Presenting and illustrating the full 3-D model would require considerable computing resources in order to obtain meaningful calculations. These resources include extensive input and forcing data derived as mentioned in the previous section. Instead, we will present a sub-component of the sigma model, namely the barotropic model (the next release will deal with the 3-D model itself, as applied to a small oceanic region such as the Sea of Japan). This model is quite simple to learn, and it should run even on a modest workstation. Yet, it is quite useful and is used extensively for practical applications such as the prediction of hurricane-induced storm surge effects (such as flooding of coastal regions, devastation and loss of life), and prediction of tidal sea surface heights in the global oceans. It is the latter application that we will describe with a real-life application: predicting the tidally-induced sea level heights in the Persian Gulf. This model (as well as the full 3-D version) proved very useful to our naval forces during Desert Storm.
Tidal sea level can be modeled by solving equations (90) to (92). In general, the right hand sides of equations (91) and (92) need to be modified to include the tide-generating gravitational potential terms due to the sun and the moon. However, for some semi-enclosed seas, such as the Persian Gulf, and most coastal oceans these terms can be neglected. Then the tides are the so-called co-oscillating tides excited by the tides generated in the adjoining primary ocean basins. It is relatively easy to prescribe these at the openings to the primary basin, in this case the Straits of Hormuz, where the tidal variations are well known. Thus the governing equations are solved with prescribed sea level conditions at the open boundary, to derive the resulting sea level fluctuations inside.
There are several components of tides that are important (see section 5.1): the semi-diurnal tides (i.e., M2, S2, N2 and K2), with roughly two tidal cycles every day; diurnal tides (K1, O1, P1 and Q1), with roughly one tidal cycle per day and the long term tides (such as the MF, MM and SSA), which are fortnightly, monthly and semi-annual in nature. In addition, in shallow water the so-called compound tides generated by non-linear interaction of semi-diurnal and diurnal tides due to shallow water depths can often be important. In this exercise, we will confine ourselves to solving for the semi-diurnal and diurnal tides in the Persian Gulf, even though the model is capable of solving for the full spectrum of tides.