中等扁圆行星上全球大气的简单几何近似
Simple geometric approximations for global atmospheres on moderately oblate planets
摘要：
某些几何近似，如广泛使用的传统浅大气层球面大地水准面（TSA-SG）和深大气层球面大地水准面（DA-SG）近似归结为空间度量张量的规范。为了消除由于SG和TSA近似引起的前阶误差，获得了在高海拔处精度增加的三个度量几何近似的序列。他们的度量张量具有一个简单的，封闭形式的解析表达式。近似捕捉到领先秩序的扁率的行星，大气柱的扩大与高度，重力的水平和垂直变化和非传统的部分科里奥利力。此外，对于前两个近似，水平度规与球面度规共形（成比例），这简化了运动方程的分析和数值公式。
英文摘要：
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.
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