An oblate‐spheroid geopotential approximation for global meteorology

Abstract

AbstractThe spherical geopotential approximation used in most meteorological global models assumes a spherical shape for the Earth and its geopotential field. Consequently, the deviation of the geoid surface from a sphere, and the observed meridional variations of the apparent gravity are not represented. These two errors are small but their effect on medium or long‐term forecasts is debated because they are systematic and might have cumulative effects. Various formulations with spheroidal iso‐geopotential surfaces have been proposed recently, but none of them combines the advantages of an accurate description for the geopotential field and of horizontal/vertical orthogonal coordinate surfaces. This article proposes a spheroidal coordinate system which meets these two requirements. The transformation and metric factors are defined analytically. The coordinate system is defined as an approximation of orthogonal horizontal/vertical coordinates in which the vertical lines are not exactly orthogonal to true horizontal surfaces. The consequences of this deviation from orthogonality are quantified and upper bounds for the resulting errors are obtained mathematically, i.e. independently of any arbitrary numerical process. The precision of the coordinate can be made as large as desired by raising the truncation of the Taylor series used to approach its exact value, and it is shown that, in practice, truncation values in the range 5 to 8 are appropriate for global numerical weather prediction.