Including the horizontal observation error correlation in the ensemble Kalman filter: idealized experiments with NICAM-LETKF

Abstract Densely-observed remote sensing data such as radars and satellites generally contain significant spatial error correlations. In data assimilation, the observation error covariance matrix is usually assumed to be diagonal, and the dense data are thinned or spatially averaged to compensate for neglecting the spatial observation error correlation. However, in theory, including the spatial observation error correlation in data assimilation can make better use of the dense data. This study performs perfect model observing system simulation experiments (OSSE) using the non-hydrostatic icosahedral atmospheric model (NICAM) and the local ensemble transform Kalman filter (LETKF) to assess the impact of assimilating horizontally dense and error-correlated observations. The condition number of the observation error covariance matrix, defined as the ratio of the largest to smallest eigenvalues, is important for the numerical stability of the LETKF computation. A large condition number makes it difficult to compute the ensemble transform matrix correctly. Reducing the condition number by reconditioning is found effective for stable computation. The results show that including the horizontal observation error correlation with reconditioning makes the analysis more accurate but requires six times more computations than the case with the diagonal observation error covariance matrix.