## 3 Methods
### Change Vector Analysis (CVA)  
The method assumes that the images at two different time phases can be represented as vectors \(\mathbf{R}\) and \(\mathbf{T}\), respectively. It quantifies the degree of change by calculating the difference vector between \(\mathbf{R}\) and \(\mathbf{T}\). A threshold value is then used to filter out regions where changes occur between the two phases [22]. \[\mathbf{R}=\left[ \begin{array}{c}r_{1}\\ r_{2}\\ \vdots\\ r_{n}\end{array} \right],\mathbf{T}=\left[ \begin{array}{c}t_{1}\\ t_{2}\\ \vdots\\ t_{n}\end{array} \right] \tag{11}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Year** & **Indicator** & **PC1** & **PC2** & **PC3** & **PC4** \\ \hline \multirow{4}{*}{2002} & NDVI & 0.562 & 0.459 & \(-\)0.541 & \(-\)0.425 \\  & WET & 0.186 & \(-\)0.697 & 0.136 & \(-\)0.679 \\  & NDBSI & \(-\)0.445 & 0.528 & 0.438 & \(-\)0.576 \\  & LST & 0.672 & 0.159 & 0.705 & 0.163 \\ \hline \multirow{4}{*}{2007} & NDVI & 0.59 & 0.379 & \(-\)0.562 & \(-\)0.439 \\  & WET & 0.169 & \(-\)0.707 & 0.211 & \(-\)0.653 \\  & NDBSI & 0.564 & \(-\)0.501 & \(-\)0.226 & 0.616 \\  & LST & \(-\)0.552 & \(-\)0.324 & \(-\)0.767 & \(-\)0.04 \\ \hline \multirow{4}{*}{2012} & NDVI & 0.549 & 0.387 & \(-\)0.559 & \(-\)0.484 \\  & WET & 0.143 & \(-\)0.739 & 0.177 & \(-\)0.632 \\  & NDBSI & 0.514 & \(-\)0.498 & \(-\)0.357 & 0.598 \\  & LST & \(-\)0.642 & \(-\)0.234 & \(-\)0.726 & \(-\)0.0766 \\ \hline \multirow{4}{*}{2017} & NDVI & 0.584 & 0.397 & \(-\)0.551 & \(-\)0.444 \\  & WET & 0.195 & \(-\)0.785 & 0.107 & \(-\)0.578 \\  & NDBSI & \(-\)0.483 & 0.428 & 0.346 & \(-\)0.68 \\  & LST & 0.622 & 0.206 & 0.751 & 0.069 \\ \hline \multirow{4}{*}{2022} & NDVI & 0.562 & 0.401 & \(-\)0.565 & \(-\)0.452 \\  & WET & 0.216 & \(-\)0.776 & 0.127 & \(-\)0.578 \\ \cline{1-1}  & NDBSI & \(-\)0.423 & 0.446 & 0.426 & \(-\)0.663 \\ \cline{1-1}  & LST & 0.677 & 0.195 & 0.695 & 0.145 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculation results of the four indicators of RSEI in the study area. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**RSEI Level** & **Poor ((0,0.2))** & **Fair ((0.2,0.4))** & **Moderate ([0.4,0.6))** & **Good ([0.6,0.8))** & **Excellent ([0.8,1.0])** \\ \hline \multirow{2}{*}{2002 Year} & Area (km\({}^{2}\)) & 9196.26 & 25,544.56 & 18,963.00 & 13,027.19 & 15,637.21 \\  & Pct. (\%) & 11.17 & 31.01 & 23.02 & 15.81 & 18.99 \\ \hline \multirow{2}{*}{2007 Year} & Area (km\({}^{2}\)) & 6213.92 & 19,830.64 & 23,569.50 & 15,811.50 & 16,939.65 \\  & Pct. (\%) & 7.54 & 24.08 & 28.62 & 19.20 & 20.57 \\ \hline \multirow{2}{*}{2012 Year} & Area (km\({}^{2}\)) & 6519.46 & 18,218.97 & 22,170.11 & 16,813.65 & 18,643.03 \\  & Pct. (\%) & 7.92 & 22.12 & 26.92 & 20.41 & 22.63 \\ \hline \multirow{2}{*}{2017 Year} & Area (km\({}^{2}\)) & 7696.82 & 19,154.39 & 18,294.59 & 16,262.18 & 20,957.22 \\  & Pct. (\%) & 9.34 & 23.26 & 22.21 & 19.74 & 25.44 \\ \hline \multirow{2}{*}{2022 Year} & Area (km\({}^{2}\)) & 6316.27 & 16,977.38 & 20,176.02 & 17,115.69 & 21,779.85 \\  & Pct. (\%) & 7.67 & 20.61 & 24.50 & 20.78 & 26.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The changes in ecological quality levels and their corresponding areas in the study area over different years. where \(n\) denotes the indicator number or the RSEI levels. The transformation vector is determined by the following equation. \[\Delta V=\mathbf{R}-\mathbf{T}=\left[ \begin{array}{c}r_{1}-t_{1}\\ r_{2}-t_{2}\\ \vdots\\ r_{n}-t_{n}\end{array} \right] \tag{12}\]  
The magnitude of the change \(|\Delta V|\) can be calculated using Equation (13). The greater the \(|\Delta V|\), the greater the likelihood that the RSEI in the region will change. \[\|\Delta V\|=\left[\left(r_{1}-t_{1}\right)^{2}+\left(r_{2}-t_{3}\right)^{2}+ \cdots+\left(r_{n}-t_{n}\right)^{2}\right]^{\frac{1}{2}} \tag{13}\]  
To identify changes in the metrics, a multi-threshold approach is employed:  
\[CV_{j}(\mathbf{R},\mathbf{T})=\left\{