Constraining the stream power law: a novel approach combining a landscape evolution model and an inversion method

T Croissant,J Braun

doi:10.5194/esurf-2-155-2014

Abstract

Abstract. In the past few decades, many studies have been dedicated to the understanding of the interactions between tectonics and erosion, in many instances through the use of numerical models of landscape evolution. Among the numerous parameterizations that have been developed to predict river channel evolution, the stream power law, which links erosion rate to drainage area and slope, remains the most widely used. Despite its simple formulation, its power lies in its capacity to reproduce many of the characteristic features of natural systems (the concavity of river profile, the propagation of knickpoints, etc.). However, the three main coefficients that are needed to relate erosion rate to slope and drainage area in the stream power law remain poorly constrained. In this study, we present a novel approach to constrain the stream power law coefficients under the detachment-limited mode by combining a highly efficient landscape evolution model, FastScape, which solves the stream power law under arbitrary geometries and boundary conditions and an inversion algorithm, the neighborhood algorithm. A misfit function is built by comparing topographic data of a reference landscape supposedly at steady state and the same landscape subject to both uplift and erosion over one time step. By applying the method to a synthetic landscape, we show that different landscape characteristics can be retrieved, such as the concavity of river profiles and the steepness index. When applied on a real catchment (in the Whataroa region of the South Island in New Zealand), this approach provides well-resolved constraints on the concavity of river profiles and the distribution of uplift as a function of distance to the Alpine Fault, the main active structure in the area.

Highlights

Because their geometry is very sensitive to external forcing such as climate or tectonics, rivers are ideal natural laboratories for studying the interactions of the various processes at play during orogenesis over geological timescales (Kirby and Whipple, 2001; Montgomery and Brandon, 2002; Duvall et al, 2004; Whittaker et al, 2007; Kirby and Whipple, 2012)
We have presented here a novel approach to constrain the coefficients of the stream power law (SPL) parameters that combines a very efficient surface process model (FastScape) and an inversion method
The inversion is constrained by a misfit function that compares a reference or observed topography with that predicted by the surface process models (SPM) under the assumption of geomorphic steady state

Summary

Introduction

Because their geometry is very sensitive to external forcing such as climate or tectonics, rivers are ideal natural laboratories for studying the interactions of the various processes at play during orogenesis over geological timescales (Kirby and Whipple, 2001; Montgomery and Brandon, 2002; Duvall et al, 2004; Whittaker et al, 2007; Kirby and Whipple, 2012) For this purpose many parameterizations of fluvial incision have been developed (Kooi and Beaumont, 1994; Sklar and Dietrich, 1998; Whipple and Tucker, 1999). An alternative is to limit the computation and the comparison with observations to 1-D river profiles, as was done by Roberts and White (2010) in Africa and Roberts et al (2012) in the Colorado Plateau to deduce information about the geometry and timing of uplift

Objectives

Discussion

Conclusion