An Analytical Model for Lateral Erosion From Saltating Bedload Particle Impacts

Abstract

AbstractThe width of bedrock rivers is set by the competition between vertical and lateral erosion in uplifting landscapes. Compared with vertical erosion rates, less is known about the lateral erosion rates that are thought to dominate when river beds are alluviated. Here, we derive an analytical model for lateral erosion by saltating bedload particle impacts that are deflected by alluvial cover. The analytical model is a simplification of the Li et al. (2020, https://doi.org/10.1029/2019jf005509) numerical model of the same process. The analytical model predicts a nonlinear dependence of lateral erosion rate on sediment supply, shear stress, and grain size, revealing the same behavior observed in the numerical model, but without tracking particle movements through time and space. The analytical model considers both uniformly distributed cover and patchy partial cover that are implemented with a fully alluviated patch along one bank and bare bedrock along the other. The model predicts that lateral erosion rate peaks when the bed is ∼70% covered for uniformly distributed alluvium, or when the bed is fully covered for patchy alluvium. Vertical erosion dominates over lateral erosion for ∼75% and >90% of sediment supply and transport stage conditions for uniformly distributed cover and patchy cover, respectively. We use the model to derive a phase diagram of channel responses (steepening, flattening, narrowing, and widening) for various combinations of transport stage and relative sediment supply. Application of our model to Boulder Creek, CA, captures the observed channel widening in response to increased sediment supply and steepening in response to larger grain size.