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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union
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Volume 5, issue 1
Earth Surf. Dynam., 5, 47-66, 2017
https://doi.org/10.5194/esurf-5-47-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Earth Surf. Dynam., 5, 47-66, 2017
https://doi.org/10.5194/esurf-5-47-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 18 Jan 2017

Research article | 18 Jan 2017

Accurate simulation of transient landscape evolution by eliminating numerical diffusion: the TTLEM 1.0 model

Benjamin Campforts1, Wolfgang Schwanghart2, and Gerard Govers1 Benjamin Campforts et al.
  • 1Division Geography, Department of Earth and Environmental Sciences, KU Leuven, Leuven, Belgium
  • 2Institute of Earth and Environmental Science, Universität Potsdam, Potsdam, Germany

Abstract. Landscape evolution models (LEMs) allow the study of earth surface responses to changing climatic and tectonic forcings. While much effort has been devoted to the development of LEMs that simulate a wide range of processes, the numerical accuracy of these models has received less attention. Most LEMs use first-order accurate numerical methods that suffer from substantial numerical diffusion. Numerical diffusion particularly affects the solution of the advection equation and thus the simulation of retreating landforms such as cliffs and river knickpoints. This has potential consequences for the integrated response of the simulated landscape. Here we test a higher-order flux-limiting finite volume method that is total variation diminishing (TVD-FVM) to solve the partial differential equations of river incision and tectonic displacement. We show that using the TVD-FVM to simulate river incision significantly influences the evolution of simulated landscapes and the spatial and temporal variability of catchment-wide erosion rates. Furthermore, a two-dimensional TVD-FVM accurately simulates the evolution of landscapes affected by lateral tectonic displacement, a process whose simulation was hitherto largely limited to LEMs with flexible spatial discretization. We implement the scheme in TTLEM (TopoToolbox Landscape Evolution Model), a spatially explicit, raster-based LEM for the study of fluvially eroding landscapes in TopoToolbox 2.

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Despite a growing interest in landscape evolution models, accuracy assessment of the numerical methods they are based on has received little attention. We test a higher-order flux-limiting finite-volume method to simulate river incision and tectonic displacement. We show that this scheme significantly influences the evolution of simulated landscapes and the spatial and temporal variability of erosion rates. Moreover, it allows for the simulation of lateral tectonic displacement on a fixed grid.
Despite a growing interest in landscape evolution models, accuracy assessment of the numerical...
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