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

Abstract

Abstract 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) 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 perturbations 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 ensemble perturbations increase the ensemble spread and successfully induce the analysis increments associated with convection 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. Significance Statement This study develops an effective method to use lightning flash observations for weather prediction. Lightning flash observations include precious information of the inner structure of clouds, but their effective use for weather prediction is not straightforward since a weather prediction model often misses observed lightning flashes. Our new method uses ensemble-generated statistical relationships to compensate for the misses and successfully improves the forecast accuracy of heavy rains in a simulated case. Our future work will test the method with real observation data.