The usual explanation of the tide in textbooks of physical geography or astronomy makes of it a simple phenomenon. It is shown that the gravitational attraction of sun and moon on the earth gives rise to forces which move the waters of the sea relative to the solid earth. It is further shown that these forces have different periods, but that the predominant ones have a period of about half a day; therefore there are two high waters and two low waters in a day. And finally it is shown that the moon plays the leading role in bringing about the tide, for the tide-producing power of a heavenly body varies directly as its mass and inversely as the cube of its distance from the earth.
On the bases of these general considerations, numerous features of the tide can be explained. Thus, at the times of new and full moon, when the tide-producing forces of sun and moon are in the same phase, the tides are greater than usual, while at the times of the moon's quadratures the tides are less than usual. In the same way, when the moon is in perigee, or nearest the earth, greater tides result than when the moon is in apogee or farthest from the earth. To be sure, it is known that the tides at different places vary in time, in range, and in other features. But these differences are ascribed to modifications brought about by local hydrographic features. And thus the whole phenomenon is seemingly reduced to simple terms.
To the navigator who is familiar with the Seven Seas, however, this very much oversimplifies the subject. For he finds that the tides at different places vary not only in time and in range, but also in character of rise and fall. Quite apart from differences in time and in range, which may be regarded as merely differences in degree, it is found that tides present striking differences in kind. There is in fact an almost bewildering variety in tides.
Take for example the actual records of the rise and fall of the tide at three such well-known places as Norfolk, Va., Pensacola, Fla., and San Francisco, Calif., for the last four days of May, 1931. These are shown in Fig. 1, the horizontal line associated with each tide curve representing the undisturbed or mean level of the sea. At Norfolk, it is seen, there are two high and two low waters in a day, morning and afternoon tides differing but little, and the high waters rising approximately the same distance above sea level as the low waters fall below it. At Pensacola, on the same days, there were but one high and one low water each day. And at San Francisco, while there were two high and two low waters each day, the morning tides differed very considerably from the afternoon tides.
It must be emphasized that the differences in the tides at the three places shown in Fig. 1 are in no way due to the disturbing effects of wind or weather. Heavy winds and rapid variations in barometric pressure do bring about very marked changes in the rise and fall of the tide. But the last four days of May, 1931, were purposely chosen because weather conditions then were relatively uniform. The features exhibited by the tides shown in Fig. 1 are characteristic features of the tide at the three places.
If we go to other places we find yet other varieties of tides. In Fig. 2 are shown the actual records of the tide for the same four days of May, 1931, at Seattle, Wash., Honolulu, Hawaii, and San Diego, Calif. At each of these places it is seen that there are two high and two low waters in a day. At Seattle, however, morning and afternoon high waters do not differ much while the morning and afternoon low waters differ strikingly. On the last day shown in Fig. 2, the afternoon low water was 10.5 feet higher than the morning low water. At Honolulu conditions are the exact reverse of those at Seattle, for at the former place the differences between morning and afternoon tides are exhibited principally by the high waters. It is of interest to note, too, that, during the last two days, the afternoon low waters at Seattle did not fall as low as sea level, while at Honolulu the morning high waters did not rise as high as sea level.
In contrast with conditions at Seattle and Honolulu, the tide curve for San Diego shows the differences between morning and afternoon tides to be exhibited in approximately equal degree by both high and low waters. The tide curve for San Diego looks much like that at San Francisco shown in the bottom diagram of Fig. 1. At the latter place, however, it is seen that there is a greater difference between the two low waters of a day than between the high waters.
Now it is a well-known fact that at any place the tide has local features with regard to times of high and low water, range of tide, or characteristics of rise and fall which distinguish it from the tide at other places. But in the tides represented in Figs. 1 and 2, time and range were disregarded, and the features considered were not minor differences but characteristics of a fundamental nature. In other words the tides at these places constitute distinct varieties.
The varieties of tides considered above do not, however, exhaust the variety in tides. In Fig. 3 are shown the records of the tides at Galveston, Tex., and at Manila, P.I., for the same four days of May, 1931. At Galveston for the first two days, there are two high and two low waters each day; but for the last two days, there are but one high and one low water a day. A characteristic feature of the tide during these last two days is the long stand of the tide which begins about four hours after high water, when for a period of about three or four hours the tide changes but little in height. At Manila there is a somewhat similar state of affairs; but whereas the stand of the tide here takes place on the rising tide, at Galveston it takes place of the falling tide. Furthermore, the stand of the tide at Galveston occurs above sea level, while at Manila it takes place below sea level.
