A new approach to the study of lightning-strike density distributions

Lightning strikes are physical phenomena which have adverse effects on power delivery systems and lines. Predicting the geographical and temporal distribution of the lightning strike densities through modeling can help power system designers to improve th e protection of the existing and new power systems and transmission lines. In order to compare th e results of the model simulations to the physical data, characterization is required. The distribution of the lightning strike densities generates patterns which ar e highly nonlinear, nonstationary, and stochastic. Traditional single-scale analyzes and measures are insufficient to characterize such structures. Multiscale analysis of these patterns indicates their self-affinity over multiple scales, which is an indication of multifractality of these structures. Con sequently, multifractal analysis methods such as the Rényi fractal dimension spectrum are appropriate candidates for characterization of these density map s. Th is paper investigates con vergence in distribution of the lightning strike maps of Manitoba from 1998 to 2004. In addition, the sensitivity of the multifractal characterization to convergence in distribution is studied. The results indicate a con vergence in statistical distribution for the lightning strike density distributions and strong sensitivity of th e Rényi spectra to th e data variations. This approach could be classified as cognitive engineering of power-delivery systems because it in eludes the sensing of th e environment and extraction of features over many scales and extended duration of time.