Correcting Correlation Errors in Ensemble Filters: An Automated Alternative to Localization

High performance ensemble Kalman filters for geophysical applications have required empirical methods to correct for errors in ensemble covariances. The two most common approaches are inflation to control errors in the variance and localization to control errors in correlation. Adaptive methods that automatically estimate appropriate values of inflation as an integral part of the ensemble filter process have been used for a number of years and work well for most applications.

Here, an alternative to localization is described in which errors in the ensemble correlations are assumed to be due to sampling errors from the use of small ensembles. An explicit estimate of the probability distribution function (PDF) for the correlation between an observation and a state variable is produced as part of the filtering algorithm. The maximum likelihood value of this correlation distribution is then used in the ensemble filter instead of the ensemble sample correlation.

Results are shown for applications of this correlation error reduction method in observing system simulation experiments with an atmospheric general circulation model. The method is able to produce ensemble analyses with significantly smaller root mean square error than can be achieved with carefully tuned traditional localization functions. The method requires no prior knowledge about the correlation distributions and can be applied without tuning in this atmospheric model. When combined with adaptive inflation, this method may be able to produce good assimilations for many types of geophysical problems without tuning.