Constraining the Earth's Dynamical Ellipticity From Ice Age Dynamics. Issue 5 (25th May 2022) - Farhat, Mohammad; Laskar, Jacques; Boué, Gwenaël
Abstract: The dynamical ellipticity of a planet expresses the departure of its mass distribution from spherical symmetry. It enters as a parameter in the description of a planet's precession and nutation, as well as other rotational normal modes. In the case of the Earth, uncertainties in this quantity's history produce an uncertainty in the solutions for the past evolution of the Earth‐Moon system. Constraining this history has been a target of interdisciplinary efforts as it represents an astro‐geodetic parameter whose variation is shaped by geophysical processes, and whose imprints can be found in the geological signal. We revisit the classical problem of its variation during ice ages, where glacial cycles exerted a varying surface loading that had altered the shape of the geoid. In the framework of glacial isostatic adjustment, and with the help of a recent paleoclimatic proxy of ice volume, we present the evolution of the dynamical ellipticity over the Cenozoic ice ages. We map out the problem in full generality identifying major sensitivities to surface loading and internal variations in parameter space. This constrained evolution is aimed to be used in future astronomical computations of the orbital and insolation quantities of the Earth. Plain Language Summary: The Earth is a deformable body subject to inner, surface, and outer forces acting together to adjust its mass distribution. This mass distribution is quantified by the dynamical ellipticity, and its evolution is largely unknown over geological timescales. As this parameter plays an important role in the evolution of the Earth's rotational motion, its uncertainty propagates to long term solutions of the Earth's orientation. To minimize this uncertainty, we present here a solution of the Earth's dynamical ellipticity over the past 50 Myr, pertaining to the surface loading contribution of the Cenozoic glacial cycles. We do so by combining oceanic proxies of glacial volume with the proper mathematical formalism to reconstruct a self‐consistent history of the glacial and oceanic loading. As the Earth's response to this loading is highly dependent on its viscosity, we perform a parametric study and constrain the possible scenarios of dynamical ellipticity evolution. Combined with other processes involving mass redistribution, such as mantle convection and the tidal response, our findings add a missing puzzle piece toward a complete history of the dynamical ellipticity, and consequently valid extended rotational solutions. Key Points: We trace the variation in the Earth's dynamical ellipticity in the context of the Earth's viscoelastic deformation during Cenozoic ice ages Its perturbation is well constrained within [−0.13%, 0.07%] over the last 3 Myr, and within [−0.11%, 0.05%] over the rest of the Cenozoic These dynamical ellipticity variations are a key element in the computation of the long term evolution of the Earth's rotational motion