Over the greater part of the world, the tide rises and falls twice daily, giving two high and two low waters in a day. At Pensacola this is not the case, for here but one high water and one low water occur each day almost without exception.
In various other features, too, the tide at Pensacola differs strikingly from the tides commonly found in the seven seas. In Fig. 1 is shown the tide curve at Pensacola for the 4-week period August 1-28, 1941. The characteristics of the tide here are most clearly revealed if we compare the tide curve of Fig. 1 with the tide curve at some place washed by the tide of the Atlantic Ocean. In Fig. 2 there is shown the tide curve at Mayport, Florida, for the same period of August, 1941. Any other Atlantic coast port would serve as well, Mayport being chosen because it, too, is in Florida, and is nearly on the same parallel of latitude as is Pensacola.
In both figures the horizontal lines associated with the tide curves, from which the rise and fall of the tide is reckoned, represent the level of the sea for the month of August, 1941. The fact that at Mayport there are two tides a day, while at Pensacola there is generally but one, appears from a glance at the two figures. And while at both places there is seen to be a fortnightly cycle of increase and decrease in range of tide, these cycles are found on examination to be different at the two places. Thus, Fig. 1 shows that this cycle at Pensacola is from a maximum range on the 4th to a minimum on the 11th, then, to a maximum again on the 19th, and back to a minimum on the 25th. At Mayport, Fig. 2 shows the fortnightly cycle to be from a maximum about the 7th to a minimum on the 14th, back to a maximum on the 23d, and then to another minimum which comes on the 29th and falls just outside Fig. 2.
If we look into a Nautical Almanac for August, 1941, we find that the fortnightly cycle at Pensacola correlates with the moon’s declination. During that month the moon’s southing occurred on the 3d and the northing on the 18th, while the moon was over the equator on the 10th and 24th. And from the previous paragraph it is seen that the day following the moon’s northing or southing, Pensacola had its maximum tides, while the day following the moon’s crossing the equator the tides had their least ranges. For May- port, on the other hand, the fortnightly cycle correlates with the moon’s phase. In August, 1941, the Nautical Almanac shows that full moon and new moon came respectively on the 6th and 22d, and the moon’s quarters on the 14th and 29th.
An examination of long continued tide observations at the two places fully confirms the features with regard to the fortnightly cycle shown in Figs. 1 and 2. At Mayport this cycle is the familiar one of spring tides about the times of new and full moon, and neap tides about the times of the moon’s quadratures. At Pensacola the maximum ranges occur about the times of the moon’s northing and southing, and the minimum ranges about the times of the moon’s crossing the equator, the tides occurring at the former times being called tropic tides, and those occurring at the latter times being called equatorial tides.
Now, the fortnightly cycle of the moon’s phase has an average period of 14 ¾ days, while the fortnightly cycle of the moon’s declination has an average period of 13f days. Hence, during the period of a year, the days of maximum range of tide at Pensacola will come at different times in relation to the days of maximum range on the Atlantic coast.
Figure 1 also brings out the fact that for two or three days, at about the time the moon crosses the equator, the tide at Pensacola shows two high waters and two low waters a day. And this is a characteristic feature of the tide at Pensacola, which may be described briefly as a daily tide, except about the time when the moon crosses the equator when two small tides a day occur for a period of one, two, or three days.
The transition from one tide a day to two tides, and vice versa, is generally not very clearly marked. The tide curve for August 10 in Fig. 1 is a case in point. From early morning till 1:30 p.m. the tide was rising more or less regularly, and the high water at 1:30 p.m. is very definitely marked. But between 3:00 a.m. and 4:30 a.m. there is very little change in elevation, except that due to wave motion. On the original tide record, which is on a much larger scale than the tide curve of Fig. 1, it is possible to read a probable high water at 3:00 a.m. and a probable low water at 4:00 a.m., the two differing by 0.02 foot. Customarily, however, heights from the tide record are tabulated to the nearest tenth of a foot; for the surface of the water is generally disturbed by wind and wave, and the attempt to read with seeming greater precision would in most cases be largely fictitious.
