Testing statistical self-similarity in the topology of river networks

Journal of Geophysical Research F: Earth Surface
By: , and 

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Abstract

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.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Testing statistical self-similarity in the topology of river networks
Series title Journal of Geophysical Research F: Earth Surface
DOI 10.1029/2009JF001609
Volume 115
Issue F3
Year Published 2010
Language English
Publisher American Geophysical Union
Contributing office(s) National Research Program - Central Branch
Description F03038: 12 p.