## 2 Materials and Methods
### Methodology
#### 2.3.1 ES Evaluation  
Using remote sensing and statistical data, the InVEST model and ArcGIS 10.6 software were used to quantitatively assess five ecosystem services: water yield [18], carbon sequestration [19; 20], soil conservation [21], habitat quality [22], and food production [23; 24] in southwestern China and reveal their spatial and temporal patterns. The spatial resolution was treated as 1 km \(\times\) 1 km, and calculations for the same are shown in Table 1.  
Figure 1: Location of study area.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**ES** & **Calculation or Formula Model** & **Parameters and Processing** \\ \hline Water Yield & Y(x) = P(x) \(-\) AET(x) & Y(x) is the average annual water yield, P(x) is the average annual precipitation, and AET is actual evapotranspiration. \\ \hline Carbon Sequestration & \(\begin{array}{c}\text{GPP}=\text{PAR}\times\text{FPAR}\times\varepsilon_{ max}\times\\ \frac{1.1814\times\left(1+\theta^{3.5\times\left(1-T_{\text{opt}}-10.7\tau_{ \text{min}}\right)}\right)}{1+\theta^{2.5\times\left(2\tau_{\text{opt}}-10.7 \tau_{\text{min}}\right)}}\times\\ \left(0.25+0.75\times\frac{\text{ET}}{\text{RN}}\right)\end{array}\) & \begin{tabular}[]{c} PAR is calculated by multiplying CERES solar radiation and the monthly PAR/SW ratio derived from the BESS data set. \(\varepsilon_{max}\) and \(T_{\text{opt}}\) (i.e., maximum LUE and optimum growth temperature) refer to various flux measurements and sun-induced chlorophyll fluorescence values [19; 20]. \\ \hline Soil Conservation & \begin{tabular}[]{c} The Sediment Delivery Ratio model \\ \(\text{RKLS}=R\times K\times LS\) \\ \(\text{USLE}=R\times K\times LS\times C\times P\) \\ \(\text{SD}=\text{RKLS}-\text{USLE}\) \\ \end{tabular} & \begin{tabular}[]{c} RKLS is the potential soil erosion (t) in the study area under specific landscape and climate conditions, USLE is the actual amount of soil erosion (t) after taking into account the interception effect of vegetation and the implementation of management engineering measures, SD is soil retention (t), \(R\) is rainfall erosion force, \(K\) is soil erodibility, \(LS\) is the slope length slope factor, \(C\) is the vegetation cover factor, and \(P\) is the soil conservation measure factor. \\ \hline Habitat Quality & \begin{tabular}[]{c} The Habitat Quality model \\ \(Q_{xj}=H_{j}\left[1-\left(\frac{D_{xj}^{c}}{D_{jj}^{c}+R^{c}}\right)\right]\) \\ \end{tabular} & \
\begin{tabular}[]{c} \(Q_{xj}\) is the habitat quality index of \(x\) grids in \(j\) habitats, \(H_{j}\) is the habitat suitability score of \(j\) habitats between 0 and 1, \(k\) is the half-saturation constant which is usually taken as 1/2 of the habitat degradation index, and \(z\) is the normalization constant, which is usually taken as the default value of 2.5. \\ \hline Food Production & \(G_{i}=\frac{G_{\text{out}}}{NDVI_{\text{loss}}}\times NDVI_{i}\) &
\begin{tabular}[]{c} \(G_{i}\) is the food production service of raster I, \(G_{\text{out}}\) is the total food production of each county, \(NDVI_{\text{loss}}\) is the sum of NDVI of arable land-like elements in the county, and \(NDVI_{i}\) is the NDVI of raster \(i\). \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calculation of ecosystem services.  
Figure 2: Framework of methodology.