We present an improved finite-difference time-domain (FDTD) method based on the moving computational domain technique for the calculation of lightning-generated fields over large-scale irregular terrain. In the improved method, a spatial window moving along with the wavefront at the speed of light is defined and, at each time step, the field components are updated only in that window. The time delay of the wavefront arrival caused by the propagation effect and the irregular terrain is considered when determining the width of the moving window. The efficiency and accuracy of the improved model are validated by comparing its results with those calculated by conventional FDTD, considering an example of