Multigrid beta filter for faster computation of ensemble covariance localization

Abstract. This study applies a multigrid beta filter (MGBF) for covariance localization in ensemble-variational (EnVar) data assimilation instead of the conventional recursive filter (RF) to achieve faster computation in a large number of processors. The parallelization efficiency of the MGBF is higher than that of the RF because all-to-all communication to change the computational region of each processor is not necessary. However, the MGBF-based localization additionally requires horizontal variable exchange between processors; its computational cost is proportional to the number of grid points and to the ensemble size, and is generally more expensive than the RF. In this study, we implement the MGBF-based localization both for the single-scale localization and for the scale-dependent localization in the regional atmospheric EnVar data assimilation system. In addition, we clarify that applying a coarser filter grid and omitting filtering except for the coarsest resolution make the computation of the MGBF-based localization several times faster than that of the RF-based one without significantly changing the EnVar analysis.