On the spherical approximation of the geopotential in geophysical fluid dynamics and the use of a spherical coordinate system

Abstract

We present an analytical, idealized yet precise model of the terrestrial gravity field. The model is meant as a basic ingredient of geophysical fluid dynamics (GFD). We explicitly deal with geopotential coordinates, show in what sense horizontal geopotential coordinate surfaces can be approximated by spherical surfaces and thus provide a clear interpretation of the “spherical approximation” of the equations of motion in GFD. The horizontal component of the gravitational force plays a crucial role in the spherical approximation. It is shown that to leading order in the relevant small parameters, the horizontal components of the gravitational force and the centrifugal force cancel each other in the spherical approximation of the geopotential field.