Optimal Angular Geometry Models of River Branching

Optimal Angular Geometry Models of River Branching *I would like to thank Michael Woldenberg for stimulating my interest in this topic and for his helpful suggestions on earlier drafts of this paper. And& G . Roy is postdoctoral fellow i n geography, University of Montreal. Geographical Analysis, Vol. 15, No. 2 (April 1983) Copyright 0 1983 by the Ohio State University Press Submitted 4182. Revised version accepted 10/82. 88 I Geographical Analysis GENERAL THEORETICAL FRAMEWORK OF HORTON'S AND HOWARD'S MODELS OF RIVER BRANCHING Horton (1926, 1932) derived his model from the assumption that overland flow on the valley slopes follows the line of steepest gradient. The angle (6) formed between the line of overland flow and the stream channel collecting the flow downslope was derived from a trigonometric model and Horton (1932) showed that where S, and S, are the channel gradient and ground slope respectively (Fig. 1). Hence 8 becomes wider as the ground slope becomes much steeper than the channel gradient. Horton (1945) later adapted the model to the case where one major stream is joined by a tributary stream. The angle of entry then is given by where So and S, denote the channel gradients of the receiving and the tributary streams, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geographical Analysis Wiley

Optimal Angular Geometry Models of River Branching

Geographical Analysis, Volume 15 (2) – Apr 1, 1983

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Publisher
Wiley
Copyright
1983 The Ohio State University
ISSN
0016-7363
eISSN
1538-4632
DOI
10.1111/j.1538-4632.1983.tb00771.x
Publisher site
See Article on Publisher Site

Abstract

*I would like to thank Michael Woldenberg for stimulating my interest in this topic and for his helpful suggestions on earlier drafts of this paper. And& G . Roy is postdoctoral fellow i n geography, University of Montreal. Geographical Analysis, Vol. 15, No. 2 (April 1983) Copyright 0 1983 by the Ohio State University Press Submitted 4182. Revised version accepted 10/82. 88 I Geographical Analysis GENERAL THEORETICAL FRAMEWORK OF HORTON'S AND HOWARD'S MODELS OF RIVER BRANCHING Horton (1926, 1932) derived his model from the assumption that overland flow on the valley slopes follows the line of steepest gradient. The angle (6) formed between the line of overland flow and the stream channel collecting the flow downslope was derived from a trigonometric model and Horton (1932) showed that where S, and S, are the channel gradient and ground slope respectively (Fig. 1). Hence 8 becomes wider as the ground slope becomes much steeper than the channel gradient. Horton (1945) later adapted the model to the case where one major stream is joined by a tributary stream. The angle of entry then is given by where So and S, denote the channel gradients of the receiving and the tributary streams,

Journal

Geographical AnalysisWiley

Published: Apr 1, 1983

References

  • The Physiological Principle of Minimum Work Applied to the Angle of Branching of Arteries
    Murray, Murray
  • Location in Continuous Space
    Wesolowsky, Wesolowsky

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