Spherical Harmonics Expansion of the Atmospheric Gravitational Potential Based on Exponential and Power Models of Atmosphere

Spherical harmonic formulation of gravitational potential of the atmosphere depends on the analytical model of the atmospheric density which is used. Exponential and power models are two well-known mathematical tools which are used in atmospheric applications. This paper presents simple formulas for the harmonic coefficients of internal and external types of the atmospheric potential based on these models which can be used in most of the gravimetric aspects. It considers the atmospheric effect on the satellite gravity gradiometry data as an example for numerical investigations. The numerical studies on these data show that the maximum atmospheric effect is about 2 mE over Fennoscandia based on both models, and their differences are less than 0.1 mE. The difference between indirect atmospheric effects reaches 2 cm and 0.02 mGal on the geoid and gravity anomaly, respectively in this region.