Efficient Concurrent Estimation of Localization for Ensemble Data Assimilation

Localization of the impact of observations is required when using computationally affordable ensemble sizes for ensemble data assimilation in large geophysical prediction models. In the earliest applications, localization was a function only of the horizontal distance between an observation and a state variable to be updated. However, it is now apparent that improved assimilation quality can be obtained using more advanced localization functions that also depend on the vertical distance between the observation and state variable, the type of the observation and the state variable, and even the details of the synoptic situation. For instance, there is evidence that a good localization of a satellite radiance observation has a much different structure from a good localization for a radiosonde temperature. Localization for a radiosonde temperature may be quite different in a quiescent atmosphere than in the presence of widespread convection. For more novel types of assimilation, for instance in coupled earth system models, there may be no good a priori estimate of how to localize the impact of an 850 hPa wind observation on the salinity at 50 meters depth or the soil moisture at 10 centimeters.

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.