Physics based interpolation techniques

Document Type

Presentation Abstract

Presentation Date

12-2-2013

Abstract

Increasingly, the demands of computational models challenge the limits of observational data. For instance, models require first and higher derivatives of velocity and thickness measurements, however numerical derivatives of data are often characterized by noise that makes their interpretation difficult. Specific examples include strain-rates and flux divergences computed from observations of velocity and thickness. Two approaches to physics based interpolation of observational data are presented here. The first is known as the "mass conserving bed", and entails using the continuity equation to interpolate between measurements of ice thickness. Our favored approach utilizes least squares rather than Lagrange multipliers, and is shown to be accurate, robust, and scalable to large problems. The second application is to InSAR surface velocity observations. In order to smooth these frequently discontinuous data we again look to the continuity equation, this time solving for vertically averaged velocity. Attaching a Lagrange multiplier to the forward model, and adding misfit over the domain, we find adjoint, control, and objective equations allowing minimization of differences between model and observed surface velocity. Bounds set in the minimization algorithm ensure optimal velocities are consistent with reported errors in thickness, surface mass balance, surface velocity, and surface rate of change. The resulting velocity field is in excellent agreement with observation, provides complete coverage, and satisfies stronger requirements for continuity. Both bed and velocity fields produced by these techniques are of use to the community for; initialization of ice sheet models, calculation of the force budget, inversion for parameter estimation, assessment of ice sheet sensitivity to perturbation, and mission planning.

Additional Details

Monday, December 2 at 3:10 p.m. in Math 103

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