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A quasi‐spheroidal system for modelling global atmospheres: geodetic coordinates
Author(s) -
White A. A.,
Inverarity G. W.
Publication year - 2011
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.885
Subject(s) - bipolar coordinates , spheroid , spherical coordinate system , cartesian coordinate system , coordinate system , spherical trigonometry , orthogonal coordinates , geographic coordinate system , geodesy , curvilinear coordinates , geodetic datum , latitude , figure of the earth , parabolic coordinates , generalized coordinates , prolate spheroidal coordinates , geometry , oblate spheroid , geographic coordinate conversion , gravitational potential , physics , log polar coordinates , mathematics , geology , classical mechanics , gravitation , chemistry , biochemistry , in vitro
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.