Facilitating Inversion of the Error Covariance Models for the Wide-Swath Altimeters

Wide-swath satellite altimeter observations are contaminated by errors caused by the uncertainties in the geometry and orientation of the on-board interferometer. These errors are strongly correlated across the track, while also having similar error structures in the along-track direction. We describe a method for modifying the geometric component of the error covariance matrix which facilitates accuracy in the removal of the respective error modes from the signal and improves computational efficiency of the data assimilation schemes involving wide-swath altimeter observations. The method has been tested using the Surface Water and Ocean Topography simulator. We show substantial computer cost savings in the pseudo-inversion of the respective error covariance matrix. This efficiency improvement comes with a few per cent error in the approximation of the original covariance model simulating uncertainties in the geometry and orientation of the on-board interferometer.