Articles | Volume 23, issue 2
Nonlin. Processes Geophys., 23, 91–93, 2016
https://doi.org/10.5194/npg-23-91-2016
Nonlin. Processes Geophys., 23, 91–93, 2016
https://doi.org/10.5194/npg-23-91-2016

Brief communication 06 Apr 2016

Brief communication | 06 Apr 2016

Brief communication: Possible explanation of the values of Hack's drainage basin, river length scaling exponent

Allen G. Hunt Allen G. Hunt
  • Department of Physics and Department of Earth & Environmental Sciences, Wright State University, 3640 Colonel Glenn Highway, Dayton, OH 45435, USA

Abstract. Percolation theory can be used to find water flow paths of least resistance. Application of percolation theory to drainage networks allows identification of the range of exponent values that describe the tortuosity of rivers in real river networks, which is then used to generate the observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law may allow interpretation of the range of exponent values based on an assessment of the heterogeneity of the substrate.

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Short summary
Percolation theory can be used to find flow paths of least resistance. Applying percolation theory to drainage networks apparently allows identification of the range of exponent values describing the tortuosity of rivers in real networks, thus generating observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law may allow interpretation of the range of exponent values based on assessment of substrate heterogeneity.