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Several localized versions of the ensemble Kalman filter have been proposed.Although tests applying such schemes have proven them to be extremelypromising, a full basic understanding of the rationale and limitations oflocalization is currently lacking. It is one of the goals of this paper tocontribute toward addressing this issue. The second goal is to elucidate therole played by chaotic wave dynamics in the propagation of information and theresulting impact on forecasts. To accomplish these goals, the principal toolused here will be analysis and interpretation of numerical experiments on a toyatmospheric model introduced by Lorenz in 2005. Propagation of the wave packetsof this model is shown. It is found that, when an ensemble Kalman filter schemeis employed, the spatial correlation function obtained at each forecast cycleby averaging over the background ensemble members is short ranged, and this isin strong contrast to the much longer range correlation function obtained byaveraging over states from free evolution of the model. Propagation of theeffects of observations made in one region on forecasts in other regions isstudied. The error covariance matrices from the analyses with localization andwithout localization are compared. From this study, major characteristics ofthe localization process and information propagation are extracted andsummarized.

On the propagation of information and the use of localization in ensemble Kalman filtering