Sea Level And The Geoid

The planar-appearing ocean surface stands in immense contrast to that of the land, where the tallest mountain peaks are more than 8 km in elevation above sea level. Beneath the ocean surface, similarly tall mountains (called sea mounts) also exist, and the ocean depth at some great trenches is greater than the height of the tallest mountains. The almost featureless ocean surface thus has an obvious appeal as an elevation reference.

The ocean surface does exhibit some height variability. There are heating, circulation, and meteorological effects on the order of 1 m and in most areas the lunar and solar tides create a semi-daily sea level variation of a meter or so. (For a comprehensive treatise on tides, consult Pugh, 1987.) But computation of a useful mean value of sea level can be achieved over an interval by a simple averaging process. There are also trends in the level of the sea, but as noted, the long-term trend of sea level at the vast majority of the world's coastlines is at present only a few millimeters per year. This rate is so small that for some purposes, such as navigation, it is often ignored.

Using sea level as an elevation reference for the coast has an intuitive appeal, but what is meant exactly by "elevation above sea level" in the middle of a continent? The concept of a level surface gives the answer. A level surface is one on which the potential energy (including the centrifugal potential due to the rotation of the earth) is everywhere the same. There are an infinite number of these surfaces; the one chosen as the reference surface in geodesy is the geoid, which most nearly coincides with the ocean surface. If there were no ocean currents or atmospheric forces on the water, the ocean surface would coincide exactly with the geoid. (If it did not, the water would flow rapidly until it did.) On land the geoid can be thought of as a surface coincident with the water surface on a network of very narrow sea level canals. Then one's elevation above sea level is in essence one's altitude (measured along the line a plumb bob would take) above the surface of a fictitious underfoot sea level canal. The subject of physical geodesy is much concerned with the geoid and determining elevations relative to it from a combination of geometric and gravimetric observations. A curious reader should consult Heiskanen and Moritz (1967), a text highly regarded by geodesists, for the mathematical details of the subject. An example of a computed geoid is shown in Fig. 1.1 (see color plate). Detailed information about it is available at the NOAA Web site This Web site is a very rich source of information concerning regional and global geoids and their computation and interpretation.

In Fig. 1.1 variations of the geoid are shown with respect to an ellipsoidal reference surface (see below). This map illustrates that the geoid over the United States has variations of a few tens of meters and is correlated with the topography to a great extent. In the conterminous United States, the geoid variations (Fig. 1.1) range from a low of —51.6 m in the Atlantic (magenta) to a high of -7.2 m (red) in the Rocky Mountains. The role played by elevations relative to the geoid is important for a number of scientific and practical concerns. As an example of the latter, if water is to flow in the correct direction in pipes and canals, then the system must have a slope relative to the geoid. Concerning their scientific importance, these geoid variations reflect underlying geophysical phenomena. For an appreciation of the relation between geophysics and geodesy, see the survey volume by Lambeck (1988).

Geoid undulations, such as those shown in Fig. 1.1, can be considered heights of the geoid relative to a "best fitting" reference surface. This reference surface is most commonly an ellipsoid of revolution with the same center of mass and orientation as the geoid. Standard reference surfaces, chosen to most closely approximate the size and shape of the geoid, are selected and sanctioned by international scientific bodies (see Chovitz (1981) for an overview). Over the entire earth, geoid undulations (and hence the mean sea surface) have a root-mean-square variation of about ±35 m, with the most extreme excursions about three times as great. These large undulations are about two orders of magnitude greater than the so-called sea surface topography, the deviations of the sea surface from level (i.e., the geoid) caused by ocean currents and meteorological processes. Satellite altimetry, a relatively new and spectacularly successful measurement technique, has resulted in a revolutionary increase in knowledge of the marine geoid by directly observing the geoidal undulations of the sea surface with a satellite-borne radar ranging system. The technique has also proven capable of measuring the meter-level sea surface topography resulting from ocean currents and their variations and apparently even has the capability to determine the global rate of sea level rise with millimeter accuracy. A discussion of this remarkable technology is reserved for Chapter 6.

As already noted, the sea surface closely approximates the geoid. Deviations from the geoid due to ocean currents and wind forcing are only about 1% (== 1 m) of the maximum amplitude of the geoid undulations. Of course, the reason that the sea surface displays so little height deviation from the geoid is that water does not possess any shear strength. The crust of the earth in contrast possesses strength sufficient to support in part or whole the topographic variations of the land. But we shall see later in Chapters 2 and 4 that the earth's crust can deform, and did so by hundreds of meters under the weight of the great ice sheets that existed at the peak of the last glacial maximum 21,000 years ago. Even though those ice sheets melted at least by 5000-4000 BP, the earth did not completely adjust to the removal of the ice load by that time. It is in fact still adjusting from removal of the load by amounts that are significant compared to the contemporary rate of global sea level rise. This means that water level measurements reflect both the global change of sea level and any local subsidence or emergence of the land that is ongoing from the last déglaciation. This continuing glacial isostatic adjustment (GIA) is one of the most important issues in the interpretation of modern sea level records because it is highly variable geographically, and difficult to model. As an illustration, consider Fig. 1.2, which presents a contour plot of 20th century trends of sea level at 70 European sites derived from tide gauge records selected on the basis of data quality. Since there is not coverage over all 360 degrees of azimuth from the load center, contours to the northeast do not close and values there are unrealistic. But the obvious bullseye pattern demonstrates the relict GIA that follows the long-ago completed melting of the Fennoscandian ice sheet. Note that in the Baltic, contemporary sea level is actually falling up to 10 mm/yr. This area is the location of the center of the Fennoscandian ice sheet, whose weight caused the earth underneath it to sink and adjacent regions to uplift. Removal of the ice load was completed long ago, but the 20th-century sea level trends show that the area is still rebounding enough to cause a fall in relative sea level. The order of magnitude of isostatic readjustment on modern vertical motion of the land is important

Mean Sea Surface Geoid
Figure 1.2 Contour plot of 20th-century European sea level trends (mm/yr).

everywhere on the planet in comparison to global estimates of sea level rise and must be accounted for.

Sea level records are also contaminated by local and regional effects such as plate tectonics, extraction of underground fluids (gas, oil, water), or seasonal/ interannual oceanographic effects such as the El Niño phenomenon. All of these have the potential to obscure or hide the long-term global rate of sea level rise.

Chapter 1 An Introduction to Sea Level 7

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  • juliane
    How does geoid affect sea levels?
    7 years ago

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