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

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, selfgravitating, 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 x 10" I vLM 5 loz3 Pa s, and assuming the form a + b(log vLM -21.3), the constants