Lightning Location System Detections as Evidence: A Unique Bayesian Framework

Abstract

Modern lightning location systems (LLSs) remotely detect propagated electromagnetic fields and geolocate them for a better understanding of the lightning phenomenon. In recent years, they have become powerful tools for assessing situations where lightning may be the cause of damage. However, due to the random errors that occur in the remote sensing of electromagnetic propagation, such systems have median location accuracies between 50 and 100 m. This means that there is always some uncertainty in reported geolocations of lightning flashes. To date, there is no effective or standardized method for quantifying this uncertainty and using LLS reports as evidence. This article presents a unique solution to this problem by developing a Bayesian framework. In the field of forensic investigation and engineering, the Bayesian approaches to reporting evidence are widely accepted in legal forums. This article describes the necessary prior probability and likelihood functions (Gaussian mixture model, bivariate Gaussian, and Students’ t-distributions, respectively), and the framework is assessed by comparison with ground-truth events—photographed lightning events to a known location, the Brixton Tower in Johannesburg, South Africa. The framework has a true positive rate between 97% and 99% and 66% and 100% and a true negative rate between 98% and 99% using the bivariate Gaussian and Students’ t-likelihood functions, respectively. Utilizing the bivariate Students’ t-likelihood function achieves a much lower false-positive rate (0.05% to 0.2%) than the bivariate Gaussian likelihood function (0.7%–2%).