A Note on Fractal Channel Networks

A Note on Fractal Channel Networks This paper studies the relation between the structure of river networks and the features of their geomorphologic hydrologic response. A mathematical formulation of connectivity of a drainage network is proposed to relate contributing areas and the network geometry. In view of the connectivity conjecture, Horton's bifurcation ratio RB tends, for high values of Strahler's order Ω of the basin, to the area ratio RA, and Horton's length ratio RL equals, in the limit, the single‐order contributing area ratio Ra. The relevance of these arguments is examined by reference to data from real basins. Well‐known empirical results from the geomorphological literature (Melton's law, Hack's relation, Moon's conjecture) are viewed as a consequence of connectivity. It is found that in Hortonian networks the time evolution of contributing areas exhibits a multifractal behavior generated by a multiplicative process of parameter 1/RB. The application of the method of the most probable distribution in view of connectivity contributes new inroads toward a general formulation of the geomorphologic unit hydrograph, in particular generalizing its width function formulation. A quantitative example of multifractal hydrologic response of idealized networks based on Peano's construct (for which RB = RA = 4, RL = 2) closes the paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

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Publisher
Wiley
Copyright
Copyright © 1991 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
DOI
10.1029/91WR02077
Publisher site
See Article on Publisher Site

Abstract

This paper studies the relation between the structure of river networks and the features of their geomorphologic hydrologic response. A mathematical formulation of connectivity of a drainage network is proposed to relate contributing areas and the network geometry. In view of the connectivity conjecture, Horton's bifurcation ratio RB tends, for high values of Strahler's order Ω of the basin, to the area ratio RA, and Horton's length ratio RL equals, in the limit, the single‐order contributing area ratio Ra. The relevance of these arguments is examined by reference to data from real basins. Well‐known empirical results from the geomorphological literature (Melton's law, Hack's relation, Moon's conjecture) are viewed as a consequence of connectivity. It is found that in Hortonian networks the time evolution of contributing areas exhibits a multifractal behavior generated by a multiplicative process of parameter 1/RB. The application of the method of the most probable distribution in view of connectivity contributes new inroads toward a general formulation of the geomorphologic unit hydrograph, in particular generalizing its width function formulation. A quantitative example of multifractal hydrologic response of idealized networks based on Peano's construct (for which RB = RA = 4, RL = 2) closes the paper.

Journal

Water Resources ResearchWiley

Published: Dec 1, 1991

References

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