An oceanographer’s guide to GOCE and the geoid

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.