A Dynamics Approach to a Low-order Climate Model

Energy Balance Models (EBM) are conceptual models which have proved useful in the study of planetary climate. The focus of EBM is placed on large scale climate components such as incoming solar radiation, albedo, outgoing longwave radiation and heat transport, and their interactions. Until recently, their study has centered on equilibrium solutions of an associated model equation, with no consideration of the dynamical nature of these solutions. In this paper we continue and expand upon recent efforts aimed at placing EBM in a more mathematical, dynamical systems context. In particular, the dynamical behavior of several variants of the Budyko-Sellers model, all but one of which involve the movement of glaciers, is shown to reduce to the study of the system on an attracting one-dimensional invariant manifold in an appropriately defined state space.