Free Oscillations in a Climate Model with Ice-Sheet Dynamics

Abstract

A study of stable periodic solutions to a simple nonlinear model of the ocean-atmosphere-ice system is presented. The model has two dependent variables: ocean-atmosphere temperature and latitudinal extent of the ice cover. No explicit dependence on latitude is considered in the model. Hence all variables depend only on time and the model consists of a coupled set of nonlinear ordinary differential equations. The globally averaged ocean-atmosphere temperature in the model is governed by the radiation balance (Budyko, 1969; Sellers, 1969). The reflectivity to incoming solar radiation, i.e., the planetary albedo, includes separate contributions from sea ice and from continental ice sheets. The major physical mechanisms active in the model are 1) albedo-temperature feedback, 2) continental ice-sheet dynamics (Weert-man, 1964, 1976) and 3) precipitation-rate variations. The model has three equilibrium solutions, two of which are linearly unstable, while one is linearly stable. For some choices of parameters, the stability picture changes and sustained, finite-amplitude oscillations obtain around the previously stable equilibrium solution. The physical interpretation of these oscillations points to the possibility of internal mechanisms playing a role in glaciation cycles.