A numerical implementation of landscape evolution models

We propose a simple and fast numerical solution for the solution of a system of three partial differential equations modeling of landscape evolution. As remarked by several authors, the main physical laws that have been proposed in landscape evolution models can be converted into a minimal system of three partial differential equations. The first one is a transport equation governing the water run-off. A second equation governs the terrain evolution by the conjugate effects of detachment-limited erosion, creep and sedimentation. The third equation governs the transport of the suspended sediment load in water. The challenge that we address is to simulate in reasonable time such a system of equations on large digital elevation models acquired by satellite or aerial imaging. We reformulate each equation as a discrete conservative scheme on a raster. Furthermore a multiscale implementation leads to extremely fast simulations. This permits to simulate water run-off on fixed landscapes, and to explore and compare in reasonable time several models and their parameters. Last but not least, we address the problem of an efficient visualisation of a three phases results : the elevation, the water height and the sediment load.