The large differences in the tidal ranges of the various portions of San Francisco Bay have never been satisfactorily explained. By use of the principle of secondary oceanic oscillations, as outlined in “Bay of Fundy Tides” in the May, 1938, issue of the Naval Institute Proceedings, a rational solution of the tidal phenomena of San Francisco Bay, as well as the Gulfs of Panama and California, will be given.
As in the reference article, the groundwork for the entire discussion was laid by the late Dr. Rollin A. Harris, of the U. S. Coast and Geodetic Survey. Figure 1 shows the oscillating systems of the North Pacific Ocean for the semidaily and the daily tide-producing forces as conceived by Harris. The Roman numerals refer to the time, in lunar hours, of high water in the several areas after the Greenwich meridian passage of the moon. The dashed lines represent the nodal lines around which the tides oscillate with a stationary wave movement, in which the tide is high on one side of the node when it is low on the other. The most familiar example of a stationary wave movement is the oscillations produced when a partly water- filled tray is raised at one end and quickly lowered.
There are two semidaily systems shown, one a complicated arrangement of bi-nodal oscillations and the other a uni-nodal system operating from the coast between Lower California to Cape Mendocino to the Polynesian Island Groups, with a node line approximately halfway to the Hawaiian Islands and paralleling the American coast. The times of high water in this system are VI and XII.
The bi-nodal system has high water at III and IX. The III area embraces the greater portion of the central Pacific basin, with the IX areas adjacent to the American and Asiatic coasts. One node extends south-southwestward from the vicinity of Acapulco, Mexico, another from the vicinity of Pt. Arguello toward the western-most of the Aleutian Islands, and a third southeastward from Japan.
Since the tides of the northern portion of the Pacific Ocean are chiefly of the mixed type, requiring a daily component, an oscillating area capable of supporting a daily tide, a brief description of such a basin is given, based on the findings of Dr. Harris.
For the North Pacific Ocean there is only one system as shown in Fig. 1. It extends from the coast of North America northward of Pt. Arguello to the Aleutian Peninsula. The opposite side is formed by the chain of islands from the Philippines to the Solomons. The node line, shown dotted near the middle of the basin, extends from the vicinity of the Hawaiian Islands to the Chishima (Kurile) Islands.
Figure 2 shows the oceanic region from the vicinity of Cape Flattery to the northwestern coast of South America, together with the mean tidal ranges of the various places as given in the U. S. Coast and Geodetic Survey Tide Tables for the Pacific Ocean; also a larger scale insert map of San Francisco Bay. The positions of the nodal lines as portrayed by Dr. Harris for the oceanic areas are authenticated by the ranges of the tide along the coasts as shown. At Acapulco, near the southern node, the tidal range is 1.6 ft., while to the southward in the Gulf of Panama ranges of 12.5 ft. are found, and 5.9 ft. at Cerros Island, on the Lower California coast, to the northward, falling again to 3.5 ft. in the vicinity of the Pt. Arguello node, and increasing again northward, with 7.4 ft. in South San Francisco Bay.
However, the large variations in the ranges cannot be explained by adhering entirely to these basic concepts, and additional facts must be found satisfactorily to account for these large variations in ranges.
The secondary semidaily oscillations shown in Fig. 2 furnish these data. Operating between the Gulf of Panama and the Gulf of California is an additional narrow band of oscillating water which has nearly the same node as the oceanic system (Acapulco), with the loop ends at the heads of the two gulfs. The southern end of the band has a broader base, covering a rather extensive portion of the coast, so that the ranges here are not so great (10.0-12.6 ft.) as found at the head of the Gulf of California (21.6 ft.).
The very deep trough lying close inshore for almost the entire distance between Panama and the Gulf of California offers itself as the oscillating basin, and, on account of the great depths on the southern portion, the position of the node is moved towards Manzanillo, which then accounts for the uniformity of the tidal range for the coast between Acapulco and Manzanillo, and explains the presence of some tide at node points through slight interference of the two oscillations.
