From Ocean Navigator #54 June/July 1993
Tides can have a very real effect on the mariner,especially low tides. Knowing what causes tides and how to calculate their extent can greatly benefit the coastal sailor.
Perhaps few natural phenomena are so well documented as the rising and falling of the tides. Some locations have tidal records going back more than 100 years. Oceanographers have been able to take this tidal data and correlate it to the actions of the moon and the sun and other natural phenomena. This has allowed them to confidently predict future tides based on the reoccurrence of these natural phenomena. Tidal predictions, therefore, tend to be based on extrapolations from the record of tidal activity in the past rather than precise knowledge of every tidal factor.
Today, physical oceanographers have developed a much great understanding of the forces that dictate the tides. However, like meteorology, some of the finer points of tidal behavior are hard to precisely quantify.
There are two basic tidal patterns and a large gray area of mixing between those two. A place with two high tides and two low tides of equal size each day is said to have a semidiurnal tide. Those with only one high tide and one low tide have a diurnal tide. Diurnal is a fancy way of saying daily cycle. A diurnal tide completes one full cycle per lunar day, about 24 hours and 50 minutes. A semidiurnal tide completes a cycle in one half of a lunar day.
Although there are many modifying factors that influence tides, the primary motivating forces are the moon and sun. Of these two, the moon has a greater effect and it is for that reason that most tides operate on a lunar day.
As the Earth and the moon weave through space, they form a gravitational system. The gravitational center of this system is not at the center of the Earth, but is actually a point (called the barycenter) between the center and the surface. With the barycenter offset, and since the Earth/moon system is revolving around this common point, centrifugal force becomes a large factor in producing tides. Any point removed from the center of a spinning object is accelerated outwards. Given a constant rotational speed, the farther from the center a point is, the faster it moves and the greater the outward acceleration. The point on Earth opposite the moon, the antipodal point, is also the point on Earth farthest from the barycenter and, therefore, the spot with the greatest outward acceleration. Ocean water moves toward this area of greater outward acceleration, creating a bulge of high water.
Interestingly, the area directly under the moon also has a bulge of high water. This occurs because the relatively weak centrifugal acceleration (weak because this point is fairly close to the barycenter) is supplemented by the gravitational pull of the moon. Because water on this side of Earth is closest to the moon, the gravitational effect is larger here than at other places on Earth—water is drawn to this side from areas experiencing less gravitational pull.
The result of these effects is the formation of two tidal bulges, one under the moon and the other on the opposite side of the Earth from the moon.
The sun has a similar, but far smaller effect (about 45% that of the moon). Thus, when there is a half moon,sun and moon are aligned at right angles relative to Earth, the effect from the sun will partially offset that from the moon, resulting in smaller tide differences. These are called neap tides. At both full moon and new moon, when the sun, moon and Earth are in line, the effects of the sun and moon are added, producing large, spring tides. Even at spring tides, the total tidal force is at most only one ten-millionth of Earth's surface gravity.
These are just the most obvious effects of the sun and moon. As all celestial navigators are aware, the declination of the moon changes significantly during the course of a month. This has a substantial effect on the type of tides experienced. When the moon's declination is fairly large, the effects generated by its presence no longer act along the equator. Instead, its strongest pull is along the latitude directly under it (the latitude that corresponds to its declination). This has an interesting result. Take, for example, a location at 25 deg; N when the moon has a 25 deg; N declination. At meridian passage of the moon, with the moon directly overhead, there will be a particularly high tide. However, about twelve and a half hours later the high tide will be much lower. The moon will, indeed be about 180 deg; of longitude from the original location and its declination still 25 deg; N. However, the antipode is now 25 deg, about 50 deg away from the location at 25 deg; N. The outward acceleration of water will be less concentrated at this location. This case where the moon has a high declination is called a tropic tide; tides when the moon's declination is close to 0 deg; are equatorial tides. In some locations the effect of a tropic tide is so great that the second high tide disappears and the location experiences diurnal tides.
It is not only moon's movement north and south which effects tides. The proximity of the moon to Earth also makes a contribution. At its closest point to Earth, called perigee, the moon will have the greater effect, causing more extreme tides. When the moon is at apogee, the point in its orbit farthest from Earth, its effect on tides will be less. Earth's elliptical orbit around the sun produces similar effects, but on a much smaller scale.
Despite tidal anomalies caused by the moon's movement north and south or closer and farther from Earth, the moon's position in its daily orbit can often be used to predict the time of a high tide. Common sense would indicate that at the moon's meridian passage, the tide should be high. Twelve hours and twenty-five minutes later, when the moon is on the opposite side of Earth, another high tide will occur. In practice, local topography has a substantial effect of advancing or delaying tides. Still, semidiurnal high tides are keyed to this pattern. Traditionally, many charts carried a correction which could be applied to the time of lunar meridian passage to determine the time of tides.
