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Spectral Signature of Landscape Channelization
  • Milad Hooshyar,
  • Gabriel G. Katul,
  • Amilcare M Porporato
Milad Hooshyar
Princeton University

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Gabriel G. Katul
Duke University
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Amilcare M Porporato
Princeton University
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Channel networks increase in complexity as the importance of erosion grows compared to diffusion by soil creep, giving rise to a channelization cascade. In this cascade, smaller channels join to form progressively larger ones with an alternation of ridges and valleys involving a multitude of wavelengths. Simulations of landscape evolution models and laboratory experiments 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 (the most energetic mode) that is related to the quasi-cyclic valleys superimposed on power-law scaling with exponent ($\alpha$) across a wide range of smaller scales. Dimensional analysis and self-similarity arguments are used to reveal the controlling factors on $\alpha$, showing that $\alpha$ is uniquely linked to the power-law relation (with exponent $m$) between erosion potential and the specific drainage area via $\alpha = 2m -3$.
28 Apr 2021Published in Geophysical Research Letters volume 48 issue 8. 10.1029/2020GL091015