## 3 Results
### Impacts of V\({}_{\text{cmax}}\) Change on GPP across Europe  
2.1 Dynamic V\({}_{\text{cmax}}\) Information Is Important for the Accurate Estimation of GPP Seasonality  
We further evaluated the seasonal variation in V\({}_{\text{cmax}}\) using three types of V\({}_{\text{cmax}}\) data: (a) V\({}_{\text{cmax}}\) derived from the LCC (i.e., LCC-derived V\({}_{\text{cmax}}\)); (b) V\({}_{\text{cmax}}\) retrieved by the model calibration method (i.e., Calibrated V\({}_{\text{cmax}}\)); and (c) V\({}_{\text{cmax}}\) based on the TRY database (i.e., TRY-based V\({}_{\text{cmax}}\)) (Figure 7). In comparison with the calibrated V\({}_{\text{cmax}}\), the LCC-derived V\({}_{\text{cmax}}\) showed major differences, without a consistent bias in any one direction. In spring and autumn, the LCC-derived V\({}_{\text{cmax}}\) reduced the overestimation of V\({}_{\text{cmax}}\) for most PFTs and reduced the underestimation for EBF; in summer, the LCC-derived V\({}_{\text{cmax}}\) reduced the overestimation of V\({}_{\text{cmax}}\) for WET, GRA, DBF, and DNF and the underestimation for CRO, SH, MF, EBF, and ENF. In comparison with the V\({}_{\text{cmax}}\) from the TRY database, we found that the TRY-based V\({}_{\text{cmax}}\) was consistently larger than the LCC-derived V\({}_{\text{cmax}}\) throughout the seasons for all biomes, especially for CRO and GRA. The seasonal pattern of the LCC-derived V\({}_{\text{cmax}}\) was very similar to those of the LAI and GPP. Figure 3: Model calibration accuracy for nine PFTs: (**a**) CRO, (**b**) DBF, (**c**) SH, (**d**) EBF, (**e**) GRA, (**f**) MF, (**g**) ENF, and (**h**) WET. The R\({}^{2}\), RMSE, and slope were estimated from the regression of the modeled GPP and EC-GPP for each biome with the intercept forced to 0. Biome abbreviations are given in Figure 2. The gray dots represent simulations constrained by seasonal dynamic V\({}_{\text{cmax}}\) using the “All” model simulations (dots in pink circles). The dashed and solid lines are the regression line and 1:1 line, respectively. Figure 4: Model validation accuracy for nine PFTs: (**a**) CRO, (**b**) DBF, (**c**) SH, (**d**) EBF, (**e**) GRA, (**f**) MF, (**g**) ENF, and (**h**) WET. Figure 5: Spatial distribution of mean annual European GPP and SIF based on different sources of data, including **(a)** FGM GPP, **(b)** BEPS GPP, **(c)** FLUXCOM GPP, **(d)** GLASS GPP, **(e)** GPP derived from GOSIF, **(f)** VPM GPP, and **(g)** original GOSIF data. Here, **(h)** illustrates the correlation matrix between these data. Consequently, these differences in V\({}_{\rm cmax}\) (Figure 8a,c) led to synchronous changes in the GPP estimated by the FGM (Figure 8b,d). In comparison with the GPP from \"PC2\" (Figure 8b), in spring and autumn, the inclusion of the LCC-derived V\({}_{\rm cmax}\) reduced the overestimation of GPP for all the PFTs, especially for MF, DBF, DNF, and ENF. In summer, the LCC-derived V\({}_{\rm cmax}\) reduced the overestimation of GPP for GRA and the underestimation of GPP for CRO, SH, MF, and EBF. In comparison with the GPP from \"PC3\", the inclusion of the LCC-derived V\({}_{\rm cmax}\) reduced the overestimation of GPP using the TRY-based V\({}_{\rm cmax}\) (Figure 8d). Figure 6: Comparison of the interannual variations in annual GPP (Pg C yr\({}^{-1}\)) simulated by the FGM and by other methods (including BEPS, MODIS, CCW, GLASS, VPM, GOSIF, FLUXCOM-RF, FLUXCOM-MARS, and FLUXCOM-ANN). (**a**) Interannual dynamics of annual GPP for Europe during 2001–2016. ** and * indicate increasing trends in the total annual GPP from 2001 to 2016 at \(p\)-value < 0.05 and \(p\)-value < 0.01, respectively. (**b**) Temporal correlation (r) between the FGM GPP and other GPP products. A total of nine global GPP products were estimated by different methods. Figure 8: Relative differences in V\({}_{\text{cmax}}\) and corresponding relative GPP differences caused by changes in V\({}_{\text{cmax}}\) with the seasons.