## 2 Materials and Methods
### Method
#### 2.2.2 Trend Analysis and Testing  
Theil-Sen Median trend analysis is a nonparametric statistical method utilized for trend detection, extensively applied in meteorological, hydrological, and vegetation data. A primary advantage of this method is its independence from specific distribution re  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ID** & **Model Name** & **Country** & **Resolution** & **Weights** \\ \hline
1 & AWI-CM-1-1-MR [65] & Germany & \(\sim\)0.9375\({}^{\circ}\)\(\times\) 0.9375\({}^{\circ}\) (-90 km) & 0.0928 \\
2 & BCC-CSM2-MR [66] & China & \(\sim\)1.125\({}^{\circ}\)\(\times\) 1.125\({}^{\circ}\) (-106.9 km) & 0.0427 \\
3 & CAS-ESM2-0 [67] & China & \(\sim\)1.4\({}^{\circ}\)\(\times\) 1.4\({}^{\circ}\) (-132.9 km) & 0.0808 \\
4 & CESM2-[68] & USA & \(\sim\)0.9375\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) (-101.4 km) & 0.0697 \\
5 & CESM2-FV2 [69] & USA & \(\sim\)0.95 \(\times\) 1.25\({}^{\circ}\) (-99.3 km) & 0.0900 \\
6 & CESM2-WACCM [70] & USA & \(\sim\)0.938\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) (-101.4 km) & 0.0912 \\
7 & CMCC-CM2-SR5 [71] & Italy & \(\sim\)0.938\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) (-101.4 km) & 0.0779 \\
8 & CMCC-ESM2 [72] & Italy & \(\sim\)0.938\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) (-101.4 km) & 0.0788 \\
9 & FIO-ESM-2-0 [73] & China & \(\sim\)0.938\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) (-101.4 km) & 0.0865 \\
10 & HadGEM3-GC31-MM [74] & UK & \(\sim\)0.556\({}^{\circ}\)\(\times\) 0.833\({}^{\circ}\) (-70.1 km) & 0.0418 \\
11 & MPI-ESM1-2-HR [75] & Germany & \(\sim\)0.938\({}^{\circ}\)\(\times\) 0.938\({}^{\circ}\) (-90 km) & 0.0361 \\
12 & MRI-ESM2-0 [76] & Japan & \(\sim\)1.125\({}^{\circ}\)\(\times\) 1.125\({}^{\circ}\) (-106.9 km) & 0.0914 \\
13 & NorESM2-MM [77] & Norway & \(\sim\)0.938\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) (-101.4 km) & 0.0353 \\
14 & TaiESM1 [78] & China, Taiwan & \(\sim\)0.938\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) (-101.4 km) & 0.0850 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic information of CMIP6 models and the assigned weights.  
quirements and its resilience to the influence of a small number of outliers [80]. The computational formula is as follows:  
\[\text{slope}=\text{median}\ (\text{Xj}-\text{Xi})/(\text{j}-\text{i})\ (\text{l}< \text{i}<\text{j}<\text{n}) \tag{3}\]  
where Xi and X are the i and j data points in the time series; when slope > 0, it indicates an improving trend in the NDVI time series; when slope < 0, it indicates a degrading trend; and when slope = 0, the NDVI time series remains essentially unchanged. The Mann-Kendall test is employed to assess the significance of Sen's slope estimate results [81; 82], with the test statistic denoted by Z. At the given significance level \(\sigma\), when \(\text{l}\,Z\,\text{l}>1.96\), it indicates that the change trend has passed the 95% significance test. Combining the slope value and \(\text{l}\,Z\,\text{l}\) value, this study categorizes the NDVI change trends in China into five levels: significant decrease (slope \(\leq-0.003/\text{year},\ \text{l}\,Z\,\text{l}>1.96\)), slight decrease (\(-0.003/\text{year}<\text{slope}\leq-0.00005/\text{year},\ \text{l}\,Z\,\text{l}>1.96\)), stable (\(-0.00005/\text{year}<\text{slope}<0.00005/\text{year},\ \text{l}\,Z\,\text{l}>1.96\)), significant increase (slope \(\geq 0.003/\text{year},\ \text{l}\,Z\,\text{l}>1.96\)), and slight increase (\(0.00005/\text{year}\leq\text{slope}<0.003/\text{year},\ \text{l}\,Z\,\text{l}>1.96\)). This classification provides a detailed assessment of vegetation dynamics across the region. In evaluating the long-term trend of NDVI at the spatial scale, this study uses the Theil-Sen Median method combined with significance testing for trend estimation. The trend component is calculated separately for the time series of each pixel. The trend results are visualized spatially using slope values, distinguishing areas with significant increase, no significant change, and significant decrease, thereby revealing the spatial heterogeneity of NDVI changes.