Using Bivariate Gaussian Distribution Confidence Ellipses of Lightning Flashes for Efficiently Computing Reliable Large Area Density Maps

This paper presents an enhanced method used to deliver the 50th percentile location uncertainty ellipse given by lightning locating systems for lightning flash density maps with very fine detail of about 100 m $\times100$ m (or less) over a vast land region spanning thousands of kilometers. Because it is founded on a rigorous mathematical method (without using convolution operators), this new technique for computing the probabilistic lightning density map coverage represents a significant improvement in terms of precision compared with other techniques identified in the literature. The technique was adapted from a method used to calculate the probability of debris collision for spacecraft, and is based on a probabilistic approach to lightning flash impact over a facility. As a proof of concept, a Java language algorithm was implemented. This algorithm was applied to a set of 11.34 million lightning flashes over the territory of Spain registered between 2003 and 2012, producing a lightning density map coverage with a cell size of 2 arcsecond (~60 m).