  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.
