## 3 Results
### GPP and Water Use Efficiency  
In the historical simulations, GPP continuously increased in most regions and dominantly followed the GHG forcing (Figure 8a,b). PR and net radiation have also increased in the near past, but they have not performed so consistently since 1850, such as GPP. Most photosynthesis models estimate the GPP and transpiration by using [PERSON]'s model [56]. This model considers photosynthetically active radiation (PAR), which is normally proportional to the incoming short-wave solar radiation although there is a limit point known as the maximum electron transport (e.g., maximum carboxylation rate) [57; 12; 58]. The photosynthesis model is also related to temperatures, humidity, CO\({}_{2}\) concentration, water, etc. [56; 58]. Among these main variables, solar energy and water are surely the key drivers of plant photosynthesis [13; 59; 60]. However, this strong GHG influence is an interesting result concerning the existence of the maximum carboxylation rate and maximum Rubisco-limited rate in the photosynthesis model. Increasing both temperature and CO\({}_{2}\) in the [PERSON] model can elevate the GPP in the GHG-only simulation, but such a dominant role of GHG over the other factors remains questionable. The role of other physiological effects may need to be investigated. Current land surface models account for key environmental conditions and physiological functions such as nutrients, plant demography, water use efficiency, and even root distribution [60; 61; 62; 63].  
Figure 8: Results of the GPP and WUE analysis: (**a**) 50-year mean start-to-end difference in GPP (1850-2010); (**b**) time series plot of global GPP; (**c**) 10-year mean start-to-end difference in WUE (1870–2010); (**d**) time series plot of global WUE. The titles above the plots and the legends within the plots are followed by the number of ensemble models in parentheses, and the estimated parameters with hats provide statistical significances. On the maps, dots indicate where the differences are significant (\(p\)-value \(\leq\) 0.05).  
In order to identify the cause of GPP increase, we estimated water use efficiency (WUE) of plants as GPP/ET [64; 65]. The result indicated that increasing GHG (CO\({}_{2}\)) elevates the efficiency of photosynthesis. The absorption of carbon dioxide (productivity) dominated ET variation (Figure 8c,d). Precipitation, water budget, soil moisture, and surface energy grew only slightly, but the photosynthesis rate abruptly increased. To a lesser extent than GHG, the influence of AER is also detected by using MLRM. As solar energy (AER effect) is a physically important driver and was statistically significant in MLRM analysis, it cannot be disregarded in future scenarios. Here, the limit of this high efficiency is not certain yet when both GHG and AER rising. The ecological resilience against GHG and AER changes should be investigated in future scenarios. In the past, high AER counterbalanced the GHG effect to some extent. However, AER has declined recently and is expected to decline in the future, so WUE could rise significantly unless GHG suddenly returns to its original state. Therefore, the study of the limit of WUE and its consequences may be necessary. Such changes in GHG and AER can result in extreme physiological stages when vegetation receive excessive solar energy and reach the WUE limit.