## 3 Results
### Comprehensive Evaluation of Ecological Environmental Quality in Incleng City  
As shown in Table 5, the eigenvalues of the six individual ecological indicators in PC1 reflect the variance contribution of each ecological index in the dataset through principal component analysis (PCA). Specifically, the larger the eigenvalue, the more variance is explained by that principal component. Therefore, these eigenvalues can be used to assess the importance of each principal component in a composite index. In contrast, the eigenvalues of PC2 to PC6 exhibited anomalies in both magnitude and sign. Notably, in PC1, the eigenvalues of the WET, NDVI, and EVI were positive, while those of the NDBSI, LST, and IDCI were negative. As illustrated in Figure 4 and Table 5, this distribution aligns with the observed environmental conditions. Figure 3: Trends in the RCEI and RSEI eigenvalues and contributions. (**a**) Comparison of trends in RCEI and RSEI eigenvalues; (**b**) Comparison of changes in RCEI and RSEI contributions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Date** & **WET** & **NDVI** & **EVI** & **NDBSI** & **LST** & **DI** \\ \hline
1990 & 0.3651 & 0.5251 & 0.3560 & \(-\)0.5081 & \(-\)0.3017 & \(-\)0.3388 \\
1996 & 0.3573 & 0.4635 & 0.0166 & \(-\)0.5468 & \(-\)0.4640 & \(-\)0.3781 \\
2002 & 0.2704 & 0.5437 & 0.2834 & \(-\)0.5907 & \(-\)0.3519 & \(-\)0.3891 \\
2006 & 0.3860 & 0.5092 & 0.0159 & \(-\)0.5498 & \(-\)0.4185 & \(-\)0.3377 \\
2008 & 0.4080 & 0.5462 & 0.0181 & \(-\)0.6164 & \(-\)0.2300 & \(-\)0.3197 \\
2013 & 0.3461 & 0.4953 & 0.3898 & \(-\)0.5347 & \(-\)0.3210 & \(-\)0.3062 \\
2018 & 0.2951 & 0.4992 & 0.3670 & \(-\)0.5438 & \(-\)0.3872 & \(-\)0.2883 \\
2022 & 0.4631 & 0.4847 & 0.3706 & \(-\)0.4958 & \(-\)0.2840 & \(-\)0.2943 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Eigenvalues of six discrete ecological indices in the principal component analysis. The principal component analysis from 1990 to 2022 revealed a positive correlation between the first principal component and key ecological indicators: the NDVI, WET and EVI. The NDVI's substantial contribution to the PC1 loading values underscores the critical role of vegetation cover in the RCEI. Concurrently, increases in the WET reflect heightened soil and vegetation moisture content, while enhancements in the EVI denote improved vegetation health. These trends collectively affirm the positive influence of these indicators on the study area's ecology. In contrast, the NDBSI, LST, and ICDI demonstrated a negative correlation with PC1 load values. Rising NDBSI values suggest escalating desiccation of surface soils and vegetation, elevated LST levels imply an intensifying greenhouse effect, and increased ICDI values signal detrimental coal dust impacts on air quality. These indicators' trajectories highlight their adverse effects on the ecological environment. In essence, the NDVI, WET, and EVI are pivotal in monitoring and evaluating regional ecosystem health, while the NDBSI, LST, and ICDI offer vital insights into ecological degradation. Figure 5 depicts the distribution of the RCEI values across eight temporal snapshots spanning the period from 1990 to 2022 in Jincheng City. Remarkably, during the years 2006, 2008, 2013, and 2022, a subset of RCEI values exceeded the 0.8 threshold, indicating robust ecological conditions. Furthermore, the lower quartile consistently remained above 0.4, while the upper quartile exceeded the 0.6 mark, indicating a generally healthy ecological state. Conversely, the years 1990, 1996, 2002, and 2018 did not exhibit any RCEI values above 0.8, reflecting periods of ecological stress. A longitudinal analysis revealed a discernible degradation in Jincheng City's ecological quality from 1990 to 2002. However, a subsequent rebound was observed from 2006 to 2022, with the exception of a brief dip in 2018, indicating a progressive improvement in the overall ecological environment. Figure 4: Results of the principal component analysis of indicators from 1990 to 2022.