Title: Estimating Heat Diffusion in the Greenland Ice Sheet

Abstract:

Estimating the rate at which heat diffuses in ice sheets is an important problem; such diffusion coefficients are assumed 'constants' in more complicated climate models. Using temperature data collected over several months from theremistors placed along the depths of boreholes in the Greenland ice sheet, specifically in the snow/firn cover, our goal is to use methods from the statistics literature, functional data analysis via parameter cascading (Xun et al., 2013 JASA) and Bayesian hierarchical modeling (Wikle, 2003, Ecology among others), to compare methodological details and estimates of the diffusion coefficient.  For the latter, we investigate the performance of different discretizations for solving the heat equation pde: Forward Euler, Backward Euler and Crank-Nicholson, as Forward Euler is potentially unstable, while the other two are stable schemes. Specifically, we examine the effect on the posterior distributions of the diffusion coefficient and the variances of the observation and process errors.  The FDA code runs much faster than the BHM, but provides less information. Our comparisons are motivated by recommendations that would be useful to our glaciologist collaborator. This is joint work with Darren Gemoets, Dylan Griffith and Neil Humphrey.

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