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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Bibliographic Details
Published in:The Cryosphere
Main Authors: Gopalan, Giridhar Raja, Hrafnkelsson, Birgir, Adalgeirsdottir, Gudfinna, Jarosch, Alexander H., Pálsson, Finnur
Other Authors: Raunvísindadeild (HÍ), Faculty of Physical Sciences (UI), Jarðvísindastofnun (HÍ), Institute of Earth Sciences (UI), Verkfræði- og náttúruvísindasvið (HÍ), School of Engineering and Natural Sciences (UI), Háskóli Íslands, University of Iceland
Format: Article in Journal/Newspaper
Language:English
Published: Copernicus GmbH 2018
Subjects:
Jöklafræði
Jöklarannsóknir
Íshvel
The Cryosphere
Online Access:https://hdl.handle.net/20.500.11815/815
https://doi.org/10.5194/tc-12-2229-2018
Description
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. The Icelandic Research Fund (RANNIS) is thanked for funding this research. Peer Reviewed

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