The 1-cm geoid after GOCE

The new satellite gravity missions (CHAMP, GRACE and GOCE) will all bring substantial improvements to our knowledge of the gravity field and thereby of the (quasi-) geoid. One of the aims of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) is to determine the geoid to within 1 cm at wavelengths down to 100 km.When determining local or regional geoids, a large part of the error is due to the error in the spherical harmonic expansion used as a reference field in remove-restore calculations. We have estimated this error for the EGM96 and for the future GOCE based model using the so-called error-degree variances associated with these models. These variances have for GOCE been determined in studies analysing the mission performance.The error-degree variances have been used in a Monte-Carlo like generation of pertubations of the EGM96 and the GOCE gravity field model in various scenarios (moderate topography, medium varying topography and Alpine topography) by scaling the error-degree variances. The error of a derived quantity like a geoid height differences have then been estimated by calculating the root-mean square variation of the results.Based on typically 50 generated models (for EGM96 and GOCE) we have estimated mean errors of geoid height differences between the continents as well as for typical levelling lines on the continents. For geoid height differences between the continents the EGM96 error is found to be between 0.45 m and 0.60 m, while the corresponding error when using GOCE decreased to between 0.05 and 0.10 m. For levelling lines of distances between 25 km and 500 km a similar improvement was found, so that maximal errors decreased from 0.88 m to 0.09 m in Alpine topography and from 0.44 m to 0.03 m in Scandinavian type topography. Obviously the use of local gravity anomalies, gravity disturbances, GPS/levelling geoid height differences as well as topographic information may further improve the results. Consequently 1-cm geoid height differences should easily be obtained in areas where these types of data are available.