Letter to the Editor
Ocean Science and Engineering
© 2018 Royal Meteorological Society High-resolution (swath) altimeter missions scheduled to monitor the ocean surface in the near future have observation-error covariances (OECs) with slowly decaying off-diagonal elements. This property presents a challenge for the majority of the data assimilation algorithms which were designed under the assumption of the diagonal OECs being easily inverted. In this note, we present a method of approximating the inverse of a dense OEC by a sparse matrix represented by the polynomial of spatially inhomogeneous differential operators, whose coefficients are optimized to fit the target OEC by minimizing a quadratic cost function. Explicit expressions for the cost function gradient and the Hessian are derived. The method is tested with an OEC model generated by the SWOT simulator.
Quarterly Journal of the Royal Meteorological Society
(2018). On the Approximation of the Inverse Error Covariances of High-Resolution Satellite Altimetry Data. Quarterly Journal of the Royal Meteorological Society, 144(715), 1995-2000.
Available at: https://aquila.usm.edu/fac_pubs/18142