The Mid-Pleistocene Transition induced by delayed feedback and bistability

The Mid-Pleistocene Transition (MPT), the shift from 41- to 100-kyr glacial–interglacial cycles that occurred roughly 1 Myr ago, is often considered as a change in internal climate dynamics. Here, we revisit the model of Quaternary climate dynamics that was proposed by Saltzman and Maasch (‘Carbon cycle instability as a cause of the late Pleistocene ice age oscillations: modelling the asymmetric response’. Glob Biogeochem Cycle 1988; 2: 177–185—from this point, referred to as SM88). We show that it is quantitatively similar to a scalar equation for the ice dynamics only when combining the remaining components into a single delayed feedback term. The delay is the sum of the internal time scales of ocean transport and ice sheet dynamics, which is on the order of 10 kyr. We find that, in the absence of astronomical forcing, the delayed feedback leads to bistable behaviour, where stable large-amplitude oscillations of ice volume and an equilibrium coexist over a large range of values for the delay. We then apply astronomical forcing using the forcing data for integrated summer insolation at 65 degrees North from Huybers and Eisenman (Integrated Summer Insolation Calculations. NOAA/NCDC Paleoclimatology Program Data Contribution #2006-079, 2006). Since the precise scaling of the forcing amplitude is not known, we perform a systematic study to show how the system response depends on the forcing amplitude. We find that over a wide range of forcing amplitudes, the forcing leads to a switch from small-scale oscillations of 41 kyr to large-amplitude oscillations of roughly 100 kyr without any change of other parameters. The transition in the forced model consistently occurs at about the same time as the MPT (between 1200 and 800 kyr BP) as observed in the data records from Lisiecki and Raymo (‘A Pliocene-Pleistocene stack of 57 globally distributed benthic δ¹⁸O records’. Paleoceanography 2005; 20:1-17). This provides evidence that the MPT could have been primarily forcing-invoked. Small additional random disturbances make the forcing-induced transition near 800 kyr BP even more robust. We also find that the forced system forgets its initial history during the small-scale oscillations, in particular, nearby initial conditions converge prior to transitioning. In contrast to this, in the regime of large-amplitude oscillations, the oscillation phase is very sensitive to random perturbations, which has a strong effect on the timing of the deglaciation events.