In fact, tide height is a variable which has more to do with local topography than with movements of celestial bodies. The Bay of Fundy, for example, has tides ranging to 50 feet. This is not because of an extraordinarily strong effect of moon and sun, but rather the shape of the underwater basin. Each physical system has a natural frequency at which it will oscillate when disturbed from a rest position (until friction brings it once more to rest, that is). This frequency is called the system's free oscillation. When the system oscillates at a frequency imposed by an outside source it is a forced oscillation. In most cases, the natural frequency of an area will not correspond to the frequency of the tidal driving force. However, when the frequency of the driving force is close to the natural frequency of the system, a large amplitude response may be obtained with the input of relatively little energy. This is called resonance and can produce large tides. It turns out the Bay of Fundy system is nearly in resonance with a semidiurnal tide. One of the most graphic examples of this can be found in a bathtub. A bather can create small waves by moving a hand through the water either rapidly or slowly. However, there is an intermediate speed at which the hand moves up and down (or back and forth) in resonance with the tub. Large waves can be created that will slop soapy water out of the tub and on to the floor.
This local topography can magnify different effects of moon and sun and change the frequency of tides. For example, some locations—like Unalaska, AK, or Galveston, TX, have tides that are predominantly semidiurnal but have a few diurnal tides in the course of a month. Others, especially on the West Coast, feature semidiurnal tides where one high and one low each day are much less extreme than others. On much of the Gulf of Mexico coast, tides are often diurnal. The truly exotic tides, however, tend to occur in exotic places. There are locations in Indonesia and other South Pacific islands where the tide adheres to the solar day, with high and low tide occurring at the same time each day.
Given all of the possible combinations and variations to consider, it is fortunate that information about tides is easily available. Tide heights and times can be obtained by the use of tide tables. These are available from many sources, both public and private. A number of computer prediction programs are available. Some of these have predictions for a vast number of locations. One nice feature of some programs is a graphical display that shows the rise and fall of tides.
NOAA publishes tables that cover thousands of stations throughout the world. These have a format that is similar to many other tables and have additional useful information often lacking in more limited compilations. The tables list a relatively small number of reference stations. Data for these stations includes the times of high and low tides as well as the height of water relative to local chart datums. This is great for those times when one is near the station, but what about all of the coastline, hundreds of miles in many cases between stations? These are covered by long lists of secondary stations in the back of the volume. Each secondary station has four differences or factors listed. These factors are corrections to, respectively, times of high tide, low tide, height of high tide and height of low tide.
The time differences are added or subtracted to the time listed at the appropriate reference station. The sign is printed with the hour and minute difference. Determining height of tide is only slightly more complex. It is usually listed as a ratio. This ratio is multiplied by the height of tide at the reference station to yield a tide height at secondary station.
Often supplementary information is also included for each station. Ranges for mean tide and spring tide are just that—the range between high and low tide. The mean tide level is the mean height between mean high and mean low. (As the mean of two means, it's about as mean a tide as possible.)
Armed with the time and height of high and low tides, it is also possible to determine the height of the tide at any intermediate time or, to put it another way, the time of any intermediate height. Unfortunately, a straight interpolation will not work here because tide rises and falls fastest midway between high and low tide and changes relatively slowly at high and low tide. The simplest method of determining the difference is to use table 3 in the back of the NOAA tide tables. Just enter this table with the time difference between low and high tide, the time difference between the nearest tide and the time in question, and the total height difference. The result pops out. Lacking this table, it is possible to construct a graph to provide the same information. Both of these presuppose that the rate of a rising and falling tide follows a cosine curve.
With the aid of a simple scientific calculator, this can also be accomplished by a navigator using tide information from any source. While the formula may seem a little involved, it is one of those things that can be written in a nav workbook or even taped to the cover of the calculator.
Here, h is the total change in tide height between high and low tide. The time ratio is the time elapsed from the previous tide divided by the time difference between the two tides.
Take a look at an example: Given a high tide at 1324 and a low tide at 1844, where the tide fell six feet in that interval, what is the tide height at 1745? To start with, six feet here, divided by two is three. To find the time ratio it is first necessary to find the time elapsed from the previous tide: 1745 - 1324 = 0421. Next, find the total time between high and low: 1844 - 1324 = 0520. Finally, divide the first by the second: 0421 ÷ 0520 = .816. This is the time ratio. Multiply 180 deg; by .816 and get 146.8 deg;. The cosine of 146.8 deg is -.8369, which must be subtracted from 1. 1 - (-.8369) = 1.8369. Finally, multiply this 1.8369 by three (h ÷ 2) and get a 5.5 feet drop from high tide.
Interestingly, similar numbers can be extracted using an old seaman's rule of thumb: the rule of twelve. This states that in the six hours between tides the level will change one-twelfth in the first hour; two-twelfths in the second hour; three-twelfths in the third and fourth hours; two-twelfths in the fifth hour and one-twelfth the last hour. This provides a quick, rough approximation.
In many cases, proper evaluation of tidal conditions allows a mariner the opportunity to safely navigate areas that in other tidal conditions might be dangerously shallow.