## 2 Study Area and Data Sources
### Methodology
#### 2.3.2 Spatial Autocorrelation Analysis  
Spatial autocorrelation is an important indicator for testing whether the ecological environmental quality of an element is related to the ecological environmental quality of its neighboring spaces. Spatial autocorrelation analysis of ecological environmental quality can describe the spatial homogeneity distribution of the ecological environmental quality in a study area. The global spatial autocorrelation index (Global Moran's I) [65] and the local spatial correlation index (Local Moran's I) were used to analyze the spatial correlation of the RCEI [66]. The Global Moran's I (GMI) measures the correlation of the attribute values between neighboring spatial units, with its value ranging from \(-1\) to \(1\). When the absolute value of Moran's I approaches \(1\), it indicates a strong spatial autocorrelation, suggesting that similar values tend to cluster together in space [67; 68]. The mathematical formula for the GMI is shown as Equation (19):  
\[\mathbf{GMI}=\frac{\mathbf{n}\sum_{i=1}^{n}\sum_{j=1}^{m}W_{ij}(\mathbf{x}_{i}-\overline{x} )\big{(}\mathbf{x}_{j}-\overline{x}\big{)}}{\Big{(}\sum_{i=1}^{n}\sum_{j=1}^{m}W_{ ij}\Big{)}\sum_{i=1}^{n}\big{(}\mathbf{x}_{i}-\overline{x}\big{)}^{2}} \tag{19}\]  
where n is the total number of elements, \(\mathbf{x}_{i}\) denotes the ecological quality value of the i position, respectively, \(\overline{x}\) denotes the average value of the ecological quality of all elements in the study area, and \(\mathbf{W}_{ij}\) is the spatial weight. The Local Moran's I (LMI) can effectively capture the correlation between the ecological quality of the grid cells within a study area. Therefore, local spatial autocorrelation analysis is important. In the absence of global spatial autocorrelation, the LMI enables the identification of potentially masked locations exhibiting local spatial autocorrelation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & \multicolumn{3}{c}{**Equation**} \\ \hline \multirow{2}{*}{WET} & \(\mathbf{WET}_{TM}\)=**0.0315\(\rho_{Blue}\)+**0.2012\(\rho_{Green}\)+**0.3102\(\rho_{Red}\)+**0.1594\(\rho_{NIR}\)**-**0.6806\(\rho_{SWIR}\)**0.6109\(\rho_{SWIR}\)**2** & (5) \\  & \(\mathbf{WET}_{OLI}\)=**0.1511\(\rho_{Blue}\)+**0.1973\(\rho_{Green}\)+**0.3283\(\rho_{Red}\)+**0.3407\(\rho_{NIR}\)**-**0.7117\(\rho_{SWIR}\)**0.4559\(\rho_{SWIR}\)**2** & (6) \\ \hline NDVI & \multicolumn{3}{c}{NDVI} \\ \hline \multirow{4}{*}{EVI} & \(\mathbf{NDVI}\)=\((\rho_{NIR}\)+\(\rho_{Red})\) & (7) \\ \cline{2-4}  & \(\mathbf{NDSVI}\)=\((\rho_{SWIR}\)+\(\rho_{Red})\) & (8) \\  & \(\mathbf{NRI}\)=\(\rho_{NIR}\)/\(\rho_{Green}\) & (9) \\  & \(\mathbf{NI}  
Conversely, when global spatial autocorrelation is present, the LMI facilitates the analysis of spatial heterogeneity. Specifically, the LMI computes the local spatial aggregation characteristics of the Regional Comprehensive Ecological Index (RCEI) and visualizes these characteristics in the local spatial context through the Local Spatial Association Indicator (LISA). The mathematical formula for calculating the LMI is shown as Equation (20):  
\[\mathbf{LMI}=\frac{\mathbf{n}(\mathbf{x}_{i}-\overline{\mathbf{x}})\sum_{j=1}^{m}\mathbf{W}_{ij}(\bm {x}_{j}-\overline{\mathbf{x}})}{\sum_{i=1}^{m}\mathbf{(x}_{i}-\overline{\mathbf{x}})^{2}} \tag{20}\]  
In this study, the GMI and LMI indices were calculated using Geo Da software (v.1.22) to assess spatial autocorrelation. Five distinct spatial aggregation patterns were identified as the following: high-high clustering (H-H), low-low clustering (L-L), low-high outlier (L-H), high-low outlier (H-L), and insignificant. Specifically, H-H indicates that both the selected area and its neighboring areas exhibit high ecological quality values. Conversely, L-L indicates low ecological quality values for both the selected area and its neighboring spaces. L-H denotes that the ecological quality of the selected area is low while its neighboring areas possess high ecological quality.