## 3 Methods
### Two-Leaf Light Use Efficiency Model  
The two-leaf light use efficiency (TL-LUE) model [45] aims to improve the MOD17 algorithm by separating the canopy into sunlit and shaded leaf groups and calculating GPP separately for them with different maximum light use efficiencies. TL-LUE considers the canopy radiative transfer processes and accounts for the different photosynthetic light responses of sunlit and shaded leaves. The basic formulas for the TL-LUE are as follows:  
\[\mathrm{GPP}=(\mathrm{APAR}_{\mathrm{su}}\times\epsilon_{\mathrm{msu}}+ \mathrm{APAR}_{\mathrm{sh}}\times\epsilon_{\mathrm{msh}})\times\mathrm{TMIN}_{ \mathrm{scalar}}\times\mathrm{VPD}_{\mathrm{scalar}} \tag{1}\]  
where \(\mathrm{APAR}_{\mathrm{su}}\) and \(\mathrm{APAR}_{\mathrm{sh}}\) denote the photosynthetically active radiation absorbed by sunlit and shaded leaves, respectively; \(\epsilon_{\mathrm{msu}}\) and \(\epsilon_{\mathrm{msh}}\) denote the maximum light use efficiency for sunlit and shaded leaves, respectively; and \(\mathrm{TMIN}_{\mathrm{scalar}}\) and \(\mathrm{VPD}_{\mathrm{scalar}}\) denote the down-regulation scalars that account for the effects of daily minimum air temperature and vapor pressure deficit, respectively, on plant light use efficiency. Further,  
\[\mathrm{APAR}_{\mathrm{su}}=(1-\alpha)\times\left[\mathrm{PAR}_{\mathrm{dir} }\times\frac{\cos\beta}{\cos\theta}+\frac{\mathrm{PAR}_{\mathrm{dir}}- \mathrm{PAR}_{\mathrm{dir,u}}}{\mathrm{LAI}}+\mathrm{C}\right]\times\mathrm{ LAI}_{\mathrm{su}} \tag{2}\]  
\[\mathrm{APAR}_{\mathrm{sh}}=(1-\alpha)\times\left[\frac{\mathrm{PAR}_{\mathrm{ dif}}-\mathrm{PAR}_{\mathrm{dir,u}}}{\mathrm{LAI}}+\mathrm{C}\right]\times\mathrm{ LAI}_{\mathrm{sh}} \tag{3}\]  
where \(\mathrm{PAR}_{\mathrm{dir}}\) and \(\mathrm{PAR}_{\mathrm{dir}}\) denote the direct and diffuse components of incoming photosynthetically active radiation, respectively; \(\mathrm{PAR}_{\mathrm{dir,u}}\) denotes the diffuse photosynthetically active radiation under the canopy and is calculated following [49]; \(\alpha\) denotes canopy albedo; \(\beta\) denotes mean leaf-sunangle; \(\theta\) denotes solar zenith angle; C denotes the contribution of multiple scattering of the total photosynthetically active radiation to the diffuse irradiance per unit leaf area within the canopy; and LAI, LAI\({}_{\text{sh}}\), and LAI\({}_{\text{su}}\) denote the leaf area index, sunlit leaf area index, and shaded leaf area index, respectively.  
The sunlit and shaded components of LAI are derived as follows:  
\[\text{LAI}_{\text{su}}=2\times\cos\theta\times\left(1-\exp\left(-0.5\times \Omega\times\frac{\text{LAI}}{\cos\theta}\right)\right) \tag{4}\]  
\[\text{LAI}_{\text{sh}}=\text{LAI}-\text{LAI}_{\text{su}} \tag{5}\]  
where LAI, LAI\({}_{\text{sh}}\), and LAI\({}_{\text{su}}\) denote the leaf area index, sunlit leaf area index, and shaded leaf area index, respectively; and \(\Omega\) is the canopy clumping index.  
Following previous studies [45; 50; 51], key parameters for the biome of deciduous broadleaf forest in TL-LUE are set as follows: \(\epsilon_{\text{msu}}=0.47\) gC M\(]^{-1}\), \(\epsilon_{\text{msh}}=2.06\) gC MJ\(]^{-1}\), TMIN\({}_{\text{min}}=-8.00\)\({}^{\circ}\)C, TMIN\({}_{\text{max}}=7.94\)\({}^{\circ}\)C, VPD\({}_{\text{min}}=0.93\) kPa, VPD\({}_{\text{max}}=4.10\) kPa, \(\alpha=0.18\), \(\beta=60\)\({}^{\circ}\), and \(\Omega=0.80\).