On the left is a schematic illustrating the model setup in an idealized rectangular channel. On the right is a contour plot of predicted ratio of lateral erosion rate to vertical erosion rate as a function of transport stage and relative sediment supply.
Left: Schematic illustrating the model setup in an idealized rectangular channel (adapted from Li et al., 2021). Saltating particles (white grain, incoming trajectory shown by white arrow) impact alluvium (immobile gray grains, impact shown by star) and are deflected towards the channel wall (black arrow) where the impact will cause erosion. Right: Contour plot of predicted ratio of lateral erosion rate Elu* to vertical erosion rate Ev* as a function of transport stage and relative sediment supply. Transport stage represents the power of the river relative to sediment grain size: the greater the stage, the greater the relative stress exerted by the flowing water. Relative sediment supply qs/qt represents the ratio of sediment supply qs to transport capacity qt: at low values, the river transports little sediment relative to what it can actually transport; a value of 1 indicates the river transports as much sediment as it can (qs = qt). Channels are predicted to widen (Elu*/ Ev* > 1, blue domain) when relative sediment supply is high as a result of increased deflection of saltating grains towards the channel walls. Vertical erosion dominates at low relative sediment supply ((Elu*/ Ev* < 1, orange domain). This result is for uniformly distributed alluvium; scenario with patchy alluvium, and the differences in erosion rates between the two walls in this scenario, are explored in the paper. Credit: Li et al. [2021], Figure 1 (modified) and Figure 7b
Source: Journal of Geophysical Research: Earth Surface

The width of bedrock channels is a key factor controlling erosion and transport processes in mountain rivers. Channel width controls flow dynamics, the force exerted on the riverbed, and therefore erosion and sediment transport rates. A narrowing river will concentrate the flow over a small area, potentially enhancing sediment transport and erosion rates, and may generate obstructions. Conversely, a widening river may undermine the hillslopes and make them more unstable, leading to increased hillslope erosion and sediment supply.

Bedrock riverbed and banks are commonly eroded by the repeated impacts of sediment grains during floods. While some models exist that relate the rate of vertical incision to a river’s sediment flux and grain size, the influence of these parameters on the erosion of bedrock walls (and therefore on channel width) is not as well understood.

In an earlier paper, Li et al. [2020] proposed a model that predicts the erosion of bedrock walls through repeated impact by sediment grains by tracking the trajectory of each grain, but such models require huge computational power and time. In a new paper, Li et al. [2021] now provide an analytical solution, that is, a series of equations that replicate the results of the earlier model without needing to track every single grain.

This new model is much faster and can easily be integrated in models of landscape evolution, thus providing a new tool to explore more completely the interactions between sediment flux, grain size, channel width and the propagation of perturbations along rivers and up valley sides.

The model shows the circumstances in which one may expect rivers to narrow or widen as a function of how much sediment is coming through the river and what its grain size is, and is tested against a real river, Boulder Creek, in California.

Citation: Li, T., Venditti, J. G., & Sklar, L. S. [2021]. An analytical model for lateral erosion from saltating bedload particle impacts. Journal of Geophysical Research: Earth Surface, 126, e2020JF006061. https://doi.org/10.1029/2020JF006061

—Mikaël Attal, Editor, JGR: Earth Surface

Text © 2021. The authors. CC BY-NC-ND 3.0
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