A new Time-Domain Method of Implementing the Sea-Level Equation in Glacial-Isostatic Adjustment

The sea-level equation (SLE) describing the redistribution of melt water in the oceans is complicated to implement in conjunction with the Laplace-transform method conventionally used to model glacial-isostatic adjustment (GIA). The recently developed spectral-finite element method (Martinec, 2000) solves the field equations governing GIA in the time domain and, thus, eliminates the need of applying the Laplace-transform method. Moreover, the spectral finite-element approach allows us to solve the SLE when modelling GIA in a 3-D viscosity model. The present test is restricted to a radially symmetric, self-gravitating, incompressible earth model consisting of a fluid core, a Maxwell-viscoelastic lower and upper mantle, and an elastic lithosphere. The Pleistocene deglaciation is simulated using the global ice model ICE-3G. To study the sensitivity of the GIA predictions, we consider three ocean models, i.e. approximations to the complete solution of the SLE. This test confirms the importance of allowing for geoid undulations and for moving coastlines when calculating the redistribution of melt water in GIA. Finally, we compare our predictions with different types of observational constraint from Canada and Fennoscandia.