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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Online Access: | https://hdl.handle.net/20.500.11815/815 https://doi.org/10.5194/tc-12-2229-2018 |
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ftopinvisindi:oai:opinvisindi.is:20.500.11815/815 2023-05-15T18:32:09+02:00 A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions Gopalan, Giridhar Raja Hrafnkelsson, Birgir Adalgeirsdottir, Gudfinna Jarosch, Alexander H. Pálsson, Finnur 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 2018-07-11 2229-2248 https://hdl.handle.net/20.500.11815/815 https://doi.org/10.5194/tc-12-2229-2018 en eng Copernicus GmbH The Cryosphere;12(7) https://www.the-cryosphere.net/12/2229/2018/tc-12-2229-2018.pdf Gopalan, G., Hrafnkelsson, B., Aðalgeirsdóttir, G., Jarosch, A. H., and Pálsson, F.: A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions, The Cryosphere, 12, 2229-2248, https://doi.org/10.5194/tc-12-2229-2018, 2018. 1994-0416 1994-0424 (eISSN) https://hdl.handle.net/20.500.11815/815 The Cryosphere doi:10.5194/tc-12-2229-2018 info:eu-repo/semantics/openAccess Jöklafræði Jöklarannsóknir Íshvel info:eu-repo/semantics/article 2018 ftopinvisindi https://doi.org/20.500.11815/815 https://doi.org/10.5194/tc-12-2229-2018 2022-11-18T06:51:38Z 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 Article in Journal/Newspaper The Cryosphere Opin vísindi (Iceland) The Cryosphere 12 7 2229 2248 |
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Open Polar |
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Opin vísindi (Iceland) |
op_collection_id |
ftopinvisindi |
language |
English |
topic |
Jöklafræði Jöklarannsóknir Íshvel |
spellingShingle |
Jöklafræði Jöklarannsóknir Íshvel Gopalan, Giridhar Raja Hrafnkelsson, Birgir Adalgeirsdottir, Gudfinna Jarosch, Alexander H. Pálsson, Finnur A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions |
topic_facet |
Jöklafræði Jöklarannsóknir Íshvel |
description |
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 |
author2 |
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 |
author |
Gopalan, Giridhar Raja Hrafnkelsson, Birgir Adalgeirsdottir, Gudfinna Jarosch, Alexander H. Pálsson, Finnur |
author_facet |
Gopalan, Giridhar Raja Hrafnkelsson, Birgir Adalgeirsdottir, Gudfinna Jarosch, Alexander H. Pálsson, Finnur |
author_sort |
Gopalan, Giridhar Raja |
title |
A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions |
title_short |
A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions |
title_full |
A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions |
title_fullStr |
A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions |
title_full_unstemmed |
A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions |
title_sort |
bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions |
publisher |
Copernicus GmbH |
publishDate |
2018 |
url |
https://hdl.handle.net/20.500.11815/815 https://doi.org/10.5194/tc-12-2229-2018 |
genre |
The Cryosphere |
genre_facet |
The Cryosphere |
op_relation |
The Cryosphere;12(7) https://www.the-cryosphere.net/12/2229/2018/tc-12-2229-2018.pdf Gopalan, G., Hrafnkelsson, B., Aðalgeirsdóttir, G., Jarosch, A. H., and Pálsson, F.: A Bayesian hierarchical model for glacial dynamics based on the shallow ice approximation and its evaluation using analytical solutions, The Cryosphere, 12, 2229-2248, https://doi.org/10.5194/tc-12-2229-2018, 2018. 1994-0416 1994-0424 (eISSN) https://hdl.handle.net/20.500.11815/815 The Cryosphere doi:10.5194/tc-12-2229-2018 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/20.500.11815/815 https://doi.org/10.5194/tc-12-2229-2018 |
container_title |
The Cryosphere |
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12 |
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7 |
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2229 |
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2248 |
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1766216209094672384 |