## 3 Results  
### Model Evaluation  
3.1.1 Including Dynamic V\({}_{\rm{cmax}}\) Information Improved GPP Estimation at EuroFLUX Sites  
We first compared the performance of the FGM between the 19 validation sites (Table 1) using the LCC-derived dynamic V\({}_{\rm{cmax}}\) (\"All\") and TRY-based constant V\({}_{\rm{cmax}}\) (\"PC3\"). While \"PC3\" used only the LAI to describe changes in vegetation status, \"All\" considered the variability in both the LAI and the V\({}_{\rm{cmax}}\) in the estimation of GPP. Compared with the TRY-based V\({}_{\rm{cmax}}\), the FGM improved the estimation of daily GPP, with the R\({}^{2}\) increased from 0.52 to 0.64 and RMSE decreased by 25%. When forcing the intercept to zero, the R\({}^{2}\) was much higher (0.95 to 0.96). Meanwhile, the scatters between the estimated GPP and EC-GPP from \"All\" were closer to the 1:1 line, with smaller biases than \"PC3\" after including the LCC-derived V\({}_{\rm{cmax}}\) (Figure 2).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**GPP** & **Spatial** & **Temporal** & \multirow{2}{*}{**Method**} & **Time** & \multirow{2}{*}{**Reference**} \\  & **Resolution** & **Resolution** & & & **Period** & \\ \hline GOSIF & 0.05\({}^{\circ}\) & Annual & Empirical model & 2001–2016 & [113; 120] \\ BEPS & 0.073\({}^{\circ}\) & Daily & TBM & 2001–2016 & [34; 37; 121; 122] \\ GLASS (v6) & 500 m & Annual & LUE model & 2001–2016 & [28; 117] \\ MODIS (6) & 500 m & Annual & LUE model & 2001–2016 & [115] \\ VPM & 500 m & Annual & LUE model & 2001–2016 & [116] \\ CCW & 0.05\({}^{\circ}\) & Annual & LUE model & 2001–2016 & [30] \\ FLUXCOM & 0.5\({}^{\circ}\) & Annual & Machine Learning & 2001–2016 & [118; 119] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Information on nine GPP products for intercomparison.  
Figure 2: Validation of model-estimated annual total GPP (g C m\({}^{-2}\) yr\({}^{-1}\)) and GPP derived from EC data for the 19 EuroFLUX sites selected for independent model validation (Table 1). GPP values estimated using the FGM were parameterized with (**a**) LCC-derived V\({}_{\rm{cmax}}\) and (**b**) TRY-based V\({}_{\rm{cmax}}\). The R\({}^{2}\) and RMSE were estimated from the regression lines for the modeled GPP and EC-GPP. The black solid lines and the red solid lines are the regression lines with the intercept forced to 0 or not, respectively.  
The FGM model generally showed a reasonable performance in predicting daily GPP compared with in situ GPP measurements across different biomes in Europe (Figures 3 and 4). Overall, the FGM captured an average of 87.5% of the variation in the EC-GPP from the validation dataset. We randomly split the forty EuroFLUX sites into 1:1 by biome to conduct independent model calibration and validation. Our independent validation indicated that the R\({}^{2}\) between the modeled GPP and EC-GPP ranged from 0.79 to 0.93, with RMSE values ranging from 0.9 to 2.73 g C m\({}^{-2}\) d\({}^{-1}\) (Figure 3). The independent validation analysis indicated the strongest model performances for MF and DBF (Figure 3b,f) and less satisfactory agreement for CRO (Figure 3a). The agricultural sites had a relatively high RMSE of 2.72 g C m\({}^{-2}\) d\({}^{-1}\) and a relatively low R\({}^{2}\) of 0.79, mainly based on deviations in amplitude and growing season periods (Figure S1). For example, in the case of DE_Seh, the FGM predicted lower GPP values than those of EC-GPP (Figure S1). The modeled GPP values were close to the values of EC-GPP in 2008 but showed lower productivity in the vegetation phase compared to the values of EC-GPP in 2007 for the same site (e.g., DE_Seh), probably due to uncertainties in the remote sensing products, such as the LAI (Figure S2). Despite some discrepancies, the FGM generally simulated the variations in the GPP on the daily time scale effectively.