## 3 Results
### The Difference in GPP by Including Spatiotemporal \(V_{\text{cmax}}\) Dynamics  
The state-of-the-art TBMs generally assume a constant \(\text{V}_{\text{cmax}}\) for a specific PFT. One typical parameterization method is to retrieve the optimal \(\text{V}_{\text{cmax}}\) from flux tower observations. The mean GPP of Europe estimated by FGM parameterized with such PFT-specific \(\text{V}_{\text{cmax}}\) values [28] was 9.90 Pg C yr\({}^{-1}\) (Figure 4a), which was 0.5 Pg C yr\({}^{-1}\) higher than GPP estimations using the \"All\" simulation. Spatially, the difference in GPP caused by changes in \(\text{V}_{\text{cmax}}\) exhibited heterogeneous spatial patterns in different countries. With the new data of spatiotemporal information on \(\text{V}_{\text{cmax}}\) (Figure 4b), we observed a pronounced decrease in GPP for Ukraine (\(-\)262.4 g C m\({}^{-2}\) yr\({}^{-1}\)), Moldova (\(-\)151.5 g C m\({}^{-2}\) yr\({}^{-1}\)), Spain (\(-\)120.7 g C m\({}^{-2}\) yr\({}^{-1}\)), Greece (\(-\)108.2 g C m\({}^{-2}\) yr\({}^{-1}\)), and Russia (\(-\)90.9 g C m\({}^{-2}\) yr\({}^{-1}\)). In contrast, vegetation in San Marino (+133.2 g C m\({}^{-2}\) yr\({}^{-1}\)), the Netherlands (+128.6 g C m\({}^{-2}\) yr\({}^{-1}\)), Luxembourg (+130.7 g C m\({}^{-2}\) yr\({}^{-1}\)), and France (+83.7 g C m\({}^{-2}\) yr\({}^{-1}\)) appeared more productive (Figure 4c).  
Figure 3: Interannual dynamics of the LAI and GPP for all of the Europe and for different plant functional types. (**a**) Comparison of interannual trends of annual total GPP based on the FGM and other methods (including BEPS, MOD17, CCW, GLASS V6, VPM, GOSIF, and FLUXCOM RF, MARS, and ANN) and the interannual trend in the mean LAI from 2001 to 2016. (**b**) Interannual dynamics of the mean LAI based on the GLASS V5 LAI product across the whole study area (including Europe and part of Russia) or only the European mainland (excluding Russia). Interannual dynamics of the mean LAI (**c**) and GPP (**d**) for five vegetation types (i.e., forests, shrub, grass, crop, and wetland). The abbreviation LUE in (**a**) stands for the light use efficiency model. The labels *** and * in (**a**) represent the interannual GPP trend at significance levels of 0.01 and 0.05, respectively. The GPP unit Tg C in (**d**) is equivalent to \(10^{-3}\) Pg C.  
In comparison with the GPP based on PFT\(-\)specific V\({}_{\text{cmax}}\), major differences emerged for the GPP for different PFTs using the \"All\" simulation, without a consistent bias in any one direction (Figure 4d). When the FGM was constrained by dynamic V\({}_{\text{cmax}}\) maps, shrubland became more productive while forests and grassland became less productive. The productivity of shrublands noticeably increased in San Marino (+162.2 g C m\({}^{-2}\) yr\({}^{-1}\)), Luxembourg (+136.8 g C m\({}^{-2}\) yr\({}^{-1}\)), the Netherlands (+124.2 g C m\({}^{-2}\) yr\({}^{-1}\)), Liechtenstein (+117.1 g C m\({}^{-2}\) yr\({}^{-1}\)), and Montenegro (+108.1 g C m\({}^{-2}\) yr\({}^{-1}\)) (Figure 4d). The largest reduction in forest productivity occurred in Slovenia (\(-\)86.7 g C m\({}^{-2}\) yr\({}^{-1}\)), followed by Bosnia and Herzegovina (\(-\)75.6 g C m\({}^{-2}\) yr\({}^{-1}\)) and Slovakia (\(-\)63.3 g C m\({}^{-2}\) yr\({}^{-1}\)). Grassland productivity decreased in Albania, Spain, Montenegro, and Greece. There is a pronounced reduction in the productivity of croplands in Ukraine (\(-\)203 g C m\({}^{-2}\) yr\({}^{-1}\)) and Moldova (\(-\)151.5 g C m\({}^{-2}\) yr\({}^{-1}\)), while the productivity of marine croplands in Belgium, Czech Republic, Poland, Hungary, Germany, and Slovakia increased moderately.