# 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 language English Factor Separation in the Atmosphere Applications and Future Prospects Cambridge University Press 5-10 6 9780521191739 9780511921414 9780521191739 https://doi.org/10.1017/CBO9780511921414.004 Published - 1 Jan 2011

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