## 3 Methods
### Ecosystem Service Function Evaluation Method  
The data used for ecosystem function evaluation indicators include Sentinel-2 data, Esri 10m resolution land use type data, GBIF species distribution data, 30m Global Fine Surface Cover Product, ERA-5 precipitation data, and HWSD V1.2 soil data. In the ecosystem function assessment, four core indicators are selected: biodiversity maintenance, carbon sequestration, water conservation, and soil and water conservation. For the evaluation of biodiversity maintenance, a comprehensive biodiversity maintenance index is used as the evaluation metric. First, the habitat irreplaceability index of the study area is calculated using the Marxan2.43 site selection model, and the protection priority and habitat irreplaceability index of each region are obtained through iterative calculations based on constraint conditions. The habitat irreplaceability index ranges from 0 to 100. By dividing this index by 100, it is normalized to a 0-1 scale. The final comprehensive biodiversity maintenance index is then obtained by adding the normalized habitat irreplaceability index to the biodiversity index. The objective function for the iterative calculation in the Marxan model is expressed as follows:  
\[\text{F}=\sum_{\text{PUs}}Cost+BLM\sum_{\text{PUs}}Boundary+\sum_{ConValue} SPF+CostTherSholdPenalty(t) \tag{10}\]  
In the formula, F is the overall objective function; \(\sum_{\text{PUs}}Cost\) represents the total cost of the planning units; \(BLM\sum_{\text{PUs}}Boundary\) denotes the total length correction value of the protected area boundary; \(\sum_{ConValue} SPF\) refers to the compensation value for protection goals that have not been met; and \(CostThreeSholdPenalty(t)\) indicates the penalty value for exceeding the cost threshold. For carbon sequestration evaluation, autotrophic respiration is used as the evaluation indicator. Autotrophic respiration is the difference between gross primary productivity (GPP) and net primary productivity (NPP). This study calculates GPP and NPP using the VPM model and the CASA model, respectively. For water conservation assessment, the amount of water conservation is selected as the key evaluation indicator. The water conservation capacity is estimated using the precipitation storage method. The runoff coefficient is determined based on studies that establish a relationship between vegetation coverage (FVC) and runoff coefficient. A polynomial fitting approach is applied to derive the corresponding equation for calculating both the bare land precipitation runoff coefficient and the ecosystem precipitation runoff coefficient. The formula is  
\[TQ=J_{0}\times K\times(R_{0}-R_{g}) \tag{11}\] \begin{table}
\begin{tabular}{c c c c c c} \hline
**Level** & **Excellent** & **Good** & **Medium** & **Low** & **Poor** \\ \hline Ecosystem Quality & EQI \(\geq\) 75 & 55 \(\leq\) EQI \(<\) 75 & 35 \(\leq\) EQI \(<\) 55 & 20 \(\leq\) EQI \(<\) 35 & EQI \(<\) 20 \\ \hline \end{tabular}
\end{table} 
Table 2: Ecosystem quality classification. In the formula, \(TQ\) is the water conservation capacity; \(J_{0}\) is the annual precipitation; \(K\) is the ratio of runoff-producing rainfall to total precipitation; \(R_{0}\) is the runoff coefficient for bare land; and \(R_{g}\) is the runoff coefficient for the ecosystem. For soil and water conservation evaluation, the modified Universal Soil Loss Equation (RUSLE) is used to calculate the soil and water conservation capacity. The driving parameters of this model include the rainfall erosivity factor, soil erodibility factor, slope length and steepness factor, vegetation cover and management factor, and conservation practice factor. These parameters are easily accessible and convenient to apply, offering reliable simulation results, which makes the model well suited for the study area.