A general approach to tidal predictions in the oceans is to gather observations over a period of roughly a year and use the time series to extract the various constituents by harmonic analysis. This method works only for places where observations are available, such as coastal stations and a few ``island'' stations in the middle of the basins. However, for the majority of the interior of the ocean basins, there exist no observations and it is necessary to resort to numerical models. It is possible to solve for the tidal response with equations such as equations (83) to (85) but with tidal potential terms on the right hand side. However for marginal seas open to primary ocean basins, and coastal oceans, it is necessary to prescribe the tidal forcing on the boundaries open to the ocean basin. In many cases, it is this forcing that is more important than the astronomical forcing. The Persian Gulf is such an example. The tides there co-oscillate with the tides entering the Gulf from the Arabian Sea through the Straits of Hormuz. The direct astronomical forcing is negligible. On the other hand, the tides in the Red Sea are primarily due to the direct astronomical forcing due to the highly constricted Straits of Bab-al-Mandeb that connects it to the Arabian Sea. For simplicity, we will present only a model of the Persian Gulf, which does not need the tidal potential terms in the governing equations of motion.
The most important parameters in a tidal model are the bottom depth and the bottom friction. Usually neither of them can be well-represented usually in a tidal model to sufficient resolution and therefore it is essential to fine-tune the model to yield good agreement with observations. It is a classical inverse-modeling problem although it is usually accomplished by trial and error. Another approach to obtain faithful tidal results is to include observations through the process of data assimilation. Both approaches can be experimented with in this model and we will come back to this in section 6.