On investigation it will be found that most tides can be referred to one or another of the varieties discussed above. Furthermore, it can be shown that these different varieties arise from different combinations of two primary constituent tides developing the tide-producing forces arising from the attraction of sun and moon, it is found that these forces have different periods, the principal ones being those having a period of a day and of half a day, respectively. The daily tide-producing forces give rise to a tidal constituent having a period of a day, and the semi-daily forces give rise to a tidal constituent having a period of half a day. And it is the varying combinations of these two constituent tides that give rise to the different varieties discussed. An example will make this clear.
Suppose that in a certain sea the tide-producing forces give rise to daily and semidaily tides with different ranges. If the semidaily constituent has much the greater range, it is clear that within that sea the tide will be much like that at Norfolk, morning and afternoon tides differing but little, and the tide will be of the semidaily type. If the range of the daily constituent is much the larger the tide will be like that at Pensacola with but one high and one low water in a day, or of the daily type.
But suppose that the two constituent tides have the same range, what is the character of the resultant tide? The rise and fall of each of these constituent tides may be represented as in Fig. 4, the semidaily constituent by the dotted curve and the daily constituent by the dashed curve. The height of the resultant tide at any moment is then clearly the sum of the heights of the constituent tides at that moment. In Fig. 4 the resultant tide is indicated by the heavy full-line curve.
Now the two constituent tides may combine in various ways in regard to time. In Fig. 4 three cases are considered. In the upper diagram the two constituent tides have such time relations that their low waters occur at the same time. The resultant tide in this case resembles the tide at Snaffle, the differences between morning and afternoon tides being wholly in the low waters. The middle diagram represents the case in which the high waters of the two constituent tides occur at the same time, and now the resultant tide resembles that at Honolulu, the differences between morning and afternoon tides being exhibited wholly in the high waters. Finally, the lower diagram represents the conditions resulting when the two constituent tides are at sea level at the same time. Now the resultant tide resembles that at San Diego, the differences in the morning and afternoon tides being exhibited in equal degree by both high and low waters.
It appears, therefore, that the varieties of tides represented by such tides as at Seattle, Honolulu, and San Diego arise from a mixture of daily and semidaily tides of approximately equal range. Such tides are known as the mixed type.
Tides in which a stand occurs, as at Galveston and Manila, can be shown to arise from a combination of a daily and a semidaily constituent in which the former has twice the range of the latter. If in the case represented by the lower diagram of Fig. 4, we take the range of the daily constituent twice that of the semi daily, it is found that the resultant tide will have but one high and one low water with a stand on the rising tide. If we take the two constituents such that are at sea level at the same instant but both rising instead of falling, as in Fig. 4, the stand will occur on the falling tide. And it is to be noted that both the daily and semidaily tide-producing forces vary in intensity from day to day, the former being greatest when the moon is at its semimonthly maximum north or south declination, and the latter being greatest when the moon is over the equator. It is in this varying relation of the magnitudes of the daily and semidaily tide-producing forces through a fortnight that we find explanation of tides which part of the time are of the mixed type and part of the time of the daily type.
The strikingly different characteristics of the varieties of tides discussed above have been traced back to the combination of daily and semidaily constituent tides of different times and ranges. The question that immediately arises is, why do the waters of the sea in different places respond differently to the tide-producing forces of sun and moon? For these tide producing forces are distributed in a regular manner over the entire earth.
To answer this question it is necessary to consider the physics of the movement, of bodies of water under the impulse of periodic forces. Briefly, it may be stated that a body of water has a natural period of oscillation which depends on the length and depth of the body of water. Furthermore, when disturbed by periodic forces that tend to upset its equilibrium, a body of water will respond best to that for the period of which most closely approximates to its natural period of oscillation.
The principal tide-producing forces of sun and moon, as has been noted before, are those having periods of half a day and a day, respectively. As these tide-producing forces sweep over the earth they put into oscillation the waters of the various oceanic basins. But the response of any given oceanic basin to these forces depends on its natural period of oscillation, which period is determined by the length and depth of the basin. Those basins whose natural periods of oscillation approximate to half a day respond best to the semidaily tide-producing forces; hence the semidaily constituent of the tide will predominate this and the tide in these basins will be of the semidaily type. Those bodies of water whose natural periods of oscillation approximate to a day will respond best to the daily tide-producing forces and thus give rise to daily tides. At the same time, those bodies of water, the natural periods of oscillation of which approximate to the semidaily forces as closely as to the semidaily forces, will respond in approximately equal degrees to both kinds of tide-producing forces and hence give rise to mixed tides.
