For most practical algorithms, the quality of error covariance estimate plays a key role in data assimilation performance. We present an approach to diagnose the estimated error structure and study data assimilation performance. The approach is an extension of E-dimension (Patil et al. 2001; Ockzowski, 2001), which is a diagnostic tool for ensemble perturbations. The E-dimension represents a local measure of ensemble perturbation that varies in both space and time and quantifies the distribution of the variance between phase space directions for an ensemble of nonlinear model solutions, and hence can be used to investigate transient local low-dimensional instabilities. Our approach, called the “E-diagnostics”, allows us to analyze the estimated error structure not only by ensemble but also hybrid error covariances. Using our approach, we investigate estimated error structures in a variety of ways, including: representation of local uncertainty in background and analysis ensembles in Ensemble Kalman filter (EnKF) and impact of data assimilation, differences in representation of error structure in Ensemble Square Filter (EnSRF) and Local Ensemble Transform Kalman Filter (LETKF), impact of different inflation schemes in EnKF, and impact of the static background error covariance in hybrid data assimilation.

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*email: ide@umd.edu
*Preference: Oral