# Constraints to Vegetation Growth Reduced by Region-Specific Changes in Seasonal Climate
## 2 Materials and Methods
### CMIP5
Sensitivity experiments: In order to assess the contribution of CO\({}_{2}\) fertilization and climate effects on vegetation separately, we used an eight-model (highlighted in Table 1) ensemble to compare three CMIP5 experiments, each of which was run for 140 years and experiences a constant CO\({}_{2}\) of preindustrial level and/or CO\({}_{2}\) increasing by 1%/year to 4 xCO\({}_{2}\): (1) In the fertilization experiment CO\({}_{2}\) increases by 1%/year to 4 xCO\({}_{2}\) for the land surface, but stays constant at preindustrial level for the atmosphere, and thus the climate effect is suppressed and the CO\({}_{2}\) fertilization effect is dominant on land (the official experiment ID is esmFixClim1); (2) in the climate experiment CO\({}_{2}\) increases for the atmosphere, but stays constant for the land surface, and hence the CO\({}_{2}\) fertilization effect is suppressed and the climate impact dominates (esmFdbk1); (3) in the combined experiment CO\({}_{2}\) concentration increases for the full Earth system (1 pctCO2). To calculate the ensemble mean, at first, we remapped all the CMIP5 data into quarter degree grid data using the bilinear interpolation method. Then, we calculated the ensemble mean for each quarter degree grid from the available modeled data. In this paper, gross primary production (GPP) was chosen from available CMIP5 land variables as the representation of photosynthesis. GPP is the amount of photosynthesis by vegetation per unit area, from which respiration is not subtracted. In the budget analysis, net biome production (NBP), which accounts for respiration and disturbance, should be the key flux of vegetation response. However, these experiments are not CO\({}_{2}\) emission driven, but rather CO\({}_{2}\) concentration driven, and the results of the carbon budget of vegetation do not change the atmospheric CO\({}_{2}\) concentration. Thus, GPP, which is equivalent to photosynthesis, can represent vegetation growth better than NBP. We also used LAI as the representative of carbon storage because LAI can be compared to satellite estimates. The vegetation response in the historical run, RCP 8.5, and combined experiments in sensitivity experiments can be simplified by the linear models as follows:  
\[\Delta GPP\ =\ a\ \Delta CO_{2}\ +\ b\ \Delta Clim\ +\ f\ \Delta Clim_{ feedback}, \tag{1}\]  
where \(\Delta CO_{2}\), \(\Delta Clim\), and \(\Delta Clim_{feedback}\) represent change in CO\({}_{2}\) concentration, change in one of the limiting climate factors but only caused by the radiative effect of the change in CO\({}_{2}\) concentration, and feedback of climate by changing GPP through the fertilization effect, respectively. The coefficients a, b, and f assume a simple linear system. The term \(\Delta Clim_{feedback}\) represents the feedback of GPP through effects on climate, such as the effect of a change in cloud cover due to increasing evapotranspiration. The fertilization experiment examines how higher CO\({}_{2}\) affects climate and vegetation via increases in leaves' internal CO\({}_{2}\) concentration, which should in turn reduce stomatal conductance transpiration. As a result, climate feedback occurs as decreasing cloud cover whilst increasing soil moisture, runoff, and solar radiation [11; 22; 23]. So, the fertilization experiment can be expressed as:  
\[\Delta GPP\ =\ a\ \Delta CO_{2}\ +\ f\ \Delta Clim_{feedback}, \tag{2}\]  
It is noteworthy that \(\Delta CO_{2}\) includes the effect of changing water use efficiency because it is directly affected by increasing CO\({}_{2}\) concentrations, not through changing climate. The climate experiment shows how higher CO\({}_{2}\) affects vegetation via the traditional greenhouse effect on climate. The fertilization effect of increasing CO\({}_{2}\) on vegetation was suppressed.