As geomorphologists we have to live with the fact that we can rarely observe the processes that shape the Earth’s surface. Instrumental records cover only a minor time span over which many geomorphic processes act, thus challenging our abilities to disentangle and understand the complex interactions of landscape evolution. Instead, much of our work has to rely on the analysis of landforms, their geometry, their assemblage, and their constituting material, as well as a blend of geochemical and numerical dating techniques of ever-increasing sophistication.
Numerical landscape evolution models (LEM) provide a useful approach to this challenge. LEMs are simulation tools that attempt to model erosion, sediment transport and deposition as well as feedbacks with vegetation and land use. They amalgamate our state of knowledge in a set of physically-based mathematical formulations and allow us to test whether these equations and their parameter values are able to generate output that is plausible and consistent with field evidence.
TTLEM, the TopoToolbox Landscape Evolution Model, is the latest addition to TopoToolbox. Spearheaded by Benjamin Campforts from KU Leuven, we have developed a LEM that allows us to simulate how mountains grow, rivers incise and hillslopes respond to tectonic and climatic forcing. We placed particular emphasis on implementing numerical models that minimize numerical diffusion. To achieve this, Benjamin has adopted a higher order flux limiting total volume method that is total variation diminishing (TVD-TVM) (Campforts and Govers 2015) to solve the partial differential equations of river incision and tectonic displacement.
In our recent manuscript under discussion in ESurf, we show that using these methods is more than just an exercise in numerical modelling. First-order approximations often smooth knickpoints in uncontrollable ways that impact on derived catchment wide erosion rates. Numerical diffusion strongly affects lateral tectonic displacement, thus restricting its simulation to models that use irregular grids and lagrangian approaches. The TVD-TVM approach solves for these issues by reducing numerical diffusion to a minimum, and thus offers a regular-grid based model with wide applications in tectonic geomorphology.
Needless to say that you can directly analyze and visualize the output using TopoToolbox. The implementation comes with a set of examples that you can directly run from the command line. Give it a try and let us know what you think!
Campforts, B., Govers, G., 2015. Keeping the edge: A numerical method that avoids knickpoint smearing when solving the stream power law. Journal of Geophysical Research: Earth Surface 120, 1189–1205. doi:10.1002/2014JF003376
Campforts, B., Schwanghart, W., Govers, G. (2016): Accurate simulation of transient landscape evolution by eliminating numerical diffusion: the TTLEM 1.0 model. Earth Surface Dynamics Discussion, in review. [DOI: 10.5194/esurf-2016-39]