## Appendix A Full Description of the SWH Model  
### General Logic  
The SWH model is developed based on the model of [PERSON] (1985), which estimates the latent heat flux from the soil surface (i.e., \(E\)) and from the canopy (i.e., \(T\)) as two separate sources. There are five resistances involved in this model: canopy stomatal resistance (\(r_{\mathrm{sc}}\)), soil surface resistance (\(r_{\mathrm{ss}}\), s\(\cdot\)m\({}^{-1}\)), aerodynamic resistance of the leaf to canopy height (\(r_{\mathrm{ac}}\), s\(\cdot\)m\({}^{-1}\)), resistance of the canopy height to reference height (\(r_{\mathrm{aa}}\), s\(\cdot\)m\({}^{-1}\)) and soil surface to canopy height (\(r_{\mathrm{as}}\), s\(\cdot\)m\({}^{-1}\)).  
Ecosystem evapotranspiration \(\lambda ET\) (W\(\cdot\)m\({}^{-2}\)) is calculated as the sum of transpiration (\(\lambda T\)) and soil water evaporation (\(\lambda E\)):  
\[\lambda ET=\lambda T+\lambda E=C_{\mathrm{c}}PM_{\mathrm{c}}+C_{\mathrm{s}}PM_{ \mathrm{s}} \tag{1}\]  
\[PM_{\mathrm{c}}=\frac{\Delta R+(\rho c_{p}D-\Delta r_{\mathrm{ac}}R_{\mathrm{ s}})/(r_{\mathrm{aa}}+r_{\mathrm{ac}})}{\Delta+\gamma(1+\left(\frac{r_{\mathrm{sc}}}{r _{\mathrm{aa}}+r_{\mathrm{ac}}}\right))} \tag{2}\]  
\[PM_{\mathrm{s}}=\frac{\Delta R+(\rho c_{p}D-\Delta r_{\mathrm{as}}R_{\mathrm{ s}})/(r_{\mathrm{aa}}+r_{\mathrm{as}})}{\Delta+\gamma(1+\left(\frac{r_{\mathrm{ ss}}}{r_{\mathrm{aa}}+r_{\mathrm{as}}}\right))} \tag{3}\]  
where \(PM_{\mathrm{c}}\) and \(PM_{\mathrm{s}}\) are terms similar to the Penman-Monteith equation to describe canopy transpiration and soil evaporation, respectively. \(C_{\mathrm{c}}\) and \(C_{\mathrm{s}}\) are the canopy resistance coefficient and soil surface resistance coefficient, respectively. \(\Delta\) is the slope of the saturation vapor pressure versus temperature curve (kPa\(\cdot\)K\({}^{-1}\)). \(\rho\) is the density of air (1.293 kg\(\cdot\)m\({}^{-3}\)), and \(c_{p}\) is the specific heat at constant pressure (1012 J\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\)). VPD is the vapor pressure deficit (kPa) in the air, and \(\gamma\) is the psychrometric constant (0.067 kPa\(\cdot\)K\({}^{-1}\)). Calculations of the resistances will be addressed later. In Equations (2) and (3), \(R\) and \(R_{\mathrm{s}}\) (W\(\cdot\)m\({}^{-2}\)) represent the available energy input above the canopy and above the soil surface, respectively, and are defined as follows:  
\[R=R_{\mathrm{n}}-G \tag{4}\]  
\[R_{\mathrm{s}}=R_{\mathrm{ns}}-G \tag{5}\]where \(R_{\rm n}\) and \(R_{\rm ns}\) (W\(\cdot\)m\({}^{-2}\)) are net radiation fluxes reaching the canopy and the substrate (W\(\cdot\)m\({}^{-2}\)), respectively. \(G\) is the soil heat flux (W\(\cdot\)m\({}^{-2}\)). \(R_{\rm ns}\) can be estimated using [PERSON]'s law:  
\[R_{\rm ns}=R_{\rm n}exp(-\lambda LAI) \tag{10}\]  
where \(\lambda\) is the light-extinction coefficient. In Equation (11), the two coefficients \(C_{\rm c}\) and \(C_{\rm s}\) are calculated as follows:  
\[C_{\rm C}=\frac{1}{1+(\frac{\rho_{\rm s}p_{\rm a}}{\rho_{\rm s}(\rho_{\rm c}+ \rho_{\rm a})})} \tag{11}\]  
\[C_{\rm s}=\frac{1}{1+(\frac{\rho_{\rm s}p_{\rm a}}{\rho_{\rm c}(\rho_{\rm c}+ \rho_{\rm a})})} \tag{12}\]  
in which \(\rho_{a},\rho_{c}\) and \(\rho_{\rm s}\) are calculated as:  
\[\rho_{a}=(\Delta+\gamma)r_{\rm aa} \tag{13}\]  
\[\rho_{c}=(\Delta+\gamma)r_{\rm ac}+\gamma r_{\rm sc} \tag{14}\]  
\[\rho_{s}=(\Delta+\gamma)r_{\rm as}+\gamma r_{\rm ss} \tag{15}\]