On the Approximation of Precision Matrices for Wide-Swath Altimetry

New observations of ocean surface topography obtained by wide-swath satellite interferometry require new capabilities to process spatially correlated errors in order to assimilate these data into numerical models. The sea surface height (SSH) variations have to be weighted against other types of assimilated data using information on their precision, as represented by the inverse of the SSH error covariance matrix $R$. The latter can be well approximated by a block-circulant (BC) structure and, therefore, allows numerically efficient implementation in operational data assimilation (DA) systems. In this note, we extend the technique of approximating $R$ for wide-swath altimeters by including the uncertainties associated with the state of the atmosphere. It is shown that such an extension keeps the BC approximation error within acceptable (±10%) bounds in a wide range of environmental conditions and could be beneficial for improving the accuracy of SSH retrievals from wide-swath altimeter observations.