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

TL;DR

This paper introduces a new nonsmooth conceptual climate model with asymmetric hemispheres that captures synchronous glacial cycles driven by Northern Hemisphere changes, extending classic energy balance models.

Contribution

It develops a nonsmooth, asymmetric Earth climate model with a discontinuous switching mechanism, demonstrating the existence of a unique attracting limit cycle for glacial cycles.

Findings

The model admits a unique nonsmooth attracting limit cycle.

Northern Hemisphere changes synchronize Southern Hemisphere glacial cycles.

The model captures realistic glacial-interglacial dynamics on orbital time scales.

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-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.