## 2 Materials and Methods
### Methodology
#### 2.2.2 Adjustment of Ecosystem Service Value
The contribution of each landscape to water production is determined by regional annual water production, which is obtained from annual precipitation minus actual evapotranspiration [76]. The InVEST water production model is utilized in this study, and the formula is as follows: \[Y(x)=\left(1-\frac{AET(x)}{P(x)}\right)\times P(x)\] (12) where \(Y(x)\) is the annual water production corresponding to grid \(x\), \(AET(x)\) is the annual actual evapotranspiration of grid \(x\), \(P(x)\) is the annual precipitation of grid \(x\), and \(\frac{AET(x)}{P(x)}\) is calculated based on the Budyko curve [77]. \[\frac{AET(x)}{P(x)}=1+\frac{PET(x)}{P(x)}-\left[1+\left(\frac{PET(x)}{P(x)} \right)^{w}\right]^{\frac{1}{b}}\] (13) where \(PET(x)\) is the annual potential evapotranspiration of grid \(x\), and \(w\) (\(x\)) is a nonphysical parameter that describes the soil properties under natural climatic conditions. * Soil retention Soil erosion is a natural process that shapes natural landscapes through the distribution of the weathering substances produced by geomorphological processes [78]. Soil retention is a general term for the role that ecosystems play in resisting soil erosion. The revised universal soil loss equation (RUSLE) can evaluate the quality of soil retention by calculating total soil conservation, in which the total soil conservation is obtained by subtracting potential soil erosion from actual soil erosion. The formula is as follows: \[SD=R\times K\times L\times S\times(1-C\times P)\] (14) where \(SD\) is the total amount of soil conservation, and \(R\), \(K\), \(L\), \(S\), \(C\), and \(P\) are the rainfall erosion factor, soil erodibility factor, slope factor, slope length factor, vegetation cover factor, and management measure factor, respectively. * Biodiversity conservation Biodiversity includes the genetic diversity, species diversity, and landscape diversity [79]. It is necessary for human survival and is of great significance to the survival and reproduction of natural species and the maintenance of a suitable environment for different species. In this study, the InVEST habitat quality model was used to calculate the supply capacity of the service. This method establishes the relationship between land use types and habitat threat sources. It evaluates habitat quality according to the influence mode and intensity of threat sources on various land use types, and then reflects the richness of the biodiversity. The formula is as follows: \[D_{xj}=\sum_{r=1}^{R}\sum_{y=1}^{Y_{r}}\left(\frac{\omega_{r}}{\sum_{r=1}^{R} \omega_{r}}\right)r_{y}i_{rxy}\beta_{x}S_{jr}\] (15) where \(D_{xj}\) is the habitat degradation degree of grid \(x\) in terms of land use type \(j\), \(R\) is the number of threat sources, \(\omega_{r}\) is the weight of threat source \(r\), \(Y_{r}\) is the grid set of threat source \(r\), \(r_{y}\) is the number of threat sources on the grid, \(\beta_{x}\) is the accessibility of threat sources to grid \(x\), \(S_{jr}\) is the sensitivity of land use type \(j\) to threat source \(r\), and \(i_{rxy}\) is the impact of grid \(y\) of the \(r\)-th threat source on habitat grid \(x\). According to different threat sources, there are two types of linear attenuation and exponential attenuation with increasing distance:  
\[i_{rxy}=1-\left(\frac{d_{xy}}{d_{rmax}}\right)\,({\rm linear}) \tag{16}\]  
\[GPP=APAR\times\varepsilon\]0  
where \(d_{xy}\) is the linear distance between habitat grid \(x\) and grid \(y\), and \(d_{rmax}\) is the maximum influence distance of threat source \(r\). \[GPP=APAR\times\varepsilon\]1  
where \(H_{j}\) is the ecological suitability of land use type \(j\), \(k\) is a semi-saturation constant that is generally set to \(1/2\) of grid resolution, and \(z\) is a scale parameter that is generally set to \(2.5\). We extracted the spatial distribution of seven types of ESs, adjusted the value of all kinds of ESs in each grid in the study area, overlayed each layer, and obtained the adjusted spatial distribution map of ESV in Sichuan Province in 2018.