## 3 Results
### Evaluation of Improved Models  
#### 3.2.1 Temporal Variations on Typical Site  
Figure 6 shows the simulated daily GPP over the year 2007 by the TL-LUE model with different modeling schemes for incorporating SM information at the grass-type site of US-Var. For the original TL-LUE model, although the simulations highly agreed with the observations during the initial drought period from the day of the year (DOY) 55 to 140, the simulations greatly overestimated from DOY 140 to 280 (Figure 6a). After  
Figure 5: Validation of daily GPP estimated by VPM with tower measurements (GPP\({}_{\rm EC}\)) at 16 sites (The red line represents the fitting line, and the dashed line represents the 1:1 line).  
incorporating SM information, all the simulations with different schemes showed clear improvements (Figure 6b-d). For these three schemes, a greatly improved performance was observed, especially during DOY 140 to 280. For Scheme 1, R\({}^{2}\) raised about 0.19, and RMSE dropped about 0.89 gCm\({}^{-2}\) day\({}^{-1}\). For Scheme 2, R\({}^{2}\) improved from 0.77 to 0.95, and RMSE decreased from 1.50 to 0.68 gCm\({}^{-2}\) day\({}^{-1}\). For Scheme 3, R\({}^{2}\) improved from 0.77 to 0.95, and RMSE decreased from 1.50 to 0.93 gCm\({}^{-2}\) day\({}^{-1}\). Overall, the simulations with Scheme 1 performed the best at the US-Var site.  
Figure 7 shows the simulated daily GPP over the year 2007 by VPM at the US-Var site. The original VPM significantly underestimated GPP during the initial period, from DOY 55 to 140 (Figure 7a). However, it greatly overpredicted GPP during DOY 140 to 280, which is similar to the case of the TL-LUE model. Clear improvements were observed in the simulations incorporating SM information. For Scheme 1, R\({}^{2}\) raised from 0.50 to 0.81, and RMSE dropped from 2.23 gCm\({}^{-2}\) to 1.34 gCm\({}^{-2}\) day\({}^{-1}\) (Figure 7b). For Scheme 2, it was in high agreement with Scheme 1, but R\({}^{2}\) further raised to 0.82 and RMSE reduced to 1.30 gCm\({}^{-2}\) day\({}^{-1}\) (Figure 7c). The performance of Scheme 3 is slightly inferior to the first two schemes but also has a significant improvement over the original model, with an R\({}^{2}\) of 0.78 and RMSE of 1.44 gCm\({}^{-2}\) day\({}^{-1}\) (Figure 7d). Overall, the simulations with Scheme 2 had the best performance at the US-Var site.  
Figure 6: The simulated daily GPP with the different schemes for incorporating SM information by the TL-LUE model against FLUXNET observations at the US-Var site during the drought episode in 2007 (**(a)** represents the original model simulation results, and **(b–d)** represent the simulation results for scheme 1–scheme 3).  
Figure 7: The simulated daily GPP with the different schemes for incorporating SM information by VPM against FLUXNET observations at the US-Var site during the drought episode in 2007 (**(a)** represents the original model simulation results, and **(b–d)** represent the simulation results for scheme 1–scheme 3).  
We conducted similar analyses at other fifteen sites (Figure 8 and Figures S1-S15). We analyzed the improvements of R\({}^{2}\) and RMSE, i.e., the difference between the indexes of the best solution and the original model.