Cost‐effective hybrid <scp>EnVar</scp> for convective‐scale data assimilation through machine‐learning‐aided background error covariances

Abstract This study introduces a cost‐effective hybrid ensemble‐variational (EnVar) radar data assimilation (DA) approach through a new machine‐learning (ML)‐aided static covariance (ML_BEC). Previous studies employed convective‐scale static BECs to compensate the deficient ensemble covariances in hybrid EnVar. The used static BECs (Z_BEC) often mix the error statistics of the rotating updraft (RU) and flank features for analyzing supercells. In contrast, ML_BEC distinguishes the RU and flank features properly. A random forest model is developed and trained with an accuracy classification score of 0.98 to guide the application of ML_BEC in proper locations. The cost‐effective hybrid EnVar with ML_BEC is demonstrated through the analyses and forecasts of two tornadic supercell cases in Oklahoma. Results show that hybrid EnVar using ML_BEC improves storm analyses and forecasts by more properly analyzing RUs during the DA cycling compared to using Z_BEC. When comparing with pure EnVar using 36‐member ensembles, Z_BEC‐based hybrid EnVar with 12‐member ensembles enhances reflectivity analyses and forecasts; however, it does not improve mesocyclone forecasts. In contrast, ML_BEC‐based hybrid EnVar with 12‐member ensembles achieves further improvements in reflectivity forecasts and produces strong mesocyclone tracks that align with observations. Furthermore, hybrid EnVar using ML_BEC with six‐member ensembles still yields superior performance in reflectivity and mesocyclone forecasts than costly pure EnVar with 36‐member ensembles and Z_BEC‐based hybrid EnVar with 12‐member ensembles, demonstrating a reduction in costs by 71% and 35%, respectively.