When the navigator desires to ascertain the time or height of the tide at any place on a given day, he naturally turns to the Tide Tables. If the particular place he is interested in is an important world port, he is sure to find daily predictions of the times and heights of the tide for that port. But if the place is not of sufficient importance to warrant daily predictions, he will look for it in the back pages of the Tide Tables where there are listed in geographic order thousands of places, for which time and height relations are given with reference to the principal ports. These data permit him to make predictions for any of these ports very readily.
Such secondary predictions are generally quite accurate in regions for which there are daily predictions for a number of principal ports. Thus, along the Atlantic coast of the United States, the Coast and Geodetic Survey Tide Tables, Atlantic Ocean, give daily predictions for 21 principal ports. At the end of the volume are listed in geographic order more than a thousand other places along the coast and inland tidal waters, for each of which are given time and height differences and ratio of ranges with reference to some near-by principal port. The navigator can, therefore, derive satisfactory predictions for practically any point along that coast.
It must be noted, however, that in deriving satisfactory secondary predictions for any place by reference to a principal port, it is not so much a question whether the two places are near each other, as that they have similar types of tide. Along the Atlantic coast of the United States, for example, the tide at any port can generally be predicted with sufficient precision by reference to some principal port even several hundred miles away, because the tide all along this coast is similar in type.
On the shores of the Philippine Islands this is not the case. Places relatively close to each other may have such different types of tide that it is impossible to predict the tides at one place from the times and heights of the tide at the other place. As an example, Manila on the west coast of Luzon Island is almost exactly on the same parallel of latitude as Port Lampon on the east coast of the island. The air-line distance between these two ports is less than 40 nautical miles. How different the tides are at the two places is shown graphically in Fig. 1, which represents a week’s rise and fall of the tide. The horizontal line associated with each of the tide curves represents mean sea level.
At Manila, for the week shown in Fig. 1, there were two high and two low waters each day for the first three days, and for the following four days but one high water and one low water per day. At Port Lampon there were two high waters and two low waters each day throughout the week. Quite apart from any differences in the progression of time or range from day to day, it is obviously impossible to derive accurate predictions at Port Lampon by reference to the tide at Manila.
In this connection it must not be overlooked that in the expression “two high waters and two low waters a day” or “one high and one low water a day” the reference is to the tidal day which has an average length of 24 hours and 50 minutes, and not to the civil day of 24 hours.
Luzon is a rather large island, and while Manila and Port Lampon are close to each other by air line, they are on different sides of the island; so that it is perhaps not surprising that the tides at the two places are quite different. In the Sulu Archipelago of the Philippines, Simisa Island is a small island about 35 miles from Jolo on neighboring Jolo Island. Here, too, the difference between the tides is striking as the week of observations shown in Fig. 2 testifies. Both Simisa and Jolo are hundreds of miles from Manila and Port Lampon. Notwithstanding this, Simisa tides resemble the tides at Port Lampon more than they do those at Jolo, while the latter show a family resemblance to the Manila tides.
If we investigate the tide on the shores of the other islands, we find, likewise, decided differences in the character of the rise and fall. Thus, Fig. 3 pictures a week of tides at Zamboanga and Davao, both on the south coast of Mindanao Island. The changes in the tide from day to day are seen to be different at the two places, and therefore accurate secondary predictions cannot be derived by reference of one to the other of these ports.
From the examples cited, it is clear that the character of the tide in Philippine waters varies considerably from place to place. For the purpose of ordinary shipping the Tide Tables, Pacific Ocean and Indian Ocean, issued annually by the Coast and Geodetic Survey, carried daily predictions for two Philippine ports, Manila and Cebu. At the end of the volume were listed nearly 300 other places for which time and height differences and ratio of ranges, with reference to either one or the other of the above ports, were given.
Beginning with the Tide Tables for 1945, daily predictions are given for two additional ports, namely, Jolo and Davao. These two additional ports will make possible better reference stations for a number of places, so that by the use of one or other of the four reference stations, satisfactory secondary predictions are possible throughout the waters of the Philippines.
A comparison of tide curves covering a fortnight brings out the differences between the tides at different places much better than comparisons for a week. In Fig. 4 are shown the predicted tide curves for the four Philippine reference stations for the fortnight beginning January 1, 1945.
The tide at any place is characterized by the times of its high and low waters, by its range, and by its features of rise and fall. It is, therefore, literally true that the tide at any place is different from the tide anywhere else. Differences of time and range, however, may be considered merely as differences of degree, but differences in features of rise and fall are more deep-seated; in fact, they are differences in kind. And with regard to differences in features of rise and fall, it is customary to divide the tides of the seven seas into three large classes or types, namely, semidaily tides, daily tides, and mixed tides.
