We present a local quasi-geoid (QG) model which combines a satellite-only global gravity model with local data sets using weighted least squares. The QG is computed for an area comprising the Netherlands, Belgium, and the southern North Sea. It uses a two-scale spherical radial basis function model complemented by bias parameters to account for systematic errors in the local gravity data sets. Variance factors are estimated for the noise covariance matrices of all involved data sets using variance component estimation. The standard deviation (SD) of the differences between the computed QG and GPS/leveling data is 0.95 and 1.52 cm for the Netherlands and Belgium, respectively. The fact that the SD of the control data is about 0.60 and 1.20 cm for the Netherlands and Belgium, respectively, points to a lower mean SD of the computed QG model of about 0.7 cm for the Netherlands and 1.0 cm for Belgium. The differences to a QG model computed with the remove-compute-restore technique range from −5.2 to 2.6 cm over the whole model domain and from −1.5 to 1.5 cm over the Netherlands and Belgium. A variogram analysis of the differences with respect to GPS/leveling data reveals a better performance of the computed QG model compared to a remove-compute-restore-based QG model for wavelengths >100 km for Belgium but not for the Netherlands. The latter is due to the fact that at the spatial scales resolved by the global gravity model, variance component estimation assigns significantly lower weights to the local data set in favor of the global gravity model.
- satellite-only global gravity model
- spherical radial basis functions
- weighted least squares