## 2 Materials and Methods
### Big-Leaf LUE-GPP Models
#### 2.5.2 MODIS Model  
The MODIS model assumes that \(LUE_{\mathrm{max}}\) is jointly affected by \(T_{\mathrm{s}}\) and \(W_{\mathrm{s}}\) rather than completely restricted by only one of them. Moreover, it uses VPD to quantify the moisture constraints on \(LUE_{\mathrm{max}}\) since APAR cannot be used for estimating GPP because leaf stomata are closed when VPD is high [21]. The MODIS model is expressed as below:  
\[GPP=PAR\times fPAR\times LUE_{\mathrm{max}}\times T_{\mathrm{s}}\times W_{ \mathrm{s}} \tag{4}\]  
\[T_{\mathrm{s}}=\left\{\begin{array}{cc}0&T_{\mathrm{min}}<0\\ \frac{T_{\mathrm{a}}-T_{\mathrm{min}}}{T_{MAX\mathrm{min}}-T_{\mathrm{min}}}&T _{\mathrm{min}}\leq T_{a}\leq T_{MAX\mathrm{min}}\\ 1&T_{a}>T_{MAX\mathrm{min}}\end{array}\right. \tag{5}\]  
\[W_{\mathrm{s}}=\left\{\begin{array}{cc}0&VPD>VPD_{\mathrm{max}}\\ \frac{VPD_{\mathrm{max}}-VPD}{VPD_{\mathrm{max}}-VPD_{\mathrm{min}}}&VPD_{ \mathrm{min}}\leq VPD\leq VPD_{\mathrm{max}}\\ 1&VPD<VPD_{\mathrm{min}}\end{array}\right. \tag{6}\]  
where \(VPD_{\mathrm{min}}\) and \(VPD_{\mathrm{max}}\) indicate the lower and upper thresholds of VPD (kPa) affecting leaf photosynthesis, which are set to 0.5 kPa and 4 kPa, respectively, and \(T_{MAX\mathrm{min}}\) indicates the temperature when \(LUE\) is at maximum and is assumed to be consistent with \(T_{\mathrm{opt}}\) in this study.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model** & **Model Structures** & **Required Parameters** & **Input Variables** \\ \hline Eddy covariance-light use & \multirow{2}{*}{PAR \(\times\) fPAR \(\times\)\(\varepsilon_{\mathrm{max}}\)\(\times\)\(Min\) (\(T_{\mathrm{s}}\), \(W_{\mathrm{s}}\))} & \(\varepsilon_{\mathrm{max}}\), \(T_{\mathrm{min}}\), \(T_{\mathrm{max}}\), \(T_{\mathrm{opt}}\) & \multirow{2}{*}{_LAI_, _PAR_, \(T_{\mathrm{a}}\), \(R_{\mathrm{n}}\), \(LE\)} \\ efficiency model (EC-LUE) & & & \\ Moderate resolution imaging & \multirow{2}{*}{PAR \(\times\) fPAR \(\times\)\(\varepsilon_{\mathrm{max}}\)\(\times\)\(T_{\mathrm{s}}\)\(\times\)\(W_{\mathrm{s}}\)} & \(\varepsilon_{\mathrm{max}}\), \(T_{\mathrm{min}}\), \(T_{\mathrm{opt}}\), \(T_{\mathrm{MAXmin}}\) & \multirow{2}{*}{_LAI_, _PAR_, \(T_{\mathrm{a}}\), \(VPD\)} \\ spectroradiometer GPP & & & \\ algorithm (MODIS) & & & \\ Vegetation photosynthesis & \multirow{2}{*}{PAR \(\times\) fPAR \(\times\)\(\varepsilon_{\mathrm{max}}\)\(\times\)\(T_{\mathrm{s}}\)\(\times\)\(\times\) model (VPM)} & \multirow{2}{*}{\(W_{\mathrm{s}}\)\(\times\)\(P_{\mathrm{s}}\)} & \multirow{2}{*}{\(T_{\mathrm{opt}}\), \(LSWI_{\mathrm{max}}\)} & \multirow{2}{*}{_LAI_, _PAR_, \(T_{\mathrm{a}}\), \(LSWI\)} \\ Model vegetation & & & \\ photosynthesis model (MVPM) & & & \\ Terrestrial ecosystem carbon flux & & & \\ model (TEC) & & & \\ Carnegie-Ames-Stanford & \multirow{2}{*}{PAR \(\times\) fPAR \(\times\)\(\varepsilon_{\mathrm{max}}\)\(\times\)\(T_{\mathrm{s}}\)\(\times\)\(W_{\mathrm{s}}\)} & \multirow{2}{*}{\(\varepsilon_{\mathrm{max}}\), \(T_{\mathrm{min}}\), \(T_{\mathrm{max}}\), \(T_{\mathrm{opt}}\), & \multirow{2}{*}{_LAI_, _PAR_, \(T_{\mathrm{a}}\), \(R_{\mathrm{n}}\), \(\lambda\), \(LE\), \(G\), \(\Delta\), \(\gamma\)} \\ approach (CASA) & & & \\ (PAR \(\times\) fPAR \(\times\)\(\varepsilon_{\mathrm{sum}}\)+ PAR \(\times\)\(\varepsilon_{\mathrm{sum}}\)+ PAR \(\times\) & \(\varepsilon_{\mathrm{max}}\), \(\varepsilon_{\mathrm{sh-max}}\), \(T_{\mathrm{min}}\), \(T_{\mathrm{opt}}\), & \multirow{2}{*}{\(R_{\mathrm{a}}\), \(R_{\mathrm{s}}\), \(\Omega\), \(C\), \(LAI\), \(PAR\), \(\overline{\theta}\), \(\mathrm{fPAR}\)\(\times\)\(\varepsilon_{\mathrm{sh-max}}\)\(\times\)\(T_{\mathrm{s}}\)\(\times\)\(W_{\mathrm{s}}\)} & \(VPD_{\mathrm{min}}\), \(VPD_{\mathrm{max}}\) & \(T_{\mathrm{a}}\), \(VPD\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model structures and parameters of the seven light use efficiency-based gross primary production (LUE-GPP) models.