## 4 Results
### Performance of the EF-LUE Model Driven by Ground Measurements at Eddy Covariance Flux Tower Sites
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Model without EF**} & \multicolumn{3}{c}{**Model with EF**} \\ \multirow{2}{*}{**Climate Type**} & \(\varepsilon_{max}\) & \(\varepsilon_{max}\) & \(\varepsilon_{max}\) & \(\varepsilon_{max}\) \\  & **(g C MJ\({}^{-1}\))** & \(T_{opt}\) (C\({}^{0}\)) & **(g C MJ\({}^{-1}\))** & \(T_{opt}\) (C\({}^{0}\)) & **\(VPD_{0}\) (kPa)** \\ \hline CRO/Cs & 2.999 & 31.037 & 0.590 & 2.725 & 30.665 & 1.262 \\ CRO/Ctb & 2.752 & 18.983 & 0.592 & 2.652 & 17.573 & 1.756 \\ CRO/Cas & 1.506 & 13.306 & 0.478 & 1.509 & 19.475 & 1.651 \\ CRO/DHa & 2.913 & 35.000 & 2.998 & 3.443 & 34.948 & 2.992 \\ CRO/Dbt & 2.272 & 18.330 & 0.745 & 2.373 & 13.903 & 1.765 \\ CRO/Dc & 2.249 & 34.964 & 0.759 & 1.959 & 26.274 & 0.646 \\ CRO/Bsk & 3.494 & 23.386 & 1.704 & 3.850 & 22.473 & 1.526 \\ CRO/Bwk & 3.999 & 32.615 & 1.853 & 3.984 & 29.279 & 1.546 \\ Average & 2.773 + 0.777 & 25.938 + 8.506 & 1.215 +0.892 & 2.812 + 0.887 & 24.824 + 2.760 & 1.643 + 0.656 \\ All & 2.811 & 34.839 & 2.905 & 2.970 & 29.494 & 2.865 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimized model parameters (\(\varepsilon_{max}\), \(T_{opt}\), and \(VPD_{0}\)) of the LUE-based model for crop GPP estimate in different climate zones (‘with EF’ denotes our new EF-LUE model; ‘without EF’ means water availability constraint was not considered). The optimized values of the model parameters in each climate zone were applied to the EF-LUE model (Equations (1)-(6)) to estimate GPP driven by the local meteorological variables (EF were calculated using flux measurements at each site) and remote sensing FPAR. For comparison, we also estimated GPP using the model 'without EF' by setting \(F_{W}=1\) in Equation (1). We compared the model results with the ground measurements at an 8-day time step to examine the model accuracy and capability in capturing the temporal variations of GPP (Figures 2-4). In general, the EF-LUE model and the model without EF driven by tower ground measurements data explained 82 % and 74% of the temporal variations in GPP across the cropland sites, respectively (Figure 2a, only used the validation sub-dataset). The overall Kling-Gupta efficiency (KGE) increased from 0.73 to 0.83, NSE increased from 0.73 to 0.81, and RMSE decreased from 2.87 to 2.39 g C m\({}^{-2}\) d\({}^{-1}\) after integrating EF in the LUE model. Furthermore, the performance of the EF-LUE model and the model without EF for water availability constraint at an 8-day time step were also verified respectively in the summer half year (between the day of vernal equinox (21 March) and the day of autumnal equinox (23 September)) and the winter half year (Figure 2b,c). The accuracy of the EF-LUE model in the summer half year improved significantly over the model without EF, with R\({}^{2}\) increased from 0.67 to 0.77 and RMSE decreased from 3.86 g C MJ\({}^{-1}\) to 3.19 g C MJ\({}^{-1}\) (Figure 2b). After incorporating EF in the LUE model, the overestimation of low values and the underestimation of high values of the GPP estimated by the LUE model without considering soil water availability were alleviated. In the winter half year, the accuracy of the model was also greatly improved after integrating EF in the LUE model, and the R\({}^{2}\) increased from 0.49 to 0.53 (Figure 2c). The performance of the EF-LUE model and the model without EF as water availability constraint were also evaluated in different climate zones as shown in Figure 3. The accuracy in the estimated GPP by the EF-LUE model was obviously improved in most climate zones. The results from the EF-LUE model showed the highest R\({}^{2}\) in the climate zones of BSk and BWk (R\({}^{2}\) > 0.9) (Figure 3a,b). In the Cfa, Cfb, and Dfb climate zones, the improvement of the EF-LUE model was most significant, with an increase of more than 0.1 in R\({}^{2}\) over the results of the model without EF (Figure 3c,d,g).