Cascade model for fluvial geomorphology

Erosional landscapes are generally scale invariant and fractal. Spectral studies provide quantitative confirmation of this statement. Linear theories of erosion will not generate scale-invariant topography. In order to explain the fractal behaviour of landscapes we have introduced a modified Fourier series that is the basis for a renormalization approach. We have introduced a non-linear dynamical model for the decay of the modified Fourier series coefficients that yield a fractal spectra. We argue that a physical basis for our approach is that a fractal (or nearly fractal) distribution of storms (floods) continually renews erosional features on all scales.