Filtered Ensemble-based Tangent Linear Model for the Operational EnVar Data Assimilation System

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.