Using Observations with Correlated Error Variance in Sequential Ensemble Filters

Observations lead the way for data assimilation, but if correlated observational error variance is ignored, they may not lead in the best direction. Sequential implementations of ensemble Kalman filters are used for many atmospheric and geophysical applications. The most common approach for dealing with correlated observational error variance (aside from ignoring it) has been to do a singular value decomposition on the error covariance matrix. When rotated to an orthogonal coordinate system defined by the singular vectors, the error covariance matrix is diagonal and the rotated observations can be assimilated sequentially. However, there are challenges in localizing the impact of the observations in the rotated space on model state variables. This method also does not work if observations assimilated in different time windows have correlated error. A second method is to explicitly model the error distribution of the correlated observations. This can be effective if there is a robust model of the time evolution of the observation error. However, if all that is known is some prior estimate of the error covariance matrix, ensemble filters suffer significant sampling error in this case.

A method that avoids the impact of this sampling error and may reduce the challenges of localization is presented. A first example is for simultaneous observations with correlated observational errors, for instance sets of retrievals generated from satellite radiance observations. A second example is for observations with temporal observational error covariance, for instance direct assimilation of radiances from a biased radiometer. Remaining challenges associated with effective localization are discussed.