Performance analysis of high-resolution ice-sheet simulations

Abstract

Numerical glacier and ice-sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or smaller, these models usually require time steps shorter than climate-coupling time scales because they update ice thickness after each velocity solution. High-resolution performance is degraded by the stability restrictions of such explicit time-stepping. This short note, which considers the shallow ice approximation and Stokes models as stress-balance end members, clarifies the scaling of numerical model performance by quantifying simulation cost per model year in terms of mesh resolution and the number of degrees of freedom. The performance of current-generation explicit time-stepping models is assessed, and then compared to the prospective performance of implicit schemes. The main results highlight the key roles played by the algorithmic scaling of stress-balance solvers and coupled, implicit-step solvers.

Increasing numerical stability of mountain valley glacier simulations: implementation and testing of free-surface stabilization in Elmer/Ice

“…It has been demonstrated for lower-order physics models, such as SIA, that when coupled to the free-surface equation governing the evolution of ice sheets and glaciers they suffer from a parabolic type time-step size constraint that is highly dependent on the ice-domain thickness (Bueler et al, 2005;Gong et al, 2017;Bueler, 2022;Robinson et al, 2022). However, for the Stokes equations the same parabolic time-step size restriction does not necessarily hold true -even for setups where the SIA and the Stokes equations gives qualitatively similar solutions (Löfgren et al, 2022).…”