A comparison of different approaches to simulate a nonlinear channel resistance in lightning return stroke models

[1] Different physical models that describe the time variation of the channel resistance are investigated in a lightning return stroke model. Such models consider one of the three following hypotheses: (1) the channel resistance decays exponentially with time; (2) the channel resistance decays with the radial expansion of the channel core, which is assumed to be described by the strong-shock approximation, or (3) the channel resistance varies with time according to three different arc resistance models (defined by Toepler, Barannik and Kushner et al.). Analyses illustrate the effect of a time-varying channel resistance on channel currents and corresponding electromagnetic fields. It is shown that the strong-shock approximation is able to predict typical features of experimentally observed lightning electromagnetic fields and return stroke speed profiles. It is also shown that results predicted by the strong-shock approximation can be qualitatively reproduced by either using simplified arc resistance equations (such as Toepler's and Barannik's ones) or considering an exponential decay of the channel resistance with attenuation constants linearly increasing with height.