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dc.contributor.authorFalkena, SKJ
dc.contributor.authorQuinn, C
dc.contributor.authorSieber, J
dc.contributor.authorFrank, J
dc.contributor.authorDijkstra, HA
dc.date.accessioned2019-06-11T09:18:48Z
dc.date.issued2019-07-17
dc.description.abstractModels 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 Nino 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.en_GB
dc.description.sponsorshipEuropean Union Horizon 2020en_GB
dc.description.sponsorshipDutch Science Foundation (NWOen_GB
dc.description.sponsorshipEngineering and Physical Sciences Research Council (EPSRC)en_GB
dc.identifier.citationVol. 475 (2227). Published online 17 July 2019.en_GB
dc.identifier.doi10.1098/rspa.2019.0075
dc.identifier.grantnumber643073en_GB
dc.identifier.grantnumber657.014.006en_GB
dc.identifier.grantnumberEP/N023544/1en_GB
dc.identifier.grantnumberEP/N014391/1en_GB
dc.identifier.urihttp://hdl.handle.net/10871/37452
dc.language.isoenen_GB
dc.publisherRoyal Societyen_GB
dc.rights© 2019 The Author(s). Published by the Royal Society. All rights reserved.
dc.subjectDelay modelsen_GB
dc.subjectMori-Zwanzigen_GB
dc.subjectReduction methodsen_GB
dc.subjectEl Niñoen_GB
dc.subjectSouthern Oscillationen_GB
dc.subjectConceptual modelsen_GB
dc.subjectFeedback effectsen_GB
dc.titleDerivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalismen_GB
dc.typeArticleen_GB
dc.date.available2019-06-11T09:18:48Z
dc.descriptionThis is the author accepted manuscript. The final version is available from The Royal Society via the DOI in this record.en_GB
dc.descriptionData access: The codes supporting this article have been uploaded as part of the supplementary material. They can also be found on the online repository figshare: https://doi.org/10.6084/m9.figshare.8085683.v1en_GB
dc.identifier.eissn1471-2946
dc.identifier.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciencesen_GB
dc.rights.urihttp://www.rioxx.net/licenses/all-rights-reserveden_GB
dcterms.dateAccepted2019-06-04
rioxxterms.versionAMen_GB
rioxxterms.licenseref.startdate2019-06-04
rioxxterms.typeJournal Article/Reviewen_GB
refterms.dateFCD2019-06-11T09:15:36Z
refterms.versionFCDAM
refterms.dateFOA2019-08-07T09:16:59Z
refterms.panelBen_GB


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