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Multiscaling properties of rainfall and bounded random cascades
Author(s) -
Menabde Merab,
Harris Daniel,
Seed Alan,
Austin Geoff,
Stow David
Publication year - 1997
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 - 10.1029/97wr02006
Subject(s) - intermittency , bounded function , multiplicative function , cascade , statistical physics , mathematics , random field , exponent , series (stratigraphy) , generalization , spectral density , mathematical analysis , statistics , physics , meteorology , geology , paleontology , linguistics , chemistry , philosophy , chromatography , turbulence
The connection among different types of exponents characterizing multiscaling properties of rainfall and a criterion for stationarity of random fields are discussed, and a new phenomenological model for rainfall time series simulation is proposed. The bounded random cascade model presented here is a generalization of the well‐known α model with the multiplicative weights of the generator converging to unity as the cascade proceeds to smaller scales. This allows one to directly simulate a multiscaling random field with an energy spectrum exponent, β>1, which is typical for rainfall time series data but which cannot be produced by a standard α model. A procedure is proposed for estimating the cascade parameters of this new bounded α model from observed data. Parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents. The bounded α model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts.