Abstact.Three gravity field models, parameterized in terms of spherical harmonic coefficients, have been computed from 71 days of GOCE (Gravity field and steady-state Ocean Circulation Explorer) orbit and gradiometer data by applying independent gravity field processing methods. These gravity models are one major output of the European Space Agency (ESA) project GOCE High-Level Processing Facility (HPF). The processing philosophies and architectures of these three complementary methods are presented and discussed, emphasizing the specific features of the three approaches. The resulting GOCE gravity field models, representing the first models containing the novel measurement type of gravity gradiometry ever computed, are analyzed and assessed in detail. Together with the coefficient estimates, full variance-covariance matrices provide error information about the coefficient solutions. A comparison with state-of-the-art GRACE and combined gravity field models reveals the additional contribution of GOCE based on only 71 days of data. Compared to combined gravity field models, large deviations appear in regions where the terrestrial gravity data are known to be of low accuracy. The GOCE performance, assessed against the GRACE-only model ITGGrace2010s, becomes superior at degree 150, and beyond. GOCE provides significant additional information of the global Earth gravity field, with an accuracy of the 2-months GOCE gravity field models of 10 cm in terms of geoid heights, and 3 mGal in terms of gravity anomalies, globally at a resolution of 100 km (degree/order 200).

The accuracy of a gravity field model depends on the amount of available data and on the variation of the gravity field. When topographic height data are available, for example, in the form of a digital terrain model, it is possible to smooth the gravity field on a local scale by removing the gravitational effects calculated from models of the topographic masses. In this way, significant improvements of the prediction results are obtained in mountainous areas. In this paper we describe methods for the calculation of such gravitational terrain effects, applicable in collocation approximation of the gravity field. The terrain effects on gravity field quantities such as gravity anomalies, deflections of the vertical, and geoid undulations are calculated using a system of rectangular prisms, representing either a quasi‐traditional model of the topography and the isostatic compensation or a residual terrain model, where only the deviation of the topography from a mean elevation surface is considered. To test the terrain reduction methods, numerical prediction experiments have been conducted in the mountainous White Sands area, New Mexico. From gravity anomalies spaced approximately 6 arc min apart, other known gravity anomalies and deflections of the vertical were predicted using collocation. When using terrain effects calculated on the basis of 0.5 × 0.5 arc min point heights, the rms errors decreased by a factor of nearly 3 to 1 arc sec for the deflections and 3–4 mGal for the gravity anomalies, quite insensitive to the actual type of terrain reduction used. The feasibility of using topographic reductions in collocation is thus effectively demonstrated.

One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally below the gravity gradient error level, which is predicted to show a 1/ f behaviour for low frequencies. In the outlier detection, the 1/ f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate for the 1/ f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow to estimate gravity gradient scale factors down to the 10 −3 level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10 −2 level with this method.

[1] The radiometer wet tropospheric correction is a limiting factor of the application of near-coastal altimetry observations in the North Sea -Baltic Sea area. Using an ECMWF model based correction instead, we increase the return rate from 70% to 95%, with observations as close as 10 km from the coast. The altimetry and 39 coastal tide gauges are referenced to the same state of the art regional geoid. The two data sets are highly correlated and reveal a consistent mean dynamic topography and two distinct correlation regimes separated by the Danish islands. The combination of the two data sets in a simple statistical model is shown to estimate the sea surface height with the same error level as state of the art operational models, indicating the potential for near-coastal applications of satellite altimetry observations.

Abstract.During the past years, the accuracy of relative positioning using differential GPS (DGPS) has been improved significantly. The present accuracy of DGPS allows us to directly estimate the differential amplitudes and Greenwich phase lags of the main semi-diurnal ocean tide loading constituents (Se, Ke, Me and Ne). For this purpose a test is carried out using two GPS stations in Alaska. One station,