## 3 Results  
### Spatial and Temporal Differences of Global GPP Estimates  
All seven LUE models showed similar spatial patterns of GPP estimates (Figure 1). The annual GPP was the highest in the humid tropics and sub-tropics, intermediate in temperate regions, and the lowest in both cold and arid regions where either temperature or water availability was the limiting factor of GPP. The seven models, however, revealed substantial differences in the GPP estimates across geographical regions and ecosystem types (Figure 1, Tables 1 and 2). For example, the CASA model simulated the lowest GPP over nearly all regions, which accounted for 68% of the highest GPP estimate from the VPRM model (Figure 1). Overall, the largest difference in the GPP estimates occurred in tropical and humid areas with high levels of production (Figure 1h). The annual GPP on the global scale ranged between 95.10 and 139.71 Pg C\(\cdot\)yr\({}^{-1}\), and the GPP estimates differed substantially at the various vegetation types (Tables 1 and 2). Three vegetation types (_i.e._, shrubland, grassland, and savanna) differed most pronounced in GPP simulations among models, as indicated by the largest coefficient of variation values (CV = 20.59%-31.07%, Table 1). Evergreen broadleaf forest, evergreen needleleaf forest, and cropland also showed considerable variability (CV = 19.07%-20.24%, Table 1). For example, evergreen broadleaf forest accounted for 22.26%-33.97% of the global GPP estimates among models, with a 19.84 Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\) difference between the maximum (EC-LUE) and the minimum (CASA) GPP estimates for this type (Tables 1 and 2). Figure 1: Spatial patterns of the global annual GPP estimates over the period 2000–2010 by **(a)** CASA; **(b)** CFix; **(c)** CFlux; **(d)** EC-LUE; **(e)** MODIS; **(f)** VPM; and **(g)** VPRM models; **(h)** the standard deviation of the GPP estimates among models. DES is no vegetation area. The long-term changes in GPP estimates differed among the seven LUE models (Figures 2 and 3). There were large differences in the long-term GPP trend from 2000 to 2010 over almost the entire vegetated areas of the globe (Figure 2). More than 50% of the vegetation areas had increasing GPP in more than half of the seven models (_i.e._, CFix, CFlux, EC-LUE, and MODIS models) (Figure 2). In terms of global annual GPP trend, three of the seven models (_i.e._, CFix, CFlux, and EC-LUE) showed a significant GPP increase from 2000 to 2010, with the trend ranging from 0.37 to 1.09 Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\), and the largest increase of GPP was found in the CFlux model (Figure 3). The CASA and MODIS models presented relatively constant long-term change (0.20 Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\), \(p=0.08\) and 0.01 Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\), \(p=0.92\), respectively), and the other two models (_i.e._, VPM and VPRM) showed slightly decreased GPP (\(-0.15\) Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\), \(p=0.34\) and \(-0.04\) Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\), \(p=0.78\), respectively) (Figure 3). All of the seven LUE models showed the decline of GPP in 2005 and then increase trend (Figure 3). Moreover, interannual variability of GPP highly correlated with the Palmer Drought Severity Index (PDSI) in the Southern Hemisphere (Figure 4). Two models (_i.e._, MODIS and VPRM) showed significant correlation (r = 0.88 and 0.71, respectively, \(p<0.05\)) between GPP and PDSI in the Southern Hemisphere. Three models (_i.e._, CASA, CFix, and VPM) showed weak correlation (r = 0.32-0.44, \(p>0.05\)).