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.
Water Resources Research – Wiley
Published: Dec 1, 1980
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