*3.1. Annual Mean Trend and Climate Feedback to Vegetation*

The multi-model ensemble mean shows pervasive future changes in vegetation structure and function by the end of this century under the high-emission RCP 8.5 scenario: LAI increases by up to 60% and GPP increases by up to 100% (Figure 2). LAI significantly increases globally except for Amazon, Mexico, and Southern Africa (Figure 2a). GPP also significantly increases for nearly the entire vegetated planet (Figure 2b), though the magnitudes may be uncertain [32]. The percentage changes are higher in the high latitude regions for LAI, while changes in magnitude of LAI and GPP are higher in both the high latitude and tropical regions. A few tropical and semi-arid areas show decreases in LAI, but none of the changes are statistically significant. The results of increasing LAI are consistent with Mahowald et al. [33].

**Figure 2.** Greening of the Earth. Simulated changes in leaf area index (LAI) and gross primary production (GPP) from the Earth system models of CMIP5. Shown are differences in annual average mean LAI (**a**) and annual total GPP (**b**) at each grid cell for 2090–2099 minus 2006–2015. Stippling shows statistically significant differences among models from a Wilcoxon signed rank test at the 95% level. Right subplots are latitude average of LAI and GPP for 2006–2015 (blue) and 2090–2099 (green).

We divided the climate (Figure 3) and the vegetation (Figure 4) response in the RCP 8.5 scenario into the temperature-limited, precipitation-limited, and radiation-limited regions. Temperature and precipitation increase for all the three regions, while radiation increases only in the radiation-limited area (Figure 3). Thus, all the climate factors contribute to vegetation growth in addition to the CO2 fertilization effect. As a result, all the three different climate-limited regions experience increases in ensemble GPP and LAI throughout the 21st century (Figure 4). LAI in the temperature-limited region shows large variability among the models compared to GPP, which implies the difficulty in modeling respiration and allocation ratios. LAI in the radiation-limited region shows a significant increase, but the magnitude of increase is small due to the saturation of the leaf increase.

By the last decade of the 21st century, the summary of the projections shows that annual climate constraints will ease for 51% of the Earth's vegetated land area (i.e., warmer in the temperature-limited region), tighten in 11% of the land area, with the remainder experiencing no change. The degree of easing varies, from 94% in the temperature-limited region and 23% in the precipitation-limited region, to 45% in the radiation-limited region (Figure 1b–d).

**Figure 3.** Climate responses from the Earth system models of CMIP5, summarized over the three climate-limiting regions. The simulations represent RCP 8.5, a pathway with the highest greenhouse gas emissions. Ensemble means and the percentiles show progressive relief of the main limiting factor for each region. Models diverge substantially towards the end of the simulation period, but almost all trends are statistically significant (see p-values in each panel). Changes in temperature (**a**–**c**), precipitation (**d**–**f**), and radiation (**g**–**i**) are expressed as percent of initial values in 2006. Outputs of Community Earth System Model, version 1–Biogeochemistry (CESM1-BGC), red line, are shown as examples of results from Earth system models incorporating nitrogen cycling. The p-value was calculated from Mann–Kendall trend test.

**Figure 4.** Vegetation responses from the Earth system models of CMIP5, summarized over the three climate-limiting regions. Same as Figure 3, except for changes in transpiration (**a**–**c**), GPP (**d**–**f**), and LAI (**g**–**i**).
