The Lightning Differential Space framework: multiscale analysis of stroke and flash behavior

Abstract. Lightning flashes play a key role in the global electrical circuit, serving as markers of deep convection and indicators of climate variability. However, this field of research remains challenging due to the wide range of physical processes and spatiotemporal scales involved. To address this challenge, this study utilizes the Lightning Differential Space (LDS), which maps lightning stroke intervals onto a parameter space defined by their temporal and spatial derivatives. Using data from the Earth Networks Total Lightning Network (ENTLN), we analyze the Number Distribution LDS clustering patterns across specific seasons in three climatically distinct regions: a tropical rainforest region (Amazon), a subtropical marine environment (Eastern Mediterranean Sea), and a mid-latitude continental region (Great Plains in the U.S.). The LDS reveals a robust clustering topography composed of “allowed” and “forbidden” interval ranges, which are consistent across regions, while shifts in cluster position and properties reflect the underlying regional meteorological conditions. As an extension of the LDS framework, we introduce the Current Ratio LDS, a new diagnostic for identifying flash initiation by mapping the ratio of peak currents between successive strokes into the LDS coordinate space. This space reveals a spatiotemporal structure that enables a clearer distinction between local and regional scales. It also reveals a distinct cluster, suggesting a possible teleconnection between remote strokes, spanning tens to hundreds of kilometers. Together, the Number Distribution LDS and the novel Current Ratio LDS provide a scalable, data-driven framework for analyzing and interpreting large datasets of CG lightning activity. This approach strengthens the ability to characterize multiscale lightning behavior, offers a framework for evaluating model representations of stroke and flash processes, and provides a basis for developing diagnostics relevant to operational monitoring and forecasting of lightning activity.