Cover and Erosion Asymmetry in Saltation-Abrasion

Erosion in bedrock-floored rivers is both driven and limited by the amount of sediment transported along the bed. Some sediment boosts wear rates, whereas too much generates a protective cover. This phenomenon determines the shape of river channels in a variety of landscapes and limits how fast they evolve. Here we reevaluate data from a well-known bedrock wear experiment to throw new light on how the saltation-abrasion process. Instead of a symmetric form for erosion versus sediment flux relative to transport capacity, we find the erosion rate peak shifts towards lower sediment fluxes when blocking of oblique saltation trajectories is taken into account. The theoretical context for this reevaluation is a cover-saltation-abrasion model, based on queueing theory (QT), for bedload transport over a planar bedrock bed. The QT approach provides some clarity in the stochastic treatment of granular impacts and cover, and generates closed-form solutions for wear rate in terms of sediment flux and simplified saltation geometry. Applied to the Sklar & Dietrich (2001) experiments in a very small recirculating flume, the two-parameter QT model fits the observed relation between erosion rate and sediment load, infers sediment flux as a function of load, admits non-negligible wear rates for a mean sediment depth of one grain, i.e., for full cover on average, but also suggests that bedrock erosion is blocked at >=50% instantaneous cover. The QT model makes testable predictions for future laboratory experiments and highlights the need for specific improvements in more comprehensive treatments of bedrock erosion and cover.