Drainage basin sensitivity to tectonic and climatic forcing: Implications of a stochastic model for the role of entrainment and erosion thresholds

Long-term average rates of channel erosion and sediment transport depend on the frequency-magnitude characteristics of flood flows 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 first-order impact on topography and patterns of dynamic response to tectonic and climate forcing. This non-linearity becomes significant when fewer than about half of flood 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 (C) 2004 John Wiley Sons, Ltd.