Computing and Mathematical Sciences Colloquium

  The flow of ice from the interior of polar ice sheets is the primary  contributor to projected sea level rise. One of the main difficulties  faced in modeling ice sheet flow is the uncertain spatially-varying  Robin boundary condition that describes the resistance to sliding at  the base of the ice. Satellite observations of the surface ice flow  velocity, along with a model of ice as a creeping incompressible  shear-thinning fluid, can be used to infer this uncertain basal  boundary condition. We cast this ill-posed inverse problem in the  framework of Bayesian inference, which allows us to infer not only the  basal sliding parameter field, but also the associated uncertainty. To  overcome the prohibitive nature of Bayesian methods for large-scale  inverse problems, we exploit the fact that, despite the large size of  observational data, they typically provide only sparse information on  model parameters. This allows us to construct low rank approximations  of the Hessian of the data-misfit functional at a cost (measured in  ice sheet Stokes solves) that is independent of the parameter and data  dimensions. We show results for Bayesian inversion of the basal  sliding parameter field for the full Antarctic continent.      This work is joint with Tobin Isaac, James Martin, Noemi Petra, and  Georg Stadler.