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Accurate simulation of transient landscape evolution by eliminating numerical diffusion

  • 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.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.show moreshow less

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Metadaten
Author:Benjamin Campforts, Wolfgang SchwanghartORCiDGND, Gerard Govers
URN:urn:nbn:de:kobv:517-opus4-418784
DOI:https://doi.org/10.25932/publishup-41878
ISSN:1866-8372
Parent Title (English):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
Subtitle (English):the TTLEM 1.0 model
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (664)
Document Type:Postprint
Language:English
Date of first Publication:2019/03/04
Year of Completion:2017
Publishing Institution:Universität Potsdam
Release Date:2019/03/04
Tag:equation; erosion; hillslopes; implicit; ranges; river incision model; stream power law; topography; transport
Issue:664
Pagenumber:20
Source:Earth Surface Dynamics 5 (2017), pp. 47–66 DOI 10.5194/esurf-5-47-2017
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 55 Geowissenschaften, Geologie / 550 Geowissenschaften
Peer Review:Referiert
Publication Way:Open Access
Licence (German):License LogoCreative Commons - Namensnennung, 4.0 International