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5 Sigma-Coordinate Model     continued...

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.