Comparison of Statistical Dynamical, Square Root and Ensemble Kalman Filters

We present a statistical dynamical Kalman filter and compare its performance to deterministic ensemble square root and stochastic ensemble Kalman filters for error covariance modeling with applications to data assimilation. Our studies compare assimilation and error growth in barotropic flows during a period in 1979 in which several large scale atmospheric blocking regime transitions occurred in the Northern Hemisphere. We examine the role of sampling error and its effect on estimating the flow dependent growing error structures and the associated effects on the respective Kalman gains. We also introduce a Shannon entropy reduction measure and relate it to the spectra of the Kalman gain.