In 1928, C. F. Gauss set the modern definition of the shape of the Earth, being described as the shape the oceans would adopt if they were entirely unperturbed and, thus, placid—a surface now called the geoid. This surface cannot be observed directly because the oceans have waves, tides, currents, and other perturbations. Nonetheless, the geoid is the ideal datum for heights, and the science of determining the location of the geoid for practical purposes is the topic of physical geodesy. The geoid is the central concept that ties together what the various kinds of height mean, how they are measured, and how they are inter-related.
The elevation of a point requires a reference surface defining zero elevation. In geodesy, this zero-reference surface has historically been mean sea level (MSL) – a vertical datum. However, the geoid, which is a particular equipotential surface of Earth’s gravity field that would coincide with mean sea level were mean sea level altogether unperturbed and placid, is the ideal datum for physical heights, meaning height associated with the flow of water, like elevations. Tidal, gravimetric, and ellipsoidal are common vertical datums that use different approaches to define the reference surface. Tidal datums average water heights over a period of approximately 19 years, gravimetric datums record gravity across Earth’s surface, and ellipsoidal datums use specific reference ellipsoids to report ellipsoid heights. Increasingly, gravity measurements, positional data from GNSS (Global Navigation Satellite System), and other sophisticated measurement technologies GRACE-FO (Gravity Recovery and Climate Experiment – Follow On) are sourced to accurately model the geoid and its geopotential surface advancing the idea of a geopotential datum. Stemming from these advancements, a new geopotential datum for the United States will be developed: North American-Pacific Geopotential Datum 2022 (NAPGD2022).
Devised by Eratosthenes of Cyrene, geographic coordinate systems date back to the 3rd century BCE and have been used in mapping locations over the globe ever since. Latitude and longitude, or geographic coordinates, are the kernel of a geographic coordinate system. However, such a system is abstract unless anchored to the Earth in some way. The geodetic datum, or terrestrial reference frame as it is now called, comprises the anchor. Geographic information systems make extensive use of geographic coordinate systems to uniquely georeference spatial data. Here it is important to understand the uncertainty of a georeferenced ground position, given in latitude and longitude, as a function of the number of decimal places specified. Geocoding is a widely used application of geographic information systems that converts between street addresses and coordinates.