## 3 Materials and Methods
### Index Weight Calculation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Index Hierarchy**} & \multirow{2}{*}{**Index**} & \multirow{2}{*}{**Symbol**} & \multicolumn{2}{c}{**Subjective**} & \multicolumn{1}{c}{**Objective**} & \multicolumn{1}{c}{**Comprehensive**} \\  & & & **Weight** & **Weight** & **Weight** \\ \hline \multirow{5}{*}{**First-level index**} & Indicators of economic development level & \(X_{1}\) & 0.21 & 0.38 & 0.30 \\  & Economic structure index & \(X_{2}\) & 0.55 & 0.24 & 0.38 \\  & Economic efficiency index & \(X_{3}\) & 0.24 & 0.38 & 0.32 \\  & Ecological carbon sequestration index & \(Y_{1}\) & 0.67 & 0.74 & 0.70 \\  & Land-cover index & \(Y_{2}\) & 0.33 & 0.26 & 0.30 \\ \hline \multirow{5}{*}{**Basic-level index**} & Per capita GDP & \(X_{11}\) & 0.25 & 0.23 & 0.24 \\  & Per capita gross industrial product & \(X_{12}\) & 0.50 & 0.57 & 0.54 \\  & Per capita disposable income of urban residents & \(X_{13}\) & 0.25 & 0.20 & 0.22 \\  & Proportion of secondary industry & \(X_{21}\) & 0.23 & 0.39 & 0.33 \\  & Proportion of tertiary industry & \(X_{22}\) & 0.23 & 0.45 & 0.35 \\  & Growth rate of tertiary industry & \(X_{23}\) & 0.40 & 0.13 & 0.25 \\  & GDP growth rate & \(X_{24}\) & 0.14 & 0.03 & 0.07 \\  & GDP energy intensity & \(X_{31}\) & 0.54 & 0.59 & 0.58 \\  & Investment in social fixed assets & \(X_{32}\) & 0.30 & 0.14 & 0.21 \\  & Total retail sales of consumer goods & \(X_{33}\) & 0.16 & 0.27 & 0.21 \\  & NPP & \(Y_{11}\) & 1.00 & 1.00 & 1.00 \\  & NDVI & \(Y_{21}\) & 0.55 & 0.77 & 0.67 \\  & NDBI & \(Y_{22}\) & 0.16 & 0.11 & 0.14 \\  & NDWI & \(Y_{23}\) & 0.29 & 0.12 & 0.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Weights of indices. Among the indicators of economic development level, the weight of per capita industrial GDP was the largest, reaching 54%, followed by 24% for per capita GDP and 22% for urban residents' disposable income. This shows that, among the three indicators affecting the level of economic development, the per capita industrial GDP was more representative and contained more information. Among the four indicators of economic structure, the proportion of the tertiary industry, the proportion of the secondary industry, and the growth rate of the tertiary industry were weighted as 35%, 33%, and 25%, respectively, considerably greater than the GDP growth rate, indicating their great impact on the economic structure. Among economic efficiency indicators, the weight of energy consumption per unit GDP was the largest, reaching 58%, followed by 21% for social fixed assets investment and 21% for total retail sales of social consumption. Among the comprehensive evaluation indicators of urban economy, the indicators of the economic development level, economic structure, and economic efficiency accounted for average weights of 30%, 38%, and 32% respectively. In the comprehensive evaluation index of the ecological environment, the weight of the ecological carbon sequestration index was 70%, and the weight of the land-cover index was 30%. Among the land-cover indicators, the weights of NDVI, NDBI, and NDWI were 67%, 14%, and 19%, respectively. There were some differences in the weight of each index. Among them, the weight of the NDVI index was the highest with a larger amount of information, while the weights of NDBI and NDWI were smaller.