Comparison of entropy-based characterization of lightning strike maps using planar and spherical coordinates

In this paper, effects of including the curvature of the Earth in the characterization of the lightning strike maps (LSMs) are studied. Lightning strikes can adversely affect the power generation and distribution systems, and behaviour prediction of such LSMs is of interest for protection and planning in the power industry. Characterization is one of the important stages of the behaviour prediction. We have shown that multifractal measures such as the Renyi fractal dimension spectrum (RS) are appropriate for characterization of such LSMs which are self-affine. The computation of the RS is based on estimating the probability density function (pdf) of the lightning strikes distribution. Since the LSMs range from very large to low densities over a large geographical area such as Manitoba, computing this pdf in planar coordinates is subject to a nonlinear error due to the curvature of the Earth. Thus, modelling and calculating the maps in spherical coordinates yields a better estimation of the pdf. The data of the LSMs have been collected by the Canadian Lightning Detection Network (CLDN) during the year 2002. The LSMs of Manitoba are characterized through regular (using planar coordinates) and modified (using spherical coordinates) RS techniques. The results indicate that regular RS technique alters the characteristics of the feature space, especially in latitudinal direction, and causes sparser features in the feature space, while using the modified RS technique alleviates all these problems, and provides a more accurate characterization which is necessary for a reliable classification of the maps