Abstract
Abstract. Identifying fast and robust numerical solvers is a critical issue that needs to be addressed in order to improve projections of polar ice sheets evolving in a changing climate. This work evaluates the impact of using advanced numerical solvers for transient ice-flow simulations conducted with the JPL–UCI Ice Sheet System Model (ISSM). We identify optimal numerical solvers by testing a broad suite of readily available solvers, ranging from direct sparse solvers to preconditioned iterative methods, on the commonly used Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models benchmark tests. Three types of analyses are considered: mass transport, horizontal stress balance, and incompressibility. The results of the fastest solvers for each analysis type are ranked based on their scalability across mesh size and basal boundary conditions. We find that the fastest iterative solvers are ∼ 1.5–100 times faster than the default direct solver used in ISSM, with speed-ups improving rapidly with increased mesh resolution. We provide a set of recommendations for users in search of efficient solvers to use for transient ice-flow simulations, enabling higher-resolution meshes and faster turnaround time. The end result will be improved transient simulations for short-term, highly resolved forward projections (10–100 year time scale) and also improved long-term paleo-reconstructions using higher-order representations of stresses in the ice. This analysis will also enable a new generation of comprehensive uncertainty quantification assessments of forward sea-level rise projections, which rely heavily on ensemble or sampling approaches that are inherently expensive.
Highlights
Fast and efficient numerical simulations of ice flow are critical to understanding the role and impact of polar ice sheets (Greenland Ice Sheet, GIS, and Antarctica Ice Sheet, AIS) on sea-level rise in a changing climate
We find that the fastest iterative solvers are ∼ 1.5–100 times faster than the default direct solver used in Ice Sheet System Model (ISSM), with speed-ups improving rapidly with increased mesh resolution
Since this study focuses on the relative performance of the tested solvers, the timing results for different methods are directly comparable, as the additional steps are consistent across the tested methods and do not bias the results
Summary
Fast and efficient numerical simulations of ice flow are critical to understanding the role and impact of polar ice sheets (Greenland Ice Sheet, GIS, and Antarctica Ice Sheet, AIS) on sea-level rise in a changing climate. As reported in the Intergovernmental Panel on Climate Change AR5 Synthesis Report (Pachauri et al, 2014), “The ability to simulate ocean thermal expansion, glaciers and ice sheets, and sea level, has improved since the AR4, but significant challenges remain in representing the dynamics of the Greenland and Antarctic ice sheets.” One of these challenges is the fact that ice-sheet models (ISMs) need to resolve ice flow at high spatial resolution (500 m to 1 km) in order to capture mass transport through outlet glaciers. This is especially the case for the GIS, which has a significant number of outlet glaciers in the 5–10 km width range (Rignot et al, 2011; Morlighem et al, 2014; Moon et al, 2015) This leads to transient iceflow simulations with highly resolved meshes, which in turn reduces the time step prescribed by the Courant–Friedrichs– Lewy (CFL) condition that is necessary to maintain convergence and avoid developing numerical instabilities.
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