The varying values of and for a given point on the earth obviously lead to varying combinations of the tide producing forces and . We may illustrate the important short period variations associated with the rotation of the earth by examining one of these forces, say that due to the moon.
The declination of the moon relative to the equator varies from about 28 S to 28 N during a lunar month (28 days). This may be compared with the declination of the sun which varies from about 23.5 S to 23.5 N during a year. At that time when the declination of the moon is zero then the distribution of the lunar tide-producing force is symmetrical with respect to the equator. In terms of of the potential tide , each point on the earth experience two maximum and two minimum tides (Fig. 2.04-8) with each culmination of the moon (24 lunar hours or 24.84 solar hours). Consequently, the apparent period of this tidal effect is 12.42 hours.
When the declination of the moon differs from zero, then the variation of the tide potential with time at a given point on the earth contains a diurnal period as well as the semidiurnal, except at the equator. The situation existing for maximum declination of the moon is illustrated in Fig. 2.04-9. The variation of at latitude 20 clearly shows the diurnal component induced by the asymmetry of the semidiurnal oscillations. At the equator the diurnal component vanishes. At the latitude , which equals (90 - ) where is the declination of the moon, the semidirnal component vanishes. The minimum value of is 62 . Consequently, at no time does the semidiurnal lunar component of the tide vanish at latitudes between 62 N and 62 S, except where its effect may tend to be offset by the solar semidiurnal tide at those times during the lunar month when the moon and sun are 90 out of phase.
The period of the principal diurnal component of the tide associated with the moon is 25.82 hours.
The tidal potential associated with the sun varies in a similar manner to that of the moon, but the periods of the diurnal and semidiurnal components differ. Also, the lunear and solar tide producing forces vary in phase relationship, thus leading to an amplitude modulation effect. Spring tides, representing a maximum range of tide, and neap tides, representing a minimum range of tide, occur twice each month when the sun and moon are in phase and 90 out of phase, respectively.
A list of the major tide components is given in The Oceans, Table 70, p. 550.