Almost Everything You Always Wanted to Know About Representing Gravity in Global Models but Were Afraid to Ask

Abstract For over 60 years, an approximation involving spherical geopotentials has underlain the representation of gravity in global numerical models of Earth's atmosphere and oceans. This article explores how departures from sphericity can be allowed by assuming spheroidal geopotentials instead. A route to more accurate model formulation is indicated, and the theoretical basis of the classical spherical‐geopotential approximation is illuminated too. An overview—from the time of Newton to the present—is given of the development of zeroth‐ and first‐order approximations to the geopotential field in terms of two small non‐dimensional parameters. The importance of using geopotential coordinate systems in atmospheric and oceanic models is emphasized. Early suggestions for such systems using non‐spherical coordinates involved qualitatively inappropriate choices of ellipsoids derived from families of confocal ellipses. Specific examples of appropriate ellipsoid choices are considered before presentation of the recently developed Geophysically Realistic, Ellipsoidal, Analytically Tractable (GREAT) system. This is based on a suitably constructed geopotential field approximation, first order accurate, from which—without further approximation—may be analytically derived equations for geopotential surfaces and surfaces orthogonal to them. GREAT coordinates satisfy stated desiderata for geopotential coordinate systems and are applicable both above and below Earth's geoid (assumed to coincide with the WGS 84 [2004, https://gis‐lab.info/docs/nima‐tr8350.2‐wgs84fin.pdf ] reference ellipsoid to an excellent approximation). GREAT‐coordinate analysis provides justification for the classical spherical‐geopotential approximation: It is revealed as a mathematical limit, but not a physically realizable one. Attention is drawn to a certain partially spherical limit that is realizable physically.