Transient Response in a Z-Level Ocean Model That Resolves Topography with Partial Cells

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 Dz/Dx. In such regions, the dispersion relation for topographic waves is inaccurate. However, bottom topography can be accurately represented in discrete zlevel 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.