Nonsmooth Invariant Manifolds in a Conceptual Climate Model
There is widespread agreement that ice sheets flowed into the ocean in tropical latitudes at sea level during the Earth's past. Whether these extreme ice ages were snowball Earth events, with the entire surface covered in ice, or whether ocean water remained ice free in regions about the equato...
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ftdatacite:10.48550/arxiv.1705.02964 2023-05-15T16:41:04+02:00 Nonsmooth Invariant Manifolds in a Conceptual Climate Model Walsh, James A. 2017 https://dx.doi.org/10.48550/arxiv.1705.02964 https://arxiv.org/abs/1705.02964 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Dynamical Systems math.DS Atmospheric and Oceanic Physics physics.ao-ph FOS Mathematics FOS Physical sciences Preprint Article article CreativeWork 2017 ftdatacite https://doi.org/10.48550/arxiv.1705.02964 2022-04-01T10:41:15Z There is widespread agreement that ice sheets flowed into the ocean in tropical latitudes at sea level during the Earth's past. Whether these extreme ice ages were snowball Earth events, with the entire surface covered in ice, or whether ocean water remained ice free in regions about the equator, continues to be controversial. For the latter situation to occur, the effect of positive ice albedo feedback would have to be damped to stabilize an advancing ice sheet shy of the equator. In this paper we analyze a conceptual model comprised of a zonally averaged surface temperature equation coupled to a dynamic ice line equation. This difference equation model is aligned with the cold world of these great glacial episodes through an appropriately chosen albedo function. Using the spectral method, the analysis leads to a nonsmooth singular perturbation problem. The Hadamard graph transform method is applied to prove the persistence of an invariant manifold, thereby providing insight into model behavior. A stable climate state with the ice line resting in tropical latitudes, but with open water about the equator, is shown to exist. Also presented are local smooth and nonsmooth bifurcations as parameters related to atmospheric CO$_2$ concentrations and the efficiency of meridional heat transport, respectively, are varied. Report Ice Sheet DataCite Metadata Store (German National Library of Science and Technology) |
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Dynamical Systems math.DS Atmospheric and Oceanic Physics physics.ao-ph FOS Mathematics FOS Physical sciences |
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Dynamical Systems math.DS Atmospheric and Oceanic Physics physics.ao-ph FOS Mathematics FOS Physical sciences Walsh, James A. Nonsmooth Invariant Manifolds in a Conceptual Climate Model |
topic_facet |
Dynamical Systems math.DS Atmospheric and Oceanic Physics physics.ao-ph FOS Mathematics FOS Physical sciences |
description |
There is widespread agreement that ice sheets flowed into the ocean in tropical latitudes at sea level during the Earth's past. Whether these extreme ice ages were snowball Earth events, with the entire surface covered in ice, or whether ocean water remained ice free in regions about the equator, continues to be controversial. For the latter situation to occur, the effect of positive ice albedo feedback would have to be damped to stabilize an advancing ice sheet shy of the equator. In this paper we analyze a conceptual model comprised of a zonally averaged surface temperature equation coupled to a dynamic ice line equation. This difference equation model is aligned with the cold world of these great glacial episodes through an appropriately chosen albedo function. Using the spectral method, the analysis leads to a nonsmooth singular perturbation problem. The Hadamard graph transform method is applied to prove the persistence of an invariant manifold, thereby providing insight into model behavior. A stable climate state with the ice line resting in tropical latitudes, but with open water about the equator, is shown to exist. Also presented are local smooth and nonsmooth bifurcations as parameters related to atmospheric CO$_2$ concentrations and the efficiency of meridional heat transport, respectively, are varied. |
format |
Report |
author |
Walsh, James A. |
author_facet |
Walsh, James A. |
author_sort |
Walsh, James A. |
title |
Nonsmooth Invariant Manifolds in a Conceptual Climate Model |
title_short |
Nonsmooth Invariant Manifolds in a Conceptual Climate Model |
title_full |
Nonsmooth Invariant Manifolds in a Conceptual Climate Model |
title_fullStr |
Nonsmooth Invariant Manifolds in a Conceptual Climate Model |
title_full_unstemmed |
Nonsmooth Invariant Manifolds in a Conceptual Climate Model |
title_sort |
nonsmooth invariant manifolds in a conceptual climate model |
publisher |
arXiv |
publishDate |
2017 |
url |
https://dx.doi.org/10.48550/arxiv.1705.02964 https://arxiv.org/abs/1705.02964 |
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Ice Sheet |
genre_facet |
Ice Sheet |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1705.02964 |
_version_ |
1766031499988041728 |