Chapter X 



The Harmonic Analysis of Tidal 

 Observations 



(1) The Preparation of Sea-level Recordings and their Scientific Use 



The dynamic theory of the tides teaches that the tide waves caused by the 

 tide-generating forces must have the period of these forces. However, due 

 to the complicated bottom configuration of the oceans and of the contours 

 of the continents, it is not possible to derive theoretically the amplitude and 

 the phase of these waves for the various points of the oceans with sufficient 

 accuracy. There is, however, no doubt that the tides obey laws. So, whereas 

 the periods of the occurring tides are determined theoretically, once for all, 

 by the harmonic analysis of the tide potential (see p. 263), their amplitudes 

 and phases remain unknown. They can, however, be computed for a locality 

 where a series of extended observations of the sea level is available. Inasmuch 

 as the tidal phenomenon constantly repeats itself within a certain interval, 

 it is to be expected that the amplitudes and phases of the tide waves derived 

 from the observations are for each locality constants, which are charac- 

 teristic for the tidal process in that particular locality. The method used 

 for this reduction is called the harmonic analysis of the tides, and since it 

 was introduced by Thomson and Darwin, it has developed into an exceedingly 

 important method of analysing tidal observations. The most important part 

 of the very extensive literature on this subject has already been given in 

 discussing the harmonic analysis of the tide potential. Important contributions 

 have been made by Borgen, and later by Rauschelbach (1924) and es- 

 pecially by Doodson (1928, p. 223). 



The procedure is based on the principle that any periodic motion or 

 oscillation can always be resolved into the sum of a series of single harmonic 

 motions. 



To a harmonic term of the tide potential as given in (VII. 17) and which 

 in general the form Q = Ccos(<rt+V ) corresponds according to the dynamic 

 theory, a component of the form 



7] = Hcos(at+V -x) (X.l) 



a is the frequency (angular velocity) of the potential component and equally 

 of the forced partial tide, V is the argument of the tide for h of the first day 

 of the series of observations to be subjected to the harmonic analysis; it can be 



