## 2 Data and Methodology
### Methodology
#### 2.3.3 Attribution Method  
We used the residual trend method [15] to identify vegetation changes disturbed by climate factors and anthropogenic activities as they affect ET and GPP. The residual trend method is a pixel-wise operation based on the positive correlation between the LAI and precipitation in ecosystems. To carry out the residual trend method, the regression equation (Equation (20) was used to compute the pixel-by-pixel predicted LAI for every year. Then, Equations (21) and (22) were, respectively, used to estimate the slope and intercept of the curve. The intercept of the regression represents the theoretical LAI when rainfall is zero. The predicted LAI highlights the climatic impacts on the LAI. However, the observed LAI is indicative of the impacts of both humans and the climate on the LAI. The residual LAI was obtained by subtracting the observed LAI from the predicted LAI. \[y=X{\overset{\wedge}{\beta}}+b \tag{20}\] \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Model** & **Parameter** & **ENF** & **EBF** & **DNF** & **DBF** & **MF** & **SHR** & **GRA** & **CRO** & **CNV** \\ \hline ET & \(g_{xx}\) & 0.005 & 0.003 & 0.005 & 0.005 & 0.006 & 0.005 & 0.008 & 0.009 & 0.009 \\ LUE & \(\varepsilon\) & 1.43 & 0.75 & 1.31 & 1.30 & 1.34 & 1.18 & 1.21 & 2.69 & 2.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimized parameter values for different land cover types. \[\dot{\beta}=\frac{n(\sum Xy)-(\sum X)(\sum y)}{n\sum X^{2}-(\sum X)^{2}} \tag{21}\]  
\[c=\overline{y}-\dot{\beta}\overline{X} \tag{22}\]  
where \(y\) is the dependent variable; \(X\) is the independent variable; \(\dot{\beta}\) is the slope of the regression; and \(c\) is the intercept. This involved first dividing the actual LAI into three components: the LAIC induced by climate, the LAIH disturbed by human activities, and a negligible residual. Variations in vegetation due to human activities were characterized by the actual LAI minus LAIC [6]. Then, we used ridge regression to identify the contributions of climatic factors and anthropogenic activities to variations in ET and GPP. The regression function can generally be described as Equation (20), and the least square method can be used to estimate the regression coefficient \(\dot{\beta}\); see Equation (23). \[\dot{\beta}=(X^{\prime}X)^{-1}X^{\prime}y \tag{23}\]  
The interactions between climatic and human activity factors can generate multi-collinearity effects, which can result in \(X^{\prime}\!X\approx 0\). Then, the variance of the unbiased estimate will be large, leading to unstable estimation. Ridge regression can add a small disturbance \(\lambda I\) to the least square function to address the situation wherein the generalized inverse value cannot be found (Equation (24)). \[\dot{\beta}(k)=(X^{\prime}X+\lambda I)^{-1}X^{\prime}y \tag{24}\]  
Ridge regression has been proven to be a useful resolution to eliminate collinearity effects among independent variables [10]. This is a roughly four-step process. 1. Each driving variable is normalized to avoid the influence of units and values. 2. The standard ridge regression coefficients of ET and GPP to each variable are obtained. 3. The standard ridge regression coefficient and trends of variables are combined to calculate the contributions of each driving factor: \[\eta_{ci}=a_{i}\cdot X_{is\_trend}\] (25) where \(i\) is the number of driving factors, \(\eta_{ci}\) denotes the contributions of the normalized driving factor to the normalized trend of ET or GPP, and \(X_{is\_trend}\) denotes the trend of the normalized driving factor. 4.