The topic of units deserves particular attention when discussing concepts of physical geodesy. Spatial data users are primarily concerned with distance units (meters, feet, etc.) as related to location and elevation. However, when building on fundamental physical concepts, the physical separation between two equipotential surfaces is defined in terms of work (i.e., force x distance). The following definitions presume an understanding that gravity is the force part of “work” and that elevation difference is the distance part. The following definitions are intended to be consistent with common usage, recent publications, and standard references such as the National Geodetic Survey (NGS; 1986); American Society of Civil Engineers, American Congress on Surveying & Mapping, and American Society of Photogrammetry & Remote Sensing (1994); and Meyer, Roman, and Zilkoski (2004).
Elevation (Generic)
Elevation is the distance above or below a reference surface. The geoid is an equi-potential reference surface that has been widely used and is closely approximated by mean sea level. Unless specifically stated otherwise, a mean sea level elevation should probably be viewed as a generic elevation.
Equipotential Surface
An equipotential surface is a continuous surface defined in terms of work units with regard to its physical environment. Although not perfect, mean sea level is often given as an example. Two objects at rest, having the same mass, and located on the same equipotential surface store the same amount of potential energy. Work is required to move any objects to a higher elevation. If the strength of gravity at point A is greater than at point B, then, for identical objects and for expenditure of the same work, the distance moved by the object at point B will be greater than at point A. The implication is that equipotential surfaces are parallel if and only if gravity is the same at both points on each respective surface. Although defined differently, a level surface and an equipotential surface are very nearly identical and, for most purposes, can be used interchangeably.
Level Surface
A level surface is a continuous surface that is always perpendicular to the local plumb line. A level surface can be at any elevation. Due to the Earth’s curvature and variations of density within the Earth, the direction of the plumb line changes as one moves from point to point on or near the surface of the Earth. Consequently, a level surface (which is always perpendicular to the plumb line) is said to be “lumpy” due to these random changes in direction of the plumb line. But, in most cases, changes in the direction of the plumb line are gradual and “lumps” in the geoid are gradual as well.
Geoid
The geoid is an equipotential surface most closely represented by mean sea level in equilibrium all over the world (i.e., constant barometric pressure at the surface, no winds, no currents, uniform density layers of water, etc.). The “ideal” conditions do not exist, and locating the geoid precisely on a global scale is an enormous challenge.
Geopotential Number
A geopotential number is a relative value computed as the infinite summation of the product of force times distance accumulated along a path of maximum gradient. A geopotential number has units of work and is rarely used in surveying and mapping applications. Dynamic heights are often used instead—see the next subsection.
Dynamic Height
Dynamic height is the geopotential number at a point divided by a constant reference gravity. Often, normal gravity at latitude 45° is used. Dynamic heights and geopotential numbers are useful when working with precise hydraulic grade lines over a large area. Standard geodesy texts contain additional information on these topics and their applications.
Orthometric Height
Orthometric height is the curved distance along the plumb line from the geoid to a point or surface in question. Few users make the distinction between the curved-line distance and the straight-line distance between the plumb line endpoints. In the past, orthometric height has been computed as the geopotential number of the equipoten-tial surface divided by gravity at the point (Zilkoski, Richards, and Young 1992). More recently (Meyer, Roman, and Zilkoski 2004), orthometric height is more specifically called a Helmert orthometric height and is computed using ellipsoid heights (from GPS) and geoid-modeling procedures. The accuracy of such a derived height is dependent upon both the quality of the GPS data and the integrity of the geoid modeling. Although elevation and orthometric height can often be used interchangeably, elevation is considered generic while orthometric height is specific.
Ellipsoid Height
Ellipsoid height is the distance as measured along the ellipsoid normal above or below the mathematical ellipsoid.
Geoid Height
Discounting curvature of the plumb line, geoid height is taken to be the distance along the ellipsoid normal between the ellipsoid and the geoid. Geoid height is computed as the ellipsoid height minus orthometric height. Within the conterminous United States, the orthometric height is always greater than the ellipsoid height, which means the geoid height is a negative number. But, on a worldwide basis, the simple relationship is
where
