Ronald C. Pacanowski and Anand Gnanadesikan.
Submitted to Monthly Weather Review, Jan 1998.
Abstract
Ocean simulations are in part determined by topographic waves with
speeds and spatial scales dependent on bottom slope. By their very
nature, discrete z-level ocean models have problems accurately
representing bottom topography when slopes are less than the grid cell
aspect ratio $\Delta z/\Delta x$. In such regions, the dispersion
relation for topographic waves is inaccurate. However, bottom
topography can be accurately represented in discrete z-level models by
allowing bottom-most grid cells to be partially filled with land.
Consequently, gently sloping bottom topography is resolved on the scale
of horizontal grid resolution and the dispersion relation for
topographic waves is accurately approximated. In contrast to the
standard approach using full-cells, partial-cells imply that all grid
points within a vertical level are not necessarily at the same depth
and problems arise with pressure gradient errors and the spurious
diapycnal diffusion. However, both problems have been effectively dealt
with. Differences in flow fields between simulations with full-cells
and partial-cells can be significant and simulations with partial-cells
are more robust than with full-cells. Partial-cells provide a superior
representation of topographic waves when compared to the standard
method employing full-cells.