The atmospheric geoid effects in Stokes’ formula

Abstract

Summary The application of Stokes’ formula requires that the atmospheric effect on the gravity anomaly is removed. We show that this direct effect reaches about − 40 cm over the Himalayas and Antarctica. The restoring of the atmospheric masses yields the indirect atmospheric effect, reaching about − 20 cm for the same regions. Consequently, the total atmospheric effect on the geoid is of the order of − 60 cm. However, for most areas close to sea level, the correction is within a few centimetres. Furthermore, the total atmospheric geoid effect is derived for the truncated as well as the modified Stokes formula. It is emphasized that the traditional (IAG) approach to adding a direct atmospheric effect to gravity may lead to a serious geoid bias in the truncated Stokes formula. However, as all the parameters of the bias are known, it can easily be corrected. In contrast, we suggest that the total atmospheric effect on the geoid be determined separately. In this approach the bias is avoided.