The factor separation methodology and the fractional approach

Tatiana Sholokhman, Pinhas Alpert

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Following Stein and Alpert (1993) (SA, in brief) The proposed method for two factors The value of any predicted field f depends on the initial and boundary conditions, as well as the model itself. If a continuous change is made in any factor ψ, the resulting field f in general changes in a continuous manner as well. This can be mathematically formulated as follows. Let the factor ψ be multiplied by a changing coefficient c so that The resulting field f is a continuous function of c: so that f(1) is the value of f in the control simulation, and f(0) is the value of f in the simulation where the factor ψ is omitted. In the notation that follows, f0 and f1 are used for f(0) and f(1), respectively. It is always possible to decompose any function f(c) into a constant part, that is independent of c, and a c-dependent component, such that. In this simple example, and It is important to understand the meaning of and, the latter being a short form for. The term represents that fraction of f that is induced by the factor ψ, while is the remaining part that does not depend on factor ψ.

Original languageEnglish
Title of host publicationFactor Separation in the Atmosphere
Subtitle of host publicationApplications and Future Prospects
PublisherCambridge University Press
Pages5-10
Number of pages6
Volume9780521191739
ISBN (Electronic)9780511921414
ISBN (Print)9780521191739
DOIs
StatePublished - 1 Jan 2011

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