The role of sediment in controlling steady-state bedrock channel slope: Implications of the saltation–abrasion incision model

The saltation–abrasion model is a mechanistic model for river incision into bedrock by saltating bedload, which we have previously derived and used experimental data to constrain all parameter values. Here we develop a method for applying the saltation–abrasion model at a landscape scale, and use the model as a reference for evaluating the behavior of a wide range of alternative incision models, in order to consider the implications of the saltation–abrasion model, as well as other models, for predicting topographic steady-state channel slope. To determine the single-valued discharge that best represents the effects of the full discharge distribution in transporting sediment and wearing bedrock, we assume all runoff can be partitioned between a low-flow and a high-flow discharge, in which all bedload sediment transport occurs during high flow. We then use the gauged discharge record and measurements of channel characteristics at a reference field site and find that the optimum discharge has a moderate magnitude and frequency, due to the constraints of the threshold of grain motion and bed alluviation by high relative sediment supply. Incision models can be classified according to which of the effects of sediment on bedrock incision are accounted for. Using the predictions of the saltation–abrasion model as a reference, we find that the threshold of motion is the most important effect that should be represented explicitly, followed in order of decreasing importance by the cover effect, the tools effect and the threshold of suspension effect. Models that lack the threshold of motion over-predict incision rate for low shear stresses and under-predict the steady-state channel slope for low to moderate rock uplift rates and rock strengths. Models that lack the cover effect over-predict incision rate for high sediment supply rates, and fail to represent the degree of freedom in slope adjustment provided by partial bed coverage. Models that lack the tools effect over-predict incision rate for low sediment supply rates, and do not allow for the possibility that incision rate can decline for increases in shear stress above a peak value. Overall, the saltation–abrasion model predicts that steady-state channel slope is most sensitive to changes in grain size, such that the effect of variations in rock uplift rate and rock strength may affect slope indirectly through their possible, but as yet poorly understood, influence on the size distribution of sediments delivered to channel networks by hillslopes.