Simple geometric approximations for global atmospheres on moderately oblate planets

TL;DR

This paper develops a sequence of simple, analytically expressible geometric approximations that improve modeling of global atmospheres on oblate planets by accounting for oblateness, gravity variation, and Coriolis effects.

Contribution

It introduces three new metric geometric approximations with closed-form expressions that reduce errors of traditional atmospheric models on oblate planets.

Findings

The approximations accurately capture planetary oblateness and atmospheric column widening.

Horizontal metrics are conformal to spherical metrics, simplifying equations.

The methods improve high-altitude atmospheric modeling accuracy.

Abstract

Certain geometric approximations such as the widely used traditional shallow-atmosphere, spherical-geoid (TSA-SG) and the deep-atmosphere, spherical-geoid (DA-SG) approximations boil down to the specification of a spatial metric tensor. In order to eliminate the leading-order errors due to the SG and TSA approximations, a sequence of three metric geometric approximations of increasing accuracy at high altitudes is obtained. Their metric tensors possess a simple, closed-form analytical expression. The approximations capture to leading order the oblateness of the planet, the widening of atmospheric columns with height, the horizontal and vertical variations of gravity and the non-traditional part of the Coriolis force. Furthermore, for the first two approximations, the horizontal metric is conformal (proportional) to the spherical metric, which simplifies analytical and numerical formulations of the equations of motion.