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C53D-01:
Large-scale Bayesian inversion of the basal friction coefficient for the Antarctic ice sheet

##### Abstract:

Model-based projections of the dynamics of the polar ice sheets play acentral role in anticipating future sea level rise. However, a number

of mathematical and computational challenges place significant

barriers on improving predictability of these models. One such

challenge is caused by the unknown model parameters that must be

inferred from heterogeneous observational data, leading to an

ill-posed inverse problem and the need to quantify uncertainties in

its solution. In this talk we discuss the problem of estimating the

uncertainty in the solution of (large-scale) ice sheet inverse

problems within the framework of Bayesian inference. The ice flow is

modeled as a three-dimensional, creeping, viscous, incompressible,

non-Newtonian fluid via the nonlinear Stokes equations.

Solving Bayesian inverse problems with expensive forward models and

high-dimensional parameter spaces is intractable on current and

anticipated supercomputers. However, under the assumption of Gaussian

noise and prior probability densities, and after linearizing the

parameter-to-observable map, the posterior density becomes Gaussian,

and can therefore be characterized by its mean and covariance. The

mean is given by the solution of a large-scale PDE-constrained

optimization problem and the posterior covariance matrix is given by

the inverse of the Hessian of the regularized data misfit

functional. Direct computation of the Hessian matrix is prohibitive,

since it would require solution of as many forward Stokes problems as

there are parameters. Therefore, we exploit the compact nature of the

data misfit component of Hessian and construct its low rank

approximation, which can be constructed at a cost (measured in number

of Stokes solves) that does not depend on the parameter or data

dimensions, thus providing scalability to problem sizes of practical

interest. We apply this framework to quantify uncertainties in the

inference of the basal friction coefficient for the Antarctic ice

sheet from InSAR satellite data.