Terrain effects in the atmospheric gravity and geoid corrections

In view of the smallness of the atmospheric mass compared to the mass variations within the Earth, it is generally assumed in physical geodesy that the terrain effects are negligible. Subsequently most models assume a spherical or ellipsoidal layering of the atmosphere. The removal and restoring of the atmosphere in solving the exterior boundary value problems thus correspond to gravity and geoid corrections of the order of 0.9 mGal and -0.7 cm, respectively.We demonstrate that the gravity terrain correction for the removal of the atmosphere is of the order of 50µGal/km of elevation with a maximum close to 0.5 mGal at the top of Mount Everest. The corresponding effect on the geoid may reach several centimetres in mountainous regions. Also the total effect on geoid determination for removal and restoring the atmosphere may contribute significantly, in particular by long wavelengths. This is not the case for the quasi geoid in mountainous regions.