## 3 Study Area and Methodologies
### Methodologies
#### 3.2.7 Exploratory Spatial Data Analysis (ESDA)  
ESDA is usually used to reveal the spatial structure and correlation of attribute values [75], mainly including global spatial autocorrelation (GSA) and local spatial autocorrelation (LSA). In order to avoid large differences in ESV caused by the different sizes of grid cells at the edge of Putian City, this study used the ESV intensity (the ratio of ESV to the area of each grid) for spatial autocorrelation analysis.  
GSA can reveal the overall agglomeration of the study area, and the global Moran's \(I\) index is used to measure and test the global autocorrelation of the ESV intensity in Putian City at 1 km \(\times\) 1 km grid scale. The equation is as follows:  
\[I_{g}=\frac{n\sum\limits_{i=1}^{n}\sum\limits_{i=1}^{n}w_{ij}(x_{i}-\overline{ x})\big{(}x_{j}-\overline{x}\big{)}}{\sum\limits_{i=1}^{n}\big{(}x_{i}- \overline{x}\big{)}\sum\limits_{i=1}^{n}\sum\limits_{j=1}^{n}w_{ij}} \tag{5}\]  
where \(I_{g}\) represents the global autocorrelation index, with a value range from \(-1\) to \(1\); \(n\) is the grid number (4296 grid cells in total in Putian City); \(x_{i}\) and \(x_{j}\) represent the attribute values of the \(i\)-th grid and the \(j\)-th grid, respectively; \(\overline{x}\) is the attribute mean; and \(W_{ij}\) is the spatial weight matrix.  
When the \(I_{g}\) value approaches 1, it indicates that the index has a clustering pattern, that is, the ESV intensity has a positive spatial correlation; when the \(I_{g}\) value approaches \(-1\), it indicates that the indicator has a dispersion mode, that is, the ESV intensity has a spatial negative correlation; when the \(I_{g}\) value is equal to 0, it means that the indicator has a random pattern, that is, there is no spatial correlation of ESV intensity.  
LSA can be used to test whether there is a clustering phenomenon between grid cells and the surrounding grid cells in space or not, analyze the clustering and differentiation characteristics of spatial elements, and reveal the local clustering characteristics of spatial cell attributes. The LISA distribution map was drawn on the basis of the z-test (\(p<0.05\)). The equation is as follows:  
\[I_{l}=z_{i}\sum\
olimits_{j}\ w_{ij}z_{j},z_{i}=\frac{n(x_{i}-\overline{x})^{ 2}}{\sum\
olimits_{i}\ (x_{i}-\overline{x})},z_{j}=x_{j}-\overline{x} \tag{6}\]  
where \(zi\) and \(z_{j}\) are the standardization of attribute values for the \(i\)-th grid and the \(j\)-th grid, respectively.  
If the \(I_{l}\) value is positive, it indicates that there are clusters with similar attributes between the two grids, including high-high clustering (\(HH\), indicating that the ESV intensity of the grid and adjacent grids is high) and low-low clustering (\(LL\), indicating that the ESV intensity of the grid and adjacent grids is low); If the \(I_{l}\) value is negative, it indicates that there are clusters with opposite attributes between the two grids, including high-low clustering (\(HL\), indicating that ESV intensity of the grid is relatively high, and the ESV intensity of the neighboring grid is low) and low-high clustering (\(LH\), indicating that the ESV intensity of the grid is low, but the ESV intensity of the surrounding grid is high).  
\begin{table}
\begin{tabular}{c c c c} \hline
**EEH** & **Coordination Type** & **EEH** & **Coordination Type** \\ \hline \(0.8\leq EEH<1\) & High coordination area & \(-0.2\leq EEH<0\) & Transition area from coordination to conflict \\ \(0.6\leq EEH<0.8\) & Relatively high coordination area & \(-0.4\leq EEH<-0.2\) & Low conflict area \\ \(0.4\leq EEH<0.5\) & Moderate coordination area & \(-0.6\leq EEH<-0.4\) & Moderate conflict area \\ \(0.2\leq EEH<0.4\) & Low coordination area & \(-0.8\leq EEH<-0.6\) & Relatively high conflict area \\ \(0\leq EEH<0.2\) & Potential crisis area & \(EEH<-0.8\) & High conflict area \\ \hline \end{tabular} Sources: Cited from the literature [38].  
\end{table}
Table 3: The classification of _EEH_.