Synchronous Glacial Cycles in a Nonsmooth Conceptual Climate Model with Asymmetric Hemispheres

We present a new conceptual model of the Earth's glacial-interglacial cycles, one leading to governing equations for which the vector field has a hyperplane of discontinuities. This work extends the classic Budyko- and Sellers-type conceptual energy balance models of temperature-albedo feedback...

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Bibliographic Details
Main Authors: Nadeau, Alice, Walsh, James, Widiasih, Esther
Format: Article in Journal/Newspaper
Language:unknown
Published: arXiv 2021
Subjects:
Dynamical Systems math.DS
Atmospheric and Oceanic Physics physics.ao-ph
FOS Mathematics
FOS Physical sciences
49J52, 37N99, 86A40
Ice Sheet
Online Access:https://dx.doi.org/10.48550/arxiv.2101.01707
https://arxiv.org/abs/2101.01707
id ftdatacite:10.48550/arxiv.2101.01707
record_format openpolar
spelling ftdatacite:10.48550/arxiv.2101.01707 2023-05-15T16:41:00+02:00 Synchronous Glacial Cycles in a Nonsmooth Conceptual Climate Model with Asymmetric Hemispheres Nadeau, Alice Walsh, James Widiasih, Esther 2021 https://dx.doi.org/10.48550/arxiv.2101.01707 https://arxiv.org/abs/2101.01707 unknown arXiv Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 CC-BY Dynamical Systems math.DS Atmospheric and Oceanic Physics physics.ao-ph FOS Mathematics FOS Physical sciences 49J52, 37N99, 86A40 Article CreativeWork article Preprint 2021 ftdatacite https://doi.org/10.48550/arxiv.2101.01707 2022-03-10T15:01:19Z We present a new conceptual model of the Earth's glacial-interglacial cycles, one leading to governing equations for which the vector field has a hyperplane of discontinuities. This work extends the classic Budyko- and Sellers-type conceptual energy balance models of temperature-albedo feedback by removing the standard assumption of planetary symmetry about the equator. The dynamics of separate Northern and Southern Hemisphere ice caps are coupled to an equation representing the annual global mean surface temperature. The system has a discontinuous switching mechanism based on mass balance principles for the Northern Hemisphere ice sheet. We show the associated Filippov system admits a unique nonsmooth and attracting limit cycle that represents the cycling between glacial and interglacial states. Due to the vastly different time scales involved, the model presents a nonsmooth geometric perturbation problem, for which we use ad hoc mathematical techniques to produce the periodic orbit. We find climatic changes in the Northern Hemisphere drive synchronous changes in the Southern Hemisphere, as is observed for the Earth on orbital time scales. : 21 pages, 5 figures Article in Journal/Newspaper Ice Sheet DataCite Metadata Store (German National Library of Science and Technology)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Dynamical Systems math.DS
Atmospheric and Oceanic Physics physics.ao-ph
FOS Mathematics
FOS Physical sciences
49J52, 37N99, 86A40
spellingShingle Dynamical Systems math.DS
Atmospheric and Oceanic Physics physics.ao-ph
FOS Mathematics
FOS Physical sciences
49J52, 37N99, 86A40
Nadeau, Alice
Walsh, James
Widiasih, Esther
Synchronous Glacial Cycles in a Nonsmooth Conceptual Climate Model with Asymmetric Hemispheres
topic_facet Dynamical Systems math.DS
Atmospheric and Oceanic Physics physics.ao-ph
FOS Mathematics
FOS Physical sciences
49J52, 37N99, 86A40
description We present a new conceptual model of the Earth's glacial-interglacial cycles, one leading to governing equations for which the vector field has a hyperplane of discontinuities. This work extends the classic Budyko- and Sellers-type conceptual energy balance models of temperature-albedo feedback by removing the standard assumption of planetary symmetry about the equator. The dynamics of separate Northern and Southern Hemisphere ice caps are coupled to an equation representing the annual global mean surface temperature. The system has a discontinuous switching mechanism based on mass balance principles for the Northern Hemisphere ice sheet. We show the associated Filippov system admits a unique nonsmooth and attracting limit cycle that represents the cycling between glacial and interglacial states. Due to the vastly different time scales involved, the model presents a nonsmooth geometric perturbation problem, for which we use ad hoc mathematical techniques to produce the periodic orbit. We find climatic changes in the Northern Hemisphere drive synchronous changes in the Southern Hemisphere, as is observed for the Earth on orbital time scales. : 21 pages, 5 figures
format Article in Journal/Newspaper
author Nadeau, Alice
Walsh, James
Widiasih, Esther
author_facet Nadeau, Alice
Walsh, James
Widiasih, Esther
author_sort Nadeau, Alice
title Synchronous Glacial Cycles in a Nonsmooth Conceptual Climate Model with Asymmetric Hemispheres
title_short Synchronous Glacial Cycles in a Nonsmooth Conceptual Climate Model with Asymmetric Hemispheres
title_full Synchronous Glacial Cycles in a Nonsmooth Conceptual Climate Model with Asymmetric Hemispheres
title_fullStr Synchronous Glacial Cycles in a Nonsmooth Conceptual Climate Model with Asymmetric Hemispheres
title_full_unstemmed Synchronous Glacial Cycles in a Nonsmooth Conceptual Climate Model with Asymmetric Hemispheres
title_sort synchronous glacial cycles in a nonsmooth conceptual climate model with asymmetric hemispheres
publisher arXiv
publishDate 2021
url https://dx.doi.org/10.48550/arxiv.2101.01707
https://arxiv.org/abs/2101.01707
genre Ice Sheet
genre_facet Ice Sheet
op_rights Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
cc-by-4.0
op_rightsnorm CC-BY
op_doi https://doi.org/10.48550/arxiv.2101.01707
_version_ 1766031426483912704

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