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Correlations, Variances, Covariances --- From GOCE Signals to GOCE Products

Wolf-Dieter Schuh(1), Hamza Alkhatib(1), Christian Boxhammer(1), Boris Kargoll(1) and Christian Siemes(1)

(1) University Bonn, Nussallee 17, D-53115 Bonn, Germany

Abstract

The great amount of data generated by the satellite mission GOCE will allow for a precise determination of the Earth's garvity field in terms of spherical harmonic parameters and their variances/covariances. To capture the detailed correlation structures present in the SGG signals, complex stochastic models must be built. Such models are implemented in an efficient manner by means of digital filters with tailored stop and band-pass regions. Unfortunately, the computational costs grow considerably when the filter captures more and more details. The first question to be addressed in this talk will be, whether the quality of the parameter estimates justifies the use of an exact filter.

The second topic of this talk is about the use of the variances and covariances of the estimated gravity field parameters for deriving secondary GOCE products such as Earth process models.The variance- covariance matrix of the parameters, which is equivalent to the inverse normal equation matrix, is a very large, fully populated, and numerically instable matrix. To make this data easier to manage, in particular easier to integrate into Earth process models, it is necessary to reduce the amount of data and to improve the stability of the variance-covariance information. For this purpose, alternative ways of representating the variance-covariance matrix by means of sparse matrices or Monte-Carlo samples will be discussed. Finally, the relationship between the parameter accuracies of such Earth process models and the rate of data compression is investigated.

 

Workshop presentation

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry