Clark 9515322 The two main goals of the proposed work are: 1) to reconstruct the change in thickness of all of the large ice sheets that once covered much of the Earth's surface during the last ice age, and 2) to explain sea-level changes and earth deformation that have occurred during late-glacial and postglacial time as a result of glacio-isostatic processes. The reconstruction of ice-age ice sheets has usually been attempted by glaciologists and Quaternary geologists who model the flow of ice sheets and assume the climate and other boundary conditions are known. Because the great weight of the ice sheets caused the earth to deform an alternative approach is to use earth deformation data (e.g. sea-level data, tide-gauge data, geodetic/GPS data or proglacial and postglacial lake shoreline tilt data) and a numerical model of viscous flow within the Earth's mantle to infer the weight of the ice sheets as they advanced and then retreated. The success of initial attempts to perform this "inversion" for the North American Laurentide ice sheet have demonstrated the feasibility of performing the global calculation. To insure that the predicted ice sheets are plausible the numerical inversion procedure utilizes quadratic programming methods to provide physical constraints upon the predicted ice sheets. The predicted ice sheets can be constrained to be always non-negative, less than a prescribed maximum thickness, with thickness profile thinning in the direction of glacier flow, and having a maximum rate of thinning or thickening. Errors can be determined for the resulting ice-sheet prediction. A recently implemented method uses "a priori" estimates of the most likely ice-sheet thickness history to "guide" the inversion process. Results are required to fit the deformatioin data using least squares criteria while the predicted ice-sheet thicknesses are still as close as possible to the a priori model. Prescribed errors of the a priori model control how strongly the predicted ice sheet is co nstrained by the a priori model, although the errors may be exceeded if the deformation data warrant it. This approach allows considerable spatial resolution in the inversion for ice-sheet history because the inverse problem is always overdetermined regardless of the number of unknown ice-sheet thicknesses. The number of equations always exceeds the number of unknowns. An additional benefit is that the procedure provides remarkable numerical stability in the determination of the matrix eigenstructure. As the ice sheets retreated their meltwater filled the ocean basins resulting in a rise in sea-level which has been observed in the geological record and recently estimated through time. This "eustatic" sealevel rise provides an important constraint upon the inversion process by indicating the volume change of the Earth's ice sheets during deglaciation while deformation data provide an estimate of the spatial distribution of this volume. Meltwater loading of the ocean floor is an important factor contribution to variation in relative sea level curves at sites distant from ice sheets. An important goal of the proposed work is to include this factor in the inverse procedure, together with the requirement that sea level remain on a gravitational equipotential surface. Understanding of the dynamic nature of ice sheets and their impact upon the earth will be valuable in global climate studies (speed of ice-sheet advance and retreat), climate modeling (ice-sheet thickness estimates affecting global circulation patterns), and geodynamic studies (component of earth movement associated with glacio- and hydro-isostasy) as well as in glacial geology.
