## 2 Materials and Methods
### Data Analysis  
#### Trending, Detrending Analysis and Standardized AET/GPP/WUE Residual Series  
Ecosystem WUE is defined and calculated as the ratio of GPP (i.e., carbon gain of g C m\({}^{-2}\)) to AET (i.e., water loss mm), \(WUE=\frac{GPP}{AET}\)[73; 74; 75]. Herein, we assessed long-term changes in GPP and WUE for spanning period from 1987 to 2017. The magnitude of these changes was quantified using [PERSON]'s slope estimator [76; 77], while the statistical significance was evaluated utilizing the nonparametric Mann-Kendall (M-K) statistics [78; 79; 80]. It is noteworthy that human activities have contributed to vegetation dynamics (land-use and land-cover change, land reclamation, overgrazing, afforestation, deforestation, and other anthropogenic factors). As a result, it is hard to distinguish the complex interactions between vegetation dynamics and influence factors (anthropogenic factors and climate variables) [81; 82; 83]. There are widely used methods to compute detrending analysis that can be classified into three categories: the regression model-based method, the biophysical model-based method, and the residual trend-based method for examining climate-human interactions in vegetation dynamics [84]. Based on the residual trend, the human activities' effects are removed to detect the climate elements' impacts (correlations) independently, calculated by the residuals of the vegetation trend models by computing the detrended analysis [37; 85; 86]. Since the GPP series is affected by many variables besides climate factors, often the annual GPP series has a positive trend, specifically in agricultural systems and forests. Thus, the detrending method will help to remove the spurious correlations caused by the human activity-induced long-term trend and accurately detect the correlationsbetween nonstationary time series or the correlations between the interannual variations of these data [85; 87]. In this study, the standardized AET, GPP and WUE series (sAET, sGPP and sWUE), i.e., the standardized detrended anomalies, were obtained from the mean (\(\mu\)) and standard deviation (\(\sigma\)) value of reference between the GPP value and the detrended value for each year separately, during the period 1982-2017 at the pixel scale. The sGPP and sWUE were calculated as follows:  
\[\text{sAET},\text{sGPP},\text{sWUE}=\frac{y_{i}^{(\text{T})}-\mu}{\sigma} \tag{1}\]  
\[y_{i}^{\text{T}}=y_{i}^{0}-y_{i}^{(\text{T})} \tag{2}\]  
where \(y_{i}^{0}\) is the observed value of AET/GPP/WUE for \(i\) year, and \(y_{i}^{(\tau)}\) is the value of the trended AET/GPP/WUE in a separate year. The detrended sAET/sGPP/sWUE series during the period 1982-2017 was calculated for each pixel using the linear regression analysis, ordinary least square method (OLS), which was calculated as the following:  
\[y_{i}^{(\tau)}=\partial+x_{i}\beta \tag{3}\]  
To fit the value of the detrended AET/GPP/WUE in a separate year, we assumed the temporal evolution (\(x_{i}\)) from 1982 to 2017 is an independent variable, and the AET/GPP/WUE series data are dependent variables (\(y^{0}\)):  
\[\beta=\frac{n\times\sum_{i=1}^{n}x_{i}\times y_{i}^{0}-\sum_{i=1}^{n}x_{i} \sum_{i}^{n}y_{i}^{0}}{n\times\sum_{i=1}^{n}x_{i}^{2}-\left(\sum_{i=1}^{n}x_{i }\right)^{2}} \tag{4}\]  
\[\partial=\overline{y}_{n}^{0}-\beta\overline{x}_{n} \tag{5}\]  
where \(n\) is the length of the studied period (\(n=36\)), while \(\beta\) is the slope ratio AET/GPP/WUE (yearly) acquired by the OLS method. \(\beta<0\) indicates that the AET/GPP/WUE tended to decrease over the studied years and vice versa.