Controls and limits on bedrock channel geometry

Data on channel geometry in naturally incising bedrock rivers reveal variable relationships between channel width, slope, and erosion rate. To explain the range of relationships between these parameters, we propose an optimized channel geometry model. The model reproduces previous theoretical and numerical modeling scaling relationships; however, to explain the field data, the model must incorporate the effects of immobile sediment cover that reduces vertical incision efficiency. Adding sediment to a system for a given rate of base level fall both widens and steepens the channel. We also find that a constant width to depth ratio is only valid for streams where the shear stress required for sediment transport is insignificant compared to the shear required to erode at the imposed base level fall. Our model offers an explanation of seemingly contradictory field observations of controls on channel width and shows that channel width fundamentally controls the erosive potential of a river especially when it carries a significant bed load.