Localization and correlation in ensemble Kalman filters

Localization of observation impacts can reduce ensemble mean RMS errors when ensemble Kalman filters are applied to large geophysical applications. Sampling error in the ensemble computation of covariances can explain at least part of the need for localization. Attempts to quantify this error and the appropriate corrective localization have been made using groups of ensembles. Other methods to adaptively estimate localization make use of the correlations between observations and state variables in a single ensemble. If an ensemble Kalman filter is viewed as a traditional Monte Carlo method for state estimation, it is possible to derive a localization that minimizes the expected RMS error of the mean. Results of applying this technique are presented for both low-order models and a simplified atmospheric general circulation model. Using an adaptive localization based on sample correlations can greatly reduce the sensitivity of ensemble Kalman filter applications to the values of inflation and fixed traditional localization width. In the GCM, this leads to reduced root mean square errors in analyses. Implications for building dynamically evolving statistical models of localization are discussed.