### Chapter 5 - Factors Influencing the Local Heights and Times of Arrival of the Tides

It is noteworthy in Fig. 6 that any one cycle of the tides is characterized by a definite time regularity as well as the recurrence of the cyclical pattern. However, continuing observations at coastal stations will reveal - in addition to the previously explained variations in the heights of successive tides of the same phase - noticeable differences in their successive time of occurrence. The aspects of regularity in the tidal curves are introduced by harmonic motions of the earth and moon. The variations noted both in observed heights of the tides and in their times of occurrence are the result of many factors, some of which have been discussed in the preceding section. Other influences will now be considered.

The earth rotates on its axis (from one meridian transit of the "mean" sun until the next) in 24 hours. But as the earth rotates beneath the envelope of tidal forces produced by the moon, another astronomical factor causes the time between two successive upper transits of the moon across the local meridian of the place (a period known as the lunar or "tidal" day) to exceed the 24 hours of the earth's rotation period - the mean solar day.

The moon revolves in its orbit around the earth with an angular velocity of approximately 12.2o per day, in the same direction in which the earth is rotating on its axis with an angular velocity of 360o per day. In each day, therefore, a point on the rotating earth must complete a rotation of 360o plus 12.2o, or 372.2o, in order to "catch up" with the moon. Since 15o is equal to one hour of time, this extra amount of rotation equal to 12.2o each day would require a period of time equal to 12.2o/15o x 60 min/hr., or 48.8 minutes - if the moon revolved in a circular orbit, and its speed of revolution did not vary. On the average it requires about 50 minutes longer each day for a sublunar point on the rotating earth to regain this position directly along the major axis of the moon's tidal force envelope, where the tide-raising influence is a maximum. In consequence, the recurrence of a tide of the same phase and similar rise (see middle diagram of Fig. 6) would take place at an interval of 24 hours 50 minutes after the preceding occurrence, if this single astronomical factor known as lunar retardation were considered. This period of 24 hours 50 minutes has been established as the tidal day.

A second astronomical factor influencing the time of arrival of tides of a given phase at any location results from the interaction between the tidal force envelopes of the moon and sun. Between new moon and first-quarter phase, and between full moon and third-quarter phase, this phenomenon can cause a displacement of force components and an acceleration in tidal arrival times (known as priming the tides) resulting in the occurrence of high tides before the moon itself reaches the local meridian of the place. Between first-quarter phase and full moon, and between third-quarter phase and new moon, an opposite displacement of force components and a delaying action (known as lagging of the tides) can occur, as the result of which the arrival of high tides may take place several hours after the moon has reached the meridian.

These are the two principle astronomical causes for variation in the times of arrival of the tides. In addition to these astronomically induced variations, the tides are subject to other accelerating or retarding influences of hydraulic, hydrodynamic, hydrographic, and topographic origin - and may further be modified by meteorological conditions.

The first factor of consequence in this regard arises from the fact that the crests and troughs of the large-scale gravity-type traveling wave system comprising the tides strive to sweep continuously around the earth, following the position of the moon (and sun).

In the open ocean, the actual rise (see middle diagram, Fig. 6) of the tidally induced wave crest is only one to a few feet. It is only when the tidal crests and troughs move into shallow water, against land masses, and into confining channels, that noticeable variations in the height of sea level can be detected.

Possessing the physical properties of a fluid, the ocean waters follow all of the hydraulic laws of fluids. This means that since the ocean waters possess a definite, although small internal viscosity, this property prevents their absolute free flow, and somewhat retards the overall movement of the tides.

Secondly, the ocean waters follow the principle of traveling waves in a fluid. As the depth of the water shallows, the speed of forward movement of a traveling wave is retarded, as deducted from dynamic considerations. In shoaling situations, therefore, the advance of tidal waters is slowed.

Thirdly, a certain relatively small amount of friction exists between the water and the ocean floor over which it moves - again slightly slowing the movement of the tides, particularly as they move inshore. Further internal friction (or viscosity) exists between tidally induced currents and contiguous current in the oceans - especially where they are flowing in opposite directions.

The presence of land masses imposes a barrier to progress of the tidal waters. Where continents interpose, tidal movements are confined to separate, nearly closed oceanic basins and the sweeps of the tides around the world is not continuous.

Topography on the ocean floor can also provide a restraint to the forward movement of tidal waters - or create sources of local-basin response to the tides. Restrictions to the advance of tidal waters imposed both by shoaling depths and the sidewalls of the channel as these waters enter confined bays, estuaries, and harbors can further considerably alter the speed of their onshore passage.

In such particularly confined bodies of water, so-called "resonance effects" between the free-period of oscillation of the traveling, tidally induced wave and that of the confining basin may cause a surging rise of the water in a phenomenon basically similar to the action of water caused to "slosh" over the sides of a wash basin by repeatedly tilting the basin and matching wave crests reflected from the opposite side of the basin.

All of the above, and other less important influences, can combine to create a considerable variety in the observed range and phase sequence of the tides - as well as variations in the times of their arrival at any location.

Of a more local and sporadic nature, important meteorological contributions to the tides know as "storm surges", caused by a continuous strong flow of winds either onshore or offshore, may superimpose their effects upon those of tidal action to cause either heightened or diminished tides, respectively. High-pressure atmospheric systems may also depress the tides, and deep low-pressure systems may cause them to increase in height.

Chapter 6 - Prediction of Tides