## 2 Materials and Methods
### Data Analyses
#### 2.3.3 Calculation of Ecosystem Services  
Given the need for socio-economic development and environmental protection in the region, we utilized carbon storage, GPP, water conservation, and crop yield for ES estimation. (1) Carbon storage  
Based on land covers and their respective carbon storage [45; 46; 47; 48; 49], a regional multi-ecosystem above-ground carbon stock calculation model was established. The model assumed that the average age of forests in 1988 was 5, 10, 15, 20, 25, and 30 years, respectively, and then calculated the ecosystem carbon storage; subsequently, the data of multiple starting years (six layers per year) were averaged to obtain the ecosystem carbon sequestration from 1988-2019. (2) GPP  
Gross primary production (GPP) was conducted with the concept of light use efficiency (LUE), and vegetation productivity was calculated from the photosynthetically active radiation absorbed by vegetation and LUE [50; 51]. The specific calculation equation is as follows:  
\[GPP=PAR\times FPAR\times\varepsilon_{max}\times TMIN_{scalar}\times VPD_{scalar} \tag{5}\]  
where \(PAR\) is light and effective radiation (MJ/m\({}^{2}\)); \(FPAR\) is the proportion of solar radiation absorbed by the vegetation canopy; \(\varepsilon_{max}\) is the maximum light energy use efficiency. \(TMIN_{scalar}\) and \(VPD_{scalar}\) are expressed as the limits of temperature and moisture environmental factors, respectively, and \(TMIN_{scalar}\) is calculated from the linear relationship between \(TMIN_{min}\) (temperature at \(\varepsilon=0\)) and \(TMIN_{max}\) (temperature at \(\varepsilon=\varepsilon_{max}\)), and \(VPD_{scalar}\) is obtained from the linear relationship between \(VPD_{min}\) (saturated water vapor pressure difference at \(\varepsilon=0\)) and \(VPD_{max}\) (saturated water vapor pressure difference at \(\varepsilon=\varepsilon_{max}\)). (3) Water conservation capacity  
The water conservation capacity is calculated through the water balance equation, which considers the different ecosystem types as a \"black box\" and focuses on the input and output of water. The difference between precipitation and evapotranspiration and other consumption is the total water quantity (TQ) [52]. The formula is as follows [53]:  
\[\text{TQ }=\sum_{i=1}^{i}(P_{i}-R_{i}-ET_{i})\times A_{i} \tag{6}\]  
where, \(P_{i}\) is the rainfall of land class \(i\); \(R_{i}\) is the surface runoff of land class \(i\), calculated from the surface runoff coefficient and annual rainfall; \(ET_{i}\) is the evapotranspiration of land class \(i\); and \(A_{i}\) is the area of land class \(i\). Surface runoff coefficient (\(\alpha\)) is the ratio of surface runoff (R) to rainfall (P), which to a certain extent reflects the capacity of the ecosystem water holding capacity. Its standard coefficient table is generally used to calculate surface runoff in the region. The formula is as follows:  
\[\text{R }=\text{ P }\times\left(\frac{\alpha}{100}\right) \tag{7}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Abbreviation** & **Category** & **Description** \\ \hline PLAND & area and edge metric & percentage of landscape: the percentage of the landscape belonging to a given class \\ FRAC & shape metric & fractal dimension index based on the patch perimeter and the patch area and describing the patch complexity \\ COHESION & aggregation metric & contiguity index: quantifies the connectivity of habitat as perceived by organisms dispersing in binary landscapes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Landscape metrics used in this study. (4) Crop yield The crop yield was calculated using the following function based on the GPP product.