The deterministic excitation paradigm, with application to the glacial-interglacial transitions

Abstract

A deterministic excitation (DE) paradigm is formulated, according to which the abrupt glacial-interglacial transitions occurred after the Mid-Pleistocene Transition correspond to the excitation by the orbital forcing, of nonlinear relaxation oscillations (ROs) internal to the climate system in the absence of any stochastic parameterization. Specific rules are derived from the DE paradigm: they parameterize internal climate feedbacks which, when activated by the crossing of certain tipping points, excite a RO. Such rules are then applied to the fluctuations of the glacial state simulated by a conceptual model subjected to realistic orbital forcing. The timing of the glacial terminations thus obtained in a reference simulation is found to be in good agreement with proxy records; besides, a sensitivity analysis insures the robustness of the timing. The role of noise in the glacial-interglacial transitions and the problems arising in the implementation of theories in which noise is crucial (such as stochastic resonance) are finally discussed. In conclusion, the DE paradigm provides the simplest possible dynamical systems characterization of the link between orbital forcing and glacial terminations implied by the Milankovitch hypothesis.