Monday, April 13, 2015
Computing and Mathematical Sciences Colloquium
Bayesian Inversion for Large Scale Antarctic Ice Sheet Flow
Professor Omar Ghattas, Jackson School of Geosciences, Department of Mechanical Engineering, and Institute for Computational Engineering & Sciences, The University of Texas at Austin
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.