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.