Regression-Based Ensemble Perturbations for the Zero-Gradient Issue Posed in Lightning-Flash Data Assimilation with an Ensemble Kalman Filter

Lightning flash observations are closely associated with the development of convective clouds and have a potential for convective-scale data assimilation with high-resolution numerical weather prediction models. A main challenge with the ensemble Kalman filter (EnKF) includes that no ensemble members have non-zero lightning flashes in the places where a lightning flash is observed. In this situation, different model states provide all zero lightning, and the EnKF cannot assimilate the non-zero lightning data effectively. This problem is known as the zero-gradient issue. This study addresses the zero-gradient issue by adding regression-based ensemble perturbations derived from a statistical relationship between simulated lightning and atmospheric variables in the whole computational domain. Regression-based ensemble perturbations are applied if the number of ensemble members with non-zero lightning flashes is smaller than a prescribed threshold (Nmin). Observing system simulation experiments for a heavy precipitation event in Japan show that regression-based ensemble perturbations increase the ensemble spread and successfully induce the analysis increments associated with convection even if only a few members have non-zero lightning flashes. Furthermore, applying regression-based ensemble perturbations improves the forecast accuracy of precipitation although the improvement is sensitive to the choice of Nmin.