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Basal boundary conditions, stability and verification in glaciological numerical models
Stockholm University, Faculty of Science, Department of Physical Geography. (Geomorphology and glaciology)ORCID iD: 0000-0003-4310-4873
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. , p. 79
Series
Dissertations from the Department of Physical Geography, ISSN 1653-7211 ; 62
Keywords [en]
Glaciology, subglacial hydrology, ice sheet modeling, basal boundary conditions, non-linear Stokes flow
National Category
Physical Geography
Research subject
Physical Geography
Identifiers
URN: urn:nbn:se:su:diva-141641ISBN: 978-91-7649-778-4 (print)ISBN: 978-91-7649-779-1 (electronic)OAI: oai:DiVA.org:su-141641DiVA, id: diva2:1088137
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: 2018-01-13Bibliographically approved
List of papers
1. Steady-state water pressures in subglacial conduits: corrections to a model and recommendations for its use
Open this publication in new window or tab >>Steady-state water pressures in subglacial conduits: corrections to a model and recommendations for its use
2015 (English)In: Journal of Glaciology, ISSN 0022-1430, E-ISSN 1727-5652, Vol. 61, no 225, p. 202-204Article in journal, Letter (Refereed) Published
National Category
Physical Geography
Research subject
Physical Geography
Identifiers
urn:nbn:se:su:diva-117409 (URN)10.3189/2015JoG14J197 (DOI)000353100100018 ()
Note

AuthorCount:3;

Available from: 2015-05-27 Created: 2015-05-19 Last updated: 2018-01-11Bibliographically approved
2. Theoretical, contemporary observational and palaeo-perspectives on ice sheet hydrology: Processes and products
Open this publication in new window or tab >>Theoretical, contemporary observational and palaeo-perspectives on ice sheet hydrology: Processes and products
2016 (English)In: Earth-Science Reviews, ISSN 0012-8252, E-ISSN 1872-6828, Vol. 155, p. 1-27Article in journal (Refereed) Published
Abstract [en]

Meltwater drainage through ice sheets has recently been a key focus of glaciological research due to its influence on the dynamics of ice sheets in a warming climate. However, the processes, topologies and products of ice sheet hydrology are some of the least understood components of both past and modem ice sheets. This is to some extent a result of a disconnect between the fields of theoretical, contemporary observational and palaeo-glaciology that each approach ice sheet hydrology from a different perspective and with different research objectives. With an increasing realisation of the potential of using the past to inform on the future of contemporary ice sheets, bridging the gaps in the understanding of ice sheet hydrology has become paramount. Here, we review the current state of knowledge about ice sheet hydrology from the perspectives of theoretical, observational and palaeo-glaciology. We then explore and discuss some of the key questions in understanding and interpretation between these research fields, including: 1) disagreement between the palaeo-record, glaciological theory and contemporary observations in the operational extent of channelised subglacial drainage and the topology of drainage systems; 2) uncertainty over the magnitude and frequency of drainage events associated with geomorphic activity; and 3) contrasts in scale between the three fields of research, both in a spatial and temporal context The main concluding points are that modem observations, modelling experiments and inferences from the palaeo-record indicate that drainage topologies may comprise a multiplicity of forms in an amalgam of drainage modes occurring in different contexts and at different scales. Drainage under high pressure appears to dominate at ice sheet scale and might in some cases be considered efficient; the sustainability of a particular drainage mode is governed primarily by the stability of discharge. To gain better understanding of meltwater drainage under thick ice, determining what drainage topologies are reached under high pressure conditions is of primary importance. Our review attests that the interconnectivity between research sub-disciplines in progressing the field is essential, both in interpreting the palaeo-record and in developing physical understanding of glacial hydrological processes and systems.

Keywords
Glacial hydrology, Ice sheet hydrology, Meltwater, Eskers, Meltwater channels, Glacial geomorphology
National Category
Earth and Related Environmental Sciences
Research subject
Physical Geography
Identifiers
urn:nbn:se:su:diva-130882 (URN)10.1016/j.earscirev.2016.01.010 (DOI)000374624800001 ()
Available from: 2016-06-07 Created: 2016-06-07 Last updated: 2017-04-27Bibliographically approved
3. Galerkin Least-Squares Stabilization in Ice Sheet Modeling - Accuracy, Robustness, and Comparison to other Techniques
Open this publication in new window or tab >>Galerkin Least-Squares Stabilization in Ice Sheet Modeling - Accuracy, Robustness, and Comparison to other Techniques
(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.

Keywords
finite element method, Galerkin Least-Squares, p-Stokes, ice sheet modeling, anisotropic mesh
National Category
Geosciences, Multidisciplinary
Research subject
Physical Geography
Identifiers
urn:nbn:se:su:diva-141635 (URN)
Available from: 2017-04-10 Created: 2017-04-10 Last updated: 2017-04-27Bibliographically approved
4. Effects of numerical implementations of the impenetrability condition on non-linear Stokes flow: applications to ice dynamics
Open this publication in new window or tab >>Effects of numerical implementations of the impenetrability condition on non-linear Stokes flow: applications to ice dynamics
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The basal sliding of glaciers and ice sheets can constitute a large part of the total observed ice velocity, in particular in dynamically active areas. It is therefore important to accurately represent this process in numerical models. The condition that the sliding velocity should be tangential to the bed is realized by imposing an impenetrability condition at the base. We study the, in glaciological literature used, numerical implementations of the impenetrability condition for non-linear Stokes flow with Navier's slip on the boundary. Using the finite element method, we enforce impenetrability by: a local rotation of the coordinate system (strong method), a Lagrange multiplier method enforcing zero average flow across each facet (weak method) and an approximative method that uses the pressure variable as a Lagrange multiplier for both incompressibility and impenetrability. An analysis of the latter shows that it relaxes the incompressibility constraint, but enforces impenetrability approximately if the pressure is close to the normal component of the stress at the bed. Comparing the methods numerically using a method of manufactured solutions unexpectedly leads to similar convergence results. However, we find that, for more realistic cases, in areas of high sliding or varying topography the velocity field simulated by the approximative method differs from that of the other methods by approx. 1% (two dimensional flow) and  > 5% when compared to the strong method (three-dimensional flow). In this study the strong method, which is the most commonly used in numerical ice sheet models, emerges as the preferred method due to its stable properties (compared to the weak method in three dimensions) and ability to well enforce the impenetrability condition.

Keywords
Non-linear Stokes, slip boundary conditions, finite element method, Lagrange multiplier method
National Category
Geosciences, Multidisciplinary
Research subject
Physical Geography
Identifiers
urn:nbn:se:su:diva-141640 (URN)
Available from: 2017-04-10 Created: 2017-04-10 Last updated: 2017-04-27Bibliographically approved

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