Testing statistical self-similarity in the topology of river networks
Article first published online: 25 SEP 2010
Copyright 2010 by the American Geophysical Union.
Journal of Geophysical Research: Earth Surface (2003–2012)
Volume 115, Issue F3, September 2010
How to Cite
2010), Testing statistical self-similarity in the topology of river networks, J. Geophys. Res., 115, F03038, doi:10.1029/2009JF001609., , and (
- Issue published online: 25 SEP 2010
- Article first published online: 25 SEP 2010
- Manuscript Accepted: 13 MAY 2010
- Manuscript Revised: 27 APR 2010
- Manuscript Received: 25 NOV 2009
- random self-similar networks;
- scale invariance;
- river networks
 Recent work has demonstrated that the topological properties of real river networks deviate significantly from predictions of Shreve's random model. At the same time the property of mean self-similarity postulated by Tokunaga's model is well supported by data. Recently, a new class of network model called random self-similar networks (RSN) that combines self-similarity and randomness has been introduced to replicate important topological features observed in real river networks. We investigate if the hypothesis of statistical self-similarity in the RSN model is supported by data on a set of 30 basins located across the continental United States that encompass a wide range of hydroclimatic variability. We demonstrate that the generators of the RSN model obey a geometric distribution, and self-similarity holds in a statistical sense in 26 of these 30 basins. The parameters describing the distribution of interior and exterior generators are tested to be statistically different and the difference is shown to produce the well-known Hack's law. The inter-basin variability of RSN parameters is found to be statistically significant. We also test generator dependence on two climatic indices, mean annual precipitation and radiative index of dryness. Some indication of climatic influence on the generators is detected, but this influence is not statistically significant with the sample size available. Finally, two key applications of the RSN model to hydrology and geomorphology are briefly discussed.