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Abstract. Bayesian hierarchical modeling can assist thestudy of glacial dynamics and ice flow properties. This approachwill allow glaciologists to make fully probabilistic predictions forthe thickness of a glacier at unobserved spatiotemporalcoordinates, and it will also allow for the derivation of posteriorprobability distributions for key physical parameters such as iceviscosity and basal sliding. The goal of this paper is to develop aproof of concept for a Bayesian hierarchical model constructed,which uses exact analytical solutions for the shallow iceapproximation (SIA) introduced by Bueler et al. ( 2005 ) . A suite of testsimulations utilizing these exact solutions suggests that thisapproach is able to adequately model numerical errors and produceuseful physical parameter posterior distributions and predictions. Abyproduct of the development of the Bayesian hierarchical model isthe derivation of a novel finite difference method for solving theSIA partial differential equation (PDE). An additional novelty ofthis work is the correction of numerical errors induced through anumerical solution using a statistical model. This error-correctingprocess models numerical errors that accumulate forward in time andspatial variation of numerical errors between the dome, interior,and margin of a glacier.

A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions