| 11. |
- Ahlkrona, Josefin
(författare)
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How much are the greenland and antarctic ice sheets melting?
- 2018
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Ingår i: XRDS: Crossroads, The ACM Magazine for Students. - : Association for Computing Machinery (ACM). - 1528-4972 .- 1528-4980. ; 25:1, s. 42-47
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Designing better simulation software to prepare for a warming world.
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| 12. |
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| 13. |
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| 14. |
- Helanow, Christian, 1981-, et al.
(författare)
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Galerkin Least-Squares Stabilization in Ice Sheet Modeling - Accuracy, Robustness, and Comparison to other Techniques
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 15. |
- Helanow, Christian, et al.
(författare)
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Stabilized equal low-order finite elements in ice sheet modeling - accuracy and robustness
- 2018
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Ingår i: Computational Geosciences. - : Springer Science and Business Media LLC. - 1420-0597 .- 1573-1499. ; 22:4, s. 951-974
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the accuracy and robustness of one of the most common methods used in glaciology for finite element discretization of the oe-Stokes equations: linear equal order finite elements with Galerkin least-squares (GLS) stabilization on anisotropic meshes. 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 reasons, other stabilization techniques, in particular the interior penalty method, result in better accuracy and are less sensitive to the choice of 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.
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| 16. |
- Kirchner, Nina, et al.
(författare)
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Shallow ice approximation, second order shallow ice approximation, and full Stokes models : A discussion of their roles in palaeo-ice sheet modelling and development
- 2016
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Ingår i: Quaternary Science Reviews. - : Elsevier BV. - 0277-3791 .- 1873-457X. ; 147, s. 136-147
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Tidskriftsartikel (refereegranskat)abstract
- Full Stokes ice sheet models provide the most accurate description of ice sheet flow, and can therefore be used to reduce existing uncertainties in predicting the contribution of ice sheets to future sea level rise on centennial time-scales. The level of accuracy at which millennial time-scale palaeo-ice sheet simulations resolve ice sheet flow lags the standards set by Full Stokes models, especially, when Shallow Ice Approximation (SIA) models are used. Most models used in paleo-ice sheet modeling were developed at a time when computer power was very limited, and rely on several assumptions. At the time there was no means of verifying the assumptions by other than mathematical arguments. However, with the computer power and refined Full Stokes models available today, it is possible to test these assumptions numerically. In this paper, we review (Ahlkrona et al., 2013a) where such tests were performed and inaccuracies in commonly used arguments were found. We also summarize (Ahlkrona et al., 2013b) where the implications of the inaccurate assumptions are analyzed for two paleo-models - the SIA and the SOSIA. We review these works without resorting to mathematical detail, in order to make them accessible to a wider audience with a general interest in palaeo-ice sheet modelling. Specifically, we discuss two implications of relevance for palaeo-ice sheet modelling. First, classical SIA models are less accurate than assumed in their original derivation. Secondly, and contrary to previous recommendations, the SOSIA model is ruled out as a practicable tool for palaeo-ice sheet simulations. We conclude with an outlook concerning the new Ice Sheet Coupled Approximation Level (ISCAL) method presented in Ahlkrona et al. (2016), that has the potential to match the accuracy standards of full Stokes model on palaeo-timescales of tens of thousands of years, and to become an alternative to hybrid models currently used in palaeo-ice sheet modelling. The method is applied to an ice sheet covering Svalbard.
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| 17. |
- Kirchner, Nina, et al.
