## 3 Results
### Local Spatial Autocorrelation for ESD Distribution  
Since global Moran's I is a general statistical indicator, it can show only the average spatial difference in ESD between a grid and its surrounding grid. The local spatial  
Figure 5: The global spatial autocorrelation change in ESD by scale and level distance. Moran’s I analysis computing was performed in 1 ArcGIS Engine node in the Computing Center. characteristics of the study area were concealed to some extent, and the spatial distribution relationship of ESD within the study area could not be fully reflected. Therefore, this paper uses Moran scatter plots and local spatial autocorrelation analysis cluster plots to further analyze the spatial distribution characteristics of ESD in the study area. The Moran scatter plot can be used to express the correlation between the standardized vector ESD (horizontal axis) of the ESD and its spatial lag vector W_ESV (vertical axis). The spatial lag of the ESD of each grid is a weighted average of the ESD of the grid and surrounding grids and is defined by a standardized spatial weighting matrix. In this study, GeoDA was applied to calculate the local spatial autocorrelation of the ESD of the 1 km \(\times\) 1 km grid in 2004, 2010 and 2016, and a Moran scatter plot was obtained, as shown in Figure 6.  
Figure 6 shows that the ESD scatter points in 2004, 2010 and 2016 are mainly distributed in the upper-right and lower-left quadrants, while the scatter points in the lower-right and upper-left quadrants are relatively small. The ESD in the study area had a significant positive spatial correlation, and the distribution of grids with a similar ESD had the characteristics of spatial agglomeration. Among them, the scatter points are concentrated in the lower left, indicating that there was little difference between the low-density grid of ESV; additionally, the scatter points in the upper right are relatively discrete, indicating that the difference between the low-density grid of ESV was relatively large. For 2004-2016, there are an increasing number of outliers in the upper-right and lower-left regions, which shows that in the areas where the ESV density had a high-high concentration and low-low concentration, the difference between the ESD of the grid and the surrounding grid becomes increasingly larger. The lower-right and upper-left regions show little change, indicating that the ESD difference between the grid and its surrounding grid remained stable in the areas where the ESD was staggered. In this study, a local spatial autocorrelation analysis agglomeration map was introduced to analyze the similarity (positive correlation) and difference (negative correlation) in ESD around the grids and their significance. This paper uses the 1 km \(\times\) 1 km scale as an example, as shown in Figures 7 and 8. Figure 7 shows that the high-high-type areas were concentrated in the east and southeast of the study area, a small number of sporadic distributions were in the west, the low-low-type areas were concentrated in the north, and a small number of small blocks were distributed in the middle. The high-low-type area was scattered in the north, and the low-high-type area was scattered in the north. From 2004-2016, the spatial cluster distribution pattern of ESD in the study area changed slightly: the high-high-type areas in the east increased rapidly and were connected with the high-high-type area in the southeast, the high-high-type areas in the southeast were reduced, and some of them were divided into \"island\" by other types. Finally, the low-low-type blocks in the north became increasingly larger. Figure 6: ESD scatter plot. Figure 8 shows that the spatial distribution pattern of the local autocorrelation significance level of the ESD in the study area was similar to that of the autocorrelation type. The local autocorrelation of ESD was not significant in most regions of the study area.