## 2 Study Area, Data and Methodology
### Estimation of ESV
\(S_{r-C2010}\), \(S_{b-C2010}\) and \(S_{p-C2010}\) are the planting areas of rice, beans and potato, respectively, accounting for the percentage of the total area of the 3 crops in 2010 for the nation; \(F_{r-C2010}\), \(F_{b-C2010}\) and \(F_{p-C2010}\) are the economic benefits per unit area of rice, beans and potato in 2010 for the nation, respectively. The ecosystem service estimation process is given in Equations (6)-(8):  
\[ESEV_{yr\_bf{}bf}=\eta_{yr\_bf{}bf}\times ESEV_{\textit{CHN2010\_bf{}bf}} \tag{6}\]  
\[ESEV_{yr\_bf{}k}=\sum_{f}ESEV_{yr\_bf{}bf} \tag{7}\]  
\[ESV_{yr}=D_{yr}\times\sum_{k}ESEV_{yr\_bf{}bf}\times A_{k} \tag{8}\]  
where \(ESEV_{yr\_bf{}bf}\) refers to the ESEV of each ecosystem service function \"\(f\)\" and land use type \"\(k\)\" in the study year; \(ESEV_{yr\_bf{}bf}\) refers to the total ESEV of each land use type \"\(k\)\" in the study year (the total item in Table 3); \(ESEV_{\textit{CHN2010\_bf{}bf}}\) refers to the ESEV of each ecosystem service function \"\(f\)\" and land use type \"\(k\)\" in 2010 for the nation, which was the basic reference, as shown in Table 2; and \(\eta_{yr\_bf{}bf}\) is the annual modified coefficients of each ecosystem service function \"\(f\)\" and land use type \"\(k\)\", calculated using Equations (1)-(5), and the results are compiled in Table 4. \(ESV_{yr}\) is the total ESV of each ecosystem service function and land use type in the study year (Table 5). \(D_{yr}\) represents 1 standard value volume of the ESEV in each study year (\(10^{3}\) Yuan\(\cdot\)hm\({}^{-2}\cdot\)a\({}^{-1}\)), and \(A_{k}\) is the total area of each land use type \"\(k\)\" in the study year. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & **FP** & **RMP** & **WP** & **GR** & **CR** & **EP** & **HR** & **SFR** & **NC** & **BP** & **AS** \\ \hline \multirow{3}{*}{Land} & 2004 & 1.03 & 1.03 & 2.6 & 1.62 & 1.62 & 1.62 & 1.62 & 1.62 & 1.62 & 1.62 & 2.13 \\  & 2010 & 1.07 & 1.07 & 2.74 & 1.86 & 1.86 & 1.86 & 1.86 & 1.86 & 1.86 & 1.86 & 2.11 \\  & 2016 & 1.12 & 1.12 & 3.41 & 1.53 & 1.53 & 1.53 & 1.53 & 1.53 & 1.53 & 1.53 & 3.55 \\ \hline \multirow{3}{*}{Water} & 2004 & 1.98 & 1.98 & 3.03 & 1.62 & 1.62 & 1.62 & 1 & 1.62 & 1.62 & 1.62 & 2.13 \\  & 2010 & 1.9 & 1.9 & 3.46 & 1.86 & 1.86 & 1.86 & 1 & 1.86 & 1.86 & 1.86 & 2.11 \\ \cline{1-1}  & 2016 & 1.92 & 1.92 & 4.28 & 1.53 & 1.53 & 1.53 & 1 & 1.53 & 1.53 & 1.53 & 3.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The annual modified coefficients for ecosystem service functions. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Land Use**} & \multicolumn{2}{c}{**2004**} & \multicolumn{2}{c}{**2010**} & \multicolumn{2}{c}{**2016**} & \multicolumn{2}{c}{**2004–2016**} \\ \cline{2-10} \multicolumn{1}{c}{**Categories**} & **Area (hm\({}^{2}\))** & \%** & **Area (hm\({}^{2}\))** & \%** & **Area (hm\({}^{2}\))** & \%** & **Area (hm\({}^{2}\))** & \%** & **\% yr** \\ \hline Built-up & 35,108.1 & 26.19 & 39,093.85 & 29.17 & 40,518.61 & 30.23 & 5411 & 15.41 & 1.2 \\ Cropland & 26,084.3 & 19.46 & 24,681.73 & 18.41 & 24,169.38 & 18.03 & \(-\)1915 & \(-\)7.34 & \(-\)0.63 \\ Forest & 4547.71 & 3.39 & 5985.44 & 4.47 & 6135.92 & 4.58 & 1588 & 34.92 & 2.53 \\ Grassland & 126.4 & 0.09 & 1308.64 & 0.98 & 1083.88 & 0.81 & 957 & 757.5 & 19.61 \\ Orchard & 17,707.32 & 13.21 & 7861.43 & 5.87 & 7478.9 & 5.58 & \(-\)10228 & \(-\)57.76 & \(-\)6.93 \\ Unused and other & 808.05 & 0.6 & 4983.58 & 3.72 & 5000.79 & 3.73 & 4193 & 518.87 & 16.4 \\ River & 35,974.58 & 26.84 & 29,326.22 & 21.88 & 29,152.83 & 21.75 & \(-\)6822 & \(-\)18.96 & \(-\)1.74 \\ Wetland and lakes & 13,678.86 & 10.21 & 20,794.43 & 15.51 & 20,495.01 & 15.29 & 6816 & 49.83 & 3.43 \\ Total & 134,035.3 & - & 134,035.3 & - & 134,035.3 & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Land use changes in the study area.