We describe how the existing sea-level equation incorrectly predicts the change in sea level (and thus the ocean load) in ice-covered, subgeoidal geographic regions during periods of deglaciation. We go on to present a new sea-level equation that overcomes this problem and we describe how this equation can be solved in a gravitationally self-consistent manner by employing a well-known spectral technique, application of the new theory to predict relative sea-level (rsl) histories and present-day, 3-D, solid surface deformation rates in northeastern Canada (based on a single earth model characterized by a lithospheric thickness of 100 km and upper and lower mantle viscosities of 5 x 10(20) and 5 x 10(21) Pa s, respectively) demonstrates that a significant error is introduced when the original theory is employed to predict the oceanic component of the surface load. Predictions of rsl curves show a discrepancy of similar to 40 per cent at sites where data have been obtained and employed to constrain models of earth viscosity structure and ice-sheet histories. This error will significantly bias estimates of mantle viscosity structure and ice thicknesses that are based on the original theory, In addition, predictions of 3-D deformation rates differ by up to 25 per cent in some regions and so future applications that employ these data to constrain models of the glacial isostatic adjustment process should adopt the improved sea-level theory. In contrast, estimates of inverse decay times from the predicted rsl curves are insensitive (to within the observational error) to the improvement in the surface load introduced by the new theory. Thus, viscosity structure inferences based on this parametrization and the original sea-level equation are unaffected by the error in the ocean load. Finally, the new theory predicts a eustatic (i.e. globally uniform) rise in sea level over the postglacial period that is similar to 11 m lower than that determined via the original theory, Therefore, estimates of the global ice budget at the last glacial maximum based on far-field rsl data and the original sea-level theory will be too small by similar to 10 per cent.
