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Stochastic model of the width function
Author(s) -
Veneziano Daniele,
Moglen Glenn E.,
Furcolo Pierluigi,
Iacobellis Vito
Publication year - 2000
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 - 10.1029/2000wr900002
Subject(s) - statistical physics , range (aeronautics) , exponent , spectral density , function (biology) , representation (politics) , mathematics , stochastic process , iterated function , probabilistic logic , power law , stochastic modelling , similarity (geometry) , computer science , mathematical analysis , physics , statistics , evolutionary biology , biology , philosophy , linguistics , materials science , image (mathematics) , artificial intelligence , politics , political science , law , composite material
A new class of probabilistic models of the width function, based on so‐called iterated random pulse (IRP) processes, is proposed. IRP processes reproduce the main characteristics of empirical width functions (nonnegativity, nonstationarity, and power law decay of the spectrum) and require few and easily accessible parameters. IRP models are based on a simple conceptualization of the geometrical structure of river basins and exploit in a natural way the self‐similarity of natural channel networks. A result that is derived from the IRP representation is that the exponent α of Hack's law, L ∼ A α , and the exponent β of the power spectral density of the width function, S (ω) ∼ |ω| −β , are related as α = 1/β. Empirical values of β are typically in the range 1.8–2.0 and are consistent with this theoretical result and the usual range of α.