Developing and exploring a theory for the lateral erosion of bedrock channels for use in landscape evolution models

Abigail L Langston,Gregory E Tucker

doi:10.5194/esurf-6-1-2018

Abstract

Abstract. Understanding how a bedrock river erodes its banks laterally is a frontier in geomorphology. Theories for the vertical incision of bedrock channels are widely implemented in the 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 and hillslope–channel coupling depends on the 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 a bedrock canyon and the other representing undercutting, slumping, and rapid downstream sediment transport that occurs in softer bedrock. Model experiments were run with a range of values for bedrock erodibility and tendency towards transport- or detachment-limited behavior and varying magnitudes of sediment flux and water discharge in order to determine the role that each plays in the development of wide bedrock valleys. The results show that this simple, physics-based theory for the lateral erosion of bedrock channels produces bedrock valleys that are many times wider than the grid discretization scale. 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.

Highlights

Understanding the processes that control the lateral migration of bedrock rivers is fundamental for understanding the genesis of landscapes in which valley width is many times the channel width
While theories that account for dynamic adjustment to bedrock channel width continue to be refined, landscape evolution models that include a relationship between sediment size and cover (Gasparini et al, 2004) and incision thresholds in bedrock channels (Tucker et al, 2001; Crave and Davy, 2001; Tucker et al, 2013) are available and widely used (Tucker and Hancock, 2010)
The most important finding of this work is that a simple, physics-based theory for lateral bedrock channel migration, when combined with a landscape evolution model, produces wide bedrock valleys that scale with drainage area, as predicted in natural systems

Summary

Introduction

Understanding the processes that control the lateral migration of bedrock rivers is fundamental for understanding the genesis of landscapes in which valley width is many times the channel width. Bedrock incision models include theories for the adjustment of channel width (e.g., Stark and Stark, 2001; Wobus et al, 2006; Turowski et al, 2009; Yanites and Tucker, 2010), the role of sediment size and bed cover (e.g., Whipple and Tucker, 2002; Sklar and Dietrich, 2004; Yanites et al, 2011), and thresholds for incision (e.g., Tucker and Bras, 2000; Snyder et al, 2003b). While theories that account for dynamic adjustment to bedrock channel width continue to be refined (for a review, see Lague, 2014), landscape evolution models that include a relationship between sediment size and cover (Gasparini et al, 2004) and incision thresholds in bedrock channels (Tucker et al, 2001; Crave and Davy, 2001; Tucker et al, 2013) are available and widely used (Tucker and Hancock, 2010)

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Discussion

Conclusion