GEOG 862
GPS and GNSS for Geospatial Professionals

Heights

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Diagram showing a spirit level run method of establishing elevetions
A Spirit Level Run
Source: Basic GIS Coordinates
Diagram showing trigonometric leveling to establish elevations, see text below
Trigonometric Leveling
Source: Basic GIS Coordinates

A point on the earth’s surface is not completely defined by its latitude and longitude. In such a context, there is, of course, a third element, that of height. Surveyors have traditionally referred to this component of a position as its elevation. One classical method of determining elevations is spirit leveling. A level, correctly oriented at a point on the surface of the earth, defines a line parallel to the geoid at that point. Therefore, the elevations determined by level circuits are orthometric; that is, they are defined by their vertical distance above the geoid as it would be measured along a plumb line. However, orthometric elevations are not directly available from the geocentric position vectors derived from GPS/GNSS measurements. In a normal course of things, a coordinate —YX, or northing easting, or latitude and longitude— is not fully a definition of a position. We've discussed also Earth-Centered, Earth-Fixed XYZ coordinates, but it is typical for a horizontal coordinate to be given a height, or elevation. This third element, was most often originally determined by spirit leveling or, in some cases, by a technique known as trigonometric leveling. Despite the surveying method that was used in the past, it was based on optical instruments oriented to gravity, therefore oriented to the geoid. Therefore, the heights were based upon gravity. There is a long legacy of benchmarks, recorded heights, and archives that are based upon this sort of methodology of determining heights. And so, this is what it follows that these values are generally what we think of as elevations —we think of orthometric heights based upon gravity.