## 3 Results
### Which Control (VPD or Soil Moisture) Can Explain Long-Term Trend in GIMMS NDVI?  
To evaluate whether the TOPS simulations are consistent with satellite observations, we calculated the differences of mean annual GPP between 2000-2009 and 1982-1999 for three simulations (_S_control_, _S_veg_, and _S_clim_) (Figure 3). Because _S_veg_ was derived from GIMMS 3g under a fixed climate, we can assume _S_veg_ to correspond to the anomaly of satellite-observed GPP. _S_control_ and _S_clim_ were very consistent with each other, while _S_veg_ showed spatial patterns of higher GPP in China, Brazil, India, and USA, indicating that TOPS underestimated GPP in these regions during the 2000s.  
Next, we calculated the difference of mean annual GPP between 2000-2009 and 1982-1999 for _S_wo_sm_ and _S_wo_vpd_ (Figure 4(c,d)). Inconsistencies between _S_wo_sm_ and _S_wo_vpd_ occurred in Brazil, Africa, and Europe, with _S_wo_sm_ showing more negative anomalies than _S_wo_vpd_ in most of the regions. In these regions, precipitation increased in 2000s (Figure 4(b)), while VPD also increased (Figure 4(a)). Estimates from _S_wo_vpd_, compared to _S_wo_sm_, are more consistent with _S_veg_ (Figure 3(b)) especially in West Brazil and Europe. Overall the effects of drought stress were more marked in the _S_wo_sm_ simulations than in _S_wo_vpd_.  
Figure 5 shows the histograms of the differences between 2000-2009 GPP and 1982-1999 GPP for the 3 simulations (_S_veg_, _S_wo_sm_, and _S_wo_vpd_), which were derived from Figures 3(b) and 4. Both _S_veg_ and _S_wo_vpd_ were positively skewed (skewness are 0.597 and 1.865, respectively), while _S_wo_sm_ was negatively skewed (skewness is -1.460). The mean of _S_veg_ (0.011 kg\(\cdot\)C\(\cdot\)yr\({}^{-1}\)) was between the means of _S_wo_sm_ (-0.008 kg\(\cdot\)C\(\cdot\)yr\({}^{-1}\)) and _S_wo_vpd_ (0.023 kg\(\cdot\)C\(\cdot\)yr\({}^{-1}\)). As a result, distribution of _S_veg_ is between _S_wo_vpd_ and _S_wo_sm_, but closer to _S_wo_vpd_ than _S_wo_sm_. These results suggest that the TOPS model overestimated the drought stress due to an overestimated VPD effect in the 2000s, and that both precipitation and VPD down regulation functions are required to simulate the long-term GPP trend.  
Figure 2: (**a**) Anomaly of global GPP estimated by the climate only run (_S_clim_), climate only run without soil moisture control (_S_wo_sm_), and climate only run without Vapor Pressure Deficit (VPD) control (_S_wo_vpd_). The time series of the CO\({}_{2}\) growth rate is shown with the black dashed line. (**b**) Time series of the correlation coefficient between GPP of the three simulations and CO\({}_{2}\) growth rate for the past 7 years.  
Figure 3: Difference of mean annual Gross Primary Production (GPP) between 2000–2009 and 1982–1999. Panel (**a–c**) are simulated with control run (_S_control_), fixed climate run (_S_veg_), and fixed vegetation run (_S_clim_), respectively.  
Figure 4: Difference of mean Vapor Pressure Deficit (VPD), precipitation, and Gross Primary Production (GPP) between 2000–2009 and 1982–1999. Panel (**a**) is annual mean VPD difference, and Panel (**b**) is annual total Precipitation difference. Panel (**c**) is the difference of annual total GPP of the simulation without-soil moisture (_S_wo_sm_), and Panel (**d**) is that of the simulation without-VPD (_S_wo_vpd_). The climatology of fPAR was used for all the simulations.  
Figure 5: Histograms of the differences between 2000–2009 Gross Primary Production (GPP) and 1982–1999 GPP for the GIMMS-3g driven simulation (_S_veg_), without-soil moisture simulation (_S_wo_sm_), and without-VPD (Vapor Pressure Deficit) simulation (_S_wo_vpd_). The maps of the differences are shown in Figure 3(b), Figure 4(c,d), respectively. The means in the legend are mean value of the difference for each scenario.