Oscillators and relaxation phenomena in Pleistocene climate theory

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

Published in the Transactions of the Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), as a contribution to the Proceedings of the workshop on Stochastic Methods in Climate Modelling, Newton Institute (23-27 August). Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), vol. 370, pp. xx-xx (2012); Source codes available on request to author and on http://www.uclouvain.be/itop

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• Relaxation oscillations in an idealized ocean circulation model
• Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles
• Mixed mode oscillations in a conceptual climate model
• State-dependence of climate sensitivity: attractor constraints and palaeoclimate regimes
• Chaotic and non-chaotic response to quasiperiodic forcing: limits to predictability of ice ages paced by Milankovitch forcing
• Effects of additive noise on the stability of glacial cycles
• Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology
• Quantifying Age and Model Uncertainties in Paleoclimate Data and Dynamical Climate Models with a Joint Inferential Analysis
• Why could ice ages be unpredictable?
• The deterministic excitation paradigm and the late Pleistocene glacial terminations