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.
|Title of host publication||Factor Separation in the Atmosphere|
|Subtitle of host publication||Applications and Future Prospects|
|Publisher||Cambridge University Press|
|Number of pages||6|
|State||Published - 1 Jan 2011|