A study of the climatic regimes of the Pleistocene using a stochastic resonance model

A global energy balance model employing the stochastic resonance mechanism, previously used to explain the climatic variability of the late Pleistocene, has now been extended to account for the climatic variations over the full Pleistocene. The possibility that extremely long-term changes (of the order of millions of years) in the boundary conditions of the climate system have altered the response of the Pleistocene climate to the external orbital forcing has been investigated. It is shown that, by slowly changing the only free parameter of the model, the system can undergo a pitchfork bifurcation. The bifurcation point separates a linear regime (identified with the early Pleistocene climate) from a strongly nonlinear regime (the late Pleistocene) where the stochastic resonance mechanism produces rapid and symmetric transitions between the two stable steady states of the system. The main differences in the dynamic features of the two regimes are the change in amplitude of the oscillations, the relative importance of the stochastic forcing, the change in shape of the probability distribution, and the corresponding change in the power centered around the 100000 year cycle: in qualitative agreement with the observed geological record. With the introduction of the external orbital forcing, now spectrally complete and included without requiring any additional hypothesis, the model reproduces the previous results, namely the good correlation with the isotopic record, the appearance of the dominant spectral peaks, as well as the redness of the power spectrum. In particular, it is shown that the orbital forcing in eccentricity acts as a pacemaker of the major glacial cycles of the late Pleistocene through the mechanism of stochastic resonance. A stochastic sensitivity analysis is then applied to validate the significance of the results and to investigate the predictability of the climate system over the time-scales of the orbital cycles.