Empirical localization of observation impact 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.