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Across Africa, perennial drainage density as a function of mean annual rainfall defines three regimes separated by threshold values of precipitation. This non-linear response of drainage to rainfall will most seriously affect regions in the intermediate, unstable, regime. A 10% decrease in precipitation in regions on the upper regime boundary (1000 mm/y) would reduce drainage by 17%, while in regions receiving 500 mm/y such a drop would cut 50% of surface drainage. Using predicted precipitation changes, we calculate that decrease in perennial drainage will significantly affect present surface water access across 25% of Africa by the end of this century.