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On the expected diameter of random channel networks
Author(s) -
Moon J. W.
Publication year - 1980
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr016i006p01119
Subject(s) - channel (broadcasting) , drainage network , drainage basin , structural basin , object (grammar) , hydrology (agriculture) , mathematics , geology , statistics , geometry , geography , computer science , geomorphology , telecommunications , geotechnical engineering , cartography , artificial intelligence
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.