26 Jun 2023
 | 26 Jun 2023

Large structures simulation for landscape evolution models

Julien Coatléven and Benoit Chauveau

Abstract. Because of the chaotic behavior of the coupling between water flow and sediment erosion and transport, without any special treatment the practical results of landscape evolution models (LEM) are likely to be dominated by numerical errors. This paper describes two areas of improvement that we believe are necessary for the successful simulation of landscape evolution models. The first one concerns the expression of the water flux that was initially rebuilt in a recent paper in a mathematically consistent way for the cell-to-cell multiple flow direction algorithms, thanks to a reinterpretation as a well chosen discretization of the Gauckler-Manning-Strickler continuous equation. Building on those results, we introduce here a general framework allowing to derive consistent expressions of the water flux for the most commonly used multiple/single flow direction (MFD/SFD) water flow routines, including node-to-node versions. If having a consistent water flux is crucial to avoid any mesh size dependence in a LEM and controlling the consistency error, the expected non-linear self amplification mechanisms of the water and sediment coupling can still lead to simulations blurred by numerical errors. Those numerical instabilities being highly reminiscent of turbulence induced instabilities in computational fluid dynamics (CFD), in the second part of our paper we present a ``large structure simulation'' (LSS) approach for LEM, mimicking the large-eddy simulations (LES) used for turbulent CFD. The LSS allows to control numerical errors while preserving the major physical based geomorphic patterns.

Julien Coatléven and Benoit Chauveau

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-687', Stefan Hergarten, 21 Jul 2023
    • AC1: 'Reply on RC1', Julien Coatléven, 24 Jul 2023
  • RC2: 'Comment on egusphere-2023-687', Anonymous Referee #2, 07 Aug 2023
Julien Coatléven and Benoit Chauveau
Julien Coatléven and Benoit Chauveau


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Short summary
The objective is to diminish the risk of producing inconsistent numerical results in non-linear LEMs. The first improvement concerns the expression of the water flux associated to MFD/SFD routing suffering from mesh dependency. We derive consistent expressions of the water flux for the most used algorithms. The second item aims at avoiding any amplification of numerical errors. We adapt the filter methodology used by CFD to manage turbulence allowing to keep only physical large structures.