## 3 Methods  
### Tseb-Sm  
The TSEB model, first proposed by [PERSON] et al. [22], is a widely used approach to simulate surface flux with various land cover types [23; 24; 25]. It is based on the energy balance principle, which can be described as follows:  
\[\mathbf{R_{n}}\approx\mathbf{H}+\mathbf{L}\mathbf{E}+\mathbf{G} \tag{1}\]  
\[\mathbf{R_{n,S}}\approx\mathbf{H_{S}}+\mathbf{L}\mathbf{E_{S}}+\mathbf{G} \tag{2}\]  
\[\mathbf{R_{n,c}}\approx\mathbf{H_{C}}+\mathbf{L}\mathbf{E_{C}} \tag{3}\]  
where \(R_{n}\) is the net radiation (i.e., incoming radiation minus outgoing radiation), \(H\) is the sensible heat flux, \(LE\) is the latent heat flux, and \(G\) is the soil heat flux. The subscripts \(C\) and \(S\) refer to the canopy and soil, respectively. Due to some additional flux that we always neglect, such as heat advection, the symbol \"\(\approx\)\" is used here. The critical process in the TSEB model is partitioning surface radiometric temperature (namely, \(T_{rad}\)) into soil and canopy temperature, which can be achieved by Equation (4):  
\[\mathbf{T_{rad}^{4}}(\theta)=\mathbf{f_{C}}(\theta)\mathbf{T_{C}^{4}}+\big{[}\mathbf{1}-\mathbf{f_ {C}}(\theta)\big{]}\mathbf{T_{S}^{4}} \tag{4}\]where \(\theta\) is the view angle, \(f_{c}(\theta)\) is the vegetation fractional cover at the viewing angle, \(T_{c}\) is the canopy surface temperature, and \(T_{s}\) is the soil surface temperature. After that, sensible heat flux of the canopy and soil can be obtained using Equations (5) and (6), respectively:  
\[\mathbf{H_{C}}=\mathbf{\rho_{air}}\mathbf{C_{P}}\frac{\mathbf{T_{S}}-\mathbf{T_{AC}}}{\mathbf{R_{X}}} \tag{5}\]  
\[\mathbf{H_{s}}=\mathbf{\rho_{air}}\mathbf{C_{P}}\frac{\mathbf{T_{S}}-\mathbf{T_{AC}}}{\mathbf{R_{X}}} \tag{6}\]  
where \(\rho_{air}\) is the density of the air (kg m\({}^{-3}\)), \(C_{P}\) is the heat capacity of the air, \(T_{AC}\) is the air temperature in the canopy, \(R_{X}\) is the boundary layer resistance of the canopy, and \(R_{S}\) is the resistance of the boundary directly above the soil surface to heat flow. Combining the Priestley-Taylor formula with the linearization approximation to the resistance approach, which is described in detail by [PERSON] et al. (2012), \(T_{c}\) was estimated using the following equations:  
\[\mathbf{T_{ci}}=\mathbf{T_{a}}+\frac{\mathbf{R_{n,c}}\mathbf{R_{ah}}}{\rho\mathbf{C_{P}}}\left( \mathbf{1}-\mathbf{\alpha_{PT}}\mathbf{g_{stress}}\frac{\mathbf{g_{stress}}}{\mathbf{g_{a}}} \frac{\mathbf{\Delta}}{\mathbf{\Delta}+\mathbf{\gamma}}\right) \tag{7}\]  
\[\mathbf{T_{s}}=\mathbf{T_{a}}+\frac{(\mathbf{R_{n,s}}-\mathbf{G_{0}})(\mathbf{R_{ah}}+\mathbf{R_{s}})} {\rho\mathbf{C_{P}}}\left(\mathbf{1}-\mathbf{\alpha_{s}}\mathbf{f_{s}}\frac{\mathbf{\Delta}}{\mathbf{ \Delta}+\mathbf{\gamma}}\right) \tag{8}\]  
where \(T_{ci}\) is the initial vegetation temperature, \(T_{a}\) is the air temperature, \(R_{n,c}\) is the soil net radiation, \(R_{a,h}\) is the aerodynamic resistance of turbulent heat transfer between the reference height and measured height of the vegetation, \(\alpha_{PT}\) is the Priestley-Taylor coefficient for vegetation (initially set to 1.26 ([PERSON], 1973), but when the soil moisture reaches saturation it will close to 2), \(f_{g}\) is the fraction of green vegetation, \(\Delta\) is the slope of the saturation vapor pressure-temperature curve, \(\gamma\) is the psychrometric constant, \(f_{s}\) is the soil water stress factor to express the influence of water stress on soil evaporation, and \(g_{stress}\)/\(g_{a}\) is the plant transpiration factor ([PERSON], 1973). The soil surface evaporation varies with soil moisture content; a soil water stress factor (\(f_{s-song}\)) was introduced to the TSEB model under a wet soil surface (an irrigated area in the growing season) by [PERSON] et al. (2016), while an analogical factor (\(f_{s-merlin}\)) under dry conditions was also introduced by [PERSON] et al. (2016) through the soil texture information.