HORTON'S LAW OF STREAM NUMBERS FOR TOPOLOGICALLY RANDOM CHANNEL NETWORKS

HORTON'S LAW OF STREAM NUMBERS FOR TOPOLOGICALLY RANDOM CHANNEL NETWORKS ACCORDING to Horton’s law of stream numbers, the bifurcation ratio in a drainage network is fairly constant with an average value between 3.5 and 4, so that the stream numbers tend to form a geometric progression. This paper investigates drainage networks whose structure is controlled by chance only. The mathematical analysis shows that the expected stream numbers also approach a geometric progression, and that the corresponding bifurcation ratios approximate the value 3.6 18. INTRODUCTION A scientific investigation of real world phenomena usually concentrates on selected properties and disregards all others. An example is the sequential pattern of merging rivers in a drainage network. The apparent hierarchy of their mergers can be studied disregarding all other components (topography, hydrology, morphometry). What remains is the information regarding the number of tributaries the system contains, and how they are interconnected, i.e., the topological structure of the network. This structure is the subject of Horton’s famous law. To understand its content, a few network parameters have to be defined. Since the original concept of stream order introduced by Horton (1945, p. 281) still contains a geometrical element (angles), the refined version of Strahler (1952, p. 1120) will be used here. The stream http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Canadian Geographer/Le Geographe Canadien Wiley

HORTON'S LAW OF STREAM NUMBERS FOR TOPOLOGICALLY RANDOM CHANNEL NETWORKS

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Publisher
Wiley
Copyright
Copyright © 1970 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0008-3658
eISSN
1541-0064
DOI
10.1111/j.1541-0064.1970.tb00006.x
Publisher site
See Article on Publisher Site

Abstract

ACCORDING to Horton’s law of stream numbers, the bifurcation ratio in a drainage network is fairly constant with an average value between 3.5 and 4, so that the stream numbers tend to form a geometric progression. This paper investigates drainage networks whose structure is controlled by chance only. The mathematical analysis shows that the expected stream numbers also approach a geometric progression, and that the corresponding bifurcation ratios approximate the value 3.6 18. INTRODUCTION A scientific investigation of real world phenomena usually concentrates on selected properties and disregards all others. An example is the sequential pattern of merging rivers in a drainage network. The apparent hierarchy of their mergers can be studied disregarding all other components (topography, hydrology, morphometry). What remains is the information regarding the number of tributaries the system contains, and how they are interconnected, i.e., the topological structure of the network. This structure is the subject of Horton’s famous law. To understand its content, a few network parameters have to be defined. Since the original concept of stream order introduced by Horton (1945, p. 281) still contains a geometrical element (angles), the refined version of Strahler (1952, p. 1120) will be used here. The stream

Journal

The Canadian Geographer/Le Geographe CanadienWiley

Published: Mar 1, 1970

References

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