Implementation of temperature variations and free surface evolution in the Shallow Ice Approximation (SIA)
Ice sheets and glaciers constitute an enormous water storage, currently corresponding to a potential sea level rise of almost 70 meters if all ice was to melt completely. The ice sheets are dynamic components of the global climate system and numerical modeling is a useful tool that can help us under...
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Uppsala universitet, Avdelningen för beräkningsvetenskap
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ftuppsalauniv:oai:DiVA.org:uu-202177 2023-05-15T16:40:43+02:00 Implementation of temperature variations and free surface evolution in the Shallow Ice Approximation (SIA) Håård, Cecilia 2013 application/pdf http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202177 eng eng Uppsala universitet, Avdelningen för beräkningsvetenskap UPTEC W, 1401-5765 13013 http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202177 info:eu-repo/semantics/openAccess Shallow Ice Approximation temperature free surface elmer matlab Other Computer and Information Science Annan data- och informationsvetenskap Student thesis info:eu-repo/semantics/bachelorThesis text 2013 ftuppsalauniv 2023-02-23T21:46:16Z Ice sheets and glaciers constitute an enormous water storage, currently corresponding to a potential sea level rise of almost 70 meters if all ice was to melt completely. The ice sheets are dynamic components of the global climate system and numerical modeling is a useful tool that can help us understand and predict how the ice sheets develop. The most accurate model available for ice sheets is given by the Stokes equations, but to solve them for a real ice sheet on a relevant time scale would be way too computationally costly. Instead approximations of the Stokes equations are used such as the Shallow Ice Approximation (SIA). The SIA is valid for areas where the aspect ratio, the ice thickness divided by the horizontal extent of the ice, is small. In this project equations for temperature and surface evolution were implemented in a Matlab version of SIA. The model already had algorithms implemented for computation of stresses, velocities and pressures for an ice sheet with fixed geometry and temperature. Implementation of temperature and free surface equations also made the problem time-dependent. The result was evaluated by solving a simple test problem and comparing the solution to a full Stokes solution obtained with the code ElmerIce. The SIA solution was closer to the Stokes solution when the aspect ratio ε and slope α were decreased simultaneously such that ε=arctanα, but a similar improvement was also obtained when only the slope was decreased. The differences between the two solutions were satisfyingly small for both temperature, surface location and velocities for an aspect ratio of ε= 7.8 10−4 and ε=arctanα. Bachelor Thesis Ice Sheet Uppsala University: Publications (DiVA) |
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Open Polar |
collection |
Uppsala University: Publications (DiVA) |
op_collection_id |
ftuppsalauniv |
language |
English |
topic |
Shallow Ice Approximation temperature free surface elmer matlab Other Computer and Information Science Annan data- och informationsvetenskap |
spellingShingle |
Shallow Ice Approximation temperature free surface elmer matlab Other Computer and Information Science Annan data- och informationsvetenskap Håård, Cecilia Implementation of temperature variations and free surface evolution in the Shallow Ice Approximation (SIA) |
topic_facet |
Shallow Ice Approximation temperature free surface elmer matlab Other Computer and Information Science Annan data- och informationsvetenskap |
description |
Ice sheets and glaciers constitute an enormous water storage, currently corresponding to a potential sea level rise of almost 70 meters if all ice was to melt completely. The ice sheets are dynamic components of the global climate system and numerical modeling is a useful tool that can help us understand and predict how the ice sheets develop. The most accurate model available for ice sheets is given by the Stokes equations, but to solve them for a real ice sheet on a relevant time scale would be way too computationally costly. Instead approximations of the Stokes equations are used such as the Shallow Ice Approximation (SIA). The SIA is valid for areas where the aspect ratio, the ice thickness divided by the horizontal extent of the ice, is small. In this project equations for temperature and surface evolution were implemented in a Matlab version of SIA. The model already had algorithms implemented for computation of stresses, velocities and pressures for an ice sheet with fixed geometry and temperature. Implementation of temperature and free surface equations also made the problem time-dependent. The result was evaluated by solving a simple test problem and comparing the solution to a full Stokes solution obtained with the code ElmerIce. The SIA solution was closer to the Stokes solution when the aspect ratio ε and slope α were decreased simultaneously such that ε=arctanα, but a similar improvement was also obtained when only the slope was decreased. The differences between the two solutions were satisfyingly small for both temperature, surface location and velocities for an aspect ratio of ε= 7.8 10−4 and ε=arctanα. |
format |
Bachelor Thesis |
author |
Håård, Cecilia |
author_facet |
Håård, Cecilia |
author_sort |
Håård, Cecilia |
title |
Implementation of temperature variations and free surface evolution in the Shallow Ice Approximation (SIA) |
title_short |
Implementation of temperature variations and free surface evolution in the Shallow Ice Approximation (SIA) |
title_full |
Implementation of temperature variations and free surface evolution in the Shallow Ice Approximation (SIA) |
title_fullStr |
Implementation of temperature variations and free surface evolution in the Shallow Ice Approximation (SIA) |
title_full_unstemmed |
Implementation of temperature variations and free surface evolution in the Shallow Ice Approximation (SIA) |
title_sort |
implementation of temperature variations and free surface evolution in the shallow ice approximation (sia) |
publisher |
Uppsala universitet, Avdelningen för beräkningsvetenskap |
publishDate |
2013 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202177 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_relation |
UPTEC W, 1401-5765 13013 http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202177 |
op_rights |
info:eu-repo/semantics/openAccess |
_version_ |
1766031131790016512 |