Mj\"olnir: A Deep Learning Parametrization Framework for Global Lightning Flash Density

Recent advances in AI-based weather forecasting models, such as FourCastNet, Pangu-Weather, and GraphCast, have demonstrated the remarkable ability of deep learning to emulate complex atmospheric dynamics. Building on this momentum, we propose Mj\"olnir, a novel deep learning-based framework for global lightning flash density parameterization. Trained on ERA5 atmospheric predictors and World Wide Lightning Location Network (WWLLN) observations at a daily temporal resolution and 1 degree spatial resolution, Mj\"olnir captures the nonlinear mapping between large-scale environmental conditions and lightning activity. The model architecture is based on the InceptionNeXt backbone with SENet, and a multi-task learning strategy to simultaneously predict lightning occurrence and magnitude. Extensive evaluations yield that Mollnir accurately reproduces the global distribution, seasonal variability, and regional characteristics of lightning activity, achieving a global Pearson correlation coefficient of 0.96 for annual mean fields. These results suggest that Mj\"olnir serves not only as an effective data-driven global lightning parameterization but also as a promising AI-based scheme for next-generation Earth system models (AI-ESMs).