Multifractal spectra of lightning strike maps using entropy and wavelet analyses

This paper describes a multifractal analysis of physical lightning strike maps obtained for Manitoba through the Canadian Lightning Detection Network. Cloud-to-ground discharges or lightning strikes are physical phenomena which may have adverse effects on power transmission and delivery. Predicting the geographical and temporal distribution of lightning strike maps through modelling can help power system designers to improve the protection of existing and new power systems and transmission lines. In order to compare the model to physical data, their characterization is required. Since lightning strike maps are highly nonlinear, nonstationary and stochastic, ordinary analyses and measures are insufficient to characterize these phenomena. Since self affinity of the lightning strike maps is the indication of multifractality, complexity measures such as the Renyi fractal dimension spectrum (RS) and Mandelbrot singularity spectrum (MS) are appropriate for such fractal analysis. In this paper, we investigate the multifractality of lightning strike maps in Manitoba through the RS and MS. Both methods generate similar results and show that the maps are multifractal. Comparing the range of results with a similar phenomenon, diffusion limited aggregates (DLA), supports the accuracy of calculations as well.