On the approximation of the inverse error covariances of high‐resolution satellite altimetry data. (28th September 2018) - Yaremchuk, Max; D'Addezio, Joseph M.; Panteleev, Gleb; Jacobs, Gregg
Abstract : 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. Abstract : In this note we propose a method of parameterizing the inverse error covariances by sparse matrices generated by spatially inhomogeneous differential operators. Columns of the sample error covariance (left) and its approximation (center) are shown. Left panel demonstrates the quality of the approximation of the entire spectrum.