Spheroidal coordinate systems for modelling global atmospheres

In meteorological dynamics it is common practice to represent the potential surfaces of apparent gravity (the geopotentials) as spheres, and consequently the use of spherical polar coordinates in models of the global atmosphere is widespread. Several writers have considered how oblate spheroidal coordinates might be used instead, thus enabling the Figure of the Earth to be better represented. It is observed here that oblate spheroidal coordinate systems are conventionally defined using confocal oblate spheroids, and that such spheroids are inappropriate representations of the geopotentials because they imply the wrong sign for the latitudinal variation of apparent gravity. Re-examination of a classical problem of Newtonian gravitation shows that, near the Earth, the geopotentials are to a very good approximation spheroids, but not spheroids of an analytically simple type. However, similar oblate spheroids are a qualitatively correct model of the near-Earth geopotentials, and are a quantitatively good approximation in so far as Newton's uniform-density model adequately describes the real Earth. An orthogonal curvilinear coordinate system based on similar oblate spheroids is proposed and examined.