Variational Methods in Ice Sheet Modelling
A complete simulation of flowing ice requires knowledge of both the fundamental physical principles that govern the stress and energy balances and a framework for assimilating data into a model to help estimate unknown parameters. Modelling ice is complex, due to the large spatial extent of ice shee...
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ftunivmontana:oai:scholarworks.umt.edu:etd-2186 2023-07-16T03:58:49+02:00 Variational Methods in Ice Sheet Modelling Brinkerhoff, Douglas John 2013-01-01T08:00:00Z application/pdf https://scholarworks.umt.edu/etd/1167 https://scholarworks.umt.edu/context/etd/article/2186/viewcontent/BRINKERHOFF_THESIS.pdf unknown University of Montana https://scholarworks.umt.edu/etd/1167 https://scholarworks.umt.edu/context/etd/article/2186/viewcontent/BRINKERHOFF_THESIS.pdf ©2013 Douglas John Brinkerhoff Graduate Student Theses, Dissertations, & Professional Papers cryosphere modelling variational techniques thesis 2013 ftunivmontana 2023-06-27T22:39:49Z A complete simulation of flowing ice requires knowledge of both the fundamental physical principles that govern the stress and energy balances and a framework for assimilating data into a model to help estimate unknown parameters. Modelling ice is complex, due to the large spatial extent of ice sheets, the multiple scales at which relevant physics operate, and the coupling between heat, stress, and ice rheology. As such, it is usually necessary to make approximations to the equations governing ice flow. At the same time, it is important to have an understanding of the specific assumptions that lead to these approximations. We develop a variational principle for Stokes flow, and neglect certain components in order to obtain the variational principle for the first-order approximation for ice flow. This result is fundamentally the result of assuming bed slopes to be much less than surface slopes, and that vertical resistive stresses are negligible. From a practical standpoint, using automatic differentiation tools on this functional yields a compact model of ice flow that automatically incorporates correct boundary condition. This model is compared to well known benchmark tests. We also present an improved model of ice thermodynamics that operates on enthalpy rather than temperature, avoiding many of the difficulties associated with phase change. We derive a method for inverting the Blatter-Pattyn ice sheet model in order to solve for the rate of basal sliding. This method uses the adjoint equations of the forward model to obtain the gradient of an error functional, and this is minimized using a quasi-Newton method. These methods are applied to an instrumented streamline of the Greenland ice sheet. We perform numerical experiments on this geometry in order to assess the sensitivity of thermal conditions at the ice sheet bed to perturbations in unknown parameters. The basal thermal regime is sensitive to changes in geothermal heat flux, with the location of the transition zone between cold and temperate ice being ... Thesis Greenland Ice Sheet University of Montana: ScholarWorks Greenland |
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University of Montana: ScholarWorks |
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ftunivmontana |
language |
unknown |
topic |
cryosphere modelling variational techniques |
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cryosphere modelling variational techniques Brinkerhoff, Douglas John Variational Methods in Ice Sheet Modelling |
topic_facet |
cryosphere modelling variational techniques |
description |
A complete simulation of flowing ice requires knowledge of both the fundamental physical principles that govern the stress and energy balances and a framework for assimilating data into a model to help estimate unknown parameters. Modelling ice is complex, due to the large spatial extent of ice sheets, the multiple scales at which relevant physics operate, and the coupling between heat, stress, and ice rheology. As such, it is usually necessary to make approximations to the equations governing ice flow. At the same time, it is important to have an understanding of the specific assumptions that lead to these approximations. We develop a variational principle for Stokes flow, and neglect certain components in order to obtain the variational principle for the first-order approximation for ice flow. This result is fundamentally the result of assuming bed slopes to be much less than surface slopes, and that vertical resistive stresses are negligible. From a practical standpoint, using automatic differentiation tools on this functional yields a compact model of ice flow that automatically incorporates correct boundary condition. This model is compared to well known benchmark tests. We also present an improved model of ice thermodynamics that operates on enthalpy rather than temperature, avoiding many of the difficulties associated with phase change. We derive a method for inverting the Blatter-Pattyn ice sheet model in order to solve for the rate of basal sliding. This method uses the adjoint equations of the forward model to obtain the gradient of an error functional, and this is minimized using a quasi-Newton method. These methods are applied to an instrumented streamline of the Greenland ice sheet. We perform numerical experiments on this geometry in order to assess the sensitivity of thermal conditions at the ice sheet bed to perturbations in unknown parameters. The basal thermal regime is sensitive to changes in geothermal heat flux, with the location of the transition zone between cold and temperate ice being ... |
format |
Thesis |
author |
Brinkerhoff, Douglas John |
author_facet |
Brinkerhoff, Douglas John |
author_sort |
Brinkerhoff, Douglas John |
title |
Variational Methods in Ice Sheet Modelling |
title_short |
Variational Methods in Ice Sheet Modelling |
title_full |
Variational Methods in Ice Sheet Modelling |
title_fullStr |
Variational Methods in Ice Sheet Modelling |
title_full_unstemmed |
Variational Methods in Ice Sheet Modelling |
title_sort |
variational methods in ice sheet modelling |
publisher |
University of Montana |
publishDate |
2013 |
url |
https://scholarworks.umt.edu/etd/1167 https://scholarworks.umt.edu/context/etd/article/2186/viewcontent/BRINKERHOFF_THESIS.pdf |
geographic |
Greenland |
geographic_facet |
Greenland |
genre |
Greenland Ice Sheet |
genre_facet |
Greenland Ice Sheet |
op_source |
Graduate Student Theses, Dissertations, & Professional Papers |
op_relation |
https://scholarworks.umt.edu/etd/1167 https://scholarworks.umt.edu/context/etd/article/2186/viewcontent/BRINKERHOFF_THESIS.pdf |
op_rights |
©2013 Douglas John Brinkerhoff |
_version_ |
1771546126498922496 |