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We analyze a set of simulations to assess the impact of climate change on global forests where MC2 dynamic global vegetation model (DGVM) was run with climate simulations from the MIT Integrated Global System Model-Community Atmosphere Model (IGSM-CAM) modeling framework. The core study relies on an ensemble of climate simulations under two emissions scenarios: a business-as-usual reference scenario (REF) analogous to the IPCC RCP8.5 scenario, and a greenhouse gas mitigation scenario, called POL3.7, which is in between the IPCC RCP2.6 and RCP4.5 scenarios, and is consistent with a 2 °C global mean warming from pre-industrial by 2100. Evaluating the outcomes of both climate change scenarios in the MC2 model shows that the carbon stocks of most forests around the world increased, with the greatest gains in tropical forest regions. Temperate forest regions are projected to see strong increases in productivity offset by carbon loss to fire. The greatest cost of mitigation in terms of effects on forest carbon stocks are projected to be borne by regions in the southern hemisphere. We compare three sources of uncertainty in climate change impacts on the world's forests: emissions scenarios, the global system climate response (i.e. climate sensitivity), and natural variability. The role of natural variability on changes in forest carbon and net primary productivity (NPP) is small, but it is substantial for impacts of wildfire. Forest productivity under the REF scenario benefits substantially from the CO₂ fertilization effect and that higher warming alone does not necessarily increase global forest carbon levels. Our analysis underlines why using an ensemble of climate simulations is necessary to derive robust estimates of the benefits of greenhouse gas mitigation. It also demonstrates that constraining estimates of climate sensitivity and advancing our understanding of CO₂ fertilization effects may considerably reduce the range of projections.