Derivation of delay equation climate models using the Mori-Zwanzig formalism

摘要: Models incorporating delay have been frequently used to understand climate variability phenomena, but often the is introduced through an ad hoc physical reasoning, such as propagation time of waves. In this paper, Mori-Zwanzig formalism a way systematically derive models from systems partial differential equations and hence provides better justification for using these delay-type models. The technique gives formal rewriting system projection onto set resolved variables, where rewritten contains memory term. computation term requires solving orthogonal dynamics equation, which represents unresolved dynamics. For nonlinear systems, it not possible obtain analytical solution approximate needs be found. Here, we demonstrate two-strip model El Nino Southern Oscillation (ENSO) explore methods solve resulting additional compared previously proposed conceptual This new leads larger ENSO period, closer that seen in observations.