Spectral signatures of characteristic spatial scales and nonfractal structure in landscapes

Authors

  • J. Taylor Perron,

    1. Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA
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  • James W. Kirchner,

    1. Department of Earth and Planetary Science, University of California, Berkeley, California, USA
    2. Swiss Federal Institute for Forest, Snow, and Landscape Research, Birmensdorf, Switzerland
    3. Department of Environmental Sciences, Swiss Federal Institute of Technology, Zurich, Switzerland
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  • William E. Dietrich

    1. Department of Earth and Planetary Science, University of California, Berkeley, California, USA
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Abstract

[1] 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.

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