## 3 Results
### Improvement Comparison Between TL-LUE and VPM  
Based on the results of Sections 3.1 and 3.2, we found that TL-LUE and VPM have a general consistency, but there were some obvious differences. Thus, we further compared the performance between the two models by calculating the difference between the R\({}^{2}\) and RMSE values of the two models (\(\Delta\)R\({}^{2}\), \(\Delta\)RMSE) at each site (Figure 11). It showed that the superiority or inferiority of the TL-LUE model versus VPM on grass ecosystems varied across sites. Among the six sites in North America, the original TL-LUE model simulations were inferior to those of the original VPM at four sites (\(\Delta\)R\({}^{2}\) = \(-\)0.05 to \(-\)0.20, \(\Delta\)RMSE = 0.21 to 1.69 gCm\({}^{-2}\) day\({}^{-1}\)). In contrast, the TL-LUE model outperformed VPM at grass-type sites in Europe. We also found that VPM generally outperformed the TL-LUE model with Scheme 2, both at the sites in North America and Europe. For the TL-LUE model, Scheme 2 accounted for both VPD and SM, whereas for VPM, it accounted for both LSWI and SM. For forest-type sites, both in North America and Europe, the original TL-LUE model performed significantly better than VPM (\(\Delta\)R\({}^{2}\) = 0.01\(--\)0.22, \(\Delta\)RMSE = \(-\)0.08 to \(-\)0.51 gCm\({}^{-2}\) day\({}^{-1}\)). Figure 10: Performance comparison of GPP estimation with different schemes for incorporating SM information by TL-LUE and VPM for non-drought years across different systems. Therefore, we conjecture whether the combination of LSWI and SM is superior to that of VPD and SM for grass-type sites and whether VPD better characterizes water stress for forest-type sites. To test this hypothesis, we examined the correlation between in situ observations of GPP and various moisture indicators (e.g., LSWI, SM, VPD) during drought years (Table 2). The GPP at all ten grass-type sites exhibited the strongest correlation with LSWI. Differently, at forest sites, the GPP displayed the strongest correlation with VPD. Therefore, we speculate that for grass-type sites, VPD may be responsible for the worse performance of the scheme multiplying VPD and SM in the TL-LUE model. On the other hand, incorporating VPD into VPM might improve the GPP simulation for forests. To support this perspective, we analyzed the use of different moisture indicators in the TL-LUE model at the grass-type sites and in VPM at the forest sites (Figures 12 and 13, and Figures S16-S31). For the TL-LUE model, we conducted the simulations at the grass-type sites using four different moisture indicators: VPD, LSWI, SM, and LSWI*SM (Figure 12). The results indicate that replacing VPD with LSWI in the TL-LUE model led to substantial improvements. For instance, at the US-Var site, replacing VPD with LSWI resulted in an increase of R\({}^{2}\) by about 0.2 with a decrease in RMSE by 0.90 gCm\({}^{-2}\) day\({}^{-1}\). Combining the results of the improvements at the 10 grass-type sites, 3 had an increase in R\({}^{2}\) of 0.1 to 0.2 (US-Var, US-SRG, and US-Wkg), and the remaining 7 sites had changes in R\({}^{2}\) of 0.02 to 0.07. For the grassland sites, the maximum R\({}^{2}\), the minimum R\({}^{2}\), and the average value of R\({}^{2}\), as well as the RMSE simulated by the SM*LSWI scheme at all the sites, performed best among all the schemes. Therefore, the SM*LSWI scheme was the optimal scheme for the grassland sites, followed by the schemes LSWI and SM, and the scheme considering only VPD showed the poorest performance. At the US-SRG site, the scheme multiplying LSWI with SM was higher in R\({}^{2}\) by 0.06 with lower RMSE by 0.11 gCm\({}^{-2}\) day\({}^{-1}\) than the scheme using only SM. This was also verified by the results at all 10 grass-type sites, which showed an increase of R\({}^{2}\) by 0.0 to 0.09 and a decrease in RMSE by 0.01 to 0.2 gCm\({}^{-2}\) day\({}^{-1}\). For all six forest sites, replacing LSWI with VPD in VPM also showed an improvement over the original model (Figure 13).