  Numerical 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,
attempts to clarify 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 result, Table 2, highlights the key roles played by the algorithmic
scaling of stress-balance and implicit-step solvers.
