Milankovic Pseudo-cycles Recorded in Sediments and Ice Cores Extracted by Singular Spectrum Analysis

Milankovic cycles describe the changes in the Earth's orbit and rotation axis and their impact on its climate over thousands of years. Singular Spectrum Analysis (SSA) is a signal processing method that is best known for its ability to find and extract pseudo-cycles in complex signals. In this short paper, we propose to apply it to three time series that have been proposed as geological reference time scales, in order to retrieve, compare and identify their Milankovic periodicities: (1) LR04, a stack of Plio-Pleistocene benthic microfossil records (Lisiecki and Raymo, 2005), (2) the CO2 and CH4 records from the Vostok ice core (Petit et al, 1999) and (3) the long-term orbital solution La04 for the insolation of Laskar et al (2004). The Vostok CO2 and CH4 series share the first 7 SSA components, three main ones (98, 104, 39 kyr), and four smaller ones (18, 22, 65, 180 kyr). CO2 displays a component at 28 kyr and a doublet at 61 and 62 kyr. CH4 displays a doublet near 50 kyr. 18/22 ky is a precession doublet, 62 kyr an insolation component, and 95/105 kyr an insolation/eccentricity doublet. The 49/50 kyr doublet in CH4 is not found in the orbital model. The SSA results for the La04 orbital solution are in excellent agreement with the values obtained by Laskar et al (2004). Four SSA components of obliquity are almost identical (rounded figures are 41, 54, 29 and 39 kyr). As far as eccentricity is concerned, the first five components are 404, 95, 124, 99, and 132 kyr. The next components are not found in our list of components for eccentricity, but they are in the SSA of insolation, at 2338, 970, 488 and 684 kyr. With more than 20 components, the LR04 stack is the richest series. In order of decreasing amplitude, one encounters 41, 95 and 75 kyr components. Next are smaller 39.5 and 53.6 kyr components, and a 22.4 kyr component. One recognizes one of the two main precession components, the doublet of obliquity components, a line at 47.4 kyr that is not found in any of the other spectra, and a doublet at 53.6 and 55.7 kyr, corresponding to the line at 54 kyr found in all four orbital quantities. Next comes a line at 63.6 kyr that may correspond to a line in insolation, CH4 and CO2. Then come components from eccentricity variations at 75.2, 94.5, 107.2, 132.1, 198.6 and 400.9 kyr. The remaining components of LR04 show up in La04. The “elusive ~200 kyr eccentricity cycle” of Hilgen et al (2020) is actually present in all three series, in the La04 orbital model as a 195 ± 6 kyr component of eccentricity and in LR04 as a 198.6 ± 5.6 kyr component. Finding not only the main expected Milankovic periodicities but also many “secondary” components with much smaller amplitudes gives confidence in our iterative SSA method (iSSA), on the quality of the La04 model and on the remarkable LR04 sedimentary stack, with more than 15 “ Milankovic periods”.