Analysis of the Static and Dynamic Fractal Dimension of Downward and Upward Discharges in Negative Downward Flashes

In this study, field records of natural downward negative lightning discharges obtained through high-speed video camera observations are analyzed. The study focuses on determining the fractal dimension as a metric for describing the structural complexity of downward negative lightning discharges; three fractal dimension estimation methods are implemented using custom-developed MATLAB algorithms. Additionally, this work investigates for the first time the fractal behavior of upward leaders, which play a critical role in the lightning attachment process. A dynamic analysis is also conducted on the development of downward negative leaders during their propagation, focusing on the morphological features and temporal evolution, in cases when high-speed video recordings were available enabling frame by-frame examinations. The estimated fractal dimensions are compared with values from previous studies for validation. Results of this study may contribute to a deeper understanding of the lightning propagation and attachment dynamics and may assist in refining lightning attachment models, thereby improving the design of lightning protection systems.