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On the main channel length‐area relationship for channel networks
Author(s) -
Mesa Oscar J.,
Gupta Vijay K.
Publication year - 1987
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/wr023i011p02119
Subject(s) - channel (broadcasting) , magnitude (astronomy) , exponential function , mathematics , open channel flow , geometry , statistical physics , statistics , physics , mathematical analysis , computer science , telecommunications , flow (mathematics) , astronomy
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 l c (m) and the main channel length; l c (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.