## 3 Results  
### Spatiotemporal Changes of EQI in Urban Agglomerations  
Figure 3 presents the grading results of the Ecological Quality Index (EQI) spatial pattern distribution in urban agglomerations of Beijing-Tianjin-Hebei (BTH), the core region of the Yangtze River Delta (CYRD), and the Pearl River Delta (PRD). In general, the spatial and temporal distribution of ecological quality in three urban agglomerations align with previous studies [90; 91], showcasing highly significant changes in EQI. Across all three, there is a consistent decrease in overall EQI as latitude rises. Pixels with higher EQI are primarily concentrated in the northeastern and southern regions of BTH and CYRD, respectively (Figure 3a,e). For PRD, the statistical distribution pattern reveals a centralization of low values with dispersed high values (Figure 3i). The observed leftward shift in the highest proportion of EQI value range indicates a deterioration in the overall ecological quality of BTH and CYRD (Figure 3c,f). The polarization trend in PRD was more pronounced evidenced by the spread of EQI towards both high and low ends. Regarding the intersection area between EQI bars in 2001 and 2020, regions with higher EQI above 0.7 in BTH and CYRD exhibited little ecological change, while that of PRD increased noticeably (Figure 3c,f,i).  
Figure 3: The spatial and statistical patterns of EQI in urban agglomerations. (**a–c**) Spatial distribution, histogram distribution, and fitted kernel density curves of EQI for BTH in 2001 and 2020. (**d–f**) Spatial and statistical distribution of EQI of CYRD in 2001 and 2020. (**g–i**) PRD.  
Table 4 quantitatively showed the changes of EQI with different levels. We found that BTH and CYRD witnessed the transformation from the pixels with \"Excellent\" and \"Good\" towards to the pixels with moderate EQI. The pixels with \"Moderate\" EQI increased 34.8%, and 151.6%, respectively for BTH and CYRD, making the ratio of \"Moderate\" pixels rise to 50.61% and 31.52%, respectively. As for PRD, the pixels with \"Excellent\" EQI and \"Poor\" EQI both increased, however the \"Excellent\" pixels account for the greatest proportion for both 2001 and 2020.  
Figure 4 presents a chord chart illustrating the EQI changes among different EQI grades, while Table 5 provides the transition matrix within each EQI grade. It is observed that the EQI grade covering the largest area continuously improves from BTH to CYRD and PRD (Figure 4a-c). The conversion of EQI grades primarily occurs between adjacent grades, with CYRD having the lowest proportion exceeding 89%. Notably, BTH and CYRD predominantly exhibit transitions from \"Good\" to \"Moderate\" and from \"Moderate\" to \"Poor,\" respectively (Figure 4a,b). This phenomenon is correlated with the urbanization level of ecologically deteriorated areas. In Figure 4 and Table 5, the main ecological deterioration pathways of BTH and CYRD are \"Good-Moderate\" with the ratio at 43.7% and 46.3%, while \"Moderate-Poor\" occupied the maximum conversion area of ecological deterioration with 3100 km\({}^{2}\) (Table 5). The ratio of EQI degradation area to EQI improvement area in CYRD is 3.6 times and 6.9 times that of the BTH and PRD.