On the expected diameter of random channel networks

On the expected diameter of random channel networks The mainstream length of river networks tends to be proportional to the area of the corresponding drainage basin raised to a power that decreases from about 0.6 for small basins to near 0.5 for large basins. Shreve (1974) calculated the expected diameter μ(D) of random channel networks with n sources for values of n up to 500. On the basis of this numerical data he concluded that it seems likely that the ratio log μ(D)/log n approaches ½ as n increases indefinitely. Our object here is to prove that this is indeed the case. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

On the expected diameter of random channel networks

Water Resources Research, Volume 16 (6) – Dec 1, 1980

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Publisher
Wiley
Copyright
Copyright © 1980 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
D.O.I.
10.1029/WR016i006p01119
Publisher site
See Article on Publisher Site

Abstract

The mainstream length of river networks tends to be proportional to the area of the corresponding drainage basin raised to a power that decreases from about 0.6 for small basins to near 0.5 for large basins. Shreve (1974) calculated the expected diameter μ(D) of random channel networks with n sources for values of n up to 500. On the basis of this numerical data he concluded that it seems likely that the ratio log μ(D)/log n approaches ½ as n increases indefinitely. Our object here is to prove that this is indeed the case.

Journal

Water Resources ResearchWiley

Published: Dec 1, 1980

References

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