Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T04:59:50.788Z Has data issue: false hasContentIssue false
  • English
  • Français

On the expected width function for topologically random channel networks

Published online by Cambridge University Press:  14 July 2016

Brent M. Troutman  and
Michael R. Karlinger
Brent M. Troutman*
Affiliation:
U.S. Geological Survey
Michael R. Karlinger*
Affiliation:
U.S. Geological Survey
*
∗Postal address: U.S. Department of the Interior, Geological Survey, Box 25046, M.S. 420, Denver Federal Center, Denver, CO 80225, USA.
∗Postal address: U.S. Department of the Interior, Geological Survey, Box 25046, M.S. 420, Denver Federal Center, Denver, CO 80225, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

An idealized river-channel network is represented by a trivalent planted plane tree, the root of which corresponds to the outlet of the network. A link of the network is any segment between a source and a junction, two successive junctions, or the outlet and a junction. For any x≧0, the width of the network is the number of links with the property that the distance of the downstream junction from the outlet is ≦x, and the distance of the upstream junction to the outlet is > x. Expressions are obtained for the expected width conditioned on N, (N, M), and (N, D), where N is the magnitude, M the order, and D the diameter of the network, under the assumption that the network is drawn from an infinite topologically random population and the link lengths are random.

Keywords

NETWORKSBRANCHING PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 836 - 849
Copyright
Copyright © Applied Probability Trust 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Billingsley, P. (1979) Probability and Measure. Wiley, New York.Google Scholar
[2] Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
[3] Gradshteyn, I. S. and Ryzhik, I. M. (1965) Table of Integrals, Series, and Products. Academic Press, New York.Google Scholar
[4] Gupta, V. K. and Waymire, E. (1983) On the formulation of an analytical approach to hydrologic response and similarity of the basin scale. J. Hydrology 65, 95–184.Google Scholar
[5] Shreve, R. L. (1966) Statistical law of stream numbers. J. Geology 74, 17–37.Google Scholar
[6] Shreve, R. L. (1967) Infinite topologically random channel networks. J. Geology 75, 178–186.Google Scholar
[7] Shreve, R. L. (1969) Stream lengths and basin areas in topologically random channel networks. J. Geology 77, 397–414.Google Scholar
[8] Shreve, R. L. (1974) Variation of mainstream length with basin area in river networks. Water Resources Res. 10, 1167–1177.Google Scholar
[9] Smart, J. S. (1968) Statistical properties of stream lengths. Water Resources Res. 4, 1001–1014.Google Scholar
[10] Smart, J. S. (1972) Channel networks. In Advances in Hydroscience, ed. Ven Te Chow, . Academic Press, New York.Google Scholar
[11] Smart, J. S. (1978) Analysis of drainage network composition Earth Surf. Proc. 3, 129–170.Google Scholar
[12] Smart, J. S. and Werner, C. (1976) Analysis of the random model of drainage basin composition. Earth Surf. Proc. 1, 219–233.Google Scholar