Empirical localization of observation impact in ensemble Kalman filters

Localization is a method for reducing the impact of sampling errors in ensemble Kalman filters. Here, the regression coefficient, or gain, relating ensemble increments for observed quantity y to increments for state variable x is multiplied by a real number α defined as a localization. Localization of the impact of observations on model state variables is required for good performance when applying ensemble data assimilation to large atmospheric and oceanic problems. Localization also improves performance in idealized low-order ensemble assimilation applications. An algorithm that computes localization from the output of an ensemble observing system simulation experiment (OSSE) is described. The algorithm produces localizations for sets of pairs of observations and state variables: for instance, all state variables that are between 300- and 400-km horizontal distance from an observation. The algorithm is applied in a low-order model to produce localizations from the output of an OSSE and the computed localizations are then used in a new OSSE. Results are compared to assimilations using tuned localizations that are approximately Gaussian functions of the distance between an observation and a state variable. In most cases, the empirically computed localizations produce the lowest root-mean-square errors in subsequent OSSEs. Localizations derived from OSSE output can provide guidance for localization in real assimilation experiments. Applying the algorithm in large geophysical applications may help to tune localization for improved ensemble filter performance.