Fractal scaling and power-law landslide distribution in a micromodel of geomorphological evolution

Abstract

Recent analyses of geographical data have shown that mountains can be well described in terms of fractals, which raises the fundamental question about the mechanisms producing fractal surfaces in geomorphological evolution. Because the formation of mountain ranges takes place over an extremely long period of time, direct observations of erosion mechanisms are hardly feasible. Therefore, we expect that model experiments on the erosion of mountain ridges taking place on a limited time scale should contribute significantly to our understanding of the emergence of fractal structures in geomorphological phenomena. During the watering of an initially smooth ridge made of a mixture of silica sand and earthy soil the surface evolves into a shape analogous to actual mountain profiles with self-affine geometry. For the exponents describing, respectively, the spatial and the temporal scaling of the surface width, α=0.78±0.05 and β=0.8±0.06 have been obtained. The former value is in a very good agreement with α=0.8±0.1 calculated for genuine transect profiles. The processes in our micromodel can be well described in terms of self-organized criticality: The system evolves into a critical state, where surface roughening takes place due to power-law distributed landslides.