The semidaily type of tide is one in which the tidal cycle is completed in half a day, that is, there are two high and two low waters a day, with but little difference between morning and afternoon tides. The daily type of tide is one in which the tidal cycle takes a full day; in other words, in this type of tide there is but one high and one low water a day. The mixed type of tide is characterized by two high and two low waters a day, but with marked differences between morning and afternoon tides.
The tide at any place changes from day to day, month to month, and year to year in consequence of the changes in relative positions of sun, moon, and earth. Hence in assigning the tide at any place to a particular type, the reference is to the predominating tide at that place. Thus, of the tides pictured in Fig. 4, that at Manila is classed with the daily type, since the tide there is predominantly daily. The tide at Cebu is classed with the mixed type, since the morning and afternoon tides generally differ considerably, while the tide at Davao is classed with the semidaily type since, here, morning and afternoon tides generally do not differ much.
Type of tide is obviously the criterion used for determining to which reference station the tide at any secondary station is to be referred. And a glance at the list of secondary stations in the Philippine Islands in the 1945 Tide Tables reveals clearly that the tide in this region varies in type from place to place. For example, for the island of Mindanao some fifty places are listed. As reference stations it was found necessary to refer one to Jolo, four to Manila, fifteen to Cebu, and the rest to Davao.
Type of tide is also the clue to an understanding of the periodic changes in rise and fall to which the tide at any place is subject. But before discussing this, it will be of advantage to consider briefly the causes that bring about different types of tide.
Starting with the tide-producing forces of sun and moon, it is found that because the orbits of these heavenly bodies, with respect to the earth, are inclined to the plane of the equator, both daily and semidaily tide-producing forces arise. These tide-producing forces are distributed over the oceans in a regular manner, varying with latitude. But the response of an ocean basin to these tide- producing forces depends primarily on its length and depth. In certain basins, length and depth are such as to favor better response to the semidaily forces while in others the dimensions are such as to favor the daily forces. Furthermore, in moving from the large and deep oceanic basins towards the coast, friction affects the daily constituents of the tide differently than the semidaily constituents. As actually observed on the shore, therefore, the tide is made up of daily constituents and semidaily constituents the relative magnitudes and phases of which are different at different places. And it is these differences of relative magnitude and relative phase that determine the type of tide.
A detailed examination of the combination of daily and semidaily constituents, which would be out of place here, brings out the following facts: If the amplitude of the daily constituent is less than half that of the semidaily, there are two high and two low waters in the day with relatively little difference between morning and afternoon tides; if the ratio of the amplitudes of the daily to semidaily constituents is more than ½ but less than 2, there will be two high and two low waters a day, but with marked differences between morning and afternoon tides; if the ratio is more than 2 but less than 4, there will be either two high and two low waters or only one high and one low water in a day, depending on the phase difference between the constituents; and if the ratio is more than 4, there will be but one high water and one low water a day.
The tide curves shown in Fig. 4 furnish good examples of the different types of tide. It will, therefore, be of interest to see how their characteristic features result from the interaction of daily and semidaily constituents.
In the upper diagram of Fig. 5 the dotted curve represents a daily constituent tide with an amplitude (semirange) of 1.90 feet which comes to high water at 21h-50m, while the dashed curve represents a semidaily constituent with amplitude of 0.64 foot which comes to its high waters at 11h-52m and 24h-17m. The resultant tide at any time is simply the sum of the heights of the constituents at that time and is shown by the full line curve. This resultant tide, on comparing with the tides shown in Fig. 4, is seen to resemble closely the tide for the first day at Manila.
The lower diagram of Fig. 5 represents a daily constituent of 1.66 feet amplitude with high water at 21h-57m and a semidaily constituent of 0.56 foot amplitude with high water at 9h-33m and 21h-58m. The resulting tide resembles fairly closely the tide at Jolo for the first day shown in Fig. 4.
The very decided difference between the tides at Manila and Jolo is thus seen to arise primarily from the difference in phase between the daily and semidaily constituents. For the relative magnitudes of the daily and semidaily constituents at both places are very nearly the same. But whereas at Jolo the high water of the semidaily constituent comes almost exactly at the same time as the low water of the daily, at Manila the high water of the semidaily constituent comes about 2 ¼ hours after the low water of the daily constituent.
In the upper diagram of Fig. 6 the daily constituent has an amplitude of 1.98 feet and comes to high water at 22h-32m, while the semidaily has an amplitude of 1.40 feet with high water at 0h-16m and 12h-41m. Comparing the resultant tide with the tide at Cebu on the first day shown in Fig. 4 reveals close agreement between the two.
The lower diagram of Fig. 6 represents a daily constituent with an amplitude of 0.79 foot coming to high water at 17h-44m and a semidaily constituent with amplitude of 1.94 feet which comes to high water at 7h-12m and 19h-37m. The resulting tide is seen to be closely similar to the tide for the first day at Davao shown in Fig. 4.
