Further Improvements of Computational Efficiency of the Multigrid Beta Filter (MGBF)

The Multigrid Beta filter (MGBF), a new technique for synthesis of covariances, is being introduced at Environmental Modeling Center (EMC) as a replacement of Recursive Filter (RF). MGBF offers a series of promising features, such as possibility for inclusion of cross-covariances within a variational approach, and the temporal component of fully four-dimensional covariances, while at the same time addresses the computational scaling problems of its predecessor in modeling of the background error. The MGBF is incorporated in the Rapid Refresh Forecast System (RRFS) version of Gridpoint Statistical Interpolation (GSI), and its performance in application to modeling of the background error covariance delivers the expected improvements of scaling and computational efficiency. Recently, through newly developed MGBF package refactored following the object-oriented programming principle, MGBF has been applied to the ensemble-variational (EnVar) data assimilation for localization of the ensemble-based background error covariance, where, where in initial test cases, using a sufficiently large size of the ensemble, MGBF underperformed the RF. This paper will discuss various strategies considered to remove this problem. It will present a series of integrations of a standalone version of the MGBF, in which different ideas were tested, resulting in an astounding turn of events, and leading to a superior performance of MGBF in application to ensemble localization. This is achieved through a better handling of computing resources within the multigrid structure and parallelization of ensemble members. Some of these techniques are also applicable to the MGBF in modeling of the background error covariance.