Estimation of lightning channel-base current from far electromagnetic field in the case of inclined channel

The inclination of a lightning return-stroke channel significantly affects the waveform of the associated electromagnetic field. In this paper, we have derived mathematical expressions to estimate the peak and waveshape of lightning return-stroke current at the channel base from the waveform of electromagnetic field observed more than some tens of kilometers away from an inclined lightning channel. Three models of the lightning return stroke are considered, which are the transmission-line (TL) model, the modified TL model with linear current decay with height (MTLL), the modified TL model with exponential current decay with height (MTLE). The peak of the lightning return-stroke current at the channel base is estimated from the peak of observed lightning electric or magnetic field using an analytical relation between the peak of channel-base current and that of the radiation field component for an inclined channel. The waveform of the channel-base current is reconstructed from the electric or magnetic field waveform using a relation between the channel-base current and the sum of induction and radiation field components for an inclined channel. It has been shown that the peak and waveshape of current at the base of an inclined channel are sufficiently accurately estimated with the proposed expressions. This work is the first attempt to solve the inverse problem (infer source parameters from electromagnetic fields) for the case of inclined lightning channel. Solving this problem is important for developing methodology of remote measurements of lightning currents.