However, these benefits do not come
without penalties. While * all* numerical ocean models experience
difficulties in handling sharp topographic changes from one grid
point to the next, the sigma-coordinate models appear to suffer
proportionately more. The problem lies in the calculation of the
pressure gradient terms in the momentum equations. In sigma
coordinates, sharp topographic change from one grid point to the
next means that the calculation of the pressure gradient involves
taking the difference between two large terms
[26]
and therefore
large roundoff errors. While this problem can be alleviated by
increased horizontal resolution, it can also be mitigated by
subtraction of horizontal averages of density from the density
terms before computing the density-gradient induced pressure
differences from one grid point to the next. However, the other
problem associated with sharp topographic changes, namely the
hydrostatic inconsistency, can be reduced in severity only by
smoothing the horizontal gradients of topography. It is generally
wise to process the bottom topography with a filter that caps the
ratio of bottom depths of adjacent grid points before using it in
the model. However care must be exercised to ensure that the
topography is not severely corrupted by this processing,
especially over the shallow coastal regions.

As mentioned earlier, the upper and bottom mixed layers constitute a significant fraction of the water column for coastal oceans and therefore play a very important role in the dynamics of the region. It is therefore essential to parameterize the vertical mixing as accurately as possible. (For a detailed discussion of solving for turbulence quantities in the geophysical context, see Mellor and Yamada [43] and Kantha and Clayson [34]). Second moment closure of turbulence, which involves solving the governing equations for Reynolds turbulence stresses (the second moments of the velocity field), provides one means of doing this. The model to be discussed incorporates this feature. The evolution of the upper mixed layer and the benthic boundary layer are therefore somewhat more realistic under both wind stirring and surface heat fluxes.