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.

闪电观测与对流云的发展密切相关，并且在高分辨率数值天气预报模式的对流尺度数据同化方面具有潜力。集合卡尔曼滤波（EnKF）面临的一个主要挑战是，在观测到闪电的地方，没有集合成员具有非零闪电。在这种情况下，不同的模式状态都给出零闪电，EnKF无法有效地同化非零闪电数据。这个问题被称为零梯度问题。本研究通过在整个计算域中添加基于回归的集合扰动来解决零梯度问题，这些扰动源自模拟闪电和大气变量之间的统计关系。如果具有非零闪电的集合成员数量小于规定的阈值（Nmin），则应用基于回归的集合扰动。对日本一次强降水事件的观测系统模拟实验表明，基于回归的集合扰动增加了集合离散度，并且即使只有少数成员具有非零闪电，也能成功地引发与对流相关的分析增量。此外，应用基于回归的集合扰动提高了降水的预报准确性，尽管这种改进对Nmin的选择很敏感。