Figure 3A. The moon's gravity when the moon is on the equator.

Figure 3B. The moon's gravity when the moon's declination is north of the equator.

Figure 3C. The effect of the moon's declination of height of tides.

The heights of the two high tides should be equal at the equator. At points north or south of the equator, an observer would still experience two high and two low tides, but the heights of the high tides would not be as great as they are at the equator. The effects of the declination of the moon are shown in Figure 3, for three cases, A, B, and C.

A. When the moon is on the plane of the equator, the forces are equal in magnitude at the two points on the same parallel of latitude and 180° apart in longitude (Figure 3A).

B. When the moon has north or south declination, the forces are unequal at such points and tend to cause an inequality in the two high waters and the two low waters each day (Figure 3B).

C. Observers at points X, Y, and Z experience one high tide when moon is on their meridian, then another high tide 12 hours 25 minutes later when at X’, Y’, and Z’. The second high tide is the same at X’ as at X. High tides at Y’ and Z’ are lower than high tides at Y and Z (Figure 3C).

The preceding discussion pertaining to the effects of the moon is equally valid when discussing the effects of the sun, taking into account that the magnitude of the solar effect is smaller. Hence, the tides will also vary according to the sun’s declination and its varying distance from the earth. A second envelope of water representing the equilibrium tides due to the sun would resemble the envelope shown in Figure 3C except that the heights of the high tides would be smaller, and the low tides correspondingly not as low.

General Features

At most places the tidal change occurs twice daily. The tide rises until it reaches a maximum height, called high tide or high water, and then falls to a minimum level called low tide or low water.
The rate of rise and fall is not uniform. From low water, the tide begins to rise slowly at first, but at an increasing rate until it is about halfway to high water. The rate of rise then decreases until high water is reached, and the rise ceases.

The falling tide behaves in a similar manner. The period at high or low water during which there is no apparent change of level is called stand. The difference in height between consecutive high and low waters is the range.

Figure 4. The rise and fall of the tide at New York during a 24-hour period.

Figure 5. The rise and fall of the tide at Boston during a 48-hour period.

Figure 6. The rise and fall of the tide at Pei-Hai, China during a 48-hour period.

Figure 7. The rise and fall of the tide on the US West Coast during a 48-hour period.

Figure 4 is a graphical representation of the rise and fall of the tide at New York during a 24-hour period. The curve has the general form of a variable sine curve.

Types Of Tide

A body of water has a natural period of oscillation, dependent upon its dimensions. None of the oceans is a single oscillating body; rather each one is made up of several separate oscillating basins. As such basins are acted upon by the tide-producing forces, some respond more readily to daily or diurnal forces, others to semidiurnal forces, and others almost equally to both. Hence, tides are classified as one of three types, semidiurnal, diurnal, or mixed, according to the characteristics of the tidal pattern.

In the semidiurnal tide, there are two high and two low waters each tidal day, with relatively small differences in the respective highs and lows. Tides on the Atlantic coast of the United States are of the semidiurnal type, which is illustrated in Figure 5 by the tide curve for Boston Harbor.

In the diurnal tide, only a single high and single low water occur each tidal day. Tides of the diurnal type occur along the northern shore of the Gulf of Mexico, in the Java Sea, the Gulf of Tonkin, and in a few other localities. The tide curve for Pei-Hai, China, illustrated in Figure 6, is an example of the diurnal type.

In the mixed tide, the diurnal and semidiurnal oscillations are both important factors and the tide is characterized by a large inequality in the high water heights, low water heights, or in both. There are usually two high and two low waters each day, but occasionally the tide may become diurnal. Such tides are prevalent along the Pacific coast of the United States and in many other parts of the world. Examples of mixed types of tide are shown in Figure 7. At Los Angeles, it is typical that the inequalities in the high and low waters are about the same. At Seattle the greater inequalities are typically in the low waters, while at Honolulu it is the high waters that have the greater inequalities.

Solar Tide

The natural period of oscillation of a body of water may accentuate either the solar or the lunar tidal oscillations. Though as a general rule the tides follow the moon, the relative importance of the solar effect varies in different areas. There are a few places, primarily in the South Pacific and the Indonesian areas, where the solar oscillation is the more important, and at those places the high and low waters occur at about the same time each day. At Port Adelaide, Australia the solar and lunar semidiurnal oscillations are equal and nullify one another at neaps.

Special Tidal Effects

As a wave enters shallow water, its speed is decreased. Since the trough is shallower than the crest, it is retarded more, resulting in a steepening of the wave front. In a few estuaries, the advance of the low water trough is so much retarded that the crest of the rising tide overtakes the low, and advances upstream as a breaking wave called a bore. Bores that are large and dangerous at times of large tidal ranges may be mere ripples at those times of the month when the range is small. Examples occur in the Petitcodiac River in the Bay of Fundy, and at Haining, China, in the Tsientang Kaing. The tide tables indicate where bores occur.
Other special features are the double low water (as at Hoek Van Holland) and the double high water (as at Southampton, England). At such places there is often a slight fall or rise in the middle of the high or low water period. The practical effect is to create a longer period of stand at high or low tide. The tide tables list these and other peculiarities where they occur.

