Error variances‐covariances of GEM‐T1: Their characteristics and implications in geoid computation

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Abstract
GEM‐TI is the first Earth potential model for which a full error variance‐covariance matrix of its coefficients was made available. This matrix offers the opportunity to look into the properties of the error covariance functions for geoid heights from GEM‐T1. They appear to be rather anisotropic and inhomogeneous. Geoid error covariance functions are used in regional geoid computations, where usually a set of potential coefficients is combined with gravity anomalies. In order to see the effect of simplification of the error variance‐covariance propagation in geoid computations, three cases were considered: the full matrix, the diagonal elements only, and the limitation to the use of error degree variances. The resulting variations in the estimated geoid errors are shown in two test areas for different cap sizes. They can reach 50 cm for a zero cap size. Finally, test computations are presented of geoid determination by least squares collocation. Since the error covariance of the observations is included in the collocation operator, the geoid heights depend upon the choice of the type of error covariance propagation of the Earth potential coefficient set, as it is a part of the observation. For the three considered cases, variations in the geoid heights amount up to 45 cm.