Reexamining the determination of the fractal dimension of river networks

Reexamining the determination of the fractal dimension of river networks In analyzing the literature on the fractal nature of river networks one can recognize several points that require clarification or additional investigations. For instance, many interpretations, with different conclusions, have been given to the important empirical results found in the previous literature on river geomorphology. Similarly, the argument concerning a possible “more likely” value of the fractal dimensions of river networks has not yet found a convincing answer. In an attempt to shed more light on the topic, particularly on the latter point, we have reexamined the basic aspects related to selfsimilarity in river networks using uniquely the fundamental concepts of fractal geometry. This approach leads to relations for the determination of the fractal dimensions which hold exactly for deterministic self‐similar trees and are compatible with related findings reported in literature. Results obtained from application of these relations to several river networks in southern Italy indicate very low variability around the average values of about 1.7, 1.5, and 1.1 for the fractal dimensions of the whole river network, of its topological equivalent, and of its individual streams, respectively. This outcome, in addition to comparable results taken from the literature, provides new arguments to the hypothesis that natural networks tend to have the same fractal dimensions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

Reexamining the determination of the fractal dimension of river networks

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Publisher
Wiley
Copyright
Copyright © 1996 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
DOI
10.1029/96WR01942
Publisher site
See Article on Publisher Site

Abstract

In analyzing the literature on the fractal nature of river networks one can recognize several points that require clarification or additional investigations. For instance, many interpretations, with different conclusions, have been given to the important empirical results found in the previous literature on river geomorphology. Similarly, the argument concerning a possible “more likely” value of the fractal dimensions of river networks has not yet found a convincing answer. In an attempt to shed more light on the topic, particularly on the latter point, we have reexamined the basic aspects related to selfsimilarity in river networks using uniquely the fundamental concepts of fractal geometry. This approach leads to relations for the determination of the fractal dimensions which hold exactly for deterministic self‐similar trees and are compatible with related findings reported in literature. Results obtained from application of these relations to several river networks in southern Italy indicate very low variability around the average values of about 1.7, 1.5, and 1.1 for the fractal dimensions of the whole river network, of its topological equivalent, and of its individual streams, respectively. This outcome, in addition to comparable results taken from the literature, provides new arguments to the hypothesis that natural networks tend to have the same fractal dimensions.

Journal

Water Resources ResearchWiley

Published: Oct 1, 1996

References

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