## 3 Model and Methods  
### Two-Leaf Light Use Efficiency Model  
The TL-LUE model [4], which is based on the MOD17 GPP model, separates the entire canopy APAR into the APAR of sunlit and shaded leaves using the BEPS model [29], and the estimation of GPP in the model is as follows:  
\[GPP=(\epsilon_{\text{msu}}\times APAR_{su}+\epsilon_{\text{msh}}\times APAR_{ sh})\times\sigma \tag{5}\]  
where \(\epsilon_{msu}\) and \(\epsilon_{msh}\) are the maximum LUE of sunlit and shaded leaves, respectively; \(APAR_{su}\) and \(APAR_{sh}\) are the APAR (MJ m\({}^{-2}\) d\({}^{-1}\)) of sunlit and shaded leaves, respectively; and \(\sigma\) is the scale of environmental stress factors such as air temperature and vapor pressure deficit to the maximum LUE. These parameters are calculated as follows:  
\[APAR_{sh}=(1-\alpha)\times\left[\frac{PAR_{dif}-PAR_{difu}}{LAI}+C\right]\times LAI _{sh} \tag{6}\]  
\[APAR_{su}=(1-\alpha)\times\left[PAR_{dif}\times\frac{\cos(\beta)}{\cos(\theta) }+\frac{PAR_{dif}-PAR_{difu}}{LAI}+C\right]\times LAI_{su} \tag{7}\]  
where \(\alpha\) is the canopy albedo for each vegetation type (Table 1); \(\beta\) is the sun-leaf angle (usually 60\({}^{\circ}\)) of the spherical canopy; \(\theta\) is the solar zenith angle; \(PAR_{dif}\), \(PAR_{dif}\), and \(PAR_{difu}\) are the PAR of diffuse, direct, and scattering PAR under a canopy, respectively [29]; \(C\) represents multiple scattering PAR inside the canopy; \(LAI_{sh}\) and \(LAI_{su}\) are the \(LAI\) of sunlit and shaded leaves [29], respectively, and the calculation of these parameters is as follows:  
\[LAI_{\text{su}}=2\times\cos(\theta)\times\left(1-e^{\frac{-0.5\times(\alpha \times LAI}{\cos(\theta)}}\right) \tag{8}\]  
\[LAI_{\text{sh}}=LAI-LAI_{\text{su}} \tag{9}\]  
where \(\Omega\) is the estimation of the vegetation CI.  
The calculation of \(\sigma\) in Equation (5) is as follows:  
\[\sigma=f(T_{\text{min}})\times g(VPD) \tag{10}\]  
\[g(T_{\text{amin}})=\left\{\begin{array}{ll}0&T_{\text{amin}}\leq T_{\text{ amin\_min}}\\ \frac{T_{\text{amin}}-T_{\text{amin\_min},\text{min}}}{T_{\text{amin\_max}}-T_{ \text{amin\_min},\text{min}}}&T_{\text{amin\_min}}<T_{\text{amin\_max}}<T_{ \text{amin\_max}}\\ 1&T_{\text{amin}}\geq T_{\text{amin\_max}}\end{array}\right\} \tag{11}\]\[f(VPD)=\left\{\begin{array}{lr}0&VPD_{\max}\leq VPD\\ \frac{VPD_{\max}-VPD}{VPD_{\max}-VPD_{\min}}&VPD_{\min}<VPD<VPD_{\max}\\ 1&VPD_{\min}\geq VPD\end{array}\right\} \tag{12}\]  
where \(T_{amin}\) and \(VPD\) are the lowest daily air temperature and vapor pressure deficit, respectively; \(T_{amin\_min}\) and \(VPD_{min}\) (Table 1) are the smallest air temperature and vapor pressure deficit, respectively, when photosynthesis decreases to 0; and \(T_{amin\_max}\) and \(VPD_{max}\) (Table 1) are the highest air temperature and vapor pressure deficit, respectively, when photosynthesis reaches the strongest level. \(VPD_{max}\), \(VPD_{min}\), \(T_{min\_min}\), and \(T_{amin\_max}\) are closely related to vegetation type [36]. In various biomes, \(f(VPD)\) and \(g(T_{amin})\) are the scales of the vapor pressure deficit and the minimum air temperature, respectively, to the maximum LUE, ranging from 0 to 1. The calculation and verification of relative parameters in the TL-LUE model have already been established using observed data from the global flux network [36; 59].