## 5 Discussion  
### Contributions of Multiple Variables to the GPP Simulation  
To quantify the contribution of climate variables (including temperature, radiation, and dew point temperature), atmospheric CO\({}_{2}\) concentrations, LAI, land cover, and vegetation indices that characterize canopy N concentrations to changes in global annual total GPP from 2001 to 2018, we fixed variable \(i\) (\(i\) = climate variables, CO\({}_{2}\) concentrations, LAI, Land cover, NI) at the initial state to simulate the interannual variation of global GPP (Figure 15). Moreover, Figure 16 showed the spatial patterns of cumulative contributions of various variables to global annual GPP from 2001 to 2018. Under the normal situation (S\({}_{\text{All}}\)), each variable changes normally over time, and the global annual GPP simulation (NI-LUE) increased at a rate of 0.53 Pg C/yr from 2001 to 2018. In contrast, the global GPP simulation (NI-LUE\({}_{\text{i0}}\)) under other situations showed different trends. With the climate variables fixed at the initial state (2001), the global annual GPP simulation (NI-LUE\({}_{\text{C10}}\)) increased at a rate of 0.52 Pg C/yr from 2001 to 2018. Among all variables, climate variables may be more of a moderator. In 2009, for example, El Nino led to higher surface temperatures, and warmer and drier climate conditions [81]. The NI-LUE GPP under the normal situation dropped suddenly in 2009, consistent with the GPP trends simulated by the two process-based biophysical models in Figure 13a, while the NI-LUE\({}_{\text{C10}}\) kept rising during the year. From 2001 to 2018, the cumulative contribution of climate variables to global GPP simulation was 12.39 Pg C. As shown in Figure 16a, the positive contributions of climate variables were mainly distributed in northern and southern South America, western Europe, central Africa, and southern China, while in eastern North America and the northern coast of South America regions, as well as the island of New Guinea in Southeast Asia, the contribution of climate variables was negative, reducing GPP in these regions. Atmospheric CO\({}_{2}\) concentrations significantly accelerated global GPP increase. The global annual GPP simulation (NI-LUE\({}_{\text{C020}}\)) increased at a rate of 0.33 Pg C/yr with the atmospheric CO\({}_{2}\) concentrations fixed in 2001. Considering CO\({}_{2}\) concentrations, the trend of global GPP interannual change increased by 60.6%. As the fuel of photosynthesis, a continued rise in atmospheric CO\({}_{2}\) contributed positively to the increase in GPP [25; 82]. In this study, atmospheric CO\({}_{2}\) concentrations cumulatively contributed 30.77 Pg C to the global GPP simulation based on the NI-LUE model from 2001 to 2018. For the spatial pattern of the cumulative contribution of CO\({}_{2}\) to GPP simulation from 2001 to 2018 (Figure 16b), it is similar to the global vegetation distribution, with higher contributions in tropical Southeast Asia, central Africa and South America, decreasing from low latitudes to high latitudes. LAI was mainly used in the NI-LUE model to distinguish shaded leaves and sunlit leaves, and calculate their APAR. With the LAI fixed in 2001, the global NI-LUE\({}_{\text{LAl0}}\) GPP still showed a significant increasing trend with a rate of 0.53 Pg C/yr. Overall, the cumulative contribution of LAI to global GPP from 2001 to 2018 was -8.12 Pg C. It was obvious that, from 2006 to 2009 and 2018, LAI played an important role in the reduction of global GPP simulations based on the NI-LUE model (Figure 15). For the spatial pattern of cumulative contributions to LAI (Figure 16c), the positive contribution of LAI was mainly distributed in northeast China, central and southern North America, and central Brazil, while the negative contribution of LAI was obvious in southern Brazil, southeastern Africa, and Australia. It was worth noting that the contribution of LAI was most likely to depend on the LAI product driving the model, and its initial value in 2001 may determine the contribution to GPP.