POSTGLACIAL SEA-LEVEL CHANGE ON A ROTATING EARTH

We present a complete derivation of the equation governing long-term s ea-level variations on a spherically symmetric, self-gravitating, Maxw ell viscoelastic planet. This new 'sea-level equation' extends earlier work by incorporating, in a gravitationally self-consistent manner, b oth a time-dependent ocean-continent geometry and the influence of con temporaneous perturbations to the rotation vector of the planet. We al so outline an efficient, pseudo-spectral, numerical methodology for th e solution of this equation, and present a variety of predictions, bas ed 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 perturbatio ns to the rotation vector can reach 7-8 m over the postglacial period in geographic regions where the rotationally induced signal is a maxim um. 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 com ponent of RSL change is sufficient to influence previous estimates of Late Holocene melting events and ongoing sea-level change due to GIA w hich were based on a RSL theory for a non-rotating Earth. In particula r, estimates of Antarctic melting over the last 5 kyr, based on the am plitude of sea-level highstands from the Australian region, may requir e an adjustment downwards of the order of 0.5 m of equivalent sea-leve l rise. Furthermore, present-day rates of sea-level change are perturb ed 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 ma ximum to the present, we predict a distinctly non-monotonic variation in the rotation-induced component of RSL. This is in agreement with ou r previous preliminary study (Milne & Mitrovica 1996), but contrasts s ignificantly with predictions presented by Han & Wahr (1989) and Bills & James (1996). We demonstrate that the disagreement arises as a cons equence of approximations adopted in the latter studies. We furthermor e refute an assertion by Bills & James (1996) that previously publishe d constraints on mantle viscosity and ice-sheet histories which did no t incorporate a rotation-induced RSL component are 'largely invalidate d' by this omission.