Does a lightning channel show a fractal?

Forecasting the striking point of a lightning flash is important for the reduction of lightning hazards. Field campaigns have been conducted, and the features of leader progression have been investigated for this final goal. Both streak and still camera observations are used, because we can obtain useful information on the leader progression manner and its velocity. A radio interferometer is another useful instrument, by which, we can capture a lightning channel image from its initiation inside the thundercloud to the attachment process to the ground. Though many laborious investigations have been performed and various results have been presented, the exact forecasting of a striking point still remains difficult. To overcome this, numerical simulations of a stepped leader near the ground surface have been carried out using the leader progression model, which has been improved by using the fractal mathematical concept. In other words, the proposed scheme in this paper is a probabilistic procedure. The finite-difference approach is applied to the two-dimensional Poisson's equation to calculate the electric field produced by the charge distribution in a thundercloud. The stepped leaders, which are initiated at the lower part of the cloud and usually proceed towards the ground, are simulated to study the theoretical stepped leader progression. The zig-zags and branches of a lightning channel can also be simulated.