%0 Journal Article
%D 2008
%T Spectral signatures of characteristic spatial scales and nonfractal structure in landscapes
%A Perron, J. Taylor
%A Kirchner, James W.
%A Dietrich, William E.
%I American Geophysical Union
%K 1824 Hydrology: Geomorphology: general
%K 1855 Hydrology: Remote sensing
%K 3205 Mathematical Geophysics: Fourier analysis
%K 4440 Nonlinear Geophysics: Fractals and multifractals
%K 4460 Nonlinear Geophysics: Pattern formation
%K fractals
%K laser altimetry
%K terrain analysis
%U http://dx.doi.org/10.1029/2007JF000866
%V 113
%X Landscapes are sometimes argued to be scale-invariant or random surfaces, yet qualitative observations suggest that they contain characteristic spatial scales. We quantitatively investigate the existence of characteristic landscape scales by analyzing two-dimensional Fourier power spectra derived from high-resolution topographic maps of two landscapes in California. In both cases, we find that spectral power declines sharply above a frequency that corresponds roughly to hillslope length, implying that the landscape is relatively smooth at finer scales. The spectra also show that both landscapes contain quasiperiodic ridge-and-valley structures, and we derive a robust measure of the ridge-valley wavelength. By comparing the spectra with the statistical properties of spectra derived from randomly generated topography, we show that such uniform valley spacing is unlikely to occur in a random surface. We describe several potential applications of spectral analysis in geomorphology beyond the identification of characteristic spatial scales, including a filtering technique that can be used to measure topographic attributes, such as local relief, at specific scales or in specific orientations.
%8 2008/10/7