## 4 Discussion
### Differences in Environmental Regulations of LUE Models  
Terrestrial ecosystem GPP variations are primarily determined by changes in environmental drivers, such as solar radiation, air temperature, water availability, and vegetation indices, because GPP estimates of LUE models mainly depend on these model inputs. In this study, most of the models found strong positive correlation between GPP estimates and the water availability across large areas and various ecosystems (Figure 5). Our results are consistent with previous global and regional studies. A study has confirmed that water availability influences the vegetation photosynthesis in 40% of the global vegetated areas in recent years [1]. At the regional scale, the spatial variations of annual GPP are positively influenced by rainfall and ET, as evaluated at 35 eddy covariance flux sites [55]. Net ecosystem production has decreased with reduced water availability observed at 14 European sites [56]. However, different LUE models showed varied areas displaying a positive correlation of water availability and GPP estimates (Table 3). Therefore, it can be inferred that different LUE models will give varied GPP estimates in the future, due to varied projections of the ecosystem water balance [57]. We found a negative correlation between GPP and solar radiation, particularly in savanna, shrubland, and grassland across the globe (Figures S1-S7b and S8), which may indicate an additional indirect effect of radiation or temperature on GPP through the water balance [58]. High levels of radiation are usually associated with high temperature and high evapotranspiration rates, which exert high stomatal conductance on the vegetation canopy and thus yield high water stress for primary production in these water-limited ecosystems [1] and vice versa. Therefore, the interannual variability of the CO\({}_{2}\) exchange in savanna, shrubland, and grassland ecosystems depends upon the duration of the wet season [59, 60, 61]. In our study, we found that radiation and water availability showed contrasting trends in these ecosystems, and the latter positively correlated with GPP (Figures S1-S7b,d), indicating that water availability plays a more important role than radiation in regulating the GPP variability due to the above interactions between water and radiation. There are debates on the impacts of radiation and drought on vegetation production in Amazon rainforest. The seven LUE models exhibited different effects of environmental variables on GPP estimates at Amazon (Figure 5). Three models (_i.e._, CFix, CFlux, and EC-LUE) showed that water dominated the GPP variations in this region (Figure 5b,c,d). Other lines of results support this conclusion that drought in Amazon area decreased the GPP [62, 63, 64]. For example, Amazon Basin accumulated 1.2-1.6 Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\) less carbon during the drought period of 2004-2005 than in previous years [62]. In contrast, CASA, VPM, and VPRM models exhibited an important role of solar radiation in regulating GPP estimates in Amazon rainforest. The decreased GPP estimates at this region are due to declined radiation for plants (Figures 5a,f,g, and 6a). Despite the large difference of water regulations on GPP estimates among models, all of the seven LUE models showed the decline of global annual GPP estimates in 2005 (Figure 3). Previous studies have reported the strong impacts of large-scale drought on vegetation production over the Southern Hemisphere, and resulted into the substantial reduction of global vegetation production [3, 65]. In this study, all seven models estimate the same decreased GPP in 2005, which implies the high confidence of model estimates. Our results also support the previous studies that drought is a major cause for the GPP anomaly in 2005 (Figure 4). Temperature shows an important influence on vegetation production at high latitudes because it is a limiting factor for plants in these regions [66]. All of the LUE models in this study integrate the impact of temperature on GPP.