The effect of Stokes’s formula for an ellipsoidal layering of the Earth’s atmosphere
2006 (English)In: Journal of Geodesy, ISSN 0949-7714, E-ISSN 1432-1394, Vol. 79, no 12, 675-681 p.Article in journal (Refereed) Published
The application of Stokes’s formula to determine the geoid height requires that topographic and atmospheric masses be mathematically removed prior to Stokes integration. This corresponds to the applications of the direct topographic and atmospheric effects. For a proper geoid determination, the external masses must then be restored, yielding the indirect effects. Assuming an ellipsoidal layering of the atmosphere with 15% increase in its density towards the poles, the direct atmospheric effect on the geoid height is estimated to be ‑5.51 m plus a second-degree zonal harmonic term with an amplitude of 1.1 cm. The indirect effect is +5.50 m and the total geoid correction thus varies between ‑1.2 cm at the equator to 1.9 cm at the poles. Finally, the correction needed to the atmospheric effect if Stokes’s formula is used in a spherical approximation, rather than an ellipsoidal approximation, of the Earth varies between 0.3 cm and 4.0 cm at the equator and pole, respectively.
Place, publisher, year, edition, pages
2006. Vol. 79, no 12, 675-681 p.
atmospheric effects, ellipsoidal effects, Stokes's formula
Earth and Related Environmental Sciences
IdentifiersURN: urn:nbn:se:kth:diva-10825DOI: 10.1007/s00190-005-0018-4ISI: 000236091500002ScopusID: 2-s2.0-33645030112OAI: oai:DiVA.org:kth-10825DiVA: diva2:228036