Quick Hillslope Response: Time to Equilibrium for Hortonian and Dunnian Flows

The development of a thin stream above the soil surface (overland flow) is associated to two mechanism of runoff generation on the hillslope: the infiltration and saturation excess mechanism. The first one, firstly proposed by Horton, typically occurs in arid and semi-arid regions, usually characterised by high rainfall intensities on soil exhibiting low infiltrabilities. For stationary rainfall of indefinite duration, the rainfall excess monotonically increases from zero (at time to ponding) to a maximum (at time to equilibrium), equal to the difference between rain intensity and saturated hydraulic conductivity. Overland flow develops along an “active” hillslope length, comparable to the total length of hillslope, which does not vary significantly during the rainstorm. The second one, firstly introduced by Hewlett and Hibbert, constitutes the main mechanism of runoff generation in humid regions, characterised by high groundwater table. The runoff is produced by contributing areas of restricted extent that expands with time, where soil water content is near to the saturation, whereas rainfall excess is (approximately) equal to its maximum (previously defined) and does not vary with time. Aim of this work is to investigate on the implications of temporal variability of rainfall excess and of temporal variability of active hillslope length on the time-scale of the hydrologic response for hortonian and dunnian mechanism of runoff generation, respectively.