LANS Informal Seminar: Noemi Petra

Seminar Title: An adjoint-based inexact Newton method for inverse problems governed by nonlinear full Stokes models of ice sheet flows
Speaker: Noemi Petra, ICES Postdoctoral Fellow, The University of Texas at Austin

Date/Time: 2011-08-24 15:00
Location: Building 240, 4301

Description:
Modeling the dynamics of polar ice sheets is critical for projections of future sea level rise. Yet, there remain large uncertainties in the basal boundary conditions and in the non-Newtonian constitutive relations employed within ice sheet models. Here, we formulate an inverse problem which involves the solution of a nonlinear full Stokes equation to infer the basal slipperiness and the rheological exponent parameter fields from surface flow velocities. For this purpose, we minimize a regularized misfit functional between observed and modeled surface flow velocities. The resulting least-squares optimization problem is solved using an adjoint-based inexact Newton-conjugate-gradient method. This method requires only Hessian-vector applications rather than computing the full Hessian matrix, which renders it attractive for large-scale inverse problems. Results show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method, and that it is insensitive to the number of inversion parameters. In addition, a numerical study for the reconstructibility of variations in basal slipperiness from surface data shows that the reconstructions converge to the exact slipperiness field as the noise in the synthetic measurements decreases, and that the nonlinear rheology makes the retrieval of the basal slipperiness more difficult. For the inversion of the stress exponent in Glen’s flow law we find that horizontally constant or smoothly varying volume fields can be reconstructed satisfactorily from noisy surface measurements.