Short communication: Analytical models for 2D landscape evolution

Abstract

Numerical modelling offers a unique approach to understand how tectonics, climate and surface processes govern landscape dynamics. However, the efficiency and accuracy of current landscape evolution models remain a certain limitation. Here, I develop a new modelling strategy that relies on the use of 1D analytical solutions to the linear stream power equation to compute the dynamics of landscapes in 2D. This strategy uses the 1D ordering, by a directed acyclic graph, of model nodes based on their location along the water flow path to propagate topographic changes in 2D. This analytical model can be used to compute in a single time step, with an iterative procedure, the steady-state topography of landscapes subjected to river, colluvial and hillslope erosion. This model can also be adapted to compute the dynamic evolution of landscapes under either heterogeneous or time-variable uplift rate. This new model leads to slope–area relationships exactly consistent with predictions and to the exact preservation of knickpoint shape throughout their migration. Moreover, the absence of numerical diffusion or of an upper bound for the time step offers significant advantages compared to numerical models. The main drawback of this novel approach is that it does not guarantee the time continuity of the topography through successive time steps, despite practically having little impact on model behaviour.