Combining EGM2008 with GOCE gravity models

The most advanced global gravity model, EGM2008, is nowadays competing with local models in terms of resolution and accuracy in the definition of the Earth gravity field. This global model, complete to spherical harmonic degree and order 2159, is however affected by several biases mainly due to datum inconsistencies and variability of the input observations density and accuracy. This article addresses the problem of improving the EGM2008 model exploiting a satellite-only model based on the Gravity and steady state Ocean Circulation Explorer (GOCE) mission. The GOCE model, apart from being more accurate in the medium frequencies, is not affected by local biases since it is obtained by a global homogeneous data set referred to a unique geocentric ellipsoid: so both effects of different data sources and inconsistent height datums are not present. The resulting combination can vary depending on the weighting of the two global models. A first simple solution is to average spherical harmonic coefficients of the same degree and order by computing the weights as the inverse of their error variance. Another attempt is to consider for the GOCE model also the error correlations of the coefficients that are available through an order-wise covariance matrix. The paper shows also a way to integrate the two available, but not fully consistent, sources of information about the EGM2008 error, i.e., the spherical harmonic coefficient variances and a geographical estimate of the geoid variance. The study has been performed on the Mediterranean area because it was required for the GOCE-Italy project and because in this area the obtained merged geoid can be validated, e.g., by using available drifter data. The main conclusion is that there is no a general criterion to chose which is the optimal way to merge the EGM2008 and GOCE models. This is because the full stochastic structure of EGM2008 is not available and only approximations can be used. This means that each case study has to be dealt with separately. In particular for the Mediterranean area the differences between the proposed combinations are here presented.