The other secondary semidaily oscillation also operates over the oceanic node (Pt. Arguello) and has its loop ends in San Francisco Bay to the north and Viscaino Bay to the south. Since the times of the tides are about 6 hours apart, the much shorter distance of the northern portion of the area should be explained to readers not familiar with tides. The period of a stationary wave is found from the formula
From these considerations, it is easily seen that the shoal waters of San Francisco Bay, beginning at the bar, introduce a small quantity for d in the denominator, resulting in a relatively large computed value for T (6 lunar hours).
The water surface of the area close to shore under the influence of the additional oscillations is shown schematically. The tide produced by the VI-XII system of Dr. Harris is not included since, being 3 hours different, it produces approximately half tide when the other oscillations are producing high or low water. It should be noted that the presence of secondary oscillating areas affects the mean sea level heights of contiguous shore areas (the only places where tide heights can be measured with any degree of precision) and thus accounts for the mean sea level differences as found by the U. S. Coast and Geodetic Survey with its precise leveling work. At the same time it makes manifest the incongruity of its method of controlling the precise level work by adjusting the level nets to so-called “mean sea level” as determined at various coastal and bay points.
In San Francisco Bay, the southern portion is best adapted by the prevailing depths to accommodate the stationary wave. Elsewhere, the farther reaches of the sloughs of the several parts of the bay also furnish the better time factor and ranges almost as great as in the south bay are found.
Figure 3 shows the tide curves reconstructed from hourly heights for 5 days for the primary tide station at the Presidio and another station at Dumbarton Bridge, furnished through the courtesy of the U. S. Coast and Geodetic Survey.
Since there must be a time difference between these places, the curves have been superimposed to show the difference in the secondary seiche factor of the tide at the two stations. Note that the seiche is constant at all high and low waters, regardless of the position of tide-producing bodies.
This constancy, shown for longer periods by the similarity of the diurnal inequalities, indicates that the secondary oscillation is rather independent of varying astronomic influences, although undoubtedly caused by the sun and moon.
The frequently made conjecture that the increase in range in South San Francisco Bay is caused by the funneling effect of the shore lines is without foundation as can be shown by comparison with the upper portions of the Bay of Fundy, where contraction effects are known to occur. From Tides at the Head of the Bay of Fundy by W. Bell Dawson, 1917, the ratio of the increase in range at Burntcoat Head, in the eastern arm of the bay, for the series of tides measured, over simultaneous tides at St. John, New Brunswick, was 2.04. However, while the diurnal inequalities of the tides are similar for Boston, Massachusetts, at the approach to the Bay of Fundy, where the mean range is 9.1 ft. and at St. John, well into the bay, mean range 20.1 ft, the rate of increase in the diurnal inequalities when greatest between Burntcoat Head and St. John was 1.4 for both the high- and low-water inequalities.
This indicates a contraction increase in the tide range, due to the shore-line convergence beginning somewhere beyond St. John, of 40 per cent of the range increase, the balance being the secondary oscillation range increase due to the closer proximity of Burntcoat Head to the loop end of the oscillating basin.
In contrast, there is no variation in the high- or low-water inequalities in South San Francisco Bay, thus precluding the probability of a contraction increase, so that the tides must enter and leave practically unimpaired.
This method of comparison of the diurnal inequalities affords an excellent criterion for the determination of range increases due to contraction since the funneling effect must take place for the full rise of the tide and thus becomes a function of the rise, thereby changing the inequalities between the original tide waves. For stations having semidaily tides, the comparison must be made with the tropic tides, when the differences are greatest.
Since the exchange of water implies currents, it should be noted that their strength is always greatest at the nodes; we therefore have a tidal current, reversing every 6 hours, in the vicinity of Pt. Arguello and Acapulco. No data are at hand for their velocities.
The rotational effect of the earth on all moving bodies is well exemplified in the variations in ranges between places on the right and left banks (with respect to the current direction) in the Gulf of California and San Francisco Bay. Since the deflection is to the right in the Northern Hemisphere, the flood tide will be deflected to the right, making the high waters higher, while the ebb tide, opposite in flow direction, will also be deflected to the right, making the low waters higher on the left bank and thereby effecting a greater range on the right bank.
The possibility of other seiches on the southern secondary loop is apparent from the variation in range at several points, but data are so sparse that a search to isolate them is not warranted.
