Analysis of lightning electromagnetic field propagation in mountainous terrain and its effects on ToA-based lightning location systems

In this paper, we analyze the propagation effects on lightning-radiated electromagnetic fields over mountainous terrain by using a three-dimensional (3-D) finite difference time domain (FDTD) method. We also discuss the time delay error in the time-of-arrival (ToA) technique currently used to locate lightning in detection networks, specifically. Furthermore, the accuracy of different approximate methods presented in the literature is discussed and tested by using our 3-D FDTD method. It is found that (1) the time delays and amplitudes of the lightning-radiated electromagnetic fields can be significantly affected by the presence of a mountainous terrain and associated diffraction phenomena; (2) for a finitely conducting ground, the time delay shows a slight increase with the increase of the observation distance, but the time delay resulting from the finite ground conductivity appears to be smaller than that caused by the mountainous terrain; and (3) the timing error associated with the ToA technique depends on the threshold times. Threshold times of 10% and 20% of the peak provide very similar results compared to those corresponding to the peak of the first derivative of the magnetic field, and the threshold time exceeds 50% of the initial rising amplitude of the signal. Furthermore, we have assessed the accuracy of two simplified methods (terrain-envelope method and tight-terrain fit method) to account for the time delays resulting from the propagation in a mountainous terrain. It is found that both methods result in time delays that are in reasonable agreement but always overestimating the results obtained using the full-wave 3-D FDTD approach for the perfectly conducting ground. These two methods represent interesting alternatives to account for the time delay over a nonflat terrain using the terrain model.