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The Earth's climate has experienced numerous critical transitions during its history, which have often been accompanied by massive and rapid changes in the biosphere. Such transitions are evidenced in various proxy records covering different timescales. The goal is then to identify, date, and rank past critical transitions in terms of importance, thus possibly yielding a more thorough perspective on climatic history. To illustrate such an angle, which inspired the punctuated equilibrium angle on the theory of evolution, we have analyzed 2 key high-resolution datasets: the CENOGRID marine compilation (past 66 Myr), and North Atlantic U1308 record (past 3.3 Myr). By combining recurrence analysis of the individual time series with a multivariate representation of the system based on the theory of the quasi-potential, we identify the key abrupt transitions associated with major regime changes that differentiate various clusters of climate variability. This allows interpreting the time-evolution of the system as a trajectory taking place in a dynamical landscape, whose multiscale features are associated with a hierarchy of tipping points., 27 pages, 5 figures plus supplementary material

Paleoclimate proxy records contain abrupt transitions that may represent former instances of the climate system crossing a tipping point (TP). Properly identifying these TPs in the Earth’s past helps determine critical thresholds in present-day climate and better understand the climate system’s underlying bifurcation mechanisms.Information contained in paleoclimate proxy records is often ambiguous because of the complexity of the system, which includes both deterministic and stochastic processes. Furthermore, paleoclimate time series differ in their time spans and periodicities, and often have high levels of noise and a nonuniform resolution. These combined sources of uncertainty highlight the need for using advanced statistical methods for robustly identifying and comparing TPs.A recently developed method that uses an augmented Kolmogorov-Smirnov test has been shown to be highly effective for transition detection in different types of records. Here, we apply this method to a set of high-quality paleoproxy records exhibiting centennial-to millennial-scale variability that have been compiled in the PaleoJump database. We thereby detect previously unrecognized transitions in these records and identify potential TPs. Furthermore, we investigate regime changes with recurrence analysis and spectral analysis. This study is supported by the H2020-funded Tipping Points in the Earth System (TiPES) project.

The Earth’s climate has experienced numerous abrupt and critical transitions during its long history. Such transitions are evidenced in precise, high-resolution records at different timescales. This type of evidence suggests the possibility of identifying a hierarchy of past critical events, which would yield a more complex perspective on climatic history of the than the classical saddle-node two-dimension representation of tipping points. Such a context allows defining a tipping, or dynamical, landscape (Lucarini and Bódai, 2020), similar to the epigenetic landscape of Waddington (1957).To illustrate a richer structure of critical transitions, we have analyzed 3 key high-resolution datasets covering the past 66 Ma and provided evidences of abrupt transitions detected with the augmented Kolmogorov-Smirnov test and a recurrence analysis (Bagniewski et al., 2021). These time series are the CENOGRID benthic d18O and d13C (Westerhold et al., 2020), the U1308 benthic d18O, d13C and the d18bulk carbonate (Hodell and Channell, 2016), and the NGRIP d18O (Rasmussen et al., 2014) records. The aim was to examine objectively the observed visual evidence of abrupt transitions and to identify among them the key thresholds indicating regime changes that differentiate among major clusters of variability. This identification is followed by establishing a hierarchy in the observed thresholds organized through a domino-like cascade of abrupt transitions that shaped the Earth’s climate system over the past 66 Ma.This study is supported by the H2020-funded Tipping Points in the Earth System (TiPES) project.ReferencesBagniewski, W., Ghil, M., and Rousseau, D. D.: Automatic detection of abrupt transitions in paleoclimate records, Chaos, 31, https://doi.org/10.1063/5.0062543, 2021.Hodell, D. A. and Channell, J. E. T.: Mode transitions in Northern Hemisphere glaciation: co-evolution of millennial and orbital variability in Quaternary climate, Clim. Past, 12, 1805–1828, https://doi.org/10.5194/cp-12-1805-2016, 2016.Lucarini, V. and Bódai, T.: Global stability properties of the climate: Melancholia states, invariant measures, and phase transitions, Nonlinearity, 33, R59–R92, https://doi.org/10.1088/1361-6544/ab86cc, 2020.Rasmussen, S. O., Bigler, M., Blockley, S. P., et al.: A stratigraphic framework for abrupt climatic changes during the Last Glacial period based on three synchronized Greenland ice-core records: refining and extending the INTIMATE event stratigraphy, Quat. Sci. Rev., 106, 14–28, https://doi.org/10.1016/j.quascirev.2014.09.007, 2014.Waddington, C. H.: The strategy of the genes., Allen & Unwin., London, 1957.Westerhold, T., Marwan, N., Drury, A. J., et al.: An astronomically dated record of Earth’s climate and its predictability over the last 66 million years, Science, 369, 1383-+, https://doi.org/10.1126/science.aba6853, 2020.