Developing and Evaluating a Theory for Lateral Erosion by Bedrock Channels in a Landscape Evolution Model

Understanding how a bedrock river erodes its banks laterally is a frontier in field-based studies, experimental studies, and modeling studies. Theory for the vertical incision of bedrock channels is widely implemented in our current generation of landscape evolution models. However, in general existing models do not seek to implement the lateral migration of bedrock channel walls. This is problematic, as modeling geomorphic processes such as terrace formation, floodplain development, and hillslope-channel coupling depend on accurate simulation of valley widening. We have developed and implemented a theory for the lateral migration of bedrock channel walls in a catchment-scale landscape evolution model. Two model formulations are presented, one representing the slow process of widening in a bedrock canyon, the other representing undercutting, slumping, and rapid downstream sediment transport that occurs in softer bedrock. Results from model calculations show that this simple, physics-based theory for the lateral erosion of bedrock channels produces bedrock valleys that are several model cells wide. The model predicts wider bedrock valleys in weaker bedrock, as many have observed in natural landscapes. Weaker bedrock also results in more channel mobility, which is a fundamental factor for developing and maintaining a bedrock valley that is several times wider than the channel it holds. Increased channel mobility and wider, more flat-bottomed valleys in the model under transport-limited conditions suggest that sediment cover on the bed that is present under transport-limited conditions is an effective way to slow vertical incision and amplify the effect of lateral erosion. This theory for the lateral erosion of bedrock channel walls and the numerical implementation of the theory in a catchment-scale landscape evolution model is a significant first step towards understanding the factors that control the rates and spatial extent of wide bedrock valleys.