The basal boundary of glaciers and ice sheets is generally not observationally accessible. This poses a major problem for glacier modeling studies, because the basal boundary condition is an essential part of a well-posed problem. The surface, however, is accessible to ground based, airborne, and satellite measurements. It is now possible to measure surface topography, ice thickness, and surface velocities over large areas. This sets up a classic inverse problem in mathematics with too many boundary conditions at the top and not enough at the bottom. Funds are provided to apply inverse methods, common in geophysics and other areas, to the problem of inferring subsurface glacier flow. A first step with a one-dimensional linear forward model has been accomplished. The funded effort will expand that work to non-linear two- and three-dimensional problems. Powerful methods of inverse theory and optimal control will be applied to solving these problems. The research goals will require obtaining new results in these two fields of mathematics as well as in numerical analysis. The resulting methods will be applied to existing data and thus no additional field work is required.
