## 3 Results
### Differences in Environmental and Vegetation Regulations of the LUE Models  
The simulated GPP of LUE models were regulated by many factors, including solar radiation, surface moisture, air temperature, and vegetation indices. In this study, almost all models showed strongly positive correlations between GPP and water availability (indicated by ET, inverted VPD, and LSWI) over the Southern Hemisphere, such as southern South America, Africa, Australia, and Northern arid areas, North America, and Western Europe (Figures 5 and S1-S7d). For most of the models, the air temperature dominated the GPP variability in the North high latitudes and the Tibetan Plateau (Figures 5 and S1-S7c). However, very weak temperature contributions to GPP were found over the high latitudes within the CFix and EC-LUE models (Figure 5b,d). Solar radiation played an important role in regulating the GPP interannual variability in Amazon rainforest within CASA, VPM, and VPRM models (Figure 5a,f,g). In contrast, three models (_i.e._, CFix, CFlux, and EC-LUE) showed strong water-dominated GPP variability over this region (Figure 5b,c,d). Figure 4: Interannual variations of annual GPP estimates and PDSI over the Southern Hemisphere (SH). Figure 3: Interannual variability of the GPP estimates of the seven light use efficiency (LUE) models from 2000 to 2010. Vegetation indices also played an important role in regulating the ecosystem GPP in most of the LUE models. More than half of the seven models positively correlated vegetation indices (shown by NDVI, EVI, and FPAR) with GPP estimates over more than half (_i.e._, 56.19%-65.02%) of the global vegetated areas (Table 3), such as Amazon, Australia, Southeast Asia, North America, and Western Europe (data not shown). In particular, CFix and EC-LUE had more vegetated areas showing positive correlations of vegetation indices with GPP compared with other models (Table 3). Figure 5: Spatial distribution of the environmental constraints to the annual GPP estimates over the period 2000–2010 of seven LUE models: **(a)** CASA; **(b)** CFix; **(c)** CFlux; **(d)** EC-LUE; **(e)** MODIS; **(f)** VPM; and **(g)** VPRM. Three environmental variables were considered: solar radiation (PAR, Green), air temperature (Blue), and water availability (Red). Differences in the model input variables resulted in significant differences in the interannual variability of GPP estimates among LUE models. Obvious spatial trends of the long-term GPP estimates were substantially different over the 11 years. Figure 6 showed that the key environmental variables and vegetation indices related with GPP, such as solar radiation, water availability, and air temperature, all changed significantly over the globe. Correlation analyses showed strong positive relationships between the GPP estimates and ET over large areas within the CFix, CFlux, and EC-LUE models (Figure 5b-d). This environmental variable increased between 2000 and 2010 in corresponding geographical regions (Figure 6d), which resulted in interannual variations of GPP estimates. At areas such as the southern South America, South Africa, North America, and Southeast Asia, GPP estimates were correlated with ET in the three models, and the increased ET led to consistent GPP increase (Figure 4b-d).