Uncertainty Quantification Techniques for Estimating Ice Sheet Initial Conditions
Abstract: Understanding the dynamics of the continental ice sheets in Antarctica and Greenland is important for predictions of sea level change. It is known that the flow of ice over long time scales can be modeled using the incompressible Stokes equation with a shear-thinning rheology, but the boundary and initial temperature conditions can only be inferred indirectly from satellite observations of the surface flow. This inference is formulated as Bayesian inverse problem (or uncertainty quantification problem), and the uncertainty in the inferred conditions due to the ill-posedness of the problem and the limited observational data is described using random variables. I will discuss the challenges involved in this problem (continental-scale simulation of ice sheets; characterization of high-dimensional probabilities) and the approximations and numerical methods needed to make solving this problem feasible (Gaussian approximations of probabilities, low-rank approximations, adjoint methods, algorithms from PDE-constrained optimization). This is joint work with Noemi Petra (Merced), Tobin Isaac (Chicago), Omar Ghattas (Austin), Steve Price (Los Alamos) and Mauro Perego (Sandia).
(Tea served in First Floor Commons Room at 3:30pm.)