Electric and Magnetic Fields Predicted by Different Electromagnetic Models of the Lightning Return Stroke Versus Measured Fields

We have compared current distributions along a vertical lightning channel above flat ground excited at its bottom by a lumped current source and electromagnetic field waveforms at different distances from the channel, calculated using the finite-difference time-domain method, for different lightning return-stroke electromagnetic models. The channel representations considered include a vertical, perfectly conducting wire surrounded by air (type 1), a vertical wire in air loaded by additional distributed series inductance L = 2.5 mu H/m and distributed series resistance R = 0.5 Omega/m (type 2), a vertical, perfectly conducting wire embedded in dielectric of relative permittivity epsilon(r) = 4 that occupies the entire half space (type 3), a vertical, perfectly conducting wire embedded in a 10-m-radius dielectric cylinder of epsilon(r) = 400 surrounded by air (type 4), and a vertical wire embedded in a 10-m-radius cylinder of epsilon(r) = 5 and relative permeability mu(r) = 5 surrounded by air (type 5). For the type-1 model, the speed of the current wave propagating along the lightning channel is essentially equal to the speed of light, upsilon = c. For type-2, type-3, and type-5 models, upsilon = 0.5c, and for the type-4 model, upsilon = 0.7c. Models of types 2 and 5 reproduce the maximum number of characteristic features of electric and magnetic field waveforms observed at distances ranging from 1 to 200 km from natural lightning and at distances ranging from tens to hundreds of meters from rocket-triggered lightning. Modifications of type-2 and type-5 models in which distributed channel resistance is not uniform can reproduce all five characteristic features. The influence of lossy ground with conductivity as low as 0.1 mS/m on vertical electric and azimuthal magnetic fields within about d = 5 km is not significant. The initial peak of vertical electric field at d = 50 km for sigma = 0.1 mS/m is 20% smaller than that for sigma = infinity. The 10%-90% rise time at d = 50 km is 5 mu s for s = 0.1 mS/m versus 1 mu s for sigma = infinity.