The varieties of tides described above are those most frequently met with in the large world ports. There are places, however, where local hydrographic features give rise to peculiarities not found at other places. Along the open sea and in coastal bodies of water, the durations of rise and fall of tide are approximately equal. This gives the rising and falling portions of the tide curve a symmetrical appearance with regard to high or low water. In the upper reaches of tidal rivers, however, especially where there is considerable fresh-water discharge, this is not the case. Thus at Albany, near the head of tide water on the Hudson River, at times of freshets the tide may rise for three or four hours and fall for eight or nine hours. This gives the tide curve in such rivers a characteristic appearance, the rise being represented by a short steep line, while the fall is represented by a longer gently sloping line.
This feature in river tides is obviously due to the resistance of the river bottom and banks to the upstream progress of the tide. Furthermore, the drainage waters which find their way into a river give rise to a current that tends to flow downstream constantly. This acts as an added element of resistance to the progress of the tide upstream. And thus the duration of rise of tide is shortened, while the duration of fall is correspondingly lengthened.
In certain rivers the tide during a portion of its rise comes as a wall of water several feet in height. This phenomenon is known as a bore and is found to occur in the upper regions of tidal rivers having large ranges of tide, the channels of which are obstructed by bars and mud flats.
This may be considered as the limiting case of river tides, in which the steepness of the rising tide becomes so great as to become vertical during a part of the rise. In North America the best known bore is that occurring in the Petitcodiac River in Canada. The largest bore is probably that found in the Tsientang, a Chinese river which empties into the China Sea. In this river the bore comes as a wall of water ten feet or more in height, its front a sloping cascade of bubbling foam.
Throughout the world, with but rare exception, the sovereignty of the moon over the tide is clearly exhibited by the retardation in the times of high and low water by about 50 minutes each day. Thus in Fig. 1 it is seen that the first high water of May 28 at Norfolk occurred at six o'clock and that each day thereafter it came about an hour later. The other high water and also the low waters are seen to have occurred approximately an hour later each day. And at Seattle, with a totally different kind of tide, a similar retardation in the times of high and low water is seen to have occurred. This merely confirms the old adage that "the tide follows the moon." For the transit of the moon over any place occurs each day later by 50 minutes, on the average.
There are some places, however, where the tide appears to follow the sun rather later the moon. That is, instead of coming later each day by about 50 minutes, the tide comes to high and low water at about the same time day after day. Thus at Tahiti in the Society Islands, it has been known for many years that high water generally comes about noon and midnight and low water about 6:00 A.M. and 6:00 P.M. In fact, it appears that the natives use the same word for midnight as for high water. At Tahiti, therefore, the tide is solar rather than lunar.
The range of the tide at Tahiti is small, less than a foot on the average. A better example of the solar type of tide has recently come to light at Tuesday Island, a small island in Torres Strait, lying about 15 miles northwesterly from the northern point of the Australian mainland. Here the range of the tide averages nearly 5 feet. The peculiar behavior of the tide here with regard to time is clearly brought out if the tide curves for a number of days are arranged in column, as in Fig. 5, which represents the tide curves for each day of the week beginning September 10, 1925.
It will be noted that the high and low waters in this figure fall practically in a vertical line; which means that instead of coming later each day by about 50 minutes, which is the state of affairs at most places in the world, the tide here comes about the same time day after day. That this is not a general feature of the tides in the South Pacific Ocean is evident from a comparison with the tide curves for Apia, Samoa, for the same week, which are shown in Fig. 6. It will be noted that here there is a distinct shift to the right in regard to the times of high and low water in following down the curves.
The mathematical process of harmonic analysis Permits the tide at any place to be resolved into its simple constituent tides. At Apia the principal lunar constituent has a range of 2.5 feet, while the principal solar constituent has a range of 0.6 foot. Hence the tide here follows the moon. At Tuesday Island, the principal lunar and solar constituents both have the same range of 3.1 feet. Hence here the tide is no longer predominantly lunar but as much solar as lunar.
The answer to the question as to why the tide at some places is governed by the sun rather than the moon is again found in the physical characteristics of the various oceanic basins and seas. Where the conditions are such as to restrict the response to the lunar tide-producing forces but not the response to the solar tide-producing forces, the latter become the more prominent and give rise to solar tides.
An interesting form of tide is found at Job, in the Sulu Archipelago, Philippine Islands. Here the high waters follow the moon but the low waters appear to follow the sun. The tide curves for the week beginning September 10, 1925, at Jolo are shown in Fig. 7. The tide here is complicated by the fact that for part of the month there are two high and two low waters in a day, while at other times there is but one high and one low water. It is seen, however, that the high waters exhibit the distinct shift to the right characteristic of lunar tides, while the low waters lie almost perpendicularly under each other.
Because of the profound influence of the hydrographic features of a body of water on the movement of the waters in response to the tide-producing forces, various other peculiarities of the tide are found at different places. But the varieties discussed above constitute the more important and most generally found varieties of the tide.