Abstract
There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase- or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). As the attracting trajectory can sometimes lie close to the boundary of its basin of attraction, a small perturbation could quite easily make climate to jump between different histories, reducing the predictability. Our study brings new insight into paleoclimate dynamics and reveals a possibility for the climate system to wander throughout different climatic histories related to preferential synchronisation regimes on obliquity, precession or combinations of both, all over the history of the Pleistocene.
Highlights
This article is a contribution to the field of paleoclimate dynamics theory, which has experienced many developments in terms of ice age models since many years notably by Le Treut and Ghil (1983), Saltzman and Maasch (1990), and many others, and remains an active research field
The dynamical systems approach outlined (1) allows for stability analysis of such synchronisation, (2) uncovers interesting effects related to the robustness of the synchronisation with respect to external perturbations, and (3) uncovers the phenomenon of multistable synchronisation that has been overlooked by previous studies
Previous studies have shown that locking mechanisms could be found in the ice ages problem (Le Treut and Ghil 1983; Hyde and Peltier 1985; Paillard 1998; Gildor and Tziperman 2000), but most of the time, the conclusions rely on a few particular realisations of the models, without providing a global analysis of the synchronisation phenomenon, like the one provided in this study
Summary
This article is a contribution to the field of paleoclimate dynamics theory, which has experienced many developments in terms of ice age models since many years notably by Le Treut and Ghil (1983), Saltzman and Maasch (1990), and many others, and remains an active research field. (Le Treut and Ghil 1983) consider a nonlinear climatic oscillator based on physical climatic mechanisms, and found frequency locking for some specific runs of their model They proposed to explain the ice age cycle in terms of a beat period (or combination tone) between the 19 and 23 kyr periods. We use a simple van der Pol oscillator model to identify and illustrate for the first time the phenomenon of generalised synchronisation between ice age cycles and astronomical forcing. For details about the van der Pol oscillator, we refer the reader mainly to van der Pol (1926), Strogatz (1994), Barnes and Grimshaw (1997), Hilborn (2000) and Balanov et al (2009)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
