An age old problem for cartographers, astronomers and atmosphere-ocean modelers alike is the gridding of the sphere. Geographic coordinates (latitude and longitude) are the most familiar but are poorly suited for modeling purposes - particularly with the finite volume methods employed in MITgcm - because lines of constant longitude (meridians) converge at the North and South poles. The spatial resolution (separation between meridians) in the zonal direction (east-west) therefore decreases to zero as one near the poles. Consequently, numerical models that must satisfy stability criteria (CFL conditions) generally require tiny time-steps and become very costly to integrate.

Instead we use the conformal expanded spherical cube. This provides a grid with nearly uniform resolution (the variations in grid-spacing are significantly smaller than for a conventional latitude-longitude grid). The only apparent difficulty is that instead of two poles (on the spherical polar grid) there are now eight. However, these poles are singularities of a different, and much more treatable nature, to the those on the lat-long grids. We have show that these singularities can be readily treated.

A paper describing the numerical algorithm can be found here:

Adcroft, A., J-M Campin, C. Hill and J. Marshall (2004) Implementation of an atmosphere-ocean general circulation model on the expanded spherical cube.  Mon. Wea. Rev., 132 (12), 2845-2863

A spectacular movie of a simulation of the global ocean using MITgcm and resolving the eddy field can be found here. The calculation was carried out on the NASA AMES, Project Columbia computing facility by Dimitris Menemenlis at JPL with help from Chris Hill and Alistair Adcroft at MIT and staff from NASA AMES. The animation shows the speed of ocean currents at 15m depth from the simulation, it can be downloaded here (its 47MB but worth waiting for!). A second animation with different perspectives and rotation can be downloaded here.

The graphics are due to Chris Henze of NASA AMES.

There is also a small web-site devoted to the cubed grid with animations.