Characterisation and modelling of lightning strikes in time and space

Lightning is inherently a spatio-temporal process with individual lightning strikes represented by their time of occurrence and spatial coordinates. In this paper, we characterise and model lightning strikes in time and space from single thunderstorms, considering each set of lightning strikes to be a set of point events. This allows for real-world datasets to characterise lightning strikes and their physical properties. We select two case studies of severe thunderstorm systems over the UK, based on their synoptic analysis information as available in the published literature. This information allows us to separate the lightning strike dataset into subsets representing individual thunderstorms producing these strikes. We first identify three supercell thunderstorms with 7955, 11988 and 5655 lightning strikes from the larger storm system that crossed the English Midlands on 28 June 2012. A second set of three structurally different severe thunderstorms with 4218, 455 and 1926 lightning strikes was selected from a severe storm system across northern England on 1 to 2 July 2015. The six lightning strike datasets are representative of individual thunderstorms and each examined with regards to three physical properties: storm movement speed, lightning inter-event time distribution and lightning spatial spread distribution about the storm track. We use a least-squares plane fit in the spatio-temporal domain to estimate a range of representative movement speed values, finding 46-52 km/h for the first storm system and 67-105 km/h for the second. For inter-event time distribution, we find that values range from 0.01 to 100 s with all thunderstorms showing two peaks in density values around 0.1 s and between 1 and 10 s. To identify temporal structure in the inter-event time series, we perform autocorrelation analysis in natural time, which returns statistically significant autocorrelation values for all thunderstorms with some storms exhibiting short-range and others long-range autocorrelation. For estimating the storm track about which the orthogonal distances are calculated between the storm track and the lightning strikes, we consider orthogonal distance regression in the two-dimensional space domain. The analysis is done similarly to inter-event times for these orthogonal distances. We find a typical range of spatial spread values to be up to 50 km in magnitude, with one thunderstorm having exceptionally high values of up to 150 km. Autocorrelation analysis of these orthogonal distance values in natural time also return significant results that vary between individual thunderstorms. Finally, we present a synthetic lightning strike model where we can freely select the number of individual storms, their starting points, direction and movement speeds. For each storm, the point events after the starting point are produced about the storm track with inter-event times and orthogonal distance values taken from synthetic time series based on the analysis done during the characterisation. The characterisation in this paper of lightning strikes in time and space is representative of real-world severe thunderstorms and can inform statistical models to simulate lightning strike events.