The Mid-Pleistocene Transition induced by delayed feedback and bistability

Abstract

The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr glacialinterglacial 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 # 2006Contribution # -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 smallscale 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 Mid-Pleistocene Transition (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 δ 18 O 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. a) c.quinn2@exeter.ac.uk arXiv:1712.07614v3 [physics.ao-ph]

Effects of Periodic Forcing on a Paleoclimate Delay Model

“…The parameter u represents the forcing amplitude of which the realistic value is uncertain. Figure 3 summarizes the most important observation of Quinn et al [32], which motivates our investigation in the following sections. For values of τ in the bistable region r el , there are two possible responses for sufficiently small u, both illustrated in Figure 3a: a smallamplitude (green in Figure 3a) and a large-amplitude (purple) response.…”

“…The term F I (t) is the forcing signal, shown in Figure 1, which is a time series of integrated summer insolation at 65 • N computed by Huybers [18] based on the model in [17]. Details, how the forcing curve in Figure 1 was obtained from publicly available data, are given in [32]. The data was obtained through numerical approximation of changes in the long-term planetary motion based on the theory for long-term variation of daily insolation by Berger [4].…”

“…In a recent study [32] we revisited a model of the Pleistocene introduced by Saltzman and Maasch [34]. This model was used to replicate the main dynamics of the ice ages, which involved perturbations in glocal ice mass, atmospheric CO 2 , and global ocean circulation.…”

“…In the original study, the authors of [34] showed this particular model was able to reproduce the MPT through a slow parameter shift. In our study [32] we reduced this model to a scalar delay differential equation (DDE) for global ice mass. Through analytical and numerical investigations we showed that the models were qualitatively equivalent.…”

Global Warming Can Lead to Depletion of Oxygen by Disrupting Phytoplankton Photosynthesis: A Mathematical Modelling Approach

“…Models of climate dynamics are usually very complicated [39] (but see [57]): indeed, a predictive model should account for many factors and processes occurring in the environment. In contrast, our model is very simple; however, it is by no means just a mathematical toy.…”