Fourier Analysis of Ocean Tides II
1. Setting up the problem
The task of tidal analysis is to take a limited sample of the tidal record, such as the two weeks readings from a tidal gauge at Bombay, and use it to predict the tides at that port in the future. In fact, for a complete calculation, a 369-day sample is the standard. The method used is harmonic analysis. Ordinarily, harmonic analysis is used for periodic functions, functions which repeat themselves exactly after a certain interval of time. But the tidal record is not periodic.
What we know from the geometry of the Sun-Earth-Moon system is that the tide-generating force at any point on the Earth's surface is a linear combination of sines and cosines whose frequencies come from a specific set: certain linear combinations, with small integral coefficients, of the fundamental astronomical frequencies governing the system. It is natural to suppose that the height of the tide, at Bombay for example, should also be a linear combination involving the same frequencies.
In practice only about 37 in all are ever used, and most ports use around 25, so the height of the tide can be written as
where the subscripts 1, 2, ... run up to about 25, the ``speeds'' vk are known a priori and the coefficients A0, A1, B1, etc, depend on the port. For example, here are the ten speeds (in degrees per hour) which figure most importantly in the tides of a port like Bridgeport, Connecticut:
This column will examine how Fourier analysis can be adapted to calculate, from the tidal record at a port, the coefficients A0, A1, B1, etc. Then the record may be extrapolated into the future, and tides for that port may be accurately predicted.
Setting up the problem
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