Postglacial sea level: energy method

The equation governing changes in sea level caused by the redistribution of ice and water masses on the earthʹs surface is rederived based on the least potential energy principle. This energy method deepens our understanding of the coupled ice–sea–Earth system, and lays the foundation of a global solution used in this study. A phenomenological parameterization of ‘realisticʹ viscosity models is proposed based on microphysical considerations. Continuously varying viscosity structures are determined using a few characteristic viscosity values (parameters) at seismically identified boundaries. By using a set of admissible ‘realisticʹ viscosity models and two models of deglaciation histories, we find that satisfactory convergence can be reached for a global solution for postglacial relative sea level (RSL) at about harmonic degree 50, and the convergence appears independent of ice model. This relatively lower tolerable truncation level is a consequence of global nature of the ice–sea–Earth system. We further examine the sensitivity of postglacial sea level to ‘realisticʹ viscosity structure and the lithospheric thickness combined. We find that variation of lithospheric thickness does not alter our previous conclusion (Fang, M., Hager, B.H., 1996. The sensitivity of post-glacial sea level to viscosity structure and ice-load history for realistically parameterized viscosity profiles. Geophys. Res. Lett. 23, 3787–3790) that there is a correlation of RSL sensitivities between ice history and viscosity structures, i.e., at sites less sensitive to the ice model, the resolving power for viscosity structure is also less. Furthermore, models having a thicker lithosphere tend to permit better resolution of lower mantle viscosity.