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Formation of evenly spaced ridges and valleys

Nature volume 460, pages 502–505 (2009)Cite this article

Abstract

One of the most striking examples of self-organization in landscapes is the emergence of evenly spaced ridges and valleys1,2,3,4,5,6. Despite the prevalence of uniform valley spacing, no theory has been shown to predict this fundamental topographic wavelength. Models of long-term landscape evolution can produce landforms that look realistic7,8,9, but few metrics exist to assess the similarity between models and natural landscapes. Here we show that the ridge–valley wavelength can be predicted from erosional mechanics. From equations of mass conservation and sediment transport, we derive a characteristic length scale at which the timescales for erosion by diffusive soil creep and advective stream incision are equal. This length scale is directly proportional to the valley spacing that emerges in a numerical model of landform evolution, and to the measured valley spacing at five field sites. Our results provide a quantitative explanation for one of the most widely observed characteristics of landscapes. The findings also imply that valley spacing is a fundamental topographic signature that records how material properties and climate regulate erosional processes.

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Figure 1: Uniform valley spacing.
Figure 2: Comparison of predicted and observed valley spacing.
Figure 3: Measurement of model parameters from topography.

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Acknowledgements

This work was supported by the National Science Foundation (J.T.P.), the Institute for Geophysics and Planetary Physics (J.W.K. and J.T.P.), and NASA (W.E.D. and J.T.P.). Laser altimetry for Gabilan Mesa was acquired and processed by NCALM (http://www.ncalm.org) with support from the National Center for Earth-surface Dynamics (NCED). We thank the Orradre family of San Ardo, California, for granting access to their land. We thank the states of Pennsylvania and Utah for making laser altimetry data publicly available. We also thank K. Whipple for his review.

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Authors and Affiliations

  1. Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA,

    J. Taylor Perron

  2. Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA,

    James W. Kirchner & William E. Dietrich

  3. Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland

    James W. Kirchner

  4. Department of Environmental Sciences, Swiss Federal Institute of Technology (ETH), Zürich, Switzerland

    James W. Kirchner

Authors
  1. J. Taylor Perron
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  2. James W. Kirchner
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  3. William E. Dietrich
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Corresponding author

Correspondence to J. Taylor Perron.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Figures S1-S3 with Legends, Supplementary Table S1 and Supplementary References. (PDF 1107 kb)

Supplementary Movie 1

This movie shows the evolution of the model landscape over 600 kyr. Competition for drainage area (a proxy for water flux) among the irregularly spaced, incipient valleys that arise in the random initial surface eventually leads to an equilibrium landscape with evenly spaced valleys. Horizontal tick interval is 200 m, vertical tick interval is 20 m. (MP4 2177 kb)

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Perron, J., Kirchner, J. & Dietrich, W. Formation of evenly spaced ridges and valleys. Nature 460, 502–505 (2009). https://doi.org/10.1038/nature08174

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