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The root of branching river networks

Nature volume 492, pages 100–103 (2012)Cite this article

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Abstract

Branching river networks are one of the most widespread and recognizable features of Earth’s landscapes and have also been discovered elsewhere in the Solar System1,2. But the mechanisms that create these patterns and control their spatial scales are poorly understood. Theories based on probability3,4,5 or optimality3,6,7,8 have proven useful9, but do not explain how river networks develop over time through erosion and sediment transport. Here we show that branching at the uppermost reaches of river networks is rooted in two coupled instabilities: first, valleys widen at the expense of their smaller neighbours, and second, side slopes of the widening valleys become susceptible to channel incision. Each instability occurs at a critical ratio of the characteristic timescales for soil transport and channel incision. Measurements from two field sites demonstrate that our theory correctly predicts the size of the smallest valleys with tributaries. We also show that the dominant control on the scale of landscape dissection in these sites is the strength of channel incision, which correlates with aridity and rock weakness, rather than the strength of soil transport. These results imply that the fine-scale structure of branching river networks is an organized signature of erosional mechanics, not a consequence of random topology.

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Figure 1: Properties of the study sites.
Figure 2: Branching instability in valley networks.
Figure 3: Growth rates of incipient valleys on inclined slopes.
Figure 4: Péclet number distributions of first- and second-order drainage basins in the study sites.

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Acknowledgements

This study was supported by the US National Science Foundation Geomorphology and Land Use Dynamics programme through award EAR-0951672 to J.T.P. and by the US Department of Defense through a National Defense Science and Engineering Graduate Fellowship to P.W.R. J.T.P. is a Scholar in the Canadian Institute for Advanced Research (CIFAR). The authors thank T. Clifton and G. Chmiel for assistance with sample preparation, and the Orradre family of San Ardo, California, and numerous landowners in Greene County, Pennsylvania, for granting access to their land.

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

    J. Taylor Perron, Paul W. Richardson & Ken L. Ferrier

  2. École et Observatoire des Sciences de la Terre, Université de Strasbourg, F-67084 Strasbourg, France,

    Mathieu Lapôtre

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Contributions

J.T.P. conceived of the study, performed the numerical modelling, and wrote the paper. J.T.P., P.W.R. and K.L.F. conducted the fieldwork. P.W.R. processed the 10Be samples, and P.W.R. and K.L.F. analysed the 10Be data. J.T.P. and M.L. performed the topographic analyses.

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Correspondence to J. Taylor Perron.

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Perron, J., Richardson, P., Ferrier, K. et al. The root of branching river networks. Nature 492, 100–103 (2012). https://doi.org/10.1038/nature11672

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