## 2 Study Area, Data and Methodology
### Estimation of ESV
\tag{1}\]  
where \(Production_{r}\), \(Production_{b}\) and \(Production_{p}\) are the total production of rice, beans and potato, respectively, and \(Total_{Area}\) is the total planting area of rice, beans and potato. \(\eta_{Food\ \&\ Material}\) is the modified coefficient of food production and raw material production services. \(CPC_{GDyr}\) and \(CPC_{CHNyr}\) are the CPCs of Guangdong and the nation in the study year, respectively. As the basic reference, \(CPC_{CHN2010}\) is the _CPC_ of the nation in 2010. The water provision service in land and water bodies was quantitatively modified by rainfall and surface runoff density. The calculation is shown in Equation (2):  
\[\left\{ \begin{aligned} &\eta_{Water(Land)}=\frac{Rf_{SAyr}}{Rf_{CHNyr}}. \frac{Rf_{CHNyr}}{Rf_{CHN2010}}\\ &\eta_{Water(WB)}=\frac{SRD_{SAyr}}{SRD_{CHNyr}}.\frac{SRD_{CHNyr} }{SRD_{CHN2010}}\end{aligned} \right. \tag{2}\]  
where \(\eta_{Water(Land)}\) and \(\eta_{Water(WB)}\) are the modified coefficients of water provision services in land and water bodies, respectively. \(Rf_{SAyr}\) and \(Rf_{CHNyr}\) are the rainfall in the study area and the nation in the study year, respectively, and \(Rf_{CHN2010}\) is the rainfall in the study area in 2010 as a basic reference. \(SRD_{SAyr}\) and \(SRD_{CHNyr}\) are the surface runoff densities of terrestrial water areas in the study area and the nation in the study year, respectively, and \(Rf_{CHN2010}\) is the surface runoff density of terrestrial water areas in the nation in 2010 as a basic reference. Regulation and supporting services were quantitatively modified by the gross primary productivity (GPP), which is an important indicator of the ecological background quality and the intensity of natural biological activities. The calculation is shown in Equation (3):  
\[\eta_{Regulation\ \&\ Support}=\frac{GPP_{SAyr}}{GPP_{CHNyr}}. \frac{GPP_{CHNyr}}{GPP_{CHN2010}} \tag{3}\]  
where \(\eta_{Regulation\ \&\ Support}\) is the modified coefficient of regulating and supporting services. \(GPP_{SAyr}\) and \(GPP_{CHNyr}\) are the GPP in the study area and the nation in the study year, respectively, and \(GPP_{CHN2010}\) is the GPP in the nation in 2010 as a basic reference. The cultural service was quantitatively modified by the ratio of tourism income to GDP according to [PERSON] et al. [27]. The calculation is shown in Equation (4):  
\[\eta_{Culture}=\frac{Tourism/GDP_{SAyr}}{Tourism/GDP_{CHNyr}}.\frac{Tourism/ GDP_{CHNyr}}{Tourism/GDP_{CHN2010}} \tag{4}\]  
where \(\eta_{Culture}\) is the modified coefficient of cultural services. \(Tourism/GDP_{SAyr}\) and \(Tourism/GDP_{CHNyr}\) are the ratios of tourism income to GDP in the study area and the nation in the study year, respectively, and \(\textit{Tourism}/\textit{GDP}_{\textit{CHN2010}}\) is the ratio of tourism income to GDP in the nation in 2010 as a basic reference. [PERSON] et al. [24] defined 1 standard value volume of ESEV as the \"\(D\) value\", which represents the economic benefit of annual grain yield in 1 unit area of cropland. The calculation process of the \(D\) value is given in Equation (5):  
\[D_{yr}=\frac{S_{r-yr}\times F_{r-yr}+S_{b-yr}\times F_{b-yr}+S_{p-yr}\times F _{p-yr}}{S_{r-C2010}\times F_{r-C2010}+S_{b-C2010}\times F_{b-C2010}+S_{p-C2010} \times F_{p-C2010}}\times D_{c-2010} \tag{5}\]  
where \(D_{yr}\) represents 1 standard value volume of the ESEV in each study year for the study area (\(10^{3}\) Yuan\(\cdot\)km\({}^{-2}\cdot\)a\({}^{-1}\)), and \(D_{c-2010}\) represents 1 standard value volume of the ESEV in 2010 for the nation (according to [PERSON] et al. [24], \(D_{c-2010}=3.4065\times 10^{3}\) Yuan\(\cdot\)hm\({}^{-2}\cdot\)a\({}^{-1}\)). \(S_{r-yr}\), \(S_{b-yr}\) and \(S_{p-yr}\) are the planting areas of rice, beans and potato accounting for the percentage of the total area of the 3 crops in the study year, respectively; \(F_{r-yr}\), \(F_{b-yr}\) and \(F_{p-yr}\) are the economic benefits per unit area of rice, beans and potato in the study year for the study area, respectively.