Glaciation cycle models and their pullback attractors

The Pleistocene climate was dominated by alternating retreat and regrowth of massive ice sheets accompanied by large variations in the global mean temperature and sea level. Partial agreement between the power spectra of global ice volume proxies and high-latitude summer insolation provides evidence that quasi-periodic changes in the earth’s orbital configuration affect the timing of glaciations and deglaciations. It remains, however, a topic of active debate whether the main cause of glacial cycles is an internal self-sustained oscillation of the climate system that merely phased locked, more or less, to orbital forcing or whether glacial cycles could not exist at all in the absence of orbital forcing. Furthermore, it is unclear whether past ice volume records should be regarded as the result of a purely deterministic process or as a randomly selected trajectory of a stochastic process. To study plausible paths of the earth’s climate system given the orbital forcing, we compute the pullback attractors of several conceptual Pleistocene models. The results are confronted with the power spectra, as well as the time series of proxy records and conclusions will be drawn about the role of internal vs. forced variability and the possible contribution of stochastic processes to the mix of causes. We argue, moreover, that the explanatory power of either a deterministically chaotic or a dynamic-stochastic model cannot be assessed by comparing the model output to observations in the time domain alone.