## 2 Data and Methods
### TL-LUE Model  
The two-leaf LUE (TL-LUE) model is based on the MOD17 algorithm and distinguishes the difference in photosynthetically effective radiation uptake between shaded and sunlit leaves. The TL-LUE model divided the canopy into shade and sunlit leaves and calculated their _APAR_ and _GPP_, respectively [33], which can lower the sensitivity of the model to sky conditions and improve the simulation of _GPP_[34; 35; 36]. The TL-LUE model simulates _GPP_ with the following equations [37]:  
\[GPP=GPP_{shade}+GPP_{sun} \tag{1}\]  
\[GPP_{shade}=(\varepsilon_{sh}\times APAR_{sh})\times T_{s}\times W_{s}\times C _{s} \tag{2}\]  
\[GPP_{sun}=(\varepsilon_{su}\times APAR_{su})\times T_{s}\times W_{s}\times C _{s} \tag{3}\]  
\(\varepsilon_{\text{msu}}\) and \(\varepsilon_{\text{msh}}\) are the maximum LUE of sunlit and shaded leaves, respectively, which were calibrated using the least squares method with the FLUXNET daily data as the reference. \(APAR_{su}\) and \(APAR_{sh}\) are the absorbed photosynthetically active radiation by sunlit and shaded leaves, respectively. They are derived as follows [31]:  
\[APAR_{sh}=(1-\alpha)\times\left(\frac{PAR_{diff}-PAR_{diff,u}}{LAI}+C\right) \times LAI_{sh} \tag{4}\]  
\[APAR_{su}=(1-\alpha)\times\left(\frac{PAR_{diff}\times cos\beta}{cos\theta} \right)+APAR_{sh} \tag{5}\]  
\[LAI_{su}=2 cos\theta\times 1-e^{-\frac{LAI_{sh}\cdot C}{2 cos\theta}} \tag{6}\]  
\[LAI_{shade}=LAI-LAI_{su} \tag{7}\]  
\[C=0.07\times\Omega\times PAR_{dir}\times(1.1-0.1 LAI)e^{-\alpha cos\theta} \tag{8}\]  
\[PAR_{diff}=PAR\times\left(0.7527+3.8453R-16.316R^{2}+18.962R^{3}-7.0802R^{4}\right) \tag{9}\]  
\[PAR_{dir}=PAR-PAR_{diff} \tag{10}\] \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Site-ID**} & \multicolumn{2}{c}{**Vegetation**} & \multirow{2}{*}{**Lon**} & \multirow{2}{*}{**Lat**} & \multirow{2}{*}{**W\({}_{\text{C}}\)**} & \multirow{2}{*}{**W\({}_{\text{P}}\)**} & \multicolumn{2}{c}{**Drought**} \\  & & & & & & & **Year** \\ \hline US-Goo & GRA & 89.87\({}^{\circ}\) W & 34.25\({}^{\circ}\) N & 0.28 & 0.11 & 2005 \\ US-ARc & GRA & 98.04\({}^{\circ}\) W & 35.55\({}^{\circ}\) N & 0.29 & 0.13 & 2006 \\ US-SRG & GRA & 110.83\({}^{\circ}\) W & 31.79\({}^{\circ}\) N & 0.24 & 0.10 & 2009 \\ US-Var & GRA & 120.95\({}^{\circ}\) W & 38.41\({}^{\circ}\) N & 0.29 & 0.12 & 2007 \\ US-Wkg & GRA & 109.94\({}^{\circ}\) W & 31.74\({}^{\circ}\) N & 0.25 & 0.11 & 2007 \\ US-AR1 & GRA & 99.42\({}^{\circ}\) W & 36.43\({}^{\circ}\) N & 0.27 & 0.12 & 2011 \\ DE-Gri & GRA & 13.51\({}^{\circ}\) E & 50.95\({}^{\circ}\) N & 0.26 & 0.11 & 2018 \\ IT-MBo & GRA & 11.05\({}^{\circ}\) E & 46.01\({}^{\circ}\) N & 0.27 & 0.14 & 2019 \\ IT-Tor & GRA & 7.58\({}^{\circ}\) E & 45.84\({}^{\circ}\) N & 0.29 & 0.12 & 2017 \\ BE-Bra & GRA & 4.52\({}^{\circ}\) E & 51.30\({}^{\circ}\) N & 0.25 & 0.14 & 2020 \\ US-MMS & DBF & 86.41\({}^{\circ}\) W & 39.32\({}^{\circ}\) N & 0.32 & 0.10 & 2011 \\ US-PFa & MF & 90.27\({}^{\circ}\) W & 45.95\({}^{\circ}\) N & 0.26 & 0.09 & 2011 \\ BE-Vie & MF & 5.99\({}^{\circ}\) E & 50.30\({}^{\circ}\) N & 0.28 & 0.14 & 2013 \\ US-GLE & ENF & 106.24\({}^{\circ}\) W & 41.36\({}^{\circ}\) N & 0.31 & 0.12 & 2005 \\ CZ-BK1 & ENF & 18.54\({}^{\circ}\) E & 49.50\({}^{\circ}\) N & 0.28 & 0.15 & 2018 \\ FR-Bil & ENF & 0.96\({}^{\circ}\) W & 44.49\({}^{\circ}\) N & 0.30 & 0.10 & 2017 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptions of flux tower sites. GRA: grass-types; DBF: deciduous broadleaf forests; MF: mixed forests; ENF: evergreen needleleaf forests; W\({}_{\text{C}}\): field capacity; W\({}_{\text{P}}\): wilting point. \[PAR_{diff,u}=PAR_{diff}\times e^{-\frac{0 SAI\times\Omega}{cos\theta}} \tag{11}\]  
\[cos\overline{\theta}=0.537+0.025\times LAI \tag{12}\]  
\(\alpha\) is albedo; \(\theta\) is the solar zenith angle; \(\beta\) is the leaf angle, which was taken as 60\({}^{\circ}\); \(\Omega\) is the clumping index; \(\alpha\) and \(\Omega\) varied with ecosystem type, and the values set here follow [PERSON] et al. (2015).