Quick and Slow Components of the Hydrologic Response at the Hillslope Scale

It is widely recognized that the Hortonian mechanism of runoff generation occurs in arid and semi-arid regions, generally characterized by high rainfall intensity on soils exhibiting low infiltrabilities. Differently, in steeply sloping forested watersheds in humid climates, by infiltrating through a highly permeable upper soil horizon, water moves beneath the soil surface determining a slow response. However, in most real cases, for example when in arid regions mountain forested areas take place, both (quick and slow) runoff generation processes coexist and together contribute to the hydrologic hillslope response. In this paper, based on analytical solutions of the hydrologic response, instantaneous response functions of both quick and slow components are defined, depending on parameters characterizing geometrical and dynamical features at the hillslope scale of immediate physical meaning. For each response component, two characteristic time-scales are defined, the mean holding time spent by a particle in its motion through the hillslope and the so-called time to equilibrium, accounting for a critical rainfall duration generating a maximum discharge at the bottom of the hillslope. Approximated instantaneous response function (IRFs) in the usual form of gamma probability density functions (pdfs) are proposed, which allowed reducing the many parameters appearing in both quick and slow response models to the scale and shape parameters, also incorporating the effect of different antecedent flow conditions. At the basin scale, the collective response of all the hillslopes is described by a representative hillslope, which combined response accounts for the relative dominance of quick and slow response.