Why do some lightning return stroke models not reproduce the far-field zero crossing?
In this paper, we investigate the reasons why some return stroke models do not reproduce one of the characteristic features of the electromagnetic fields radiated by lightning, namely the far-field inversion of polarity with a zero crossing occurring in the tens of microseconds range. This study leads to physical insights into the behavior of the return stroke attenuation and speed as a function of height. Making reference to the properties of time domain far fields, we show that any one of the existing lightning return stroke channel models, including the electromagnetic models, sometimes known as Antenna Theory models, and the engineering models, should be able to predict a zero crossing in the far field as long as the duration of the return stroke current and the height of the channel are finite. However, the present versions of most of the available engineering and electromagnetic models predict the zero crossing to occur at times that fall well beyond those observed experimentally. We identify three mechanisms responsible for the time of occurrence of the reversal of polarity in the far fields: the current attenuation along the channel, the duration of the return stroke current, and the return stroke speed. The analysis of the MTLE and MTLL engineering models shows that the higher the attenuation of the current along the channel, the earlier the polarity reversal of the vertical electric field. Also, for a given value of the attenuation factor, higher propagation speeds correspond to earlier polarity reversal times. For the TCS model, in which the only adjustable parameter is the return-stroke speed, we show that the far-field zero crossing occurs considerably later than the values predicted by both the MTLE and the MTLL models. This is shown to be essentially due to the fact that the decrease of the current wave along the channel according to the TCS model is less pronounced than the current attenuation predicted by the MTLE and MTLL models. Furthermore, it is shown that, in the electromagnetic models, a uniformly distributed resistance along the channel does not lead to a zero crossing in the tens of microseconds range even for large resistance values. This is due to the significant increase of the current pulse duration, as it propagates along the channel as a result of the dispersion effect. The correct zero crossing time, however, can indeed be successfully reproduced if a nonlinear channel resistance is used, which prevents the significant increase of the current pulse duration as it propagates up the channel. Finally, based on the predictions of the MTLE, MTLL, and TCS models, it is shown that the zero crossing time decreases as the observation point moves farther away from the lightning channel, with the amount of variation of less than 10%.