Improved mean sea surface estimation by gravity field error covariance weighting

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Abstract
Geodesists are finding increasing value in the use of satellite‐borne radar altimeters by fully exploiting the geophysical information contained in the data. The high degree of accuracy necessary for extracting this information requires independent knowledge of the geocentric satellite position to a comparable level of accuracy. The accuracy of sea surface height measurements on length scales greater than a few thousand kilometers is limited primarily by the radial errors contained in the estimated satellite orbits, the most significant contribution being the result of inadequacies in the modeling of the earth's gravity field. Additionally, such orbit errors are geographically correlated to some extent. These geographically correlated orbit errors result in a bias to the estimated sea surface heights, and have not been accounted for in previous global mean sea surfaces which have been derived from satellite altimetry data. This study quantifies the impact of errors in the GEM‐L2 gravity field model on the accuracy of the estimated global sea surface heights to be obtained by the TOPEX/Poseidon mission. A correlation matrix is constructed that describes the statistical relationship between geographically defined radial errors. This correlation matrix is used as a weighting covariance for the altimetric observations in the least‐squares estimation of the mean sea surface. Variance reduction of the height error is demonstrated for realizations of the radial error surface generated from the covariance matrix of the GEM‐L2 gravity model coefficient errors. The ratios of the standard deviations of the weighted estimates to the standard deviations of the unweighted estimates show reductions in uncertainty everywhere over the surface, with reductions as great as 56% in some locations.

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