Anticipation of Oligocene's climate heartbeat by simplified eigenvalue estimation

TL;DR

This paper introduces a simplified eigenvalue estimation method to analyze climate transition signals in sediment data, revealing potential early indicators of the Oligocene's climate shift from greenhouse to icehouse conditions.

Contribution

It presents a novel autoregression-based eigenvalue estimation technique for detecting bifurcations in paleoclimate time series, with validation and application to Eocene-Oligocene data.

Findings

Identified a potential bifurcation point 34 million years ago.

Demonstrated the method's robustness across parameter ranges.

Suggested early warning signals for climate regime shifts.

Abstract

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 $CaCO_3$ 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 $CaCO_3$ 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$\widehat{=}$"million years ago" and Ma$\widehat{=}$"million years" throughout the article.)