(författare)
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Shallow ice approximation, second order shallow ice approximation, and full Stokes models : A discussion of their roles in palaeo-ice sheet modelling and development
- 2016
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Ingår i: Quaternary Science Reviews. - : Elsevier BV. - 0277-3791 .- 1873-457X. ; 135, s. 103-114
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Forskningsöversikt (refereegranskat)abstract
- Full Stokes ice sheet models provide the most accurate description of ice sheet flow, and can therefore be used to reduce existing uncertainties in predicting the contribution of ice sheets to future sea level rise on centennial time-scales. The level of accuracy at which millennial time-scale palaeo-ice sheet simulations resolve ice sheet flow lags the standards set by Full Stokes models, especially, when Shallow Ice Approximation (SIA) models are used. Most models used in paleo-ice sheet modeling were developed at a time when computer power was very limited, and rely on several assumptions. At the time there was no means of verifying the assumptions by other than mathematical arguments. However, with the computer power and refined Full Stokes models available today, it is possible to test these assumptions numerically. In this paper, we review (Ahlkrona et al., 2013a) where such tests were performed and inaccuracies in commonly used arguments were found. We also summarize (Ahlkrona et al., 2013b) where the implications of the inaccurate assumptions are analyzed for two paleo-models - the SIA and the SOSIA. We review these works without resorting to mathematical detail, in order to make them accessible to a wider audience with a general interest in palaeo-ice sheet modelling. Specifically, we discuss two implications of relevance for palaeo-ice sheet modelling. First, classical SIA models are less accurate than assumed in their original derivation. Secondly, and contrary to previous recommendations, the SOSIA model is ruled out as a practicable tool for palaeo-ice sheet simulations. We conclude with an outlook concerning the new Ice Sheet Coupled Approximation Level (ISCAL) method presented in Ahlkrona et al. (2016), that has the potential to match the accuracy standards of full Stokes model on palaeo-timescales of tens of thousands of years, and to become an alternative to hybrid models currently used in palaeo-ice sheet modelling. The method is applied to an ice sheet covering Svalbard.
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| 18. |
- Löfgren, André, 1992-, et al.
(författare)
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Increasing Numerical Stability of Mountain Valley Glacier Simulations : Implementation and Testing of Free-Surface Stabilization in Elmer/Ice
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- This paper concerns a numerical stabilization method for free-surface ice flow called the free-surface stabilizationalgorithm (FSSA). In the current study, the FSSA is implemented into the numerical ice-flow software Elmer/Ice and tested onsynthetic two-dimensional (2D) glaciers, as well as on the real-world glacier of Midtre Lovénbreen, Svalbard. For the synthetic2D cases it is found that the FSSA method increases the largest stable time-step size at least by a factor of ten for the case of agently sloping ice surface ( 3◦), and by at least a factor of five for cases of moderately to steeply inclined surfaces ( 6◦ − 12◦) .5Furthermore, the FSSA method increases the overall accuracy for all surface slopes. The largest stable time-step size is foundto be smallest for the case of a low sloping surface, despite having overall smaller velocities. For Midtre Lovénbreen the FSSAmethod doubles the largest stable time-step size, however, the accuracy is in this case slightly lowered in the deeper parts ofthe glacier, while it increases near edges. The implication is that the non-FSSA method might be more accurate at predictingglacier thinning, while the FSSA method is more suitable for predicting future glacier extent. A possible application of the10larger time-step sizes allowed for by the FSSA is for spin-up simulations, where relatively fast changing climate data can beincorporated on short time scales, while the slowly changing velocity field is updated over larger time scales.
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| 19. |
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| 20. |
- Löfgren, André, et al.
(författare)
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Increasing stable time-step sizes of the free-surface problem arising in ice-sheet simulations
- 2022
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Ingår i: Journal of Computational Physics: X. - : Elsevier BV. - 2590-0552. ; 16
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Tidskriftsartikel (refereegranskat)abstract
- Numerical models for predicting future ice mass loss of the Antarctic and Greenland ice sheets require accurately representing their dynamics. Unfortunately, ice-sheet models suffer from a very strict time-step size constraint, which for higher-order models constitutes a severe bottleneck; in each time step a nonlinear and computationally demanding system of equations has to be solved. In this study, stable time-step sizes are increased for a full-Stokes model by implementing a so-called free-surface stabilization algorithm (FSSA). Previously this stabilization has been used successfully in mantle-convection simulations where a similar viscous-flow problem is solved. By numerical investigation it is demonstrated that instabilities on the very thin domains required for ice-sheet modeling behave differently than on the equal-aspect-ratio domains the stabilization has previously been used on. Despite this, and despite the different material properties of ice, it is shown that it is possible to adapt FSSA to work on idealized ice-sheet domains and increase stable time-step sizes by at least one order of magnitude. The FSSA method presented is deemed accurate, efficient and straightforward to implement into existing ice-sheet solvers.
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