2019 CSDMS meeting-028: Difference between revisions

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|CSDMS meeting abstract title=Implicit-spectral solution for a simple landscape evolution model
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|CSDMS meeting abstract=In this study, a spectral solution to a simple two-dimensional landscape evolution model (LEM) is considered. Spectral methods are powerful tools for solving elliptical partial differential equations and are widely used in other fields, though they have received comparatively little attention in landscape evolution modelling. In the LEM considered, the land surface elevation is altered by three processes: regional uplift, fluvial incision, and hillslope diffusion. In the simplest case, these processes act in an undifferentiated way across the entire landscape. Even with this model, the dependence of the fluvial incision term on contributing area makes numerical solutions to this problem challenging. As a result of this term, the governing equation has the form of an integral PDE, which is resistant to implicit schemes. For this reason, many LEMs are solved explicitly. When the desired grid is large, an explicit method may be restricted by stability to a time step too small for the timescales of interest. To solve the problem implicitly, I draw the comparison between this LEM and a heat equation with a nonlinear sink (the fluvial incision term) and solve the diffusional problem with an implicit-spectral method by enforcing periodicity in one dimension. I compare this with an explicit solution and draw some preliminary conclusions on the usefulness of this method for landscape evolution modeling.
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Implicit-spectral solution for a simple landscape evolution model

David Litwin, Johns Hopkins University Baltimore Maryland, United States. dlitwin3@jhu.edu


In this study, a spectral solution to a simple two-dimensional landscape evolution model (LEM) is considered. Spectral methods are powerful tools for solving elliptical partial differential equations and are widely used in other fields, though they have received comparatively little attention in landscape evolution modelling. In the LEM considered, the land surface elevation is altered by three processes: regional uplift, fluvial incision, and hillslope diffusion. In the simplest case, these processes act in an undifferentiated way across the entire landscape. Even with this model, the dependence of the fluvial incision term on contributing area makes numerical solutions to this problem challenging. As a result of this term, the governing equation has the form of an integral PDE, which is resistant to implicit schemes. For this reason, many LEMs are solved explicitly. When the desired grid is large, an explicit method may be restricted by stability to a time step too small for the timescales of interest. To solve the problem implicitly, I draw the comparison between this LEM and a heat equation with a nonlinear sink (the fluvial incision term) and solve the diffusional problem with an implicit-spectral method by enforcing periodicity in one dimension. I compare this with an explicit solution and draw some preliminary conclusions on the usefulness of this method for landscape evolution modeling.