Elevation

Vertical Datum

Vertical measures of elevation are meaningful only as they are relative to some form of reference surface. This reference surface is often known as a vertical datum. Perhaps the most obvious and common datum to use in the context of measuring elevations over the earth's surface is the geoid. The U.S. National Geodetic Survey Geodetic Glossary defines the geoid as the “equipotential surface of the earth's gravity field which best fits, in a least squares sense, mean sea level.” Vertical measures of elevation above the geoid (usually measured 90° to the datum) are known as orthometric heights.

Both the modeling of the geoid and the spatial variation of the geoid across the earth are quite complex, largely due to variations in the density and resultant local gravity anomalies of the earth. Consequently, simpler local models of the geoid based on local sea level have been historically employed to establish a workable vertical datum for local areas. Of course, sea levels fluctuate, and the definition of what constitutes [Page 124]“sea level” usually refers to mean sea level (msl) established over a period of time. All measures of elevation relative to sea level, in fact, refer to mean sea level usually established at a single point, often termed local mean sea level (lmsl). For example, in Great Britain, vertical measures of elevation reported on maps are made relative to Ordnance Datum Newlyn (ODN). This is a time series of sea level variations measured by tide gauge for the period 1915 to 1921 at the port of Newlyn (Cornwall). In Ireland, the datum used is calculated in a similar way for a location at Malin Head (County Donegal). The North American Vertical Datum of 1988 (NAVD 88) is distinct in that although derived from sea level datum, it is a composite of various leveled locations across North America relative to a single point at Pointeau-Père (Québec, Canada).

Figure 1 Examples of Benchmarks Used in Great Britain

Source: Images courtesy of Ordnance Survey. © Crown Copyright. All rights reserved.

Of course, the direct measurement of all inland elevations relative to a single datum in a coastal location in this way would be rather impractical, even for a local area. Points of known elevation in relation to this datum are often established inland as a series of fixed, leveled benchmarks (see Figure 1).

An alternative vertical datum to use in place of the geoid might be some sort of more simplified geometric representation of the earth. The use of various ellipsoids of rotation (often abbreviated to ellipsoid) is common for this task. For example, such an ellipsoid is used as part of the World Geodetic System 1984 (WGS84) datum used for global positioning system (GPS) measurements. GPS satellites fix three-dimensional positions relative to the center of the earth; and vertical measures of elevation above the ellipsoid, so-called ellipsoidal heights, can be obtained in relation to this reference ellipsoid. Of course, vertical measures of elevation obtained this way are of limited use, particularly if they are to be associated with more traditional orthometric heights derived from maps and surveying. Ellipsoidal heights can be converted to orthometric heights in conjunction with an accurate model of the geoid (for example, the USGG2003 geoid model for locations in the United States). Typical GPS software usually incorporates a model of the geoid in order to allow transformation of ellipsoidal heights to orthometric heights.

...