21 Apr 2021

21 Apr 2021

Review status: a revised version of this preprint is currently under review for the journal ESurf.

Short communication: Analytical models for 2D landscape evolution

Philippe Steer Philippe Steer
  • Univ Rennes, CNRS, Géosciences Rennes - UMR 6118, F-35000 Rennes, France

Abstract. Numerical modelling offers a unique approach to understand how tectonics, climate and surface processes govern landscape dynamics. However, the efficiency and accuracy of current landscape evolution models remain a certain limitation. Here, I develop a new modelling strategy that relies on the use of 1D analytical solutions to the linear stream power equation to compute in 2D the dynamics of landscapes. This strategy uses the 1D ordering, by a directed acyclic graph, of model nodes based on their location along the water flow path to propagate topographic changes in 2D. I demonstrate that this analytical model can be used to compute in a single time step, with an iterative procedure, the steady-state topography of landscapes subjected to river, colluvial and hillslope erosion. This model can also be adapted to compute the dynamic evolution of landscapes under either heterogeneous or time-variable uplift rate. This new model leads to slope-area relationships exactly consistent with predictions and to the exact preservation of knickpoint shape throughout their migration. Moreover, the absence of numerical diffusion or of an upper bound for the time step offer significant advantages compared to numerical models. The main drawback of this novel approach is that it does not guarantee the time-continuity of the topography through successive time steps, despite practically having little impact on model behaviour.

Philippe Steer

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on esurf-2021-35', Liran Goren, 20 May 2021
    • AC1: 'Reply on RC1', Philippe Steer, 12 Jul 2021
  • RC2: 'Comment on esurf-2021-35', Sebastien Carretier, 16 Jun 2021
    • AC2: 'Reply on RC2', Philippe Steer, 12 Jul 2021

Philippe Steer

Model code and software

Salève Philippe Steer

Philippe Steer


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Short summary
How landscapes respond to tectonic and climatic changes is a major issue in Earth Sciences. I have developed a new model that solves for landscape evolution in two dimensions using analytical solutions. Compared to numerical models, this new model is quicker and more accurate. It can compute in a single time step the topography at equilibrium of a landscape or be used to describe its evolution through time, for instance during changes in tectonic or climatic conditions.