Efficient Concurrent Estimation of Localization for Ensemble Data Assimilation
A number of methods for estimating appropriate localization have been developed in recent years. Several of these assume that localization is required primarily because of sampling error due to small ensembles. For instance, the group filter runs several ensemble filters in parallel and estimates localization from differences in the Kalman gain coefficients. Direct sampling error correction methods make prior assumptions about the distribution of the gain and produce corrections to localizations. Empirical localization functions can be computed using the output of an ensemble OSSE in which the truth is known.
However, these methods require significantly more computation to find good estimates of localization than is required for a single ensemble assimilation. New methods that adaptively estimate good localizations concurrently with a single ensemble filter assimilation are presented. These methods update the estimate of localization at each assimilation time as the ensemble filter proceeds. These methods can converge relatively quickly to effective localization estimates and entail only minimal additional computational cost. The methods are described and the results are compared to the much more expensive methods previously documented. When combined with adaptive inflation algorithms, it is possible to develop completely automated filters that do not require any tuning for some applications.