## 2 Materials and Methods
### SIF Based GPP Models  
Recent space-borne SIF observations offer new methods for monitoring vegetation photosynthesis at regional and global scales and contain information about APAR and LUE [22; 23; 33; 36; 53]. GPP can be calculated by the following formula [33; 36; 54; 55]:  
\[GPP\ =\ SIF\times\frac{\varepsilon_{g}}{\varepsilon_{f}\times f_{esc}}\approx SIF \times\frac{\varepsilon_{g}}{\varepsilon_{f}} \tag{8}\]  
where \(\varepsilon_{g}\) represents LUE; \(\varepsilon_{f}\) is the LUE for SIF (i.e., the fraction of APAR photons that are then emitted from the canopy as SIF photons); and \(f_{esc}\) is a term that accounts for the fraction of SIF photons that escape from the canopy to space. While the leaves of grasses and crops have high leaf area index, they have relatively simple plant structure and low absorptance on the near-infrared wavelengths. Thus, \(f_{esc}\) has been used as a relative constant for a given vegetation type, and we assume \(f_{esc}\approx 1\)[33].  
Previous studies at the leaf and canopy scale indicated that the \(\varepsilon_{g}\) and \(\varepsilon_{f}\) terms tend to covary, and their ratios tend to be constant under the conditions of satellite measurements [21; 33; 48; 56; 57]. Despite the changes in the fPAR, PAR, or stress, SIF should be a good constraint on the photosynthetic rate if the ratio of \(\varepsilon_{g}/\varepsilon_{f}\) is constant [58]. Therefore, a simple regression model based on space-borne SIF is able to link SIF with GPP for both cropland and grassland and has been developed for GPP estimation [33]. However, several studies have indicated that \(\varepsilon_{f}\) is weakly sensitive to the photosynthetic pathway type, a large discrepancy in \(\varepsilon_{g}\) between crops and grasses leads to a difference in the slopes, and crop (C4) and grass (C3) species should be considered separately when SIF is used to estimate GPP by applying the linear regression model [20; 27; 57; 59]. Hence, a biome-specific (crop and grass) linear model was used to estimate GPP in our study. The GPPs derived from flux towers via the EC technique were frequently used as validation data in previous studies. However, these studies focused on generally simple and small areas (<1 km\({}^{2}\)). To match the 0.5\({}^{\circ}\) grid cells of the SIF and vegetation index data, we developed a scale conversion coefficient for GPP from flux towers by using the EVI ratio in our study [5; 60]. Specifically, 1 km\({}^{2}\) and 0.5\({}^{\circ}\) grid cells based on the coordinates of the flux towers were used to extract EVI data to match the GPP from flux towers and the SIF from OCO-2 and GOME-2 during the study period, respectively. The EVI ratios for the 0.5\({}^{\circ}\) and 1 km\({}^{2}\) grid cells were calculated; then, the ratios were averaged during the growing season and used as the conversion coefficients. The GPP values from the flux towers were scaled up from a 1 km\({}^{2}\) grid cell to a 0.5\({}^{\circ}\) grid cell spatial  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Site ID** & **T\({}_{\max}\) (\({}^{\circ}\)C)** & **T\({}_{\min}\) (\({}^{\circ}\)C)** & **T\({}_{opt}\) (\({}^{\circ}\)C)** & \(\varepsilon_{0}\) (g C MJ\({}^{-1}\) APAR) \\ \hline Daman & 45 & 0 & 19 & 2.66 \\ A’rou & 35 & 0 & 12 & 1.6 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the VPM at the Daman and A’rou sites.  
scale by using the conversion coefficients. The model performance was evaluated using the coefficient of determination (R\({}^{2}\)) and the root mean square error (RMSE).