In tabulating the high and low waters at Pensacola, it is therefore customary to tabulate a high or low water when its height differs by at least one-tenth of a foot from a preceding or succeeding low or high water. If it is less than a tenth of a foot, it is disregarded as a tide for the purposes of high and low water tabulation.
This procedure of disregarding tides with ranges of less than a tenth of a foot works very well as far as the tabulation of tides is concerned. But when it comes to determining mean high water, mean low water, and mean range of tide at Pensacola, difficulties appear. The first difficulty is the matter of definition. For example, mean high water at any place is defined simply as the average of all the high waters at that place over a sufficiently long period of time. Where there are two tides a day, as at Mayport, the determination of mean high water is, in principle, very simple. It is merely necessary to sum the heights of all the high waters over a sufficiently long period of time and then derive the average height.
But if we attempt to get the heights of all the high waters at Pensacola over a considerable period of time, we are immediately confronted by the fact that each fortnight there are periods of small tides during which it is difficult to decide which do and which do not constitute tides. The tide curve on August 10, previously considered, is a good example. Shall the possible high water at 3:00 a.m. be included in the determination of mean high water?
Then, too, there is a difficulty of a technical nature. The height to which high water rises at any place varies from day to day, month to month, and year to year within a cycle of 18.6 years. To base a determination of mean high water altogether on observations, it is thus necessary to secure a series covering a period of about 19 years. But in the case of tides like those occurring at Mayport, techniques have been developed by means of which sufficiently accurate determinations of mean high water may be secured from a year of observations or even less. These techniques depend on correcting the values derived from short series by use of simple factors depending on theoretical considerations. But for tides like those at Pensacola, the correction to mean values of results from short series of observations is extremely difficult if it is attempted to include all the high waters.
The tidal engineer has gotten round the difficulty by treating the tide at Pensacola as if it were always of the daily type. That is, for purposes of determining mean high water or mean low water, he disregards the secondary tides completely, and on days when there are two tides he uses the higher high water as the high water of the day, and the lower low water as the low water of the day. This procedure at once eliminates the question of whether or not the high waters of extremely small tides should be included in the determination of mean high water. And at the same time, it reduces the technical difficulties of correcting the results from a short series of observations to mean values.
With the above-described procedure of using but one tide a day in the calculations, the mean range of tide at Pensacola is 1.27 feet from a 19-year series of observations covering the period 1923-41. The yearly value of the range shows a distinct periodicity with a maximum average of 1.40 feet for the year 1932 and a minimum average of 1.12 feet for 1941. This periodic yearly variation in the range of tide correlates with the 18.6-ycar period of variation in the declination of the moon, the declination having been at its maximum in 1932 and at its minimum in 1941.
Since the sun also plays a part in the production of the tide, it is reasonable to look for some relation of the tide at Pensacola to the declination of the sun. Investigation proves this to be the case. To the sun’s yearly declinational cycle from vernal equinox to summer solstice and then to autumnal equinox and winter solstice, the tide at Pensacola responds in a cycle of increasing and decreasing rise and fall. Figure 3 shows this cycle graphically, as derived from the 19-year series of tide observations at Pensacola. The horizontal line, corresponding to the value of 1.27 feet, represents the mean rise and fall of tide at Pensacola, while the open circles represent the average rise and fall for the corresponding months of the year.
Figure 3 shows that during the year the rise and fall of the tide at Pensacola is least in March and September and greatest in June and December. Figure 3 further shows that the minimum of March and maximum of June are secondary, while those of September and December are the primary.
In 1932, the moon had its maximum declination. We should therefore expect that in December of 1932 at the time of the moon’s northing or southing to find the tide at Pensacola to have a considerably larger range than usual. From the Nautical Almanac, we find that in December, 1932, the moon had its northing on the 13th and its southing on the 26th. And from the tide record of Pensacola for that month, we find the range to have been 1.7 feet on the 13th and 2.2 feet on the 26th,
In the year 1941, the moon’s declination had its minimum value. And from Fig. 3 the range of the tide at Pensacola has its least value in September. On examining the tide record of Pensacola for September, 1941, we find that for the entire month the range averaged 0.96 feet. On the 7th and 21st of that month when the moon crossed the equator, the tide had a range of but 0.4 and 0.5 foot, respectively.
