## 2 Materials and Methods
### Quantifying ES Supply
#### 2.3.3 Assessment of ES Supply Index  
Since each ES has its own measurement unit, we individually standardized the ES values and then summarized them within each county to mitigate the influence of magnitude and variability. We employed min-max normalization to standardize the values of the five ES indicators [63; 64]. This normalization method removes the units of the input data and scales them to a common range. After standardization, the standardized values were accumulated to obtain the ES supply index (ESSI), which represents the total ecosystem service supply. The calculation equation for ESSI is as follows:  
\[\text{ES}_{\text{ij}}=\frac{\text{ES}_{\text{ij}}-\text{minES}_{\text{j}}}{ \text{maxES}_{\text{j}}-\text{minES}_{\text{j}}} \tag{1}\]  
\[\text{ESSI}_{\text{i}}=\sum_{\text{j}=1}^{\text{n}}\text{ES}_{\text{ij}} \tag{2}\]  
where \(\text{ESSI}_{\text{i}}\) is the ES supply index of county i; \(\text{ES}_{\text{ij}}\) is the standardized value for ES j of county i; \(\text{ES}_{\text{ij}}\) is the initial value for ES j of county i; \(\text{max ES}_{\text{j}}\) is the maximum value of ES over 107 counties, and min ES denotes the minimum value of ES; n = 5.  
\begin{table}
\begin{tabular}{l l l l l} \hline
**ES Indicator** & **Code** & **Model or Proxy** & **Unit** & **Assessment Process** \\ \hline Crop production & Cro & Crop yield per square kilometer & ton/km\({}^{2}\) & Crop production was calculated by dividing the crop yield of each county by its territory to illustrate per-unit provision service. \\ Water retention & Wet & Water balance equation & m\({}^{3}\)/km\({}^{2}\) & \(TQ=\frac{1}{\sum_{i=1}^{L}{(P-R_{i}-ET_{i})}}\) \\  & Wet & Water balance equation & m\({}^{3}\)/km\({}^{2}\) & \(TQ\) is water conservation, \(P\) is the annual average rainfall (mm), \(R_{i}\) is the annual average surface runoff (mm), and \(ET_{i}\) is the annual evapotranspiration (mm), \(ADA=K\times K\times K\times(S-C\times P)\) \\  & & & \(\Delta\Delta\) = soil conservation (\(t\)/ (hm\({}^{2}\)/d)). R = rainfall capacity index \\ Soil conservation & Scon & USLE (Universal Soil Loss Equation) & t/(hm\({}^{2}\)/m\({}^{2}\)). & \(\Delta\) = soil capability factor (\(t\)/hm\({}^{2}\)/d) = soil capability factor (\(t\)/hm\({}^{2}\)/d) = soil capability factor (\(t\)/hm\({}^{2}\)/d) = soil capability factor (unless), \(P\) = conservation practice factor (unless). C = power and management factor from [PERSON] and [PERSON] [57], for Iron Williams [58], L is from [PERSON] et al. [99] and [PERSON] et al. [60], C from [PERSON] et al. [61], and P from [PERSON] et al. [62]. \\ Carbon sequestration & Sceq & CASA (Carnegie-Ames-Stanford approach) & kg C/km\({}^{2}\) & \(NPP=\) net primary productivity (g C/m\({}^{2}\)), \(APR=\) absorbed photosynthetic active radiation (M/m), \(\xi\) = the utilization rate of light energy (g C/M). \\ Outdoor recreation & Rec & Tourists per square kilometer & persons/km\({}^{2}\) & Outdoor recreation was calculated via the area of forest land in each county. \\ \hline \end{tabular}
\end{table}
Table 2: ES indicators from the MA categories and their quantitative methods, units, and ES variable requirements.