Spectral Signature of Landscape Channelization

Channel networks increase in complexity as the importance of erosion grows compared to diffusion by soil creep, giving rise to a channelization cascade. Simulations, laboratory experiments, and data from a natural landscape are used to uncover the signature of such a cascade in the wavenumber spectrum of elevation fluctuations. Power spectra at intermediate distances from the boundaries are characterized by a peak wavenumber that is related to the quasi-cyclic valleys superimposed on a power-law scaling with exponent (α) at smaller scales. Dimensional analysis and self-similarity arguments show that α is uniquely linked to the power-law relation (with exponent m) between erosion potential and the specific drainage area via α = 2m − 3. This finding connects the spectral behavior of erosional surfaces to the exponent m that distinguishes between the steep landscapes with debris-flow-dominated channels and relatively flat fluvial landscapes and directly controls the shape of the channel profile.