On self‐similarity and self‐affinity of drainage basins

On self‐similarity and self‐affinity of drainage basins An approach is proposed which allows consideration from common positions the self‐similar and self‐affine properties of river drainage basins and which introduces respective characteristics of their fractal structure. Horton's (1945) model has been assumed as the basis of this study. It is shown that self‐similarity of river drainage basins is characterized by the self‐similarity dimension DS = ln RB/ln RL. In the case of self‐affinity, two scaling indices DL = ln RB/ln RL and Dw = ln RB/ln (RA/RL) are required, the combinations of which determine the Hurst H = DL/DW index (characterizing the degree of drainage basins self‐affinity) and the lacunary dimension DG = 2DLDW/(DL + DW) (characterizing the degree of lacunarity or noncompactness of drainage basins). On the basis of analysis of published data from rivers in the United States, Italy, Russia, and Romania, the conclusion is drawn that river drainage basins are generally noncompact (DG < 2) and self‐affine (H < 1) fractal objects. Besides, for a quantitative description of river drainage basins, a new parameter is introduced, which characterizes the degree to which a large catchment is filled with smaller ones. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

On self‐similarity and self‐affinity of drainage basins

Water Resources Research, Volume 30 (1) – Jan 1, 1994

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Publisher
Wiley
Copyright
Copyright © 1994 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
DOI
10.1029/93WR02017
Publisher site
See Article on Publisher Site

Abstract

An approach is proposed which allows consideration from common positions the self‐similar and self‐affine properties of river drainage basins and which introduces respective characteristics of their fractal structure. Horton's (1945) model has been assumed as the basis of this study. It is shown that self‐similarity of river drainage basins is characterized by the self‐similarity dimension DS = ln RB/ln RL. In the case of self‐affinity, two scaling indices DL = ln RB/ln RL and Dw = ln RB/ln (RA/RL) are required, the combinations of which determine the Hurst H = DL/DW index (characterizing the degree of drainage basins self‐affinity) and the lacunary dimension DG = 2DLDW/(DL + DW) (characterizing the degree of lacunarity or noncompactness of drainage basins). On the basis of analysis of published data from rivers in the United States, Italy, Russia, and Romania, the conclusion is drawn that river drainage basins are generally noncompact (DG < 2) and self‐affine (H < 1) fractal objects. Besides, for a quantitative description of river drainage basins, a new parameter is introduced, which characterizes the degree to which a large catchment is filled with smaller ones.

Journal

Water Resources ResearchWiley

Published: Jan 1, 1994

References

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