The rotational stability of an ice-age earth

Predictions of glaciation-induced changes in the Earth\textquoterights rotation vector exhibit sensitivities to Earth structure that are unique within the suite of long-wavelength observables associated with glacial isostatic adjustment (henceforth GIA), and, despite nearly a quarter of a century of research, these sensitivities remain enigmatic. Previous predictions of present-day true polar wander (TPW) speed driven by GIA have indicated, for example, a strong sensitivity to variations in the thickness of the elastic lithosphere and the treatment (phase or chemical?) of the density discontinuity at 670-km depth. Nakada recently presented results that suggest that the predictions are also sensitive to the adopted rheology of the lithosphere; however, his results have introduced an intriguing paradox. In particular, predictions generated using a model with an extremely high-viscosity lithospheric lid do not converge to results for a purely elastic lithosphere of the same thickness. Mitrovica (as cited by Nakada) has suggested that the paradox originates from an inaccuracy in the traditional rotation theory (e.g. Wu \& Peltier) associated with the treatment of the background equilibrium rotating form upon which any load- and rotation-induced perturbations are superimposed. We revisit these issues using a new treatment of the linearized Euler equations governing load-induced rotation perturbations on viscoelastic earth models. We demonstrate that our revised theory, in which the background form of the planet combines a hydrostatic component and an observationally inferred excess ellipticity, resolves the apparent paradox. Calculations using the revised theory indicate that earlier predictions based on earth models with purely elastic lithospheric lids are subject to large errors; indeed, previously noted sensitivities of TPW speed predictions to the thickness and rheology (elastic versus viscous) of the lithosphere largely disappear in the application of the new theory. Significant errors are also incurred by neglecting the stabilizing influence of the Earth\textquoterights excess ellipticity. Finally, we demonstrate that the contribution from rotational feedback on predictions of present-day rates of change of the geoid (sea surface) and crustal velocities are overestimated by the traditional rotation theory, and this has implications for analyses of ongoing satellite (e.g. GRACE) missions and geodetic GPS surveys.