Abstract
In Part I of this two-part study, a new theory for optimal linear filtering of covariances sampled from an ensemble of forecasts was detailed. This method, especially designed for data assimilation (DA) schemes in numerical weather prediction (NWP) systems, has the advantage of using optimality criteria that involve sample estimated quantities and filter output only. In this second part, the theory is tested with real background error covariances computed using a large ensemble data assimilation (EDA) at the convective scale coupled with a large EDA at the global scale, based respectively on the Applications of Research to Operations at Mesoscale (AROME) and ARPEGE operational NWP systems. Background error variances estimated with a subset of this ensemble are filtered and evaluated against values obtained with the remaining members, which are considered as an independent reference. Algorithms presented in Part I show relevant results, with the homogeneous filtering being quasi optimal. Heterogeneous filtering is also successfully tested with different local criteria, yet at a higher computational cost, showing the full generality of the method. As a second application, horizontal and vertical localization functions are diagnosed from the ensemble, providing pertinent localization length scales that consistently depend on the number of members, on the meteorological variables, and on the vertical levels.
