July - September 2003
Frequently research and technology endeavors have unforeseen but positive outcomes. When European explorers set out to find a shortcut to India, they discovered the New World. When a staphylococci bacteria culture was mistakenly contaminated with a common mold, the clear area between the mold and the bacterial colony led to the conclusion that the mold, Penicillin notatum, produced a compound that inhibited the growth of bacteria. This chance discovery led to the development of the antibiotic penicillin.
That the earth does not have a geometrically perfect shape is well established, and the geoid is used to describe the unique and irregular shape of the earth. However, only recently have the more substantial irregularities in the surface created by the global mean sea level (MSL) been observed. These irregularities are an order of magnitude greater than experts had predicted. Controlled by the gravitational potential of the earth, these irregularities form very gentle but massive "hills" and "valleys." This astonishing finding was made possible through the use of GPS, a technology designed by the United States Department of Defense to revolutionize navigation for the U.S. Navy and Air Force. GPS has done thatand a lot more.
What Is Mean Sea Level?
For generations, the only way to express topographic or bathymetric elevation was to relate it to sea level. Geodesists once believed that the sea was in balance with the earth's gravity and formed a perfectly regular figure. MSL is usually described as a tidal datum that is the arithmetic mean of hourly water elevations observed over a specific 19-year cycle. This definition averages out tidal highs and lows caused by the changing effects of the gravitational forces from the moon and sun.
MSL is defined as the zero elevation for a local area. The zero surface referenced by elevation is called a vertical datum. Unfortunately for mapmakers, sea level is not a simple surface. Since the sea surface conforms to the earth's gravitational field, MSL also has slight hills and valleys that are similar to the land surface but much smoother. However, zero elevation as defined by Spain is not the same zero elevation defined by Canada, which is why locally defined vertical datums differ from each other.
The MSL surface is in a state of gravitational equilibrium. It can be regarded as extending under the continents and is a close approximation of the geoid. By definition, the geoid describes the irregular shape of the earth and is the true zero surface for measuring elevations. Because the geoid surface cannot be directly observed, heights above or below the geoid surface can't be directly measured and are inferred by making gravity measurements and modeling the surface mathematically. Previously, there was no way to accurately measure the geoid so it was roughly approximated by MSL. Although for practical purposes, at the coastline the geoid and MSL surfaces are assumed to be essentially the same, at some spots the geoid can actually differ from MSL by several meters.
GPS has transformed how altitude at any spot is measured. GPS uses an ellipsoid coordinate system for both its horizontal and vertical datums. An ellipsoidor flattened sphereis used to represent the geometric model of the earth.
Conceptually, this precisely calculated ellipsoid, called an oblate ellipsoid of revolution, was intended to replicate the MSL as the main geodetic reference or vertical datum. If this ellipsoid vertical datum is used, height above the ellipsoid will not be the same as MSL and direct elevation readings for most locations will be embarrassingly off. This is caused, in part, because the GPS definition of altitude does not refer to MSL, but rather to a gravitational surface called the reference ellipsoid. Because the reference ellipsoid was intended to closely approximate the MSL, it was surprising when the two figures differed greatly.
The TOPEX/POSEIDON satellite, launched in 1992, was specifically designed to perform very precise altimetric observations. These measurements have demonstrated that neither human error nor GPS inaccuracies are responsible for the sometimes substantial discrepancies between ellipsoid and MSL measurements. In fact, the three-dimensional surface created by the earth's sea level is not geometrically correct, and its significant irregularities could not be mathematically calculated; this explains the difference between the ellipsoid-based GPS elevation readings and elevations shown on accurate topographic maps.
A brief examination of elevation readings for Esri headquarters in Redlands, California, demonstrates these differences. The campus elevation is shown on topographic quadrangle maps and high-resolution digital elevation models (DEMs) for the area as approximately 400 meters above MSL. However, a precise, nonadjusted GPS reading for the same location typically shows the elevation as 368 meters.
Why is there a 32-meter difference? The GPS receiver uses a theoretical sea level estimated by a World Geodetic System (WGS84) ellipsoid, which does not perfectly follow the theoretical MSL. The MSL, approximated by an ellipsoid, is related to gravity or the center of mass of the earth. Discrepancies between a WGS84 ellipsoid, and the geoid vary with location. To continue with this example, elevation readings for Yucaipa, a city located less than 10 miles east of Redlands, differ by 31.5 meters.
Continued on page 2