## 2 Materials and Methods
### Driving Variables of ES Coordination
#### 2.6.2 Effects of Driving Variables on Coordination via Geo-Detector Model  
The geo-detector model (GDM) can help identify the most influential factors or variables that contribute to specific spatial patterns, and reveal how different factors interact in a spatial context. It offers insights into the potential effects of human activities on ecosystems, water resources, or air quality. In this study, we employed the GDM to assess the spatial correlation between the explanatory variables and the dependent variables through spatial variance analysis (SVA) [73; 74]. The GDM is a valuable analytical tool to identify and quantify the spatial associations between driving factors and specific outcomes. This insight can guide decision making by highlighting where interventions or ecological resource allocation should be focused for maximum impact. By employing statistical and spatial analytical techniques, the GDM enables researchers to identify dominant driving factors and their interactive effects, as well as explore spatial patterns and trends in complex geographical processes [75]. The fundamental assumption of the GDM is as follows: if an independent variable X significantly affects a dependent variable Y, then the spatial distributions of X and Y should exhibit similarity. SVA is used to compare the spatial consistency between the dependent variable and independent variables. Based on this comparison, the interpretation of independent variables in relation to the dependent variable can be quantified.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variable** & **Code** & **Description** & **Unit** \\ \hline Elevation & DEM & Derived from the SRTM3 global digital elevation model & Meter \\ Slope & SLOPE & Derived from the SRTM3 global digital elevation model & Degree \\ Precipitation & PRE & Annual trends of precipitation for the period 1956–2017 & mm \\ Temperature & TEM & Annual trends of temperature for the period 1956–2017 & \({}^{\circ}\)C \\ Normalized Difference & NDVI & Vegetation cover & \% \\ Vegetation Index & & & \\ Cropland & CROP & County land area that is occupied by area that is & \% \\  & & classified as cropland & \\ Forestland & FOREST & County land area that is occupied by area that is & \% \\  & & classified as forest & \\ Grassland & GRASS & County land area that is occupied by area that is & \% \\  & & classified as grassland & \\ Construction land & CON & County land area that is occupied by area that is & \% \\ Population & POP & Annual total population & person \\ Economic level & GDP & Gross domestic product & yuan \\ Urbanization rate & URBAN & Urban population proportion & \% \\ Distance to the nearest county & COUNTY & Distance to the nearest county center & km \\ \hline \hline \end{tabular}
\end{table}
Table 3: Details of the driving variables for coupling coordination between ESSI and ESDI in this study.  
The spatial distribution hierarchy of ESDI was weaker compared to ESSI (Figure 4). In both 2000 and 2020, ESDI displayed spatial distribution characteristics with higher values in the central areas and lower values in the outer areas of the study area, which closely resemble the spatial distribution of construction land. The areas with the highest and higher ESS grades were primarily concentrated in central Shanxi, southeastern areas, and the northern plains, indicating a relatively concentrated distribution. The areas with the lowest demand were contiguous and distributed in mountainous regions such as Mount Luliang in the west and Mount Taihang in the east. From 2000 to 2020, due to population growth and economic development in the study area, there was a clear increase in ESDI. The number of counties with higher grades of ESS increased, while the counties with the lowest demand decreased. Some areas with medium demand in 2000 shifted to higher demand categories by 2020, indicating a transformation from relatively lower to higher grades. Overall, the spatial distribution of ESDI displayed noticeable differences between the outskirts and the middle regions of the study area.