Lightning can be seen as a large-scale cooperative phenomenon, which may evolve in self-similar cascaded way. Using the electric field waveforms recorded by the slow antenna system, the mono-and multifractal behaviors of 115 first return strokes in negative cloud-to-ground discharges have been investigated with wavelet multi-resolution based multifractal method. The results show that the return stroke process, in term of its electric field waveform, has apparent fractality and strong degree of multifractality. The multifractal spectrums obtained for the 115 cases are all well fitted to a modified version of the binomial cascade multifractal model. The width of the multifractal spectrums, which measure the strength of multifractality, is 1.6 in average. The fractal dimension of the electric field waveforms ranges from 1.2 to 1.5 with an average of 1.3, a similar value to the fractal dimension of the lightning channel obtained by others. This suggests that the lightning-produced electric fields may appear the same fractal dimension as its channel. The relationship between the peak current of a return stroke and the charge deposition in its channel was also discussed. The results suggest that the wavelet and scaling analysis may be a powerful tool in interpretation of the lightning-produced electric fields and therefore in understanding of the lightning.

The effect of ground altitude on lightning striking distance has been investigated based on a bi-directional leader model. The model, which is a development of that proposed originally by Mazur and Ruhnke in 1998, enables the calculation of leader channel parameters, such as leader charge density, leader current, leader potential, and lightning striking distance to flat ground. In the model, the lightning striking distance is directly related to the critical electric field in the negative streamer zone in front of the leader tip and to the leader potential. The former may vary with the ground altitude above sea level and the latter may also be affected by it. Based on this thought and on the bi-directional leader model, the effect of regional ground altitude on lightning striking distance was investigated. The result shows that the striking distance increases significantly as the ground altitude increases. This is because the critical electric field necessary for sustaining the negative streamer zone decreases as the ground altitude increases. The result is useful to both physical and engineering application.

[1] This paper presents the first analysis of fractal dynamics of lightning initiation process with a coherent approach. Using experimental data obtained from a broadband interferometer system operating at a bandwidth of 25-100 MHz, the sequences of inter-pulse time interval of the VHF radiation pulses emitted during the lightning initial breakdown process were analyzed with the multifractal detrended fluctuation analysis (MF-DFA) method. For 63 lightning flashes analyzed, it was found that there is an apparent long-range time correlated and nonlinear cascade behavior within the initiation breakdown process of the lightning. This result suggests that the initiation of lightning may be associated with progressively building up of correlated strong electrical field regions by self-similar scaling up (inverse cascading) of discharges across scales from small to large. The result may be promising toward our understanding of lightning initiation. Citation: Gou, X., M. Chen, Y. Du, and W. Dong (2010), Fractal dynamics analysis of the VHF radiation pulses during initial breakdown process of lightning, Geophys.