Comptes Rendus
Glacier flow modelling: a comparison of the Shallow Ice Approximation and the full-Stokes solution
[Modélisation de l'écoulement des glaciers : comparaison entre l'approximation de la couche mince et les équations de Stokes complètes.]
Comptes Rendus. Physique, Volume 5 (2004) no. 7, pp. 709-722.

De nombreuses approches, plus ou moins complexes, sont envisageables pour modéliser l'écoulement des glaciers et des calottes polaires. Parmi ces méthodes, l'approximation de la couche mince (Shallow Ice Approximation, SIA) semble être la plus utilisée, notamment pour sa grande simplicité. La SIA, essentiellement utilisée pour modéliser l'écoulement des calottes polaires, repose sur le faible rapport d'aspect ζ caractéristique de ces objets glaciaires. Pour des objets plus petits, comme les glaciers Alpins, la question de l'applicabilité de la SIA se pose puisque sa validé diminue lorsque ζ augmente. Avec comme objectif de définir le domaine de validité de cette méthode, les résultats de la SIA sont comparés à ceux obtenus en résolvant complètement les équations de Stokes à l'aide d'un code aux éléments finis. A partir de tests bidimensionnels, on montre que la solution donnée par la SIA est plus détériorée lorsque la pente du socle augmente que lorsque l'accumulation augmente, même si une augmentation de l'accumulation conduit à une augmentation de ζ. Par conséquent, lorsque la pente du socle devient importante, c'est elle qui doit être considérée, et non plus le rapport d'aspect, indiquant que la pente est donc le plus sévère des critères de validité de la SIA pour les applications glaciaires. Des simulations tridimensionnelles montrent que la non prise en compte des contraintes de cisaillement longitudinal dans la SIA contribue significativement à la différence avec la solution complète de Stokes.

Several different approaches of various complexities have been used in glacier and ice sheet modelling studies. Amongst them, owing to its simplicity, the Shallow Ice Approximation appears to be the most widely adopted method. This approach, essentially used for ice sheets, owes its success to the shallow aspect of the modelled ice mass embodied in an aspect ratio ζ. When considering smaller ice bodies like alpine-type glaciers, the question arises as to whether the SIA is still valid, given that the method is all the more accurate as ζ is small. In order to test the domain of applicability of the method, results of a SIA finite difference model are compared to those of a finite element model in which the flow equations are fully considered. From a set of two-dimensional flow tests, it is shown that the accuracy of the method is much more deteriorated with increasing bedrock slopes than it is with increasing accumulation rates, even if higher accumulations lead to thicker glaciers with a larger ζ. This leads to the conclusion that when slopes become pronounced, it is a bedrock-related aspect ratio that becomes of relevance such that the bedrock slope should be the most important parameter to consider for assessing the validity of the SIA Method. A 3-dimensional simulation shows that longitudinal shear stresses explain a large part of the misfit between SIA and full-Stokes approaches.

Publié le :
DOI : 10.1016/j.crhy.2004.10.001
Keywords: Glacier flow modelling, Shallow Ice Approximation, Stokes solution
Mot clés : Modélisation de l'écoulement des glaciers, Approximation de la couche mince de glace, Solution de Stokes
Emmanuel Le Meur 1 ; Olivier Gagliardini 1 ; Thomas Zwinger 2 ; Juha Ruokolainen 2

1 Laboratoire de glaciologie et géophysique de l'environnement du CNRS (associé à l'université Joseph Fourier), 54, rue Molière, BP 96, 38402 Saint Martin d'Hères, France
2 Scientific Computing Ltd., P.O. Box 405, 02101 Espoo, Finland
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Emmanuel Le Meur; Olivier Gagliardini; Thomas Zwinger; Juha Ruokolainen. Glacier flow modelling: a comparison of the Shallow Ice Approximation and the full-Stokes solution. Comptes Rendus. Physique, Volume 5 (2004) no. 7, pp. 709-722. doi : 10.1016/j.crhy.2004.10.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2004.10.001/

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