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Mathematical Paradigms of Climate Science pp 93–113Cite as

Effects of Additive Noise on the Stability of Glacial Cycles

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Abstract

It is well acknowledged that the sequence of glacial-interglacial cycles is paced by the astronomical forcing. However, how much is the sequence robust against natural fluctuations associated, for example, with the chaotic motions of atmosphere and oceans? In this article, the stability of the glacial-interglacial cycles is investigated on the basis of simple conceptual models. Specifically, we study the influence of additive white Gaussian noise on the sequence of the glacial cycles generated by stochastic versions of several low-order dynamical system models proposed in the literature. In the original deterministic case, the models exhibit different types of attractors: a quasiperiodic attractor, a piecewise continuous attractor, strange nonchaotic attractors, and a chaotic attractor. We show that the combination of the quasiperiodic astronomical forcing and additive fluctuations induces a form of temporarily quantised instability. More precisely, climate trajectories corresponding to different noise realizations generally cluster around a small number of stable or transiently stable trajectories present in the deterministic system. Furthermore, these stochastic trajectories may show sensitive dependence on very small amounts of perturbations at key times. Consistently with the complexity of each attractor, the number of trajectories leaking from the clusters may range from almost zero (the model with a quasiperiodic attractor) to a significant fraction of the total (the model with a chaotic attractor), the models with strange nonchaotic attractors being intermediate. Finally, we discuss the implications of this investigation for research programmes based on numerical simulators.

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Notes

  1. 1.

    In the following, 1 ka = 1,000 years and 1 Ma = 1,000 ka.

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Acknowledgements

MC is senior research associate with the Belgian National Fund of Scientific Research. This research is a contribution to the ITOP project, ERC-StG 239604 and to the Belgian Federal Policy Office project BR/121/A2/STOCHCLIM.

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Authors and Affiliations

  1. Earth and Life Institute, George Lemaître Centre for Earth and Climate Research, Université catholique de Louvain, BE-1348, Louvain-la-Neuve, Belgium

    Takahito Mitsui & Michel Crucifix

  2. Belgian National Fund of Scientific Research, Rue d’Egmont, 5, BE-1000, Brussels, Belgium

    Michel Crucifix

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  1. Takahito Mitsui
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Editors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Padova, Padova, Italy

    Fabio Ancona

  2. Dipartimento di Matematica, Università di Roma - Tor Vergata, Roma, Italy

    Piermarco Cannarsa

  3. Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina, USA

    Christopher Jones

  4. Scienze Agrarie, Forestali e Alimentari, Università degli Studi di Torino, Torino, Italy

    Alessandro Portaluri

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Mitsui, T., Crucifix, M. (2016). Effects of Additive Noise on the Stability of Glacial Cycles. In: Ancona, F., Cannarsa, P., Jones, C., Portaluri, A. (eds) Mathematical Paradigms of Climate Science. Springer INdAM Series, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-39092-5_6

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