| Abstract: | Long‐term average rates of channel erosion and sediment transport depend on the frequency–magnitude characteristics of ?ood ?ows that exceed an erosion threshold. Using a Poisson model for rainfall and runoff, analytical solutions are developed for average rates of stream incision and sediment transport in the presence of such a threshold. Solutions are derived and numerically tested for three erosion/transport formulas: the Howard–Kerby shear‐stress incision model, the Bridge–Dominic sediment transport model, and a generic shear‐stress sediment transport model. Results imply that non‐linearity resulting from threshold effects can have a ?rst‐order impact on topography and patterns of dynamic response to tectonic and climate forcing. This non‐linearity becomes signi?cant when fewer than about half of ?ood events are capable of detaching rock or sediment. Predicted morphology and uplift‐gradient scaling is more closely consistent with observations and laboratory experiments than conventional slope‐linear or shear‐linear erosion laws. These results imply that particle detachment thresholds are not details that can be conveniently ignored in long‐term landscape evolution models. Copyright © 2004 John Wiley & Sons, Ltd. |
