Oscillators and relaxation phenomena in Pleistocene climate theory

TL;DR

This paper reviews dynamical system models of Pleistocene climate oscillations, highlighting their bifurcation structures, synchronization mechanisms, and the impact of stochastic fluctuations on ice age and rapid climate events.

Contribution

It draws parallels between climate theories and dynamical systems concepts, analyzing their bifurcation structures and stochastic effects in a comprehensive review.

Findings

Most theories involve a limit cycle in ocean circulation.

Synchronization with astronomical forcing is common across theories.

Stochastic fluctuations can cause phase dispersion and resonance.

Abstract

Ice sheets appeared in the northern hemisphere around 3 million years ago and glacial-interglacial cycles have paced Earth's climate since then. Superimposed on these long glacial cycles comes an intricate pattern of millennial and sub-millennial variability, including Dansgaard-Oeschger and Heinrich events. There are numerous theories about theses oscillations. Here, we review a number of them in order to draw a parallel between climatic concepts and dynamical system concepts, including, in particular, the relaxation oscillator, excitability, slow-fast dynamics and homoclinic orbits. Namely, almost all theories of ice ages reviewed here feature a phenomenon of synchronisation between internal climate dynamics and the astronomical forcing. However, these theories differ in their bifurcation structure and this has an effect on the way the ice age phenomenon could grow 3 million years ago. All theories on rapid events reviewed here rely on the concept of a limit cycle in the ocean circulation, which may be excited by changes in the surface freshwater surface balance. The article also reviews basic effects of stochastic fluctuations on these models, including the phenomenon of phase dispersion, shortening of the limit cycle and stochastic resonance. It concludes with a more personal statement about the potential for inference with simple stochastic dynamical systems in palaeoclimate science. Keywords: palaeoclimates, dynamical systems, limit cycle, ice ages, Dansgaard-Oeschger events