identity derivation, a method for attributing evapotranspiration (runoff) change is proposed: The contribution of precipitation, potential evapotranspiration (ET p ) and water-heat coupling control parameter ω can be expressed as: where α is the weight coefficient, and the value range is [0,1].
The value of α is recommended to be equal to 0.5 in this study.
The semi-empirical formula is used to distinguish the contribution of M and S, after obtaining the relative contributions (RC) of M and S to the change of ω, the contributions of M and S to ET change can be expressed as: RC(M) and RC(S) represent the contribution rate of vegetation coverage and climate seasonal index to ET change, which can be calculated by the following formula: In this study, mean absolute error (MAE), the square root of the mean square error (RMSE) and Nash-Sutcliffe coefficient of efficiency (NSE) were selected to describe the deviation between estimated ET a and measured ET a by the water-heat coupling control parameter ω.
where i represents the time series, n represents the length of the time period, and ET estimated,i and ET measured,i represent the estimated and measured values of the actual evapotranspiration of a basin in a certain year.

Quantification of the climatic and vegetation indices
The annual temperature and precipitation of WRW and XRW showed a rising trend ( Figure 2).  (Table 1 and Figure 3(a)). It can be seen from the ANOVA analysis results that significant differences have been found between the variations of the vegetation cover trends (p < 0.05, F > F-crit, Table 1).

Similar increasing trends
In terms of the climate seasonality index (S), it is shown that a contradictory trend has been found in the two watersheds. In WRW and XRW, the slope of S is 0.02 and -0.001 respectively (Figure 3(b)). For the WRW, the S tends to show an overall upward trend, ranging from 0.06 to 0.   that large significant difference between the S values of the two watersheds have been found (p < 0.01, F > F-crit) ( Table 1).

Validation of the estimated ET a
Based on the Budyko framework, the relationships between the water-heat coupling control parameter ω and the veg-  (Table 3). Therefore, we deduce that Fu's method could be more applicable in estimating actual evapotranspiration in this study.

Attribution of ET a variations to climatic and vegetation factors
The results showed that the ET a presented a significant increasing trend in the two watersheds based on the MODIS ET data ( Figure 5). The ET a of these two watersheds  (13) and (14).  However, the climate seasonality index tends to lead to a decreasing trend of ET a in the two watersheds, with negative contribution rates of 11.48 and 13.47 mm, respectively (Table 4).
According to the results analysis of the contribution, the contribution of precipitation is second only to vegetation (Table 4). The precipitation is more sensitive than other climate factors in this area (Figure 8).

Attribution of actual evapotranspiration in arid regions
In this study we used the observed meteorological data from two reservoir watersheds in DRB. Additionally, we applied the data of climate factor and vegetation coverage to analyze the variation of ET a in WRW and XRW of DRB. The results     Some studies, however, have come to the opposite con-

Uncertainty
There are certain uncertainties in our study, which may come from the uncertainty of methods, data and parameters.
We use the total differential method for attribution analysis under the Budyko framework. The partial derivative coefficients in the total differential method should be calculated by the complete Taylor expansion method so as to obtain accurate results. However, in our study, the partial derivative coefficient is estimated as a first-order approximation. Yang et al. () showed that ignoring the higher-order coefficients of the Taylor expansion would lead to an underestimation of the contribution of climate change to hydrological processes as precipitation increases. And since the R 2 of the semi-empirical formula is less than 0.5, the change of vegetation coverage M and climate seasonal index S cannot fully explain the interannual variation of parameter ω. In this study, we used MODIS datasets to analyze the actual evapotranspiration. Results showed that ET a data of MODIS is slightly higher than the ground-based observed data. This may lead to a higher value for the study of the con- Moreover, a proxy strategy is to choose crops that use less water and are suitable for growing in arid regions. Findings of this study tend to be a reference in exploring the complex climate-vegetation-hydrology relationships in arid mountainous regions.