A theory of Pleistocene glacial rhythmicity
Authors: Verbitsky Mikhail Y. , Crucifix Michel , Volobuev Dmitry M. 
Published: August 2018

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.