Abstract

In this talk, we start by reviewing some models for landscape evolution, many of which are hybrid models, combining fundamental physical laws with empirical modeling. Such models can be valid near equilibrium. Nevertheless, this situation is not satisfactory from the mathematical standpoint, since such models will be valid only for a given landscape or class of landscapes.

We propose a simple landscape model, deduced from mathematical principles, coping with the main features of all models. This model singles out three spatially distributed scalar state variable, namely the landscape elevation, the water elevation, and the sediment concentration in water. These state variables are linked by three partial differential equations. Two of these equations are mere conservation laws. A third equation copes with the three main features identified in the literature as the main phenomena shaping a landscape: erosion, sedimentation and creep.

Numerical results show that a variety of common landscape features can be reproduced. Furthermore changing various parameters in the model can alter the morphology of the landscape and the various features observed, even for the same initial landscape. The conjectured mathematical instability and non-uniqueness of landscape evolution is illustrated numerically. On the other hand numerical stability of real landscape topographies under realistic values for their evolution is also observed. Lastly, the model presented also shows promise in the field of channel network restoration, as river networks tend to become sharper with the proper choice of parameters in the erosion model.