# On the main channel length‐area relationship for channel networks

On the main channel length‐area relationship for channel networks Motivated by the empirical relationship between the main channel length and the basin area for river networks, a similar equation is derived analytically using the random model postulates and the additional assumption that link lengths have a common exponential probability distribution. Specifically, it is shown that in networks with large magnitude m, the main channel length l(m), and the magnitude are related by l(m) ∼ β(2π)½(2π)½, where β is mean link length. This result is utilized to explain another empirical relationship between the distance to the center of gravity lc(m) and the main channel length; lc(m) ∼ l(m)/2. The observed deviations of the random model prediction regarding the main channel length from empirical observations is used to discuss some important open problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

# On the main channel length‐area relationship for channel networks

Water Resources Research, Volume 23 (11) – Nov 1, 1987
4 pages

/lp/wiley/on-the-main-channel-length-area-relationship-for-channel-networks-hQlZF0Ec9K
Publisher
Wiley
ISSN
0043-1397
eISSN
1944-7973
D.O.I.
10.1029/WR023i011p02119
Publisher site
See Article on Publisher Site

### Abstract

Motivated by the empirical relationship between the main channel length and the basin area for river networks, a similar equation is derived analytically using the random model postulates and the additional assumption that link lengths have a common exponential probability distribution. Specifically, it is shown that in networks with large magnitude m, the main channel length l(m), and the magnitude are related by l(m) ∼ β(2π)½(2π)½, where β is mean link length. This result is utilized to explain another empirical relationship between the distance to the center of gravity lc(m) and the main channel length; lc(m) ∼ l(m)/2. The observed deviations of the random model prediction regarding the main channel length from empirical observations is used to discuss some important open problems.

### Journal

Water Resources ResearchWiley

Published: Nov 1, 1987

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