Ocean Science www.ocean-sci.net 1812-0784 1812-0792 4 1 2008 10.5194/os-4-15-2008 http://www.ocean-sci.net/4/15/2008/ http://www.ocean-sci.net/4/15/2008/os-4-15-2008.html http://www.ocean-sci.net/4/15/2008/os-4-15-2008.pdf 15 29 2008-01-24 An Oceanographer's Guide to GOCE and the Geoid C. W. Hughes cwh@pol.ac.uk R. J. Bingham Proudman Oceanographic Laboratory, 6 Brownlow St., Liverpool L3 5DA, UK A review is given of the geodetic concepts necessary for oceanographers to make use of satellite gravity data to define the geoid, and to interpret the resulting product. The geoid is defined, with particular attention to subtleties related to the representation of the permanent tide, and the way in which the geoid is represented in ocean models. The usual spherical harmonic description of the gravitational field is described, together with the concepts required to calculate a geoid from the spherical harmonic coefficients. A brief description is given of the measurement system in the GOCE satellite mission, scheduled for launch shortly. Finally, a recipe is given for calculation of the ocean dynamic topography, given a map of sea surface height above a reference ellipsoid, a set of spherical harmonic coefficients for the gravitational field, and defining constants. Bingham, R. J., Haines, K., and Hughes, C. W.: Calculating the ocean's mean dynamic topography from a mean sea surface and a geoid, J. Atmos. Ocean. Tech, in press, 2008. Chelton, D. B., Walsh, E. J., and MacArthur, J. L.: Pulse compression and sea level tracking in satellite altimetry, J. Atmos. Ocean. Tech, 6, 407–438, 1989. Ekman, M.: Impacts of geodynamic phenomena on systems for height and gravity, Bulletin Géodésique, 63, 281–296, 1989. ESA: Gravity field and steady-state ocean circulation mission, report for mission sellection of the four candidate earth explorer missions, ESA report SP-1233 (1), 217 pp., available at http://www.esa.int/livingplanet/goce, 1999. Forsberg, R. and Skourup, H.: Arctic Ocean gravity, geoid and sea-ice freeboard heights from ICESat and GRACE, Geophys. Res. Lett., 32, L21502, doi:10.1029/2005GL023711, 2005. Gill, A. E.: Atmosphere-Ocean Dynamics. Academic Press, London and Orlando, Florida, 662 pp., 1982. Heiskanen, W. and Moritz, H.: Physical Geodesy, W. H. Freeman and Co,. San Francisco and London, 364 pp., 1967. Hwang, C., Hsiao, Y.-S., Shih, H.-C., Yang, M., Chen, K.-H., Forsberg, R., and Olesen, A. V.: Geodetic and geophysical results from a Taiwan airborne gravity survey: Data reduction and accuracy assessment, J. Geophys. Res., 112, B04407, doi:10.1029/2005JB004220, 2007. Knudsen, P. and 19 coauthors: Combining altimetric/gravimetric and ocean model mean dynamic topography models in the GOCINA region, in: Dynamic Planet—Monitoring and Understanding a Dynamic Planet With Geodetic and Oceanographic Tools, Int. Assoc. Geod. Symp., Vol. 130, edited by: Rizos, C. and Tregoning, P., Springer, New York, 3–10 2007. Lambeck, K.: The Earth's variable rotation: Geophysical causes and consequences, Cambridge University Press, 1980. Moritz, H.: Geodetic Reference System 1980, Bulletin Géodésique, 54, 395–405, 1980a. Moritz, H.: Advanced Physical Geodesy, Herbert Wichmann Verlag (West Germany) and Abacus Press (Great Britain), 500 pp., 1980b. Rapp, R. H.: The treatment of permanent tidal effects in the analysis of satellite altimeter data for sea surface topography, Manuscripta Geodaetica, 14, 368–372, 1989. Rummel, R. and Rapp, R. H.: The treatment of permanent tidal effects in the analysis of satellite altimeter data for sea surface topography, Manuscripta Geodaetica, 14, 368–372, 1989. Smith, W. H. F. and Sandwell, R. H.: Global sea floor mapping from satellite altimetry and ship depth soundings, Science, 277(5334), 1956–1962, 1997. Smith, D. A.: There is no such thing as "The" EGM96 geoid: Subtle points on the use of a global geopotential model, IGeS Bulletin No. 8, International Geoid Service, Milan, Italy, 17–28, 1998. Tapley, B., Ries, J., Bettadpur, S., Chambers, D., Cheng, M., Condi, F., Gunter, B., Kang, Z., Nagel, P., Pastor, R., Pekker, T., Poole, S., and Wang, F.: GGM02 – An improved Earth gravity field model from GRACE, J. Geod, 79, 467–478 2005. Vermeille, H.: Direct transformation from geocentric coordinates to geodetic coordinates, J. Geodesy, 76, 451–454, 2002.