Publication Date:
2014-01-17
Description:
It is customary in atmospheric britishmodelling to approximate the equi-geopotential surfaces of apparent gravity as spheres, and to use spherical polar coordinates to represent the global atmosphere. However Earth's mean surface is more accurately approximated by a spheroid of revolution than by a sphere, and therefore the geopotential surfaces are better represented as spheroidal surfaces than spherical ones. Several authors have considered how to develop a spheroidal coordinate system. The keystone for this is a sufficiently-accurate, yet simple and flexible, mathematical approximation of the geopotential for a spheroidal Earth. Geopotential approximation is a compromise between the extremes of being either too simple, with deficient representation of the essentials of the underlying physics, or too complicated, leading to overly-complicated coordinate systems. A new spheroidal geopotential approximation is proposed herein. It is relatively simple, and analytically tractable, yet properly represents the underlying physics. Using this new approximation, a new, relatively simple, quasi-orthogonal spheroidal coordinate system is developed. It is then straightforward to obtain the customary spherical geopotential approximation, with its associated use of spherical polar coordinates, as an asymptotic limit of this new formulation. This confirms a previous finding, obtained using a different quasi-orthogonal coordinate system. The spheroidal geopotential approximation, and quasi-orthogonal coordinate system, proposed herein are however much simpler, yet no less accurate. They thereby lead to a much simpler, more direct, yet equally rigorous, justification for the spherical geopotential approximation.
Print ISSN:
0035-9009
Electronic ISSN:
1477-870X
Topics:
Geography
,
Physics
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