# Constraints to Vegetation Growth Reduced by Region-Specific Changes in Seasonal Climate
## 3 Results
### Decomposing Vegetation Growth Into Three Factors  
The results indicate that the climate feedback substantially contributed to the growth of vegetation by relaxing climate constraints. Although it is well known that the climate feedback can positively or negatively influence the growth of vegetation, it has not been quantitatively assessed at the global scale. The sensitivity experiments allow us to quantitatively evaluate the climate feedback to vegetation (\(f\)\(\Delta\)\(Clim_{feedback}\) in Equation (1)). We assumed that the ratio of GPP change to change in climate variables is constant (i.e., b = f = _const._). At first, we calculated \(\Delta\)\(GPP\) / \(\Delta\)\(Clim\) (i.e., b) in the climate experiment using the linear regression of annual GPP on annual mean climate variables. Then, we calculated _a_\(\Delta\)\(CO_{2}\) by subtracting \(f\)\(\Delta\)\(Clim_{feedback}\) from GPP increase in Equation (2). Finally, _b_\(\Delta\)\(Clim\) was derived from Equation (3) by subtracting _a_\(\Delta\)\(CO_{2}\) and \(f\)\(\Delta\)\(Clim_{feedback}\) by assuming the additive relationship of the fertilization effect and the climate change effect.  
The percentage ratios of the contribution of each term (i.e., _a_\(\Delta\)\(CO_{2}\), _b_\(\Delta\)\(Clim\), and \(f\)\(\Delta\)\(Clim_{feedback}\)) were shown for each limited region in Figure 11. In the temperature-limited region, all the three terms substantially contributed to the increase in GPP, and the annual average of the climate feedback contribution was 17%. The snow-albedo feedback can account for the climate feedback [38; 39]. The climate feedback added 37% more increase in GPP than the radiative warming effect alone. The total contribution of climate feedback and climate is 63%, which is the highest contribution among the three climate-limited regions. The contribution is much higher in winter than summer because the temperature did not limit GPP in the summer.  
In the precipitation limited area, there was almost no contribution of the climate feedback effect. This result can be explained by the relatively low water-recycling ratio compared to the humid area [40]. The moisture from the other regions controls the precipitation trend in the water-limited region, so that the influence of changing water use efficiency on the region is negligible.  
In the radiation-limited area, the contribution of the climate feedback is 7%, while the radiative climate change negatively affects 24% of the increase in GPP. The feedback was caused by the decreasing trend in cloud cover through change in water use efficiency [35]. The magnitude of the contribution of the climate feedback changes with model selection due to the difficulty in modeling clouds in GCMs. Thus, the feedback contribution can be underestimated, especially when a low resolution GCM cannot  
Figure 10: Spatial distribution of the additive and counteracting impacts of CO\({}_{2}\) on vegetation. Same as Figure 8 except for transpiration, **a**, **d**, **g**; GPP, **b**, **e**, **h**; and LAI, **c**, **f**, **i**.  
represent well the increase in regional convective clouds caused by the enhanced water cycle that results from added vegetation growth.