Can we model the statistical distribution of lightning location system errors better?

Lightning location systems geolocate lightning strokes. Given assumptions made in the geolocation models, errors in the reported locations can occur. Modelling these errors as a bivariate Gaussian distribution of historic stroke detections has found success in the form of confidence ellipses. However, the presence of outliers - strokes with large location errors - indicate that there is a better model for these errors. The Students’ t-distribution is a “heavier” tailed distribution. This paper investigates whether the bivariate Students’ t-distribution is a better model for such errors. A methodology for modelling and evaluating the distribution of location errors using maximum likelihood estimation, expectation-maximization and a Mahalanobis distance quality-of-fit test is described. This method is applied to stroke reports from the South African Lightning Detection Network and the Austrian Lightning Detection and Information System time-correlated with photographed lightning events to the Brixton Tower, South Africa and current measurements to the Gaisberg Tower, Austria respectively. In both cases, we find outliers in the distribution of location errors - even as the performance of the networks increase. Using the Mahalanobis test, we find the bivariate Students’ t-distribution to be a better statistical model for both the South African and the Austrian events.