Referenzeellipsoid

The Referenzeellipsoid, or reference ellipsoid, is a mathematically defined ellipsoid used as the reference surface in geodesy to approximate the Earth's shape and to define geodetic coordinate systems. It provides a smooth, global surface on which latitude and longitude are defined and serves as the basis for many map projections and spatial calculations.

It is characterized by its equatorial radius a and flattening f (or inverse flattening 1/f). Flattening describes the difference between the equatorial and polar radii. The ellipsoid is not the geoid; the geoid is a separate surface defined by gravity potential. Heights can be expressed as ellipsoidal heights relative to the ellipsoid or orthometric heights relative to the geoid.

Common reference ellipsoids include WGS 84 (a = 6378137.0 m, 1/f = 298.257223563), GRS80 (a = 6378137.0 m, 1/f = 298.257222101), International 1924 (Hayford) (a = 6378388.0 m, 1/f = 297.0), and Clarke 1866 (a = 6378206.4 m, b = 6356583.8 m; 1/f ≈ 294.9787).

Usage: The referenzeellipsoid underpins GPS and GNSS positioning, map projection definitions, and cadastral surveying. A datum defines the relationship between the ellipsoid and the Earth’s surface, and transforming between datums requires transformation parameters.

Selection: Global applications often use WGS 84; regional or national projects may adopt a local ellipsoid to reduce mapping errors in a specific area. The choice depends on accuracy requirements, the region of interest, and the available datum transformations.