https://doi.org/10.5194/gmd-2020-397
https://doi.org/10.5194/gmd-2020-397

Submitted as: development and technical paper 17 Dec 2020

Submitted as: development and technical paper | 17 Dec 2020

Review status: a revised version of this preprint was accepted for the journal GMD and is expected to appear here in due course.

# Assessment of numerical schemes for transient, finite-element ice flow models using ISSM v4.18

Thiago Dias dos Santos1,2, Mathieu Morlighem1, and Hélène Seroussi3 Thiago Dias dos Santos et al.
• 1Department of Earth System Science, University of California, Irvine, CA, USA
• 2Centro Polar e Climático, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil
• 3Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA, USA

Abstract. Time dependent simulations of ice sheets require two equations to be solved: the mass transport equation, derived from the conservation of mass, and the stress balance equation, derived from the conservation of momentum. The mass transport equation controls the advection of ice from the interior of the ice sheet towards its periphery, thereby changing its geometry. Because it is based on a hyperbolic partial differential equation, a stabilization scheme needs to be employed when solved using the finite element method. Several stabilization schemes exist in the finite element method framework, but their respective accuracy and robustness have not yet been systematically assessed for glaciological applications. Here, we compare classical schemes used in the context of the finite element method: (i) Artificial Diffusion, (ii) Streamline Upwinding, (iii) Streamline Upwind Petrov-Galerkin, (iv) Discontinuous Galerkin, and (v) Flux Corrected Transport. We also look at the stress balance equation, which is responsible for computing the ice velocity that `advects' the ice dowstream. To improve the velocity computation accuracy, the ice sheet modeling community employs several sub-element parameterizations of physical processes at the grounding line, the point where the grounded ice starts to float onto the ocean. Here, we introduce a new sub-element parameterization for the driving stress, the force that drives the ice sheet flow. We analyze the response of each stabilization scheme by running transient simulations forced by ice shelf basal melt. The simulations are based on an idealized ice sheet geometry for which there is no influence of bedrock topography. We also perform transient simulations of the Amundsen Sea Sector, West Antarctica, where real bedrock and surface elevations are employed. In both idealized and real ice sheet experiments, stabilization schemes based on artificial diffusion lead systematically to a bias towards more mass loss in comparison to the other schemes, and therefore, should be avoided or employed with a sufficiently high mesh resolution in the vicinity of the grounding line. We also run diagnostic simulations to assess the accuracy of the driving stress parameterization, which in combination with an adequate parameterization for basal stress, provides improved numerical convergence in ice speed computations and more accurate results.

Thiago Dias dos Santos et al.

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Thiago Dias dos Santos et al.

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