Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Galerkin Least-Squares Stabilization in Ice Sheet Modeling - Accuracy, Robustness, and Comparison to other Techniques
Stockholm University, Faculty of Science, Department of Physical Geography.ORCID iD: 0000-0003-4310-4873
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We investigate the accuracy and robustness of one of the most common methods used in glaciology for the discretization of the p-Stokes equations: equal order finite elements with Galerkin Least-Squares (GLS) stabilization. Furthermore we compare the results to other stabilized methods. We find that the vertical velocity component is more sensitive to the choice of GLS stabilization parameter than horizontal velocity. Additionally, the accuracy of the vertical velocity component is especially important since errors in this component can cause ice surface instabilities and propagate into future ice volume predictions. If the element cell size is set to the minimum edge length and the stabilization parameter is allowed to vary non-linearly with viscosity, the GLS stabilization parameter found in literature is a good choice on simple domains. However, near ice margins the standard parameter choice may result in significant oscillations in the vertical component of the surface velocity. For these cases, other stabilization techniques, such as the interior penalty method, result in better accuracy and are less sensitive to the choice of the stabilization parameter. During this work we also discovered that the manufactured solutions often used to evaluate errors in glaciology are not reliable due to high artificial surface forces at singularities. We perform our numerical experiments in both FEniCS and Elmer/Ice.

Keyword [en]
finite element method, Galerkin Least-Squares, p-Stokes, ice sheet modeling, anisotropic mesh
National Category
Geosciences, Multidisciplinary
Research subject
Physical Geography
Identifiers
URN: urn:nbn:se:su:diva-141635OAI: oai:DiVA.org:su-141635DiVA: diva2:1087896
Available from: 2017-04-10 Created: 2017-04-10 Last updated: 2017-04-27Bibliographically approved
In thesis
1. Basal boundary conditions, stability and verification in glaciological numerical models
Open this publication in new window or tab >>Basal boundary conditions, stability and verification in glaciological numerical models
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

To increase our understanding of how ice sheets and glaciers interact with the climate system, numerical models have become an indispensable tool. However, the complexity of these systems and the natural limitation in computational power is reflected in the simplifications of the represented processes and the spatial and temporal resolution of the models. Whether the effect of these limitations is acceptable or not, can be assessed by theoretical considerations and by validating the output of the models against real world data. Equally important is to verify if the numerical implementation and computational method accurately represent the mathematical description of the processes intended to be simulated. This thesis concerns a set of numerical models used in the field of glaciology, how these are applied and how they relate to other study areas in the same field.

The dynamical flow of glaciers, which can be described by a set of non-linear partial differential equations called the Full Stokes equations, is simulated using the finite element method. To reduce the computational cost of the method significantly, it is common to lower the order of the used elements. This results in a loss of stability of the method, but can be remedied by the use of stabilization methods. By numerically studying different stabilization methods and evaluating their suitability, this work contributes to constraining the values of stabilization parameters to be used in ice sheet simulations. Erroneous choices of parameters can lead to oscillations of surface velocities, which affects the long term behavior of the free-surface ice and as a result can have a negative impact on the accuracy of the simulated mass balance of ice sheets.

The amount of basal sliding is an important component that affects the overall dynamics of the ice. A part of this thesis considers different implementations of the basal impenetrability condition that accompanies basal sliding, and shows that methods used in literature can lead to a difference in velocity of 1% to 5% between the considered methods.

The subglacial hydrological system directly influences the glacier's ability to slide and therefore affects the velocity distribution of the ice. The topology and dominant mode of the hydrological system on the ice sheet scale is, however, ill constrained. A third contribution of this thesis is, using the theory of R-channels to implement a simple numerical model of subglacial water flow, to show the sensitivity of subglacial channels to transient processes and that this limits their possible extent. This insight adds to a cross-disciplinary discussion between the different sub-fields of theoretical, field and paleo-glaciology regarding the characteristics of ice sheet subglacial hydrological systems. In the study, we conclude by emphasizing areas of importance where the sub-fields have yet to unify: the spatial extent of channelized subglacial drainage, to what degree specific processes are connected to geomorphic activity and the differences in spatial and temporal scales.

As a whole, the thesis emphasizes the importance of verification of numerical models but also acknowledges the natural limitations of these to represent complex systems. Focusing on keeping numerical ice sheet and glacier models as transparent as possible will benefit end users and facilitate accurate interpretations of the numerical output so it confidently can be used for scientific purposes.

Place, publisher, year, edition, pages
Stockholm: Department of Physical Geography, Stockholm University, 2017. 79 p.
Series
Dissertations from the Department of Physical Geography, ISSN 1653-7211 ; 62
Keyword
Glaciology, subglacial hydrology, ice sheet modeling, basal boundary conditions, non-linear Stokes flow
National Category
Physical Geography
Research subject
Physical Geography
Identifiers
urn:nbn:se:su:diva-141641 (URN)978-91-7649-778-4 (ISBN)978-91-7649-779-1 (ISBN)
Public defence
2017-05-31, De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 13:00 (English)
Opponent
Supervisors
Projects
Greenland Analogue Project
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.

Available from: 2017-05-08 Created: 2017-04-11 Last updated: 2017-05-03Bibliographically approved

Open Access in DiVA

No full text

Other links

arXiv:1702.08369

Search in DiVA

By author/editor
Helanow, Christian
By organisation
Department of Physical Geography
Geosciences, Multidisciplinary

Search outside of DiVA

GoogleGoogle Scholar

Total: 7 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf