Intense rainstorms are a prevalent feature of current weather. Evidence is presented showing that simulation of flood hydrographs shown to be dominated by subsurface flow requires watershed model parameterisation to vary between periods of different rainstorm intensity, in addition to varying with antecedent basin storage. The data show an emerging global relation between flood response and the intensity of rainstorms. Flood responses are quantified as watershed residence times (strictly time constants of nonlinear transfer-function models) identified directly from information contained within 15-min rainfall and streamflow observations. The emerging monotonic, curvilinear relation indicates that (subsurface) watershed residence time decreases as mean intensity rises, and is seen over a wide range of synoptic conditions from temperate and tropical climates. Projected increases in rainstorm intensity would then result in a greater likelihood of river floods in subsurface-dominated watersheds than is currently simulated by systems models omitting this additional nonlinearity.