The deterministic excitation paradigm and the late Pleistocene glacial terminations

A deterministic excitation (DE) paradigm is formulated, according to which the abrupt late Pleistocene glacial terminations 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 output of an energy-balance model simulating the fluctuations induced by realistic orbital forcing on the glacial state. The timing of the glacial terminations, thus, obtained in a reference simulation is found to be in good agreement with proxy records. A sensitivity analysis insures the robustness of the timing. The potential irrelevance of noise allowing DE to hold is discussed, and a possible explanation of the 100-kyr cycle problem based on DE is outlined. 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.