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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 nonlinear 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 millimeters per year) would reduce drainage by 17%, whereas in regions receiving 500 millimeters per year, such a drop would cut 50% of surface drainage. By using predicted precipitation changes, we calculate that a decrease in perennial drainage will significantly affect present surface water access across 25% of Africa by the end of this century.