Ice age True Polar Wander in a compressible and non-hydrostatic Earth

Issues related to long timescale instability in the Earth's rotation, named True Polar Wander (TPW), have continuously been debated, after the pioneering works of the sixties. We show ice age TPW results from a newly developed compressible model, based on the numerical integration in the radial variable of the momentum and Poisson equations and on the contour integration in the Laplace domain which allows us to deal with the non-modal contribution from continuous radial rheological variations. We thus fully exploit the long term behaviour of the Earth's rotation and we quantify the effects of the compressible rheology, compared to the widely used incompressible one. We discuss the so-called 'traditional approach' to the Earth's rotation developed during the eighties and nineties, both for ice age and mantle convection TPW and we explain within this approach the sensitivity of TWP predictions to the elastic and viscoelastic rheologies of the lithosphere. We agree on the necessity to include the effects of the non-hydrostatic bulge from mantle convection to obtain realistic ice age TPW rates in the lower mantle viscosity range [10(21), 10(22)] Pa s, as first indicated by Mitrovica et al. Their analysis represents a first attempt to couple the effects on TPW from mantle convection and glacial forcing, by including the non-hydrostatic bulge due to mantle convection but not the other time-dependent driving terms. This partial coupling freezes in space the non-hydrostatic contribution due to mantle convection, thus damping the present-day ice age TPW and forcing the axis of instantaneous rotation to come back to its initial position when ice ages started as discussed in Mitrovica et al. We also describe a peculiar behavior of the new ice age TPW predictions exhibiting a dampened pendulum motion, with the axis of instantaneous rotation overcrossing the position it had before ice ages started. We argue that a viscoelastic rather than elastic lithosphere should be adopted in the modelling of TPW although, on the time of ice ages, it is difficult to disentangle the effects of lithospheric rheology and of mantle convection. We discuss the implication of self-consistent convection calculations of the non-hydrostatic contribution and its impact on the long term Earth's rotation stability during ice ages. The ice age TPW cannot account for more than 70 per cent of the observed one, at least for lower mantle viscosities lower than 1022 Pa s: mantle convection must therefore contribute to the observed TPW.