A Theory of Pleistocene Glacial Rhythmicity
Authors: Verbitsky Mikhail Y. , Crucifix Michel , Volobuev Dmitry M. 
Published: March 2018

Abstract. Variations of Northern Hemisphere ice volume over the past 3 million years have been described in numerous studies and well documented. These studies depict the mid-Pleistocene transition from 40-ky oscillations of global ice to predominantly 100-ky oscillations around 1 million years ago. It is generally accepted to attribute the 40-ky period to astronomical forcing, and to attribute the transition to the 100-ky mode to a phenomenon caused by a slow trend which, around the mid-Pleistocene, enabled the manifestation of non-linear processes. However, both the physical nature of this non-linearity, and its interpretation in terms of dynamical systems theory, are debated. Here, we show that ice sheet physics, coupled with a linear ocean feedback, conceal enough dynamics to satisfactorily explain the system response over the full Pleistocene. There is no need, a priori, to call for a non-linear response of the carbon cycle. Without astronomical forcing, the obtained dynamical system evolves to equilibrium. When it is astronomically forced, then, depending on the values of parameters involved, the system is capable of producing different modes of non-linearity and consequently – different periods of rhythmicity. The crucial factor that defines a specific mode of system response is the relative intensity of glaciation and ocean feedbacks. To measure this factor, we introduce a dimensionless variability number V. When ocean positive feedback is weak (V ~ 0), the system exhibits fluctuations with dominating periods of about 40 ky which is in fact a combination of doubled precession period and (to smaller extent) obliquity period. When ocean positive feedback increases (V ~ 0.75), the system evolves with a roughly 100-ky period due to doubled obliquity period. If ocean positive feedback increases further (V ~ 0.95), the system produces fluctuations of about 400 ky. When V-number is gradually increased from its low early Pleistocene values to its late Pleistocene value of V ~ 0.75, the system reproduces mid-Pleistocene transition from mostly 40-ky fluctuations to 100-ky-period rhythmicity. Since V-number is a combination of multiple parameters, it implies that multiple scenarios are possible to account for the mid-Pleistocene transition. Thus, our theory is capable to explain all major features of the Pleistocene climate such as mostly 40-ky fluctuations of the early Pleistocene, a transition from an early Pleistocene type of non-linear regime to a late Pleistocene type of non-linear regime, and 100-ky fluctuations of the late Pleistocene. When the dynamical climate system is expanded to include Antarctic glaciation, it becomes apparent that ocean positive feedback (or its absence) plays a crucial role in the Southern Hemisphere as well. While Northern Hemisphere insolation impact is amplified by the ocean and eventually affects Antarctic climate, the Antarctic ice sheet area of glaciation is limited by the area of the Antarctic continent, and therefore it cannot engage strong positive feedback from the ocean. This may serve as a plausible explanation of the synchronous response of the Northern and Southern Hemispheres to Northern Hemisphere insolation variations. Given that the V-number is dimensionless, we consider that this model could be used as a framework to investigate other physics which may possibly be involved in producing ice ages. In such a case, the equation currently representing ocean temperature would describe some other climate component of interest, and as long as this component is capable of producing an appropriate V-number, it may perhaps be considered a feasible candidate.