## 2 Materials and Methods
### Determining Drivers for the Coupling Coordination Degree between ES Supply and Demand  
The GDM was utilized to identify the most influential socio-ecological drivers for the coupling coordination between ES supply and demand. The factor detection results for thirteen socio-ecological variables yielded the influencing coefficients (\(q\)-statistic values) and significance levels (\(p\)-values) (Figure 6). In 2000 and 2020, the variables SLOPE, PRE, and COUNTY did not pass the significance tests. Meanwhile, the variable TEM was a statistically significant driving variable (\(p\)-value \(<\) 0.001) in 2000, but its significance level was greater than 0.1 in 2020. Conversely, the variable URBAN was not significant in 2000 (\(p\)-value \(>\) 0.1) but became a significant driving variable in 2020 (\(p\)-value \(<\) 0.05). Figure 6 presents the sorting results for the \(q\)-statistic values for significant variables (\(p\)-value \(\leq\) 0.05), revealing their influencing coefficients on CCD in 2000 and 2020. The influencing coefficients of CON, POP, and GDP were greater than 0.5 and higher than the other factors in both 2000 and 2020. This demonstrates \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & **ESSI** & \multicolumn{2}{c}{**ESDI**} & \multicolumn{2}{c}{**CCD**} \\ \hline
**Year** & **2000** & **2020** & **2000** & **2020** & **2000** & **2020** \\ \hline Minimum value & 0.528 & 0.512 & 0.649 & 0.638 & 0.002 & 0.059 \\ Maximum value & 0.859 & 0.870 & 0.979 & 0.980 & 0.566 & 0.427 \\ Mean value & 0.670 & 0.649 & 0.044 & 0.067 & 0.212 & 0.196 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The statistical values of standardized values of ES supply, ES demand, and coupling coordination degree in 2000 and 2020. Figure 6: Factor-detected results of socio-ecological variables of CCD using GDM in 2000 (**a**) and 2020 (**b**). \"\"\"\" \(p<\) 0.001, \"\"\"\" \(p<\) 0.01, \"\"\"\" \(p<\) 0.05. Panels (**a**) and (**b**) display the prominent influencing factors of CCD in 2000 and 2020, respectively. All factors are organized in descending order based on their influencing coefficients (\(q\)-statistic values). that these variables were the main drivers of the spatial pattern of CCD during both time periods. GRASS, CROP, and DEM were considered sub-high determinate variables based on their \(q\)-statistic values. Notably, the variables TEM, NDVI, and FOREST had weak effects on CCD in 2000, whereas in 2020, the variables URBAN, FOREST, and NDVI had a weak effect. This suggests that the impact of forest coverage on the coordination relationship was relatively small in the study area. Furthermore, the interaction detector module of GDM assessed the influencing coefficients of any two socio-ecological variables (Figure 7) and compared them with their separate influencing coefficients (\(q\)-statistic values). The results reveal two interaction modes of socio-ecological variables on CCD: nonlinear enhancement and mutual enhancement. This indicates that the explanatory power of the interaction between any two variables for CCD is greater than that of any single variable. The interactive effects on CCD between CON and the other variables were the strongest, with \(q\)-statistic values exceeding 0.85. After interacting with POP and GDP in both 2000 and 2020, the \(q\)-statistic values of all variables were above 0.65, which was higher than the values for the separate effects of POP and GDP on CCD. It is important to note that SLOPE, PRE, and COUNTY did not exhibit significant effects on CCD in the single-factor detection results (Figure 6). However, after interacting with CON, POP, and GDP, the influencing coefficients of SLOPE, PRE, and COUNTY were 0.88, 0.67, and 0.68 in 2000, respectively, and similar results were observed in 2020. This suggests that even if individual socio-economic variables do not have a significant effect on the spatial distribution of CCD, they may play a key role via interaction with variables that have high influencing coefficients.