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.
Water Resources Research – Wiley
Published: Nov 1, 1987
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