Abstract
The long-term variations in the orbit of the Earth govern the insolation on its surface and hence its climate. The use of the astronomical signal, whose imprint has been recovered in the geological records, has revolutionized the determination of the geological timescales. However, the orbital variations beyond 60 Myr cannot be reliably predicted because of the chaotic dynamics of the planetary orbits in the Solar System. Taking this dynamical uncertainty to account is necessary for a complete astronomical calibration of geological records. Our work addresses this problem with a statistical analysis of 120 000 orbital solutions of the secular model of the Solar System ranging from 500 Myr to 5 Gyr. We obtain the marginal probability density functions of the fundamental secular frequencies using kernel density estimation. The uncertainty of the density estimation is also obtained here in the form of confidence intervals determined by the moving block bootstrap method. The results of the secular model are shown to be in good agreement with those of the direct integrations of a comprehensive model of the Solar System. Application of our work is illustrated on two geological data sets: the Newark-Hartford records and the Libsack core.
Highlights
Milankovitch (1941) hypothesized that some of the past large climate changes on the Earth originated from the long-term variations in its orbital and rotational elements
If we look at some specific properties of the probability density functions (PDFs), such as its mean, the differences between the secular model and the complete model are on the same order as the variability of the results from the same secular model
In this work we give a statistical description of the evolution of the fundamental frequencies of the Solar System beyond 60 Myr, that is, beyond the predictability horizon of the planetary motion, with the aim to quantify the uncertainty induced by its chaotic behavior
Summary
Milankovitch (1941) hypothesized that some of the past large climate changes on the Earth originated from the long-term variations in its orbital and rotational elements. The climate rhythms found in the geological records are directly related to the Earth’s precession constant and to the fundamental secular frequencies of the Solar System: the precession frequencies (gi)i=1,8 of the planet perihelia and the precession frequencies (si)i=1,8 of their ascending nodes The evolution of these fundamental frequencies is accurately determined up to 60 Myr (Laskar et al 2004, 2011a; Laskar 2020). Geological constraints should likewise be retrieved in a statistical setting In this spirit, a recent Bayesian Markov chain Monte Carlo (MCMC) approach has been proposed to provide geological constraints on the fundamental frequencies (Meyers & Malinverno 2018).
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