Papers › Anticipation of Oligocene's climate heartbeat by simplified eigenvalue estimation
Anticipation of Oligocene's climate heartbeat by simplified eigenvalue estimation
Martin Heßler, Oliver Kamps
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The Eocene-Oligocene transition marks a watershed point of earth's climate history. The climate shifts from a greenhouse state to an icehouse state in which Antarctica glaciated for the first time and periodic dynamics arise which are still relevant for our current climate. We analyse a CaCO₃ concentration time series which covers the Eocene-Oligocene transition and which is obtained from a Pacific sediment core at site DSDP1218. Therefore, we introduce a simplified autoregression-based variant of the dominant eigenvalue (DEV) estimation procedure. The DEV works as leading indicator of bifurcation-induced transitions and enables us to identify the bifurcation type. We confirm its reliability in a methodological study and demonstrate the crucial importance of proper detrending to obtain unbiased results. As a remark, we discuss also possible pathways to estimate the stability of limit cycles based on the DEV and the alternative drift slope as a proof of principle. Finally, we present the DEV analysis results of the CaCO₃ concentration time series which are reproducible in a wide parameter range. Our findings demonstrate that the onset of Oligocene's periodic dynamics might be announced by a Neimark-Sacker/Hopf bifurcation in course of the Eocene-Oligocene transition 34 mya. (We follow the convention and use mya="million years ago" and Ma="million years" throughout the article.)
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