In global atmospheric models, the geopotentials of apparent gravity are usually represented as spheres following minor but systematic approximations, including neglect of the ellipticity of the Figure of the Earth and of the latitude variation of the magnitude of apparent gravity, g. Improved representation using families of simple spheroids encounters various problems. Confocal oblate spheroids are technically convenient but qualitatively unsuitable as regards the implied latitude variation of g and vice versa for similar oblate spheroids. Representation of geopotentials by the quasi-spheroidal surfaces of the geodetic coordinate system (used in aircraft navigation and satellite geodesy) is considered here. A single reference spheroid represents the Figure of the Earth, and exterior geopotentials are represented by surfaces of constant perpendicular distance from the reference spheroid. These surfaces are not precise spheroids, and latitude variation of g is not represented. The (orthogonal) coordinates are longitude, geographic latitude and perpendicular height above the reference spheroid. The geodetic system has many desirable features, including ease of transformation to Cartesian coordinates and hence derivation of the metric factors (not required for geodesy or navigation). Transformation from Cartesian coordinates is not analytically straightforward, but is amenable to perturbation or efficient numerical solution. A comparison is made with precisely spheroidal coordinate systems. Copyright © 2011 British Crown copyright, the Met Office. Published by John Wiley & Sons Ltd.