Postglacial sea-level change on a rotating Earth

We present a complete derivation of the equation governing long-term sea-level variations on a spherically symmetric, self-gravitating, Maxwell viscoelastic planet. This new 'sea-level equation' extends earlier work by incorporating, in a gravitationally self-consistent manner, both a time-dependent ocean-continent geometry and the influence of contemporaneous perturbations to the rotation vector of the planet. We also outline an efficient, pseudo-spectral, numerical methodology for the solution of this equation, and present a variety of predictions, based on a suite of earth models, of relative sea level (RSL) variations due to glacial isostatic adjustment (GIA). These results show that the contribution to the predicted RSL signal from GIA-induced perturbations to the rotation vector can reach 7-8 m over the postglacial period in geographic regions where the rotationally induced signal is a maximum. This result is sensitive to variations in the adopted lower-mantle viscosity and is relatively insensitive to variations in the adopted lithospheric thickness. We also show that the rotationally induced component of RSL change is sufficient to influence previous estimates of Late Holocene melting events and ongoing sea-level change due to GIA which were based on a RSL theory for a non-rotating Earth. In particular, estimates of Antarctic melting over the last 5 kyr, based on the amplitude of sea-level highstands from the Australian region, may require an adjustment downwards of the order of 0.5 m of equivalent sea-level rise. Furthermore, present-day rates of sea-level change are perturbed by as much as similar to 0.2 mm yr(-1) by the rotational component of sea-level change, and this has implications for GIA corrections of the global tide gauge record. Over the period from the last glacial maximum to the present, we predict a distinctly non-monotonic variation in the rotation-induced component of RSL. This is in agreement with our previous preliminary study (Milne & Mitrovica 1996), but contrasts significantly with predictions presented by Han & Wahr (1989) and Bills & James (1996). We demonstrate that the disagreement arises as a consequence of approximations adopted in the latter studies. We furthermore refute an assertion by Bills & James (1996) that previously published constraints on mantle viscosity and ice-sheet histories which did not incorporate a rotation-induced RSL component are 'largely invalidated' by this omission.