Time Correlations of Lightning Flash Sequences in Thunderstorms Revealed by Fractal Analysis

By using the data of lightning detection and ranging system at the Kennedy Space Center, the temporal fractal and correlation of interevent time series of lightning flash sequences in thunderstorms have been investigated with Allan factor (AF), Fano factor (FF), and detrended fluctuation analysis (DFA) methods. AF, FF, and DFA methods are powerful tools to detect the time-scaling structures and correlations in point processes. Totally 40 thunderstorms with distinguishing features of a single-cell storm and apparent increase and decrease in the total flash rate were selected for the analysis. It is found that the time-scaling exponents for AF (α _AF) and FF (α _FF) analyses are 1.62 and 0.95 in average, respectively, indicating a strong time correlation of the lightning flash sequences. DFA analysis shows that there is a crossover phenomenon—a crossover timescale (τ _c) ranging from 54 to 195 s with an average of 114 s. The occurrence of a lightning flash in a thunderstorm behaves randomly at timescales <τ _c but shows strong time correlation at scales >τ _c. Physically, these may imply that the establishment of an extensive strong electric field necessary for the occurrence of a lightning flash needs a timescale >τ _c, which behaves strongly time correlated. But the initiation of a lightning flash within a well-established extensive strong electric field may involve the heterogeneities of the electric field at a timescale <τ _c, which behave randomly.