## Appendix A Input Data of InVEST Models  
### Water Yield Module  
According to the basic requirement of data input for this module, we calculated a number of key parameters. \(AET_{xj}\) is a function of reference evapotranspiration, the depth of the root-restricting layer, plant available water content and LULC. It therefore follows that \(\frac{AET_{xj}}{P_{x}}\), the approximate value of the Budyko curve, can be calculated as follows:  
\[\frac{AET_{xj}}{P_{x}}=\frac{1+\omega_{x}R_{xj}}{1+\omega_{x}R_{xj}+\frac{1}{R _{xj}}} \tag{1}\]  
In this expression, \(R_{xj}\) refers to [PERSON]'s aridity index of LULC type \(j\) in a given grid cell, \(x\), and is equivalent to the ratio of potential evapotranspiration to precipitation. In contrast, \(\omega_{x}\) is dimensionless, denotes the water available to a plant and is used to estimate annual precipitation. Applying the definition of [PERSON] et al. (2016), this non-physical parameter can also be used to describe soil attributes affected by natural climate and is calculated as follows:  
\[\omega_{x}=Z\frac{AWC_{x}}{P_{x}} \tag{2}\]  
In this expression, \(AWC_{x}\) denotes the water available to a plant (mm) and will depend on both soil texture and depth, while \(Z\) refers to seasonal precipitation distribution and depth. [PERSON]'s aridity index is calculated as follows:  
\[R_{xj}=\frac{k_{xj}ET_{0x}}{P_{x}} \tag{3}\]In this expression, \(ET_{0}\) is reference evapotranspiration, while \(k_{xj}\) is the coefficient of evapotranspiration of LULC type \(j\) in a given grid cell, \(x\), as determined by vegetation type.  
We therefore defined average annual precipitation, \(ET_{0}\), soil depth, plant available water content (_PAWC_), LULC, root depth, elevation, biophysical table and the Z parameter as inputs to this water yield module. Of these, _PAWC_ refers to the water fraction stored in the soil profile that is available for land use; this was calculated based on physical and chemical soil properties, following the method presented by [PERSON] [67], as follows:  
\[\begin{array}{ll}PAWC&=54.509-0.312\times sand\%-0.003\times(sand\%)^{2}-0.055\times sil\%\\ &-0.006\times(silt\%)^{2}-0.738\times clay\%+0.007\times(clay\%)^{2}\\ &-2.688\times OM\%+0.501\times(OM\%)\end{array} \tag{10}\]  
This expression incorporates values for relative sand (sand%), silt (silt%), clay (clay%) and organic matter content (OM%).  
We calculated the annual mean reference ET\({}_{0}\) using the Food and Agriculture Organization of the United Nations (FAO) Penman-Monteith equation (Equation (11), below) as listed in the user guide to the InVEST model [68], corrected using:  
\[LE=\frac{\Delta(R_{n}-G)+\rho C_{p}[e_{s}(T_{a}-e_{a})]}{\Delta+\frac{\gamma( r_{a}-r_{s})}{r_{a}}} \tag{11}\]  
In this expression, \(LE\) is latent heat flux; \(D\) is the slope of the temperature saturated vapor pressure curve; \(Rn\) is net surface radiation; G is soil heat flux; \(r\) is air density; \(C_{p}\) is specific heat at constant pressure; \(T_{a}\) is air temperature; \(e_{s}\) (\(T_{a}-e_{a}\)) denotes the vapor pressure difference at a reference height; \(\gamma\) is the psychrometric constant; \(r_{a}\) is aerodynamic resistance; and \(r_{s}\) is surface impedance.