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 chal-lenge with the ensemble Kalman filter (EnKF) is that no ensemble members have nonzero 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 nonzero 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 perturba-tions are applied if the number of ensemble members with nonzero lightning flashes is smaller than a prescribed threshold (Nmin). Observing system simulation experiments for a heavy precipitation event in Japan show that regression-based en-semble perturbations increase the ensemble spread and successfully induce the analysis increments associated with convec-tion even if only a few members have nonzero lightning flashes. Furthermore, applying regression-based ensemble perturbations improves the forecast accuracy of precipitation although the improvement is sensitive to the choice of Nmin.