Effect of limited storm duration on landscape evolution, drainage basin geometry, and hydrograph shapes

[1] Landscape evolution models that calculate erosion as a function of discharge usually assume steady state runoff conditions and compute discharge as a power law function of the contributing area. This assumption is appropriate for small catchments and for regions in which the climate is characterized by long-lasting rainfall events. With larger catchments or shorter storms, however, the travel time of a water particle from the divide to the catchment outlet is typically longer than the characteristic storm duration. Hence a hydrologic steady state cannot be reached. This paper offers an analytic solution for nonsteady state peak discharge and investigates how changes in storm duration alter hydrograph characteristics and the shape of the resulting equilibrium landscape. An asymptotic function is used to incorporate the effect of storm duration into a landscape evolution model. We demonstrate with numerical simulations and analytical results that decreasing relative storm duration results in downstream-decreasing equilibrium channel concavity and decreasing valley density. It is also shown that this nonsteady state runoff system is less stable than the system of steady state runoff processes. Under certain conditions, no fixed dynamic equilibrium state exists. Furthermore, analysis of the shape of runoff hydrographs reveals feedback mechanisms manifested between hydrograph shape, erosion, and morphogenesis, demonstrating a compensatory mechanism between external precipitation input and internal runoff production.