A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions
Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatiotemporal coordinates, and it will also allow for the derivation of poster...
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Published in | The cryosphere Vol. 12; no. 7; pp. 2229 - 2248 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Katlenburg-Lindau
Copernicus GmbH
11.07.2018
Copernicus Publications |
Subjects | |
Online Access | Get full text |
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Summary: | Bayesian hierarchical modeling can assist the
study of glacial dynamics and ice flow properties. This approach
will allow glaciologists to make fully probabilistic predictions for
the thickness of a glacier at unobserved spatiotemporal
coordinates, and it will also allow for the derivation of posterior
probability distributions for key physical parameters such as ice
viscosity and basal sliding. The goal of this paper is to develop a
proof of concept for a Bayesian hierarchical model constructed,
which uses exact analytical solutions for the shallow ice
approximation (SIA) introduced by Bueler et al. (2005). A suite of test
simulations utilizing these exact solutions suggests that this
approach is able to adequately model numerical errors and produce
useful physical parameter posterior distributions and predictions. A
byproduct of the development of the Bayesian hierarchical model is
the derivation of a novel finite difference method for solving the
SIA partial differential equation (PDE). An additional novelty of
this work is the correction of numerical errors induced through a
numerical solution using a statistical model. This error-correcting
process models numerical errors that accumulate forward in time and
spatial variation of numerical errors between the dome, interior,
and margin of a glacier. |
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ISSN: | 1994-0424 1994-0416 1994-0424 1994-0416 |
DOI: | 10.5194/tc-12-2229-2018 |