Preprints
https://doi.org/10.5194/tc-2021-239
https://doi.org/10.5194/tc-2021-239

  07 Sep 2021

07 Sep 2021

Review status: this preprint is currently under review for the journal TC.

A comparison of the performance of depth-integrated ice-dynamics solvers

Alexander Robinson1,2,3,4, Daniel Goldberg5, and William H. Lipscomb4 Alexander Robinson et al.
  • 1Complutense University of Madrid, Madrid, Spain
  • 2Geosciences Institute CSIC-UCM, Madrid, Spain
  • 3Potsdam Institute for Climate Impact Research, Potsdam, Germany
  • 4Climate and Global Dynamics Laboratory, National Center for Atmospheric Research, Boulder, CO 80305, USA
  • 5School of GeoSciences, University of Edinburgh, Edinburgh, UK

Abstract. In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics approximations have emerged as fast solvers capable of resolving the relevant physics of ice sheets at the continen- tal scale. However, the numerical stability of these schemes has not been studied systematically to evaluate their effectiveness in practice. Here we focus on three such solvers, the so-called Hybrid, L1L2-SIA and DIVA solvers, as well as the well-known SIA and SSA solvers as boundary cases. We investigate the numerical stability of these solvers as a function of grid resolution and the state of the ice sheet. Under simplified conditions with constant viscosity, the maximum stable timestep of the Hybrid solver, like the SIA solver, has a quadratic dependence on grid resolution. In contrast, the DIVA solver has a maximum timestep that is independent of resolution, like the SSA solver. Analysis indicates that the L1L2-SIA solver should behave similarly, but in practice, the complexity of its implementation can make it difficult to maintain stability. In realistic simulations of the Greenland ice sheet with a non-linear rheology, the DIVA and SSA solvers maintain superior numerical stability, while the SIA, Hybrid and L1L2-SIA solvers show markedly poorer performance. At a grid resolution of ∆x = 4 km, the DIVA solver runs approximately 15 times faster than the Hybrid and L1L2-SIA solvers. Our analysis shows that as resolution increases, the ice-dynamics solver can act as a bottleneck to model performance. The DIVA solver emerges as a clear outlier in terms of both model performance and its representation of the ice-flow physics itself.

Alexander Robinson et al.

Status: open (until 02 Nov 2021)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Alexander Robinson et al.

Alexander Robinson et al.

Viewed

Total article views: 279 (including HTML, PDF, and XML)
HTML PDF XML Total Supplement BibTeX EndNote
212 65 2 279 41 1 1
  • HTML: 212
  • PDF: 65
  • XML: 2
  • Total: 279
  • Supplement: 41
  • BibTeX: 1
  • EndNote: 1
Views and downloads (calculated since 07 Sep 2021)
Cumulative views and downloads (calculated since 07 Sep 2021)

Viewed (geographical distribution)

Total article views: 270 (including HTML, PDF, and XML) Thereof 270 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
1
 
 
 
 
Latest update: 21 Sep 2021
Download
Short summary
Here we investigate the numerical stability of several commonly used methods, in order to determine which of them are both capable of resolving the complex physics of the ice flow and are also computationally efficient. We find that the so-called DIVA solver outperforms the others. Its representation of the physics is consistent with more complex methods, while it remains computationally efficient at high resolution.