## 3 Results
### Impacts of V\({}_{\text{cmax}}\) Change on GPP across Europe
(**a**) The relative differences in V\({}_{\text{cmax}}\) between LCC-derived V\({}_{\text{cmax}}\) and TRY-based V\({}_{\text{cmax}}\); (**b**) the corresponding relative difference in GPP caused by changes in V\({}_{\text{cmax}}\). (**c**) The differences between LCC-derived V\({}_{\text{cmax}}\) and the calibrated V\({}_{\text{cmax}}\); (**d**) the corresponding difference in GPP caused by changes in V\({}_{\text{cmax}}\). Figure 7: Seasonal dynamics of V\({}_{\text{cmax}}\) (blue), LAI (green), and GPP (black) for nine PFTs: (**a**) evergreen needleleaf forest (ENF), (**b**) evergreen broadleaf forest (EBF), (**c**) deciduous needleleaf forest (DNF), (**d**) deciduous broadleaf forest (DBF), (**e**) mixed forest (MF), (**f**) shrublands (SH), (**g**) grasslands (GRA), (**h**) croplands (CRO), and (**i**) wetland (WET). 2.2 Including Dynamic V\({}_{\rm cmax}\) Information Improved the Estimation of the GPP Spatial Pattern  
The conventional method of fixing V\({}_{\rm cmax}\) using the model calibration method and TRY database overestimated the European GPP by 0.5 Pg C yr\({}^{-1}\) (Figure 9a) and 2.9 Pg C yr\({}^{-1}\) (Figure 9b), respectively. Compared with \"PC2\", using spatiotemporally explicit V\({}_{\rm cmax}\) information, the terrestrial ecosystem productivity mainly increased for regions in marine climate zones between 43\({}^{\circ}\)N-60\({}^{\circ}\)N and 0\({}^{\circ}\)E-30\({}^{\circ}\)E but decreased for most of the regions in other climate zones (Figure 9c). In contrast, the FGM driven by the TRY-based V\({}_{\rm cmax}\) overestimated the GPP for almost all the regions, especially for cropland (Figure 9d). Including dynamic V\({}_{\rm cmax}\) information improved the FGM's performance in simulating the variability in European GPP based on the spatial correlations between the estimated annual GPP and other GPP products or GOSIF data (Figure 9e). Figure 9: Spatial pattern of mean annual GPP (g C m\({}^{-2}\) yr\({}^{-1}\)) when V\({}_{\rm cmax}\) was parameterized in the FGM as a PFT-specific constant with two types of data: (**a**) calibrated V\({}_{\rm cmax}\) (“PC2”) and (**b**) TRY-based V\({}_{\rm cmax}\) (“PC3”). (**c**) and (**d**) represent the differences in GPP due to the different V\({}_{\rm cmax}\) parameterizations, i.e., GPP in “All” minus GPP in (**a**) and (**b**). (**e**) Spatial correlation (r) between the FGM GPP for three different simulations (“All”, “PC2”, and “PC3”) and other GPP products (including BEPS, FLUXCOM, GLASS, and GOSIF GPP products) and GOSIF data. 2.3 Interannual Changes in V\({}_{\rm cmax}\) Only Have a Minor Effect on GPP in a Limited Period of 16 Years  
We further evaluated the V\({}_{\rm cmax}\) change effect on GPP on annual time scales (Figure 10). Compared with \"PC2\", the annual GPP of cropland, grassland, and forests demonstrated reductions of 8%, 21%, and 9%, respectively, with the inclusion of the LCC-derived V\({}_{\rm cmax}\). However, we also noticed a slight 8% increase in the GPP for shrubland. Using the TRY-based V\({}_{\rm cmax}\), the FGM overestimated the annual GPP of cropland, grassland, shrubland, and forests by 49%, 34%, 26%, and 15%, respectively. Figure 10: The V\({}_{\rm cmax}\) change effect on GPP on annual time scales. (**a**) Difference in mean annual total GPP and (**b**) interannual variations in total GPP from 2001 to 2016 for the four dominant vegetation types (i.e., crop, forest, shrub, and forest) in the simulations w/o the V\({}_{\rm cmax}\) constraint. (**c**) The V\({}_{\rm cmax}\) change effect on interannual variations in total GPP across Europe simulated by the FGM in four model simulations (i.e., “All”, “PC1”, “PC2” and “PC3”) using the LCC-derived dynamic V\({}_{\rm cmax}\) from 2001 to 2016 (“All”), LCC-derived dynamic V\({}_{\rm cmax}\) from 2001 to 2016 (“PC1”), calibrated constant V\({}_{\rm cmax}\) (“PC2”), and TRY-based constant V\({}_{\rm cmax}\) (“PC3”). Section 2.2.3 contains descriptions of these four simulation experiments.