1
Sea Level Dynamics

As discussed in the Preface, one of the more complex aspects of water boundaries is the dynamic nature of the land/water interface. A major cause of that variation is constantly changing water level. That fluctuation is due to a variety of causes including the tides, metrological conditions, and global sea level changes. Traditionally, sea level variations are classified by the period of variation, ranging from surface gravity waves with periods varying from 1 to 20 seconds; to seiches and tsunamis with periods of up to an hour; to astronomic tides with dominant periods of one‐half and one lunar day; to storm surges with periods ranging from a few hours to several days; to long term, apparently nonperiodic trends caused by geological and climatological effects with periods of thousands of years.

In addition to varying periods, sea level variations also vary considerably in amplitude. Variations range from those associated with seiches and surface waves with amplitudes as small as a few centimeters to tsunamis with amplitudes in the tens of meters.

1.1 Short‐Term Sea Level Variation (Other than Tides)

1.1.1 Surface Gravity Waves

Possibly the most noticeable sea level variations are surface gravity waves (Figure 1.1), which are generally called either wind waves or swell. Wind waves are the effect of wind on water and always travel in the same direction that the wind is blowing. Wind waves continuing for longer than a few hours gain sufficient energy to take on a distinct character known as swell, which move across open areas of water even though not under the influence of the wind. Wind waves generally have periods from 1 to 15 seconds. Swell has longer periods, generally between 12 and 25 seconds, and appears less steep than wind waves. Also, swell will not normally break in open water, while wind waves will often break.

Figure 1.1 Surface Gravity Waves.

The height of waves is usually expressed as the vertical distance from peak to trough. Since there can be considerable differences in height between individual waves in an area, another measurement used to describe heights is the significant wave height. That measure is the average height of the highest one‐third of waves over an observational period, generally about 20 minutes. Wave heights up to 30 m have been measured.

1.1.2 Seiches

Seiches are the periodic change in sea level that occur in enclosed waters and which are set in motion by some disturbance such as a strong wind, atmospheric pressure changes, or boat traffic. Basically, seiches represent water sloshing back and forth within an enclosed basin with periods ranging from a few minutes to a few hours depending upon the size of the basin. The amplitude of seiches is generally in the tenths of a foot range or less (Figure 1.2).

Figure 1.2 Prominent Seiche Superimposed on Tidal Variation for Typical Day, Isla Magueyes, Puerto Rico.

Source: www.tidesandcurrents.noaa.gov/NOAA/Public Domain.

Knowledge of seiches is important for the design and operation of harbors and other areas where berthing of deep draft vessels occur. In addition, knowledge of these variations is important in tidal studies since they can easily distort tidal measurements.

1.1.3 Storm Surges

As previously discussed, surface waves are created by the drag or stress of atmospheric wind on the sea surface. Changes in the level of the sea surface are also related to another atmosphere phenomenon called the inverse barometer effect. The combination of the effect of wind drag (which is proportional to the square of the wind speed) and effect of atmospheric pressure (which decreases sea level by one centimeter per millibar) can result in huge sea level surges being generated by storm systems, especially in shallow water bodies.

In simple terms, a mound of water can be produced by a storm moving across a water body. The storm wind moving cyclonically around the storm can push the water causing it to pile up as it approaches the shore. Since tropical storm winds have a counterclockwise motion in the northern hemisphere, the storm surge in that hemisphere is typically greatest in height to the right of an approaching storm. The height of a storm surge in a particular location depends on a number of different factors including storm intensity, forward speed, angle of approach to the coast, central pressure, and the shape and bathymetric characteristics of coastal features such as bays and estuaries, and the width and slope of the continental shelf. A shallow slope will potentially produce a greater storm surge than a steep shelf. As a result, a storm approaching an area such as the Louisiana coastline with a very wide and shallow continental shelf may produce a 20‐ft storm surge, while the same hurricane approaching the eastern U.S. coastline with a steeper continental shelf would result in a much smaller surge. Often, storm surges cause greater damage than the winds in a storm (Figure 1.3).

Figure 1.3 Storm Surge of Hurricane Katrina as Observed in Biloxi, MS (Note that the gauge was lost near the height of the storm surge).

Source: NOAA/https://tidesandcurrents.noaa.gov/predma2.html, last accessed 13 November 2023.

1.1.4 Tsunamis

A tsunami is a series of waves created by a displacement of the water column caused by an undersea disturbance of some type. That disturbance may be undersea earthquakes, landslides, volcanic eruptions, or even explosions or meteorite impacts. The period of the waves varies from minutes to greater than an hour, depending on the nature of the disturbance creating the tsunami. Once generated, the waves travel rapidly across the open ocean with a speed equal to the square root of the product of the water depth and the acceleration of gravity (9.8 m/s2), with speeds often over 620 kmph (IOC 2006). The wavelength may be as long as 80 km. At sea, the wave height may be less than a meter in height, so the waves are virtually unnoticeable at sea. Yet, as the tsunami waves approach shoaling water, the water piles up which creates waves as high as 30 m or more (Figure 1.4).

Figure 1.4 Tsunami Waves Resulting from the Japanese Earthquake of 3/10/2011, as Observed in Crescent City, California.

Source: www.tidesandcurrents.noaa.gov/NOAA/Public Domain.

1.2 Tidal Variation and Datum Planes

1.2.1 Tidal Cycles

Tides are sea level variations caused by the gravitational forces of the sun and moon as well as solar radiation. Tidal variations are cyclic and follow periodic patterns due to the cyclic nature of those astronomical phenomena. As a result, tides may be distinguished from other types of sea level variations.

The primary driving force of the tides is the gravitational pull of the moon as it rotates around the earth. Due to that force, there is an uplifting of the sea under the moon caused by its gravitational pull on the fluid water. On the side of the earth opposite the moon, the lesser gravitational force due to the greater distance to the moon and the centrifugal force caused by the earth’s spin causes a second higher water. Although interrupted by intervening land masses, these two high water waves, with their intervening low waters, follow the moon in its revolution about the earth and represent the primary constituents of the observed tide. Since one‐half of the average interval between consecutive transits of the moon is 12.42 hours, the moving high waters generally take the form of a sine wave with a period of that interval.

There is a similar, although somewhat lesser, effect on the level of the seas caused by the gravitational pull of the sun on water on the rotating earth. That wave may be represented as a sine wave with a period of 12.00 hours. Changes in sea level caused by several other relationships between the moon, sun, and earth may also be considered as sine wave constituents of the observed tide. For example, the elliptical orbit of the moon about the earth results in a constituent with a period of 27.55 days with highest water at the time of perigee (when the moon is closest to the earth) and lowest water when the moon is the greatest distance away. Also, there is a constituent period of one year associated with the declination of the sun.

When the constituent cycles associated with the cycles of the moon and sun are “in phase” (when the peaks are occurring at approximately the same time), tides with greater than normal ranges occur. Such is the case twice a month near the time of the new and full moon when the earth, moon, and sun are in a line. At those times, the constituent waves associated with the sun and moon are in phase and produce the so‐called spring tides. Much smaller neap tides are those which occur at the time of the quarter or three‐quarter moon when the sun and moon are at 90 degrees to each other as measured from the earth. Their respective following waves are then out of phase and result in smaller tidal ranges (Figure 1.5).

Figure 1.5 The Relationship Between the Semi‐diurnal Constituents of the Moon (M 2) and Sun (S 2) for a Spring Tide and a Neap Tide...