Periodicity in a Conceptual Model of Glacial Cycles in the Absence of Milankovitch Forcing

Previously, McGehee and Widiasih coupled Budyko's Energy Balance Model with dynamics of a latitudinal ice-line incorporating the albedo feedback effect. They reduced this model to a two-dimensional equation of global mean temperature and a latitudinal ice-line. With this conceptual model, we now include dynamics of the ablation and accumulation of ice, to form a three-dimensional system that partitions the regions of the Earth latitudinally into an accumulation zone, ablation zone, and ice-free zone. Motivated by the findings of Abe-Ouchi et al that the fast retreat of ice-sheets is due to an increased rate of ablation via the effects of delayed isostatic rebound, we incorporate a simple switching mechanism to the model which increases the rate of ablation during periods of glacial retreat. This forms a discontinuous system of the Earth's temperature and ice-volume in which we find a stable periodic orbit. This can be interpreted as a intrinsic cycling of the Earth's climate in the absence of Milankovitch forcing.