Submitted as: development and technical paper
10 Oct 2023
Submitted as: development and technical paper |  | 10 Oct 2023
Status: this preprint is currently under review for the journal GMD.

Numerical stabilization methods for level-set-based ice front migration

Gong Cheng, Mathieu Morlighem, and G. Hilmar Gudmundsson

Abstract. Numerical modeling of ice sheet dynamics is a critical tool for projecting future sea-level rise. Among all the processes responsible for the loss of mass of the ice sheets, enhanced ice discharge triggered by the retreat of marine terminating glaciers is one of the key drivers. Numerical models of ice sheet flow are therefore required to include ice front migration in order to reproduce today's mass loss and be able to predict their future. However, the discontinuous nature of calving poses a significant numerical challenge for accurately capturing the motion of the ice front. In this study, we explore different stabilization techniques combined with varying reinitialization strategies to enhance the numerical stability and accuracy of solving the level-set function, which tracks the position of the ice front. Through rigorous testing on an idealized domain with a semicircular and a straight-line ice front, including scenarios with diverse front velocities, we assess the performance of these techniques. The findings contribute to advancing our ability to model ice sheet dynamics, specifically calving processes, and provide valuable insights into the most effective strategies for simulating and tracking the motion of the ice front.

Gong Cheng et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on gmd-2023-194', Michael Wolovick, 13 Nov 2023
    • AC1: 'Reply on CC1', Gong Cheng, 13 Nov 2023
      • CC2: 'Reply on AC1', Michael Wolovick, 14 Nov 2023
        • AC2: 'Reply on CC2', Gong Cheng, 14 Nov 2023
  • RC1: 'Comment on gmd-2023-194', Matt Trevers, 17 Nov 2023
  • RC2: 'Comment on gmd-2023-194', Anonymous Referee #2, 20 Nov 2023

Gong Cheng et al.

Video supplement

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Gong Cheng et al.


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Short summary
We conducted a comprehensive analysis of the stabilization and reinitialization techniques currently employed in ISSM and Ua for solving level-set equations, specifically those related to the dynamic representation of moving ice fronts within numerical ice sheet models. Our results demonstrate that the Streamline Upwinding Petrov Galerkin (SUPG) method outperforms the other approaches. We found that excessively frequent reinitialization can lead to exceptionally high errors in simulations.