## 2 Materials and Methods
### Methods
#### 2.3.2 [PERSON] et al. [32] developed the EC-LUE model which is mainly driven by FAPAR, PAR, the air temperature, and the Bowen ratio of sensible to latent heat flux. Because of the weak simulation of sensible and latent heat fluxes on a large spatial scale, adopting the Bowen ratio for presenting water stress factors (\(\text{W}_{s}\)) will hinder EC-LUE model application on a large scale [75]. In this study, VPD was used to replace sensible and latent heat fluxes to calculate \(\text{W}_{s}\)[21]. The GPP in EC-LUE is estimated as follows:  
\[\text{GPP}=\text{ FAPAR}*\text{IPAR}*\varepsilon_{\text{max}}*\text{Min}(\text{T}_{ \text{S}},\text{W}_{\text{S}})\] (2a) where FAPAR is obtained from the OLCI FAPAR product (OGVI). IPAR is the same as in the MODIS GPP algorithm. \[\varepsilon_{\text{max}}\] is the potential LUE without environmental stress and is set  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Description** \\ \hline \(\varepsilon_{\text{max}}\) & The maximum light use efficiency \\ \(\text{TMIN}_{\text{max}}\) & Daily minimum temperature where \(\varepsilon=\varepsilon_{\text{max}}\) \\ \(\text{TMIN}_{\text{min}}\) & Daily minimum temperature at which \(\varepsilon=0.0\) \\ \(\text{VPD}_{\text{max}}\) & Daylight average vapor pressure deficit at which \(\varepsilon=\varepsilon_{\text{max}}\) \\ \(\text{VPD}_{\text{min}}\) & Daylight average vapor pressure deficit at which \(\varepsilon=0.0\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Biome properties look-up table parameters for daily gross primary production (GPP) [50;74].  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Biome Types** & **ENF** & **DBF** & **MF** & **CSH** & **OSH** & **WSA** & **GRA** & **CRO** \\ \hline \(\varepsilon_{\text{max}}(\text{gC}/\text{m}^{2}/\text{d}/\text{M}\text{J})\) & 0.962 & 1.165 & 1.051 & 1.281 & 0.841 & 1.239 & 0.860 & 1.044 \\ \(\text{TMIN}_{\text{max}}\) (\({}^{\circ}\)C) & \(-8.00\) & \(-6.00\) & \(-7.00\) & \(-8.00\) & \(-8.00\) & \(-8.00\) & \(-8.00\) \\ \(\text{TMIN}_{\text{min}}\) (\({}^{\circ}\)C) & 8.31 & 9.94 & 9.50 & 8.61 & 8.80 & 11.39 & 12.02 & 12.02 \\ \(\text{VPD}_{\text{max}}\) (Pa) & 650.0 & 650.0 & 650.0 & 650.0 & 650.0 & 650.0 & 650.0 \\ \(\text{VPD}_{\text{min}}\) (Pa) & 4600.0 & 1650.0 & 2400.0 & 4700.0 & 4800.0 & 3200.0 & 5300.0 & 4300.0 \\ \hline \hline \end{tabular}
\begin{tabular}{c} ENF: evergreen needleleaf forests; DBF: deciduous broadleaf forests; MF: mixed forests; CSH: closed shrulbands; OSH: open shrulbands; WSA: woody savannas; GRA: grasslands; and CRO: croplands. \\ \end{tabular}
\end{table}
Table 3: Biome properties look-up table for the moderate resolution imaging spectroradiometer (MODIS) GPP algorithm [50].  
to 2.14 (gC/m\({}^{2}\)/d) [33]. T\({}_{\rm s}\) and W\({}_{\rm s}\) are the downward-regulation scalars for the individual influences of temperature and humidity on LUE. Min denotes the minimum value of T\({}_{\rm s}\) and W\({}_{\rm s}\). T\({}_{\rm s}\) indicates a limiting influence of temperature on vegetation photosynthesis, based on the algorithm of the temperature limiting factor in the Terrestrial Ecosystem Model (TME) [76; 77]:  
\[\rm T_{s}=\frac{(T-T_{min})(T-T_{max})}{(T-T_{min})(T-T_{max})-\left(T-T_{opt} \right)^{2}} \tag{2b}\]  
where T is the average air temperature (\({}^{\circ}\)C), and T\({}_{\rm min}\), T\({}_{\rm max}\), and T\({}_{\rm opt}\) represent the minimum, maximum, and optimum air temperatures (\({}^{\circ}\)C), respectively, for photosynthetic activities. If the air temperature is below T\({}_{\rm min}\) or exceeds T\({}_{\rm max}\), Ts is set to zero. According to [32], this study set T\({}_{\rm min}\) and T\({}_{\rm max}\) to 0 and 40 \({}^{\circ}\)C, respectively, and T\({}_{\rm opt}\) was determined to be 20.33 \({}^{\circ}\)C through nonlinear optimization. The W\({}_{\rm s}\) can be expressed as follows:  
\[\rm W_{s}=\frac{VPD_{0}}{VPD_{0}+VPD} \tag{2c}\]  
where VPD\({}_{0}\) is the half-saturation coefficient of the Equation (2c), obtained from previous research (Table 4) [21].