Success at the latest climate talks will be a recognition by the world’s nations that incremental change will not do the job, says Johan Rockström.

Ensuring that the world's food needs are met by 2050 will take a doubling of global food production. To improve agricultural yields on that scale will require a radical rethink of global water-management strategies and policies. Sub-Saharan Africa is the epicentre of this challenge. Ninety-five per cent of sub-Saharan agriculture depends on 'green water': moisture from rain held in the soil. In large parts of the continent, most rain evaporates before it generates 'blue water', or run-off, so little of it recharges rivers, lakes and groundwater.