While the parties to the UNFCCC agreed in the December 2009 Copenhagen Accord that a 2°C global warming over pre-industrial levels should be avoided, current commitments on greenhouse gas emissions reductions from these same parties will lead to a 50 : 50 chance of warming greater than 3.5°C. Here, we evaluate the differences in impacts and adaptation issues for water resources in worlds corresponding to the policy objective (+2°C) and possible reality (+4°C). We simulate the differences in impacts on surface run-off and water resource availability using a global hydrological model driven by ensembles of climate models with global temperature increases of 2°C and 4°C. We combine these with UN-based population growth scenarios to explore the relative importance of population change and climate change for water availability. We find that the projected changes in global surface run-off from the ensemble show an increase in spatial coherence and magnitude for a +4°C world compared with a +2°C one. In a +2°C world, population growth in most large river basins tends to override climate change as a driver of water stress, while in a +4°C world, climate change becomes more dominant, even compensating for population effects where climate change increases run-off. However, in some basins where climate change has positive effects, the seasonality of surface run-off becomes increasingly amplified in a +4°C climate.