MITgcm is discretized by carving up the fluid in to "finite volumes" with six sides. In the interior of the fluid this creates a grid of box shaped elements. Where the topography (solid bottom) intersect the grid we shape the volume to fit the topography. This can be done in varying degrees of approximation, such as piecewise constant or discontinuous partial steps ("lopping"), piecewise linear or even higher order.

In contrast, the finite difference method used in ocean models until recently would fit the topography to the grid; there is clearly a large representation error.

Our use of topography using finite volumes also opens up as yet unexplored possibilities, as suggested by the figures below.