Light intensity emitted from the lightning channel: comparison of different return stroke models

Abstract

The intensity of the light pulse emitted from the lightning channel during the return stroke process is analysed. For the most frequently accepted value of the real lightning return stroke velocity, the time dependence of the apparent height and the apparent velocity are calculated by the causality consideration. The experimentally observed decrease of the apparent return stroke velocity along the channel of more than 25% is partly explained. Five return stroke models are considered and compared: Bruce-Golde (BG), transmission line, modified transmission line (MTL), travelling current source (TCS) and Diendorfer-Uman (DU) models. The expression for the total emitted light intensity, its rise-time and the peak light intensity along the channel are carried out. At close distances the BG, the TCS and the DU models give approximately the same shape of total light intensity as the channel-base current. The substantially longer rise-time of the emitted light signal at medium distances is explained by the relatively slow geometrical growth of the lightning channel. All models except the TL model propose the exponential decrease of the peak light intensity with the channel height which is in agreement with the experimental data. Simple expressions connecting the channel decay constant of the light intensity, return stroke velocity and the current-decay constant at the channel base in the case of the BG, the TCS and the DU models are derived. None of the models can adequately describe the increase of the light intensity rise-time along the channel observed at heights above 1 km. It is concluded that simultaneous measurements of the channel decay constant and the parameters of the channel-base current are necessary to prove the validity of any particular model as well as to calculate the return stroke velocity.