On the Budyko-Sellers energy balance climate model with ice line coupling

Title:
On the Budyko-Sellers energy balance climate model with ice line coupling
Authors:
Walsh, James; Rackauckas, Christopher
Abstract:
Over 40 years ago, M. Budyko and W. Sellers independently introduced low-order climate models that continue to play an important role in the mathematical modeling of climate. Each model has one spatial variable, and each was introduced to investigate the role ice-albedo feedback plays in influencing surface temperature. This paper serves in part as a tutorial on the Budyko-Sellers model, with particular focus placed on the coupling of this model with an ice sheet that is allowed to respond to changes in temperature, as introduced in recent work by E. Widiasih. We review known results regarding the dynamics of this coupled model, with both continuous (``Sellers-type") and discontinuous (``Budyko-type") equations. We also introduce two new Budyko-type models that are highly effective in modeling the extreme glacial events of the Neoproterozoic Era. We prove in each case the existence of a stable equilibrium solution for which the ice sheet edge rests in tropical latitudes. Mathematical tools used in the analysis include geometric singular perturbation theory and Filippov's theory of differential inclusions.
Citation:
Walsh, James, and Christopher Rackauckas. 2015. "On the Budyko-Sellers energy balance climate model with ice line coupling." Discrete and Continuous Dynamical Systems - Series B 20(7): 2187-2216.
Publisher:
American Institute of Mathematical Sciences
DATE ISSUED:
2015-09
Department:
Mathematics
Type:
Article
PUBLISHED VERSION:
10.3934/dcdsb.2015.20.2187
PERMANENT LINK:
http://hdl.handle.net/11282/582393

Full metadata record

DC FieldValue Language
dc.contributor.authorWalsh, Jamesen
dc.contributor.authorRackauckas, Christopheren
dc.date.accessioned2015-11-19T17:20:27Zen
dc.date.available2015-11-19T17:20:27Zen
dc.date.issued2015-09en
dc.identifier.citationWalsh, James, and Christopher Rackauckas. 2015. "On the Budyko-Sellers energy balance climate model with ice line coupling." Discrete and Continuous Dynamical Systems - Series B 20(7): 2187-2216.en_US
dc.identifier.issn1531-3492en
dc.identifier.urihttp://hdl.handle.net/11282/582393en
dc.description.abstractOver 40 years ago, M. Budyko and W. Sellers independently introduced low-order climate models that continue to play an important role in the mathematical modeling of climate. Each model has one spatial variable, and each was introduced to investigate the role ice-albedo feedback plays in influencing surface temperature. This paper serves in part as a tutorial on the Budyko-Sellers model, with particular focus placed on the coupling of this model with an ice sheet that is allowed to respond to changes in temperature, as introduced in recent work by E. Widiasih. We review known results regarding the dynamics of this coupled model, with both continuous (``Sellers-type") and discontinuous (``Budyko-type") equations. We also introduce two new Budyko-type models that are highly effective in modeling the extreme glacial events of the Neoproterozoic Era. We prove in each case the existence of a stable equilibrium solution for which the ice sheet edge rests in tropical latitudes. Mathematical tools used in the analysis include geometric singular perturbation theory and Filippov's theory of differential inclusions.en
dc.language.isoen_USen
dc.publisherAmerican Institute of Mathematical Sciencesen
dc.identifier.doi10.3934/dcdsb.2015.20.2187en
dc.subject.departmentMathematicsen_US
dc.titleOn the Budyko-Sellers energy balance climate model with ice line couplingen_US
dc.typeArticleen
dc.identifier.journalDiscrete and Continuous Dynamical Systems - Series Ben
dc.subject.keywordClimate modelingen_US
dc.subject.keywordIce-albedo feedbacken_US
dc.subject.keywordSingular perturbationsen_US
dc.subject.keywordDifferential inclusionsen_US
dc.identifier.volume20en_US
dc.identifier.issue7en_US
dc.identifier.startpage2187en_US
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