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

Abstract

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-alb edo feedback by removing the standard assumption of planetary symmetry about the equator. The dynamics of distinct Northern and Southern Hemisphere ice caps are coupled through 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 that 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 timescales involved, the model presents a nonsmooth geometric perturbation problem, for which we use ad hoc mathematical techniques to produce the periodic orbit. We find that climatic changes in the Northern Hemisphere drive synchronous in-phase changes in the Southern Hemisphere due to the coupling provided by the annual global mean surface temperature. This behavior is observed for the Earth on orbital timescales.

Publisher

SIAM Publications

Publication Date

1-1-2021

Publication Title

SIAM Journal on Applied Dynamics Settings

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1137/21M1390098

Keywords

Nonsmooth dynamical systems, Virtual equilibria, Nonsmooth return map, Ice-alb edo feedback, Paleoclilmate, Glacial cycles

Language

English

Format

text

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