## 4 Results
### Performance of the EF-LUE Model Driven by Ground Measurements at Eddy Covariance Flux Tower Sites
In the Csa  
Figure 2: Comparisons of GPP between estimation by the models and ground measurements by eddy covariance system at cropland flux tower sites (using validation dataset): (**a**) whole year; (**b**) summer half year (Spring Equinox (21 March) to Autumn Equinox (23 September)); and (**c**) winter half year. EF data were from flux tower measurements. The blue and red points represent GPP estimated by the EF-LUE model and by the model without EF, respectively. The solid lines are the regression lines, and the gray dashed lines are the 1:1 line. there were too few data samples to give a credible conclusion though both models showed favorable results (Figure 3e,h). Figure 4 gave the results at each flux tower site, the GPP estimated by the EF-LUE model showed higher R\({}^{2}\) and lower RMSE in most sites compared with the results by LUE model without EF, especially at CH-Oe2, DE-Geb, DE-Seh, US-Ne2, and US-Ne3. The coefficient of determination (R\({}^{2}\)) increased from 0.53 to 0.78, and the RMSE decreased from 3.12 to 2.17 at CH-Oe2 sites. The KGE increased from 0.62 to 0.81 at the US-Ne3 site. The NSE increased from 0.73 to 0.88 at the DE-Geb site. However, although the EF-LUE model generally improved the accuracy in the estimated GPP compared to the method without EF, it performed unsatisfactorily at some sites such as the FR-Gri, US-ARM, and DE-Seh sites (R\({}^{2}<\) 0.7) (Figure 4). The results were biased by uncertainty in the satellite-based FAPAR data (figures not shown), which could be improved further by improving the quality of the FAPAR product. Figure 3: Comparisons between GPP estimated by the model and GPP measured by eddy covariance at cropland flux tower sites (using validation dataset) in the following climate zones: (**a**) BSk; (**b**) BWk; (**c**) Cfa; (**d**) Cfb; (**e**) Casa; (**f**) Dfa; (**g**) Dfb; (**h**) Dfc. To further explore the model performance in capturing the temporal variation, we plotted the time series of the estimated GPP together with the ground measurements for the validation sub-dataset at four sites, i.e., DE-Geb, YC, US-ARM, and US-Ne2 (Figure 5). The EF-LUE model could effectively reproduce temporal variations in the GPP observations at these cropland sites. The GPP estimated by the EF-LUE model performed well in tracking the ground-measured GPP at the beginning and the end of the growing season (Figure 5). Moreover, the GPP estimated by the EF-LUE model was closer to the GPP measured by eddy covariance system during the hot summer period at these sites. Soil water availability, expressed by EF, regulated the changes in GPP in the early growing stage and aging stage, as well as during hot summer when soil water stress often occurred. On the contrary, the estimated GPP by the model without EF showed an early start in the beginning of the growing season and a lag in the end of the growing season, in particularly at the site US-Ne2. However, deviation between the estimated GPP by the EF-LUE model and the measured GPP still existed, which might be attributed to the uncertainties in the forcing data, in particularly the satellite observation-based FAPAR. Another possible source of errors could be the different spatial footprints between the ground flux measurements and the 1 km pixel size for GPP estimate. Figure 4: Comparisons between GPP estimated by the LUE models (with and without EF) and GPP measured by eddy covariance at flux tower sites (using validation sub-dataset): (**a**) R\({}^{2}\); (**b**) RMSE; (**c**) Bias; (**d**) KGE; (**e**) NSE. Solid and open circles represent the results from the EF-LUE model (i.e., with EF) and the LUE model without EF, respectively, driven by meteorological data from flux tower sites.