Variations In Range

Though the tide at a particular place can be classified as to type, it exhibits many variations during the month. The range of the tide varies according to the intensity of the tide-producing forces, though there may be a lag of a day or two between a particular astronomic cause and the tidal effect.

The combined lunar-solar effect is obtained by adding the moon’s tractive forces vectorially to the sun’s tractive forces. The resultant tidal bulge will be predominantly lunar with modifying solar effects upon both the height of the tide and the direction of the tidal bulge. Special cases of interest occur during the times of new and full moon. With the earth, moon, and sun lying approximately on the same line, the tractive forces of the sun are acting in the same direction as the moon’s tractive forces (modified by declination effects). The resultant tides are called spring tides, whose ranges are greater than average.

Between the spring tides, the moon is at first and third quarters. At those times, the tractive forces of the sun are acting at approximately right angles to the moon’s tractive forces. The results are tides called neap tides, whose ranges are less than average.

With the moon in positions between quadrature and new or full, the effect of the sun is to cause the tidal bulge to either lag or precede the moon. These effects are called priming and lagging the tides.

Thus, when the moon is at the point in its orbit nearest the earth (at perigee), the lunar semidiurnal range is increased and perigean tides occur. When the moon is farthest from the earth (at apogee), the smaller apogean tides occur. When the moon and sun are in line and pulling together, as at new and full moon, spring tides occur (the term spring has nothing to do with the season of year); when the moon and sun oppose each other, as at the quadratures, the smaller neap tides occur. When certain of these phenomena coincide, perigean spring tides and apogean neap tides occur.

These are variations in the semidiurnal portion of the tide. Variations in the diurnal portion occur as the moon and sun change declination. When the moon is at its maximum semi-monthly declination (either north or south), tropic tides occur in which the diurnal effect is at a maximum;. When it crosses the equator, the diurnal effect is a minimum and equatorial tides occur.

When the range of tide is increased, as at spring tides, there is more water available only at high tide; at low tide there is less, for the high waters rise higher and the low waters fall lower at these times. There is more water at neap low water than at spring low water. With tropic tides, there is usually more depth at one low water during the day than at the other. While it is desirable to know the meanings of these terms, the best way of determining the height of the tide at any place and time is to examine the tide predictions for the place as given in the tide tables, which take all these effects into account.

Tidal Cycles

Tidal oscillations go through a number of cycles. The shortest cycle, completed in about 12 hours and 25 minutes for a semidiurnal tide, extends from any phase of the tide to the next recurrence of the same phase. During a lunar day (averaging 24 hours and 50 minutes) there are two highs and two lows (two of the shorter cycles) for a semidiurnal tide. The moon revolves around the earth with respect to the sun in a synodical month of about 29 1/2 days, commonly called the lunar month. The effect of the phase variation is completed in one-half a synodical month or about 2 weeks as the moon varies from new to full or full to new. The effect of the moon’s declination is also repeated in one-half of a tropical month of 27 1/3 days or about every 2 weeks. The cycle involving the moon’s distance requires an anomalistic month of about 27 1/2 days. The sun’s declination and distance cycles are respectively a half year and a year in length. An important lunar cycle, called the nodal period, is 18.6 years (usually expressed in round figures as 19 years). For a tidal value, particularly a range, to be considered a true mean, it must be either based upon observations extended over this period of time, or adjusted to take account of variations known to occur during the nodal period.

Time Of Tide

Since the lunar tide-producing force has the greatest effect in producing tides at most places, the tides “follow the moon.” Because the earth rotates, high water lags behind both upper and lower meridian passage of the moon. The tidal day, which is also the lunar day, is the time between consecutive transits of the moon, or 24 hours and 50 minutes on the average. Where the tide is largely semidiurnal in type, the lunitidal interval (the interval between the moon’s meridian transit and a particular phase of tide) is fairly constant throughout the month, varying somewhat with the tidal cycles. There are many places, however, where solar or diurnal oscillations are effective in upsetting this relationship. The interval generally given is the average elapsed time from the meridian transit (upper or lower) of the moon until the next high tide. This may be called mean high water lunitidal interval or corrected (or mean) establishment. The common establishment is the average interval on days of full or new moon, and approximates the mean high water lunitidal interval.

In the ocean, the tide may be in the nature of a progressive wave with the crest moving forward, a stationary or standing wave which oscillates in a seesaw fashion, or a combination of the two. Consequently, caution should be used in inferring the time of tide at a place from tidal data for nearby places. In a river or estuary, the tide enters from the sea and is usually sent upstream as a progressive wave so that the tide occurs progressively later at various places upstream.