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


Falkena, SKJ and Quinn, C and Sieber, J and Frank, J and Dijkstra, HA, Derivation of delay equation climate models using the Mori-Zwanzig formalism, Proceedings of the Royal Society A, 475, (2227) Article 20190075. ISSN 1364-5021 (2019) [Refereed Article]

Copyright Statement

2019 The Author(s) Published by the Royal Society. All rights reserved.

DOI: doi:10.1098/rspa.2019.0075


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

Item Details

Item Type:Refereed Article
Keywords:delay models, Mori-Zwanzig, reduction methods, El Niņo southern oscillation, conceptual models, feedback effects
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Dynamical systems in applications
Objective Division:Environmental Policy, Climate Change and Natural Hazards
Objective Group:Understanding climate change
Objective Field:Climate variability (excl. social impacts)
UTAS Author:Quinn, C (Dr Courtney Quinn)
ID Code:149467
Year Published:2019
Web of Science® Times Cited:7
Deposited By:Mathematics
Deposited On:2022-03-31
Last Modified:2022-05-24

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