*2.1. CMIP5*

CMIP5 is a set of model experiments for assessing past and future climate change in the Intergovernmental Panel for Climate Change Assessment Report number 5 (IPCC AR5) [19]. To objectively select datasets, the models of CMIP5 data used in this paper met the following criteria.


We used three sets of outputs from 21 models from CMIP5 (Table 1).

**Table 1.** Coupled Model Intercomparison Project Phase 5 (CMIP5) models and the forcing characteristics. Models used in the sensitivity analysis (experiment IDs are esmFixClim1, esmFdbk1, and 1pctCO2) shown in the analysis are highlighted in red.


The experiments are:

1. Historical run: Runs covering the historical period 1850–2005. For this period, model forcings include: greenhouse gases (GHG), volcanoes, aerosols, and land cover.

2. RCP 8.5: Projections forced by pre-determined increasing CO2 concentrations covering 2006 to 2100. For this analysis we chose the RCP 8.5 scenario, a pathway with the highest greenhouse gas emissions, leading to 8.5 W/m<sup>2</sup> radiative forcing at the end of the 21st century [20]. Although just a decade passed since 2006, it has been reported that the emission concentration in 2100 is projected to follow RCP 8.5 [21].

3. Sensitivity experiments: In order to assess the contribution of CO2 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 CO2 of preindustrial level and/or CO2 increasing by 1%/year to 4xCO2: (1) In the fertilization experiment CO2 increases by 1%/year to 4xCO2 for the land surface, but stays constant at preindustrial level for the atmosphere, and thus the climate effect is suppressed and the CO2 fertilization effect is dominant on land (the official experiment ID is esmFixClim1); (2) in the climate experiment CO2 increases for the atmosphere, but stays constant for the land surface, and hence the CO2 fertilization effect is suppressed and the climate impact dominates (esmFdbk1); (3) in the combined experiment CO2 concentration increases for the full Earth system (1pctCO2).

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 CO2 emission driven, but rather CO2 concentration driven, and the results of the carbon budget of vegetation do not change the atmospheric CO2 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:

$$
\Delta GPP = a\,\Delta CO2 + b\,\Delta Clm + f\,\Delta Clm\_{fredback\_{Ar}} \tag{1}
$$

where Δ*CO*2, Δ*Clim*, and Δ*Climf eedback* represent change in CO2 concentration, change in one of the limiting climate factors but only caused by the radiative effect of the change in CO2 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 Δ*Climf eedback* 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 CO2 affects climate and vegetation via increases in leaves' internal CO2 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:

$$
\Delta GPP = \left\| \begin{array}{c} \Delta CO\_2 \ \ + \ f \ \Delta Clim\_{fendback} \end{array} \right\| \tag{2}
$$

It is noteworthy that Δ*CO*<sup>2</sup> includes the effect of changing water use efficiency because it is directly affected by increasing CO2 concentrations, not through changing climate.

The climate experiment shows how higher CO2 affects vegetation via the traditional greenhouse effect on climate. The fertilization effect of increasing CO2 on vegetation was suppressed. The climate experiment can be expressed as:

$$
\Delta GPP = b \,\Delta \text{Clim}\_{\prime} \tag{3}
$$

For mapping purposes, the outputs were firstly re-gridded to 0.5 × 0.5 degree resolution, using the bilinear interpolation method, to be consistent with the limiting factor data [9].

### *2.2. GIMMS-LAI3G*

The GIMMS-LAI3G data were derived from the Global Inventory Modeling and Mapping Studies (GIMMS) Normalized Differential Vegetation Index (NDVI) using the neural network algorithm [24]. We aggregated the 1/12 degree spatial resolution LAI data into the half degree data prior to monthly and annual analysis. To be consistent with historical CMIP5 runs that end in 2005, we used GIMMS-LAI3g data from overlapping the period 1982–2005.
