This study demonstrates the advantages of scale- and variable-dependent localization (SDL and VDL) on three-dimensional ensemble variational data assimilation of the hourly-updated high-resolution regional forecast system, the Rapid Refresh Forecast System (RRFS). SDL and VDL apply different localization radii for each spatial scale and variable, respectively, by extended control vectors. Single-observation assimilation tests and cycling experiments with RRFS indicated that SDL can enlarge the localization radius without increasing the sampling error caused by the small ensemble size and decreased associated imbalance of the analysis field, which was effective at decreasing the bias of temperature and humidity forecasts. Moreover, simultaneous assimilation of conventional and radar reflectivity data with VDL, where a smaller localization radius was applied only for hydrometeors and vertical wind, improved precipitation forecasts without introducing noisy analysis increments. Statistical verification showed that these impacts contributed to forecast error reduction, especially for low-level temperature and heavy precipitation.

The ensemble-based tangent linear model (ETLM), which evolves the static background error covariance (BEC) in time in the data assimilation window, is beneficial for improving the analysis and avoids the need for developing the tangent linear forecast model and its adjoint as in four-dimensional variational data assimilation (4DVar). This study proposes to apply the filtered ETLM (FETLM), which is composed of ensemble perturbations at limited time slots and localized with a quasi-Gaussian filter in the way that avoids calculation of the inverse matrix. Tests with the Lorenz (1996) model showed that FETLM evolved the static BEC as in 4DVar and improved the analysis. In experiments with the FETLM implemented in the hourly-updated regional forecast system, the Rapid Refresh Forecast System, the imbalance of the analysis was mitigated due to the flow-dependent BEC. Moreover, the cross-variable covariance in the FETLM made it possible to assimilate radar reflectivity effectively even without hydrometeors as control variables.

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.