Linear and nonlinear couplings between orbital forcing and the marine δ18O record during the Late Neocene

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Abstract
Previous investigations of the response of Plio‐Pleistocene climatic records to long‐term, orbitally induced changes in radiation have considered a linear response of climate. While the second‐order statistics of power spectra and cross spectra provide necessary information on linear processes, insight into the nonlinear characteristics of Pliocene and Pleistocene climate is not provided by these statistical quantities. Second‐order statistics do not contain the phase information necessary to investigate nonlinear, phase‐coupled processes. Such information is provided by higher‐order statistical quantities. In particular, bispectral analysis indicates that nonlinear couplings are present in the climatic (radiative) forcing at the Milankovitch frequencies. Through a linear transfer, this forcing produces similar nonlinear couplings in deep‐sea sedimentary oxygen isotope records (ODP site 677 and DSDP site 607) from 1.0 to 0 Ma during the late Neogene. This analysis suggests that during the late Pleistocene, the dominance of the 100,000 year cycle in the climate record is consistent with a linear, resonant response to eccentricity forcing. In the period from 2.6 to 1.0 Ma, a change in the nature of the climatic response to orbital forcing is indicated, as phase couplings present in the isotopic time series are not similar to the phase couplings present in the insolation forcing. Third‐order moments (skewness and asymmetry) are used to quantify the shape of the climatic response. From 2.6 Ma to present, an increase in the asymmetry (sawtoothness) of the oxygen isotopic records is accompanied by a corresponding decrease in the skewness (peakedness) of the records. This indicates an evolution in the nature of the phase coupling within the climate system. These results may provide important constraints useful in development of models of paleoclimate.