Numerical Simulation of Landscape Evolution Models

This paper gives the complete numerical schemes implementing the main physical laws proposed in landscape evolution models (LEMs). These laws can be modeled by a system of three partial differential equations governing water runoff, stream incision, hill slope evolution and sedimentation. The goal of the presented algorithm, code and online demo is to be able to test these equations on digital elevation models (DEMs) of any resolution, and to illustrate its potential to simulate the fine structure of the river network, and to understand the landscape morphology and its causes. The equations simulate plausible evolutions. We illustrate experiments on DEMs of several sites, including one site, La Réunion where the DEM is given at three different resolutions: the SRTM resolution (90m), and then 12m and 4m on DEMs derived from several Pléiades pairs. Other many DEMs are proposed in the online demo, which allows to upload and tests other DEMs.