A probabilistic framework for the cover effect in bedrock erosion

The cover effect in fluvial bedrock erosion is a major control on bedrock channel morphology and long-term channel dynamics. Here, we suggest a probabilistic framework for the description of the cover effect that can be applied to field, laboratory, and modelling data and thus allows the comparison of results from different sources. The framework describes the formation of sediment cover as a function of the probability of sediment being deposited on already alluviated areas of the bed. We define benchmark cases and suggest physical interpretations of deviations from these benchmarks. Furthermore, we develop a reach-scale model for sediment transfer in a bedrock channel and use it to clarify the relations between the sediment mass residing on the bed, the exposed bedrock fraction, and the transport stage. We derive system timescales and investigate cover response to cyclic perturbations. The model predicts that bedrock channels can achieve grade in steady state by adjusting bed cover. Thus, bedrock channels have at least two characteristic timescales of response. Over short timescales, the degree of bed cover is adjusted such that the supplied sediment load can just be transported, while over long timescales, channel morphology evolves such that the bedrock incision rate matches the tectonic uplift or base-level lowering rate.