Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo
As Arctic sea ice extent decreases with increasing greenhouse gases, there is a growing interest in whether there could be a bifurcation associated with its loss, and whether there is significant hysteresis associated with that bifurcation. A challenge in answering this question is that the bifurcat...
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ftdatacite:10.48550/arxiv.1509.00059 2023-05-15T13:10:26+02:00 Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo Hill, Kaitlin Abbot, Dorian S. Silber, Mary 2015 https://dx.doi.org/10.48550/arxiv.1509.00059 https://arxiv.org/abs/1509.00059 unknown arXiv https://dx.doi.org/10.1137/15m1037718 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 49J52, 37N05 Primary, 37B55, 37G15 Secondary article-journal Article ScholarlyArticle Text 2015 ftdatacite https://doi.org/10.48550/arxiv.1509.00059 https://doi.org/10.1137/15m1037718 2022-04-01T12:05:04Z As Arctic sea ice extent decreases with increasing greenhouse gases, there is a growing interest in whether there could be a bifurcation associated with its loss, and whether there is significant hysteresis associated with that bifurcation. A challenge in answering this question is that the bifurcation behavior of certain Arctic energy balance models have been shown to be sensitive to how ice-albedo feedback is parameterized. We analyze an Arctic energy balance model in the limit as a smoothing parameter associated with ice-albedo feedback tends to zero, which introduces a discontinuity boundary to the dynamical systems model. Our analysis provides a case study where we use the system in this limit to guide the investigation of bifurcation behavior of the original albedo-smoothed system. In this case study, we demonstrate that certain qualitative bifurcation behaviors of the albedo-smoothed system can have counterparts in the limit with no albedo smoothing. We use this perspective to systematically explore the parameter space of the model. For example, we uncover parameter sets for which the largest transition, with increasing greenhouse gases, is from a perennially ice-covered Arctic to a seasonally ice-free state, an unusual bifurcation scenario that persists even when albedo-smoothing is reintroduced. This analysis provides an alternative perspective on how parameters of the model affect bifurcation behavior. We expect our approach, which exploits the width of repelling sliding intervals for understanding the hysteresis loops, would carry over to other positive feedback systems with a similar natural piecewise-smooth limit, and when the feedback strength is likewise modulated with seasons or other periodic forcing. : 29 pages, 12 figures, 2 tables Text albedo Arctic Sea ice DataCite Metadata Store (German National Library of Science and Technology) Arctic |
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DataCite Metadata Store (German National Library of Science and Technology) |
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language |
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topic |
Dynamical Systems math.DS Atmospheric and Oceanic Physics physics.ao-ph FOS Mathematics FOS Physical sciences 49J52, 37N05 Primary, 37B55, 37G15 Secondary |
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Dynamical Systems math.DS Atmospheric and Oceanic Physics physics.ao-ph FOS Mathematics FOS Physical sciences 49J52, 37N05 Primary, 37B55, 37G15 Secondary Hill, Kaitlin Abbot, Dorian S. Silber, Mary Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo |
topic_facet |
Dynamical Systems math.DS Atmospheric and Oceanic Physics physics.ao-ph FOS Mathematics FOS Physical sciences 49J52, 37N05 Primary, 37B55, 37G15 Secondary |
description |
As Arctic sea ice extent decreases with increasing greenhouse gases, there is a growing interest in whether there could be a bifurcation associated with its loss, and whether there is significant hysteresis associated with that bifurcation. A challenge in answering this question is that the bifurcation behavior of certain Arctic energy balance models have been shown to be sensitive to how ice-albedo feedback is parameterized. We analyze an Arctic energy balance model in the limit as a smoothing parameter associated with ice-albedo feedback tends to zero, which introduces a discontinuity boundary to the dynamical systems model. Our analysis provides a case study where we use the system in this limit to guide the investigation of bifurcation behavior of the original albedo-smoothed system. In this case study, we demonstrate that certain qualitative bifurcation behaviors of the albedo-smoothed system can have counterparts in the limit with no albedo smoothing. We use this perspective to systematically explore the parameter space of the model. For example, we uncover parameter sets for which the largest transition, with increasing greenhouse gases, is from a perennially ice-covered Arctic to a seasonally ice-free state, an unusual bifurcation scenario that persists even when albedo-smoothing is reintroduced. This analysis provides an alternative perspective on how parameters of the model affect bifurcation behavior. We expect our approach, which exploits the width of repelling sliding intervals for understanding the hysteresis loops, would carry over to other positive feedback systems with a similar natural piecewise-smooth limit, and when the feedback strength is likewise modulated with seasons or other periodic forcing. : 29 pages, 12 figures, 2 tables |
format |
Text |
author |
Hill, Kaitlin Abbot, Dorian S. Silber, Mary |
author_facet |
Hill, Kaitlin Abbot, Dorian S. Silber, Mary |
author_sort |
Hill, Kaitlin |
title |
Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo |
title_short |
Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo |
title_full |
Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo |
title_fullStr |
Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo |
title_full_unstemmed |
Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo |
title_sort |
analysis of an arctic sea ice loss model in the limit of a discontinuous albedo |
publisher |
arXiv |
publishDate |
2015 |
url |
https://dx.doi.org/10.48550/arxiv.1509.00059 https://arxiv.org/abs/1509.00059 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
albedo Arctic Sea ice |
genre_facet |
albedo Arctic Sea ice |
op_relation |
https://dx.doi.org/10.1137/15m1037718 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1509.00059 https://doi.org/10.1137/15m1037718 |
_version_ |
1766229852630810624 |