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arXiv · 2008.07219

A Delay Equation Model for the Atlantic Multidecadal Oscillation

Swinda K. J. Falkena·Courtney Quinn·Jan Sieber·Henk A. Dijkstra
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Abstract

A new technique to derive delay models from systems of partial differential equations, based on the Mori-Zwanzig formalism, is used to derive a delay difference equation model for the Atlantic Multidecadal Oscillation. The Mori-Zwanzig 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 Atlantic Multidecadal Oscillation. The resulting delay difference model is of a different type than the delay differential model which has been used to describe the El Ni\~no- 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 Mori-Zwanzig 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.

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Swinda K. J. Falkena, Courtney Quinn, Jan Sieber, Henk A. Dijkstra. 2020-08-17. A Delay Equation Model for the Atlantic Multidecadal Oscillation. https://doi.org/10.1098/rspa.2020.0659

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