## 2 Methodology
### Research Method  
#### 2.4.1 Indicator Evaluation Method  
To evaluate the indicator system, we used the linear weighted-sum method to evaluate the comprehensive level of the indicators. The details are shown in Equation (4):  
\[\mathrm{U_{i}}=\sum_{\mathrm{i=1}}^{\mathrm{m}}\sum_{\mathrm{j=1}}^{\mathrm{n}} \omega_{\mathrm{j}}\times y_{\mathrm{ij}} \tag{4}\]  
where \(\mathrm{U_{i}}\) represents the comprehensive value of various indicators in city i, \(\omega_{\mathrm{j}}\) represents the weight of indicator j in the corresponding indicator system, \(y_{\mathrm{ij}}\) represents the normalized value of indicator j in city i, and m and n represent the number of provinces and indicators, respectively. There are subjective weighting methods and objective weighting methods for determining indicator weights. In this study, we combined subjective and objective evaluation and used the entropy method (Equation (1)) and the Analytic Hierarchy Process for comprehensive calculation. The entropy method is an objective weighting method that uses the amount of information provided by the entropy value of an indicator to determine the weight of that indicator, i.e., the lower the information entropy, the higher the weight [46; 47]. However, the entropy method is highly objective and tends to ignore the errors in the data itself, thus deviating from the true situation. The Analytic Hierarchy Process uses the concept of hierarchy to layer the indicators, which are evaluated by relevant experts, so as to obtain the weight value of the evaluation indicators. Nonetheless, the results of subjective methods are prone to bias due to subjective factors [48]. In order to reflect the intrinsic connection between data, we combined subjective evaluation with objective evaluation and used the arithmetic mean to express the indicator weights (Equation (5)), making the evaluation results more accurate and realistic. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**System**} & \multirow{2}{*}{**Service Type**} & \multicolumn{5}{c}{**Ecosystem Service Value (CNY/hm\({}^{-2}\))**} \\  & & **Grassland** & **Woodland** & **Farmland** & **Wettands** & **Water Body** & **Unused Land** \\ \hline \multirow{4}{*}{Regulating services} & Gas regulation & 707.9 & 3097.00 & 515.89 & 1547.10 & 0.00 & 0.00 \\  & Climate regulation & 796.4 & 2389.10 & 569.09 & 14,697.50 & 407.00 & 0.00 \\  & Hydrological regulation & 707.9 & 2831.50 & 533.06 & 13,322.30 & 18,033.20 & 26.50 \\  & Waste treatment & 1159.2 & 1159.20 & 936.56 & 15,625.70 & 16,086.60 & 8.80 \\  & Food production & 265.5 & 88.50 & 267.98 & 257.90 & 88.50 & 8.80 \\  & Raw material & 44.2 & 2300.60 & 301.48 & 60.20 & 8.80 & 0.00 \\  & Soil maintenance & 1725.5 & 3450.90 & 1261.87 & 1469.70 & 8.80 & 17.70 \\  & Biodiversity maintenance & 964.5 & 2884.60 & 652.33 & 2148.80 & 2203.30 & 300.80 \\  & Aesthetic landscapes & 35.4 & 1132.60 & 92.62 & 4770.20 & 3840.20 & 8.80 \\  & Total value & 6406.5 & 19,334.00 & 5130.88 & 53,899.40 & 40,676.40 & 371.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The value of ecological services for each land use type. Equation (5) based on the entropy method is written below:  
\[ \begin{split} Y_{ij}&=\frac{X^{\prime}_{ij}}{\sum_{i=1}^ {m}X^{\prime}_{ij}}\\ H_{j}&=\frac{1}{\ln m}\sum_{i=1}^{m}Y_{ij}\ln Y_{ij} \\ \eta_{j}&=\frac{1}{n-\sum_{i=1}^{n}H_{j}}\end{split}  \tag{5}\]  
where \(X^{\prime}_{ij}\) denotes the standard value of indicator j in the ith province; m and n denote the number of provinces and indicators, respectively; \(Y_{ij}\) denotes the proportion of indicator j in the ith province; \(H_{j}\) denotes the information entropy of indicator j; \(\eta_{j}\) denotes the weight of indicator j (the specific calculated weights are in the 5 th column of Tables 1-3).