Controls on width in bedrock rivers

One of the fundamental open questions in geomorphology is: What controls the width of bedrock rivers? Landscape evolution models scale width with drainage area, which is used as a proxy for channel discharge, but observations often do not support width-drainage area scaling. This study explores controls on width in bedrock rivers by 1) developing mechanistic models for lateral erosion by bedload and suspended load impacts, 2) partitioning shear stresses on the bed and banks using model simulations and field observations, and 3) proposing a method for predicting steady-state channel width. A numerical model is developed for lateral erosion by bedload particles that are deflected by bed roughness, which reproduces the erosional patterns observed in the flume experiments. An analytical solution of the numerical model is derived, which shows that lateral erosion rate dominates at high sediment supply when the bed is near fully covered, while vertical erosion dominates at low-to-intermediate sediment supply when the bed is largely exposed to particle impacts. Partitioning bed and wall stresses, which are the key parameters of the lateral erosion model, shows that the observed wall stress is larger than the observed bed stress in many studied canyons due to the complex three-dimensional flow structure and rough bedrock walls in natural bedrock rivers. A model for lateral erosion by bedload and suspended load advected by turbulent eddies is developed to incorporate the role of suspended load and is combined with the model for lateral erosion by bedload impacts. The combined model shows that finer sediment dominates lateral erosion at low sediment supply, but coarser sediment plays an important role at high sediment supply. The model for lateral erosion from bedload impacts is coupled with the vertical erosion model to predict steady channel width at local and drainage basin scale. Results reveal that local channel width is controlled by sediment supply instead of water discharge. Channel width scales sediment supply and caliber at drainage basin scale, which can give the appearance of width-drainage area scaling.