Articles | Volume 23, issue 2
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

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Cited articles

Gray, D. M.: Interrelationships of watershed characteristics, J. Geophys. Res., 66 1215–1223, 1961.
Hack, J. T.: Studies of longitudinal profiles in Virginia and Maryland. USGS Professional Papers 294-B, Washington DC, 46–97, 1957.
Hunt, A. G., Ewing, R. P., and Ghanbarian, B.: Percolation Theory for Flow in Porous Media, 3rd Edn., Springer, Berlin, 2014.
Lopez, E., Buldyrev, S. V., Braunstein, L. A., Havlin, S., and Stanley, H. E.: Possible connection between the optimal path and flow in percolation clusters, Phys. Rev. E, 72, 056131,, 2005.
Maritan, A., Rinaldo, A., Rigon, R., Giacometti, A., and Rodriguez-Iturbe, I.: Scaling laws for river networks, Phys. Rev. E, 53, 1510–1515, 1996.
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.