Several tidal puzzles of long standing are easily solved in the light of this new concept, including the continuous seiche in Los Angeles Harbor, the rotary tidal currents found off the coast, the increases in the ranges in the various bays of Southern California, and variations in mean sea level.
The secondary oscillation, riding the primary tidal oscillation, produces differences in water height between the narrow band and the adjacent waters. Since the band passes close outside the Channel Islands off the Southern California coast, the differences in head existing between the band and the basin produced by the partially submerged San Nicholas range and the shore keeps this basin in continuous oscillation. At only four times every tidal day are the waters of the “band” and the basin (were there no additional seiches therein) at the same level so that there is a constant source of tidal energy to keep this basin in continuous oscillation. The seiches as found in Los Angeles Harbor are then “part and parcel” of the tide. Figure 4 shows these seiches on a portion of a typical marigram for Los Angeles Harbor, as well as a weekly record from another gauge which reads from right to left. This record shows the magnitude which the seiches reached when the tidal wave produced by the seaquake in the vicinity of the Aleutian Islands on November 10, 1938, impinged on the outer rim of the basin. This wave, when it reached Honolulu, produced there a tide of 0.5 ft. in height, with one smaller recurrence imperceptible at San Francisco. When this wave, probably no greater than at Honolulu, added an extra impulse to the sensitive Los Angeles Harbor basin, the hourly oscillations at times reached 2.5 ft. from trough to crest and retained their violence almost unimpaired for two days, then began to diminish in amplitude, and wore themselves out in about 10 days. Naturally, with this rapid change in water height, strong currents were experienced in the harbor and several ships had difficulty in mooring.
Furthermore, the additional pressure from the “band” passing close to shore forces the waters to rise to a greater height in the bays opening on the coast along which the band operates. The bays act as water barometers and respond to the increases in pressure (additional head) by a corresponding increase in water height within the bay. It thus accounts for the increases in range or superior high-water heights found in San Diego Bay, Newport Bay, and Los Angeles Harbor in comparison with the ranges at the entrances to these bays. Naturally, as the node is approached, the differences in pressures becomes less so that a greater increase in range should be expected in San Diego Bay than in bays northward, other features being considered equal.
Also, the pressure differences functioned to better advantage to increase ranges during the time when Los Angeles and Long Beach Harbors were not sheltered by breakwaters, which act as barriers and nullify the former tendency to have greater ranges in the bay than on the open coasts.
The Bay of Fundy-Maraca Island (Brazil) secondary oscillation off the Atlantic coast of the United States produces similar range increases in the bays where the entrance area (in relation to the bay area) is large enough to permit the ingress and egress of sufficient water so that the pressure differences can function. The branching of the streams in San Francisco Bay is analogous to the branch of the Bay of Fundy secondary oscillation which enters Long Island Sound and produces there a tide practically similar to that in the Bay of Fundy, except for the ranges. This similarity is seen by comparing the published predicted tides for stations near the heads of the two oscillating areas, St. John, New Brunswick, for the Bay of Fundy, and Willetts Point, New York, for Long Island Sound, keeping in mind that hydrographic features affect both times and heights.
The range increases in various bays along the Atlantic coast are only partially due to the pressure differences. Part of the increase, as previously shown, is caused by hydrographic features of the coast, such as tunneling, direction of the bay opening in relation to the advancing tide wave, size of opening in relation to the bay area, etc. Examination of the diurnal inequalities, when greatest, for ports for which predicted tides are available, discloses the increases at the heads of embayments. Since the primary tides on the Atlantic coast of the United States are simple and alike for the entire coast, the inequalities should be alike, but those for such ports as Tybee Roads (entrance to Savannah, Georgia) and Mayport (entrance to Jacksonville, Florida) near the head of the coastal embayment are greater than at Wilmington, North Carolina, near a coastal salient of the embayment, indicating a contraction rise.
These secondary oscillations, while deduced purely from theoretical considerations, offer satisfactory answers for so many features of tidal phenomena in the region covered which heretofore had been unexplained, that their existence may be considered proved.
Furthermore, the validity of Dr. Harris’ stationary wave theory of all tidal phenomena is likewise further demonstrated by these findings.