On the a priori estimation of collocation error covariance functions: a feasibility study

Error covariance estimates are necessary information for the combination of solutions resulting from different kinds of data or methods, or for the assimilation of new results in already existing solutions. Such a combination or assimilation process demands proper weighting of the data, in order for the combination to be optimal and the error estimates of the results realistic. One flexible method for the gravity field approximation is least-squares collocation leading to optimal solutions for the predicted quantities and their error covariance estimates. The drawback of this method is related to the current ability of computers in handling very large systems of linear equations produced by an equally large amount of available input data. This problem becomes more serious when error covariance estimates have to be simultaneously computed. Using numerical experiments aiming at revealing dependencies between error covariance estimates and given features of the input data we investigate the possibility of a straightforward estimation of error covariance functions exploiting known characteristics of the observations. The experiments using gravity anomalies for the computation of geoid heights and the associated error covariance functions were conducted in the Arctic region north of 64° latitude. The correlation between the known features of the data and the parameters variance and correlation length of the computed error covariance functions was estimated using multiple regression analysis. The results showed that a satisfactory a priori estimation of these parameters was not possible, at least in the area considered.