Adaptive Localization of Observation Impact in Ensemble Data Assimilation

Localization of the impact of observations on state variables is essential to obtain good performance from ensemble filters for geophysical data assimilation problems. In general, the localization for a particular application has been obtained by tuning the width of an approximately gaussian function of the distance between an observation and a state variable. Evaluating the effect of a given localization choice is so expensive for realistic applications that very little work has been done on exploring the impact of more general localization functions.

Estimates of the localization required to minimize the impacts of sampling error in ensemble filters can be obtained by running two or more ensemble filters that differ only in their initial ensemble conditions. A more sophisticated algorithm runs two or more filters that adaptively estimate localization during the assimilation and applies this localization in each of the filters. This latter method is an extension of the group filter algorithm that has been used to tune localization in some large geophysical applications.

These two methods for estimating localization will be described and evaluated in a sequence of observing system simulation experiments. The estimated localizations will be compared to estimates that are obtained by optimizing the fit of an ensemble assimilation posterior to the truth in an observing system simulation experiment. Differences between these estimates of localization quantify how much of the need for localization is due to causes other than ensemble sampling error such as nonlinearity and nongaussianity. Implications for building improved localization for large geophysical] applications are discussed.