Multivariate Correlations in Ensemble Data Assimilation: Balance Operators and Localization

In numerical weather prediction, the ensemble derived background error covariance contains sampling error due to limited computational resources.  Spatial localization is typically applied, eliminating long distance correlations that are likely spurious, but also frequently disrupting balance.  In this work, we apply a balance operator, traditionally implemented in variational systems, to two ensemble data assimilation schemes to increase the balance in the presence of localization.  We show that the type of spatial localization, either performed on the observation or background error covariance matrix, greatly affects the impact of the balance operator.  Results from an intermediate complexity model and preliminary findings from NCEP’s Global Forecast System (GFS) will be presented.

With limited ensemble size, spurious correlations can also exist between variable types that are not physically related.  Like spatial localization, correlations between these variables can be removed through modifying the observation or background error, referred to as variable localization.  We present a unified view of variable localization applied in several ensemble methods.  These methods will become critical for coupled data assimilation systems in the future.  In the nearer term, it has the potential for improving the analysis of cloud water which can be contaminated by spurious, low amplitude correlations.  The viability of this method will be explored within the GFS.