A GOCE-Only Global Gravity Field Model by the Space-Wise Approach

The global gravity field model computed by the spacewise approach is one of three official solutions delivered by ESA from the analysis of the GOCE data. The model consists of a set of spherical harmonic coefficients and the corresponding error covariance matrix. The main idea behind this approach is to exploit the spatial correlation of the gravity field to estimate grids of potential and its second order radial derivatives at mean satellite altitude; from these grids, spherical harmonic coefficients are then derived by numerical integration. The filtering strategy includes also a Wiener filter along the orbit to reduce the noise variance and correlation before gridding the data. In the first release of the space-wise approach, based on a period of about two months, some prior information coming from existing gravity field models entered into the solution especially at low degrees and low orders. In this work, the strategies adopted to remove these dependencies on external data are described. Mainly two modifications have been implemented. The first is an improved modelling of the error covariance matrix of the estimated along-track gravitational potential to remove the dependency on EGM08 at very low degrees; the second is an internally computed GOCE-only prior model to be used in place of the official quick-look model, thus removing the dependency on EIGEN5C especially in the polar gaps. Once the procedure to obtain a GOCE-only solution has been outlined, a new global gravity field model has been computed by applying the space-wise approach to eight months of GOCE orbit and gradiometer data. The results are presented and discussed in this paper, also comparing them with respect to the previous solution. 1. THE SPACE-WISE APPROACH AND THE RATIONALE OF THIS WORK The space-wise approach is a multi-step collocation procedure [8][16], developed in the framework of the GOCE HPF [17] data processing for the estimation of the spherical harmonic coefficients of the Earth gravitational field and their error covariance matrix. The solution is based both on the satellite-to-satellite tracking (SST) data derived from the on-board GPS receiver and on the satellite gravity gradients (SGG) observed by the on-board electrostatic gradiometer. In particular, the low frequency part of the field is estimated from kinematic orbits [11][21] by means of the energy conservation approach [4][20]. The high frequency part is then derived by combining the estimated along-track gravitational potential with the observed gravity gradients. Finally spherical harmonic coefficients are computed by integrating estimated grids of potential and of its second radial derivatives at mean satellite altitude [2]. The error covariance matrix of the estimated coefficients is derived by Monte Carlo simulations [9]. The first release of the space-wise model (SPW) [10] had been delivered during the ESA Living Planet Symposium at Bergen in July 2010. It was based on the first two months of GOCE data and it had been computed in such a way that it represented a solution in between a pure GOCE-only model (time-wise approach, TIM, [13]) and a combined model (direct approach, DIR, [1]). See also [12] for details on these delivered models. Afterwards, it was decided to switch towards a spacewise GOCE-only model, removing dependencies on prior models based on external data. Such dependencies can be summarized as follows: • the EGM08 model [15] had been used to modify the estimated potential along the orbit so to reduce its error at very low frequency; • the GOCE quick-look model [6] had been used as prior model for the space-wise solution, but this is not a GOCE-only model since in it both reduced dynamic orbits [21] and polar gaps regularization [7] come from EIGEN5C [3]. Besides removing such dependencies on data not provided by the GOCE mission, other two main features have been incorporated in the space-wise scheme: • a semi-automatic pre-processing of the data to detect and repair outliers, data gaps, etc. • a combination method to merge space-wise solutions based on data covering different time periods. The latter has been made necessary because the model presented here is a GOCE-only solution derived from about eight months of data, which is definitively a too