A delay equation model for the Atlantic Multidecadal Oscillation

Abstract

A new technique to derive delay models from systems of partial differential equations, based on the Mori–Zwanzig (MZ) formalism, is used to derive a delay-difference equation model for the Atlantic Multidecadal Oscillation (AMO). The MZ formalism gives a rewriting of the original system of equations, which contains a memory term. This memory term can be related to a delay term in a resulting delay equation. Here, the technique is applied to an idealized, but spatially extended, model of the AMO. The resulting delay-difference model is of a different type than the delay differential model which has been used to describe the El Niño Southern Oscillation. In addition to this model, which can also be obtained by integration along characteristics, error terms for a smoothing approximation of the model have been derived from the MZ formalism. Our new method of deriving delay models from spatially extended models has a large potential to use delay models to study a range of climate variability phenomena.