If we calculate the ratios of the amplitudes of the daily to the semidaily constituents for the examples shown in Figs. 5 and 6, we derive the following figures: Manila, 2.97; Jolo, 2.96; Cebu, 1.41; Davao, 0.41. And referring back to the general discussion of the combination of daily and semidaily constituents, we see that since the ratio at Manila and Jolo is between 2 and 4, the tide at these places will at times be of the daily type. At Cebu the ratio is between ½ and 2 and therefore the tide is of the mixed type. At Davao the ratio is less than ½ and therefore the tide here is of the semidaily type.
Parenthetically it should perhaps be noted that in actually making the primary predictions for any port, a number of semidaily and a number of daily constituents must be taken into account. In the examples of Figs. 5 and 6 only one of each type was used, for the semidaily the principal lunar semidaily and for the daily a combination of the principal lunar daily and the principal solar daily. And that is why the curves of Figs. 5 and 6 deviate somewhat from the prototypes of Fig. 4.
Now the daily constituents of the tide depend in part on the declination of the sun but in much the larger part on the declination of the moon. The moon’s declination goes through a cyclic change in the period of a fortnight. When the moon is over the equator, the lunar daily constituents become small, while when the moon is at its semi-monthly northing and southing the daily constituents are at a maximum. The moon’s declination is further subject to a cyclic change in a period of 18.6 years, during which the declination at the moon’s northing or southing varies from a maximum of 28.6° to a minimum of 18.3° and back again to a maximum of 28.6°. As a result, the daily constituents of the tide at any place are subject to relatively greater variations than are the semidaily constituents.
Hence when we know the type of tide at any place, we know the character of the changes to which the tide at that place is subject. Where the tide is of the semidaily type, we know immediately that there are two high waters and two low waters a day with but little difference between morning and afternoon tides. Furthermore, the change in time and height of tide from day to day follows a relatively simple pattern. The times of high and low water become later each day on the average by about 50 minutes. The heights change principally with the change in the moon’s phase, the maximum ranges coming about the times of new and full moon and the minimum ranges about the times of the moon’s first and third quarters.
Where the tide is of the daily type the change from day to day is of a more complicated pattern than in the semidaily tide and varies in accordance with the phase and amplitude relations of the daily and semidaily constituents. The heights of the tide vary primarily with the change in the moon’s declination, the greatest ranges occurring about the times of the moon’s northing and southing and the smallest ranges about the times when the moon is over the equator.
In places where the mixed type of tide occurs there are as a rule two high waters and two low waters a day but with marked differences between forenoon and afternoon tides. In some places this difference is featured principally by the high waters, in others principally in the low waters, and in still others in approximately equal degree in both high and low waters, depending on the phase difference between the daily and semidaily constituents.
In the light of these general considerations, we can now summarize briefly the features of the tide at the four ports which are used as reference stations for the tides in Philippine waters.
At Manila the tide is of the daily type for a little more than half the time. The range of tide averages about If feet, varying through the month from less than half a foot when the moon is over the equator, to about 4f feet at the times of the moon’s northing or southing. During the periods when there are but one high water and one low water a day, the rise of the tide takes about 16 hours, while the fall of the tide takes about 9 hours.
At Jolo the tide is of the daily type about half the time. The range averages a little over a foot and varies from less than half a foot when the moon is over the equator to about 4 feet at times of the moon’s northing or southing. When the larger ranges of the tide occur, the fall takes about 8 hours, and is followed by a period of about 8 hours during which the tide is practically at a stand, after which comes the rise taking about 8 hours.
The tide at Cebu is of the mixed type, but with such large differences between morning and afternoon tides that occasionally there is but one high water and one low water a day. The range of tide averages about 3 ½ feet and varies in relation both to the moon’s phase and declination. At times of new and full moon the range becomes about 4§ feet, and at times of the moon’s northing and southing the smaller range averages about half a foot while the larger range averages 5 ½ feet. It follows, therefore, that at times when the moon is full or new and at the same time near its monthly northing or southing, the large range may be as great as 7 feet.
On the average the two high waters of a day at Cebu differ by about 2 feet, while the average difference between the two low waters is about 1 ¼ feet. At the time of the moon’s northing or southing these differences average, respectively, 3 feet and 2 ¼ feet. The tides of a day occur generally in the following order: higher high water is followed by lower low water then by lower high water and higher low water.
At Davao the tide is of the semidaily type with a range averaging about 4 feet, and varying from 5 ¾ feet at springs to 2 feet at neaps. The durations of rise and fall are approximately equal, averaging 6 ¼ hours each.
With the characteristics of the four reference stations known, the characteristics at any other Philippine port listed in the tide tables become known by noting to which reference port it is referred.