A theory of Pleistocene glacial rhythmicity

Abstract

Variations in 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 kyr oscillations of global ice to predominantly 100 kyr oscillations around 1 million years ago. It is generally accepted to attribute the 40 kyr period to astronomical forcing and to attribute the transition to the 100 kyr mode to a phenomenon caused by a slow trend, which around the mid-Pleistocene enabled the manifestation of nonlinear processes. However, both the physical nature of this nonlinearity and its interpretation in terms of dynamical systems theory are debated. Here, we show that ice-sheet physics coupled with a linear climate temperature feedback conceal enough dynamics to satisfactorily explain the system response over the full Pleistocene. There is no need, a priori, to call for a nonlinear response of the carbon cycle. Without astronomical forcing, the obtained dynamical system evolves to equilibrium. When it is astronomically forced, depending on the values of the parameters involved, the system is capable of producing different modes of nonlinearity and consequently different periods of rhythmicity. The crucial factor that defines a specific mode of system response is the relative intensity of glaciation (negative) and climate temperature (positive) feedbacks. To measure this factor, we introduce a dimensionless variability number, V. When positive feedback is weak (V ∼ 0), the system exhibits fluctuations with dominating periods of about 40 kyr which is in fact a combination of a doubled precession period and (to smaller extent) obliquity period. When positive feedback increases (V ∼ 0.75), the system evolves with a roughly 100 kyr period due to a doubled obliquity period. If positive feedback increases further (V ∼ 0.95), the system produces fluctuations of about 400 kyr. When the V number is gradually increased from its low early Pleistocene values to its late Pleistocene value of V ∼ 0.75, the system reproduces the mid-Pleistocene transition from mostly 40 kyr fluctuations to a 100 kyr period rhythmicity. Since the 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 of explaining all major features of the Pleistocene climate, such as the mostly 40 kyr fluctuations of the early Pleistocene, a transition from an early Pleistocene type of nonlinear regime to a late Pleistocene type of nonlinear regime, and the 100 kyr fluctuations of the late Pleistocene.When the dynamical climate system is expanded to include Antarctic glaciation, it becomes apparent that climate temperature positive feedback (or its absence) plays a crucial role in the Southern Hemisphere as well. While the Northern Hemisphere insolation impact is amplified by the outside-of-glacier climate and eventually affects Antarctic surface and basal temperatures, the Antarctic ice-sheet area of glaciation is limited by the area of the Antarctic continent, and therefore it cannot engage in strong positive climate feedback. This may serve as a plausible explanation for the synchronous response of the Northern and Southern Hemisphere 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 that may possibly be involved in producing ice ages. In such a case, the equation currently representing climate 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.