The variation in the rise and fall of the tide at Pensacola is thus very considerable. This variation is related primarily to the declination of moon and sun, rather than to the moon’s phase, as is the case with the tides in the Atlantic Ocean.
The question of why there is generally but one tide a day at Pensacola, and why the variation in rise and fall is related to the declination of the heavenly bodies, leads first to a consideration of the tide- producing forces. A mathematical development of the tide-producing forces of sun and moon shows that the principal forces are those having a period of half a day and a day, respectively. Furthermore, the tide-producing forces having a period of a day, vary with the declination of the heavenly bodies, being greatest when these bodies have their greatest declination and practically vanishing when the heavenly bodies are over the equator.
But the tide-producing forces of sun and moon, being of astronomical origin, are distributed over the earth’s surface in a regular manner, varying with the latitude. Then, why should these same forces bring about two tides a day at Mayport, which is practically on the same parallel of latitude as Pensacola, and only one tide a day at Pensacola?
The search for an answer to this question leads to a consideration of the movement of a body of water under the impulse of periodic forces. In brief, it may be said that each body of water, large or small, has a natural period of oscillation which depends on the length and depth of the body of water. And when acted upon by periodic forces that disturb its equilibrium, a body of water will respond best to that force the period of which most closely approximates to its own natural period of oscillation.
Now, as the tide-producing forces of sun and moon sweep over the earth, they put into oscillation the waters of the various seas and oceans. But the response of any given basin of sea or ocean to these tide- producing forces depends on its natural period of oscillation, this period being 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 tide-producing forces of half-day period, while those bodies of water whose natural period of oscillation approximate to a day will respond best to the tide-producing forces of daily period.
By means of the mathematical process known as harmonic analysis, the tide at any place can be resolved into its simple constituent tides. At Pensacola, the two principal constituents of daily period have together an amplitude of 0.82 foot, while the two principal constituents of half-day period have an amplitude of 0.08 foot. In other words, the daily constituents of the tide at Pensacola are more than ten times as large as the half-daily. At Mayport, on the other hand, the harmonic analysis shows that the daily constituents are less than one-fifth as large as the half-daily. And parenthetically it may be noted that while the ratio between the daily and half-daily constituents of the tide varies from place to place, all along the Atlantic coast of the United States the daily constituents are less than the half-daily.
Westward from the 85th meridian all along the north coast of the Gulf of Mexico, the daily constituents of the tide arc several times greater than the half-daily constituents. And this is likewise true for the western coast and for the western part of the southern coast as far east as Yucatan Peninsula.
Another feature of the daily constituents of the tide in the Gulf of Mexico that is of importance in this connection is that of time of tide. Investigation shows that the time of high water of the daily constituents is practically the same over the whole area of the gulf considered in the preceding paragraph.
If now we study the tides in the Caribbean Sea, we find that here, too, for the most part the daily constituents of the tide are larger than the half-daily. Furthermore in the Caribbean Sea, too, the time of high water of the daily constituents of the tide is practically the same for the whole sea. And as compared with the time of high water of the daily constituents in the Gulf of Mexico, this time is about 12 hours different.
This 12 hours’ difference in time of high water of the daily constituents as between the Gulf of Mexico and the Caribbean Sea leads to the inference that the gulf and the Caribbean form a single oscillating basin so far as the daily constituents of the tide are concerned. If this basin were of rectangular shape and of uniform depth, the natural period of its oscillation would be given by the formula 2L ÷ √gh, in which L is the length of the basin in the direction of oscillation, g the acceleration of gravity, and h the depth of the water. But with the actual irregularities of shape and depth of these two bodies of water, it becomes impossible to compute the period of oscillation from a simple formula. However, several investigators, after making certain simplifying assumptions, have found from theoretical considerations that the basin composed of the Gulf of Mexico and the Caribbean has an oscillating period of approximately 24 hours.
It appears, therefore, that the relatively large magnitude of the daily constituents of the tide at Pensacola, and the Gulf of Mexico as a whole, finds its explanation in the fact that the Gulf of Mexico and the Caribbean Sea constitute a basin whose depth and dimensions are such as to oscillate in a period of approximately 24 hours, and thus respond better to the daily tide- producing forces than to the forces with a period of half a day.