Abstract
AbstractComputing predictions of future sea level that include well-defined uncertainty bounds requires models that are capable of robustly simulating the evolution of ice sheets and glaciers. Ice flow behaviour is known to be sensitive to the location and geometry of dynamic ice boundaries such as the grounding line (GRL), terminus position and ice surface elevation, so that any such model should track these interfaces with a high degree of accuracy. To address this challenge, we implement a numerical approach that uses the level-set method (LSM) that accurately models the evolution of the ice–air and ice–water interface as well as capturing topological changes in ice-sheet geometry. This approach is evaluated by comparing simulations of grounded and marine-terminating ice sheets to various analytical and numerical benchmark solutions. A particular advantage of the LSM is its ability to explicitly track the moving margin and GRL while using a fixed grid finite-difference scheme. Our results demonstrate that the LSM is an accurate and robust approach for tracking the ice surface interface and terminus for advancing and retreating ice sheets, including the transient marine ice-sheet interface and GRL positions.
Highlights
The Greenland and Antarctic ice sheets have been losing mass at an accelerated rate (Bevis and others, 2019; Rignot and others, 2019) and ice-sheet margins have recently undergone dramatic changes (Bunce and others, 2018; Konrad and others, 2018)
We aim to demonstrate that the level-set method (LSM) is an effective approach for accurately tracking the evolution of the ice–air and ice–water interfaces, as well as the terminus position for ice sheets and the grounding line (GRL) position of marine ice sheets
When steady xg are presented as a function of the grid size of the velocity solver the gap reduces to 150 m and we find that the GRL converges to a value near 730 km at the lowest resolution (Fig. 9b)
Summary
The Greenland and Antarctic ice sheets have been losing mass at an accelerated rate (Bevis and others, 2019; Rignot and others, 2019) and ice-sheet margins have recently undergone dramatic changes (Bunce and others, 2018; Konrad and others, 2018). Any choice of numerical algorithm must be guided by the need to accurately capture dynamically evolving boundaries, and to ensure reliable predictions of ice volume and extent and to minimize uncertainty in sea-level rise estimates To address these challenges, we aim to demonstrate that the level-set method (LSM) is an effective approach for accurately tracking the evolution of the ice–air and ice–water interfaces, as well as the terminus position for ice sheets and the GRL position of marine ice sheets. Other alternatives include the location-based moving mesh approach of Goldberg and others (2009) where the challenge is to define a suitable monitor function to position nodes, or the velocity-based moving-point approach proposed by Bonan and others (2016) to track the ice-sheet margin, but not yet applied to addressing the GRL problem These difficulties addressed above can be readily handled by the use of the LSM which can capture complex evolving geometries without requiring adaptive mesh refinement, and with the further advantage of being relatively straightforward to implement. Our implementation uses the finite-difference method on a regular fixed grid, which further highlights the strength and versatility of the LSM by demonstrating that moving ice boundaries can be tracked accurately without requiring local mesh refinement
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