Glaciation-induced variations in the Earth's precession frequency, obliquity and insolation over the last 2.6 Ma

Abstract

Summary We compute, using many-body orbital integration routines, perturbations in the Earth's orbital elements (e.g. precession frequency, obliquity) and solar insolation associated with predicted, glaciation-influenced, time-series of the precession constant H(t). The time-series are computed, in an a priori calculation, using spherically symmetric, self-gravitating, Maxwell viscoelastic earth models, gravitationally self-consistent ocean loads and two ice models constrained to yield eustatic sea-level variations that match the observed fluctuations in oxygen isostope records over the last 0.8 and 2.6 Ma. We also perform a series of orbital integrations that assume a time-independent perturbation to the precession constant, relative to the present-day value, for periods extending over the last 12 Ma. Recent analyses have suggested that the relationship between the precession constant and precession frequency may depart significantly from linearity in the event that glaciation-induced perturbations to H reduce it by more than 0.15 per cent from its present-day value. We confirm this suggestion; however, we also show that the glaciation-induced perturbations to the dynamic ellipticity of the planet must remain at this level for more than 6 Ma in order for the non-linearity, which is linked to an external forcing associated with the orbits of Jupiter and Saturn, to have a significant effect on the precession frequency. In the case of integrations extending over only the last 2.6 Ma we have parametrized our main results in terms of a simple linear scaling with the logarithm of lower-mantle viscosity (vLM). In the range 2 times 1021≤vLM≤ 1023 Pa s, and assuming the form a+b(log vLM - 21.3), the constants (a, b) for the mean relative perturbation to the precession constant, and the perturbations to the precession frequency and the frequency of the obliquity variation are (relative to the present-day values): (-0.0003, -0.86), (-0.01 ′′yr-1, -0,05′′ yr-1) and (-0.01′′ yr-1, -0.05′′ yr-1) The rate of change of the temporal shift between our prediction of the mean daily solar insolation at a high-latitude geographic site, relative to the nominal solution, maybe parametrized using the same form with (-0.1 ka Ma-1, -0.8 ka Ma-1). We also present preliminary results for the influence of ‘climatic friction’ on the secular trend in the obliquity over the last 2.6 Ma. We find that this rate may be as high as 0.06° Ma-1. However, plausibly small values of the lag time between insolation variations and ice-sheet growth reduce this trend significantly. As a final point, predictions of glaciation-induced perturbations to the precession constant described herein are consistent with those presented in our earlier, more limited, analyses (Mitrovica, Pan & Forte 1994; Mitrovica & Forte 1995), but they disagree with subsequent predictions by Peltier & Jiang (1994) and Jiang & Peltier (1996). We show that the latter set of predictions (and the conclusions based upon them) are in error.