A conceptual model for glacial cycles and the middle Pleistocene transition

Abstract

Milankovitch’s astronomical theory of glacial cycles, attributing ice age climate oscillations to orbital changes in Northern-Hemisphere insolation, is challenged by the paleoclimatic record. The climatic response to the variations in insolation is far from trivial. In general the glacial cycles are highly asymmetric in time, with slow cooling from the interglacials to the glacials (inceptions) and very rapid warming from the glacials to the interglacials (terminations). We shall refer to this fast-slow dynamics as the “saw-tooth” shape of the paleoclimatic record. This is non-linearly related to the time-symmetric variations in the orbital forcing. However, the most pronounced challenge to the Milankovitch theory is the middle Pleistocene transition (MPT) occurring about one million years ago. During that event, the prevailing 41 kyr glacial cycles, corresponding to the almost harmonic obliquity cycle were replaced by longer saw-tooth shaped cycles with a time-scale around 100 kyr. The MPT must have been driven by internal changes in climate response, since it does not correspond to any apparent changes in the orbital forcing. In order to identify possible mechanisms causing the observed changes in glacial dynamics, it is relevant to study simplified models with the capability of generating temporal behavior similar to the observed records. We present a simple oscillator type model approach, with two variables, a temperature anomaly and a climatic memory term. The generalization of the ice albedo feedback is included in terms of an effective multiplicative coupling between this latter climatic memory term (representing the internal degrees of freedom) and the external drive. The simple model reproduces the temporal asymmetry of the late Pleistocene glacial cycles and suggests that the MPT can be explained as a regime shift, aided by climatic noise, from a period 1 frequency locking to the obliquity cycle to a period 2–3 frequency locking to the same obliquity cycle. The change in dynamics has been suggested to be a result of a slow gradual decrease in atmospheric greenhouse gas concentration. The critical dependence on initial conditions in the (non-autonomous) glacial dynamics raises fundamental questions about climate predictability.