Rivers as linear elements in landform evolution models

Stefan Hergarten

doi:10.5194/esurf-8-367-2020

Abstract

Abstract. Models of detachment-limited fluvial erosion have a long history in landform evolution modeling in mountain ranges. However, they suffer from a scaling problem when coupled to models of hillslope processes due to the flux of material from the hillslopes into the rivers. This scaling problem causes a strong dependence of the resulting topographies on the spatial resolution of the grid. A few attempts based on the river width have been made in order to avoid the scaling problem, but none of them appear to be completely satisfying. Here a new scaling approach is introduced that is based on the size of the hillslope areas in relation to the river network. An analysis of several simulated drainage networks yields a power-law scaling relation for the fluvial incision term involving the threshold catchment size where fluvial erosion starts and the mesh width. The obtained scaling relation is consistent with the concept of the steepness index and does not rely on any specific properties of the model for the hillslope processes.

Highlights

Fluvial incision is a major if not dominant component of long-term landform evolution in orogens
Linear diffusion is the simplest model here; it was considered in the context of landform evolution by Culling (1960) even before models of fluvial erosion came into play
This study presents a simple scaling relation for the fluvial incision term in landform evolution models involving detachment-limited fluvial erosion and hillslope processes

Summary

Introduction

Fluvial incision is a major if not dominant component of long-term landform evolution in orogens. Restriction to the detachment-limited regime considerably simplifies the equations. The generic differential equation for the topography H (x1, x2, t) of a landform evolution model with detachment-limited fluvial erosion reads ∂H = U − E − divq, (1). The third term describes a local transport process at the hillslopes, where q is the flux density and div the 2-D divergence operator. Linear diffusion is the simplest model here; it was considered in the context of landform evolution by Culling (1960) even before models of fluvial erosion came into play. There are more sophisticated models for q that take the nonlinear dependencies of hillslope processes on topography into account (e.g., Andrews and Bucknam, 1987; Howard, 1994; Roering et al, 1999)

Objectives

Findings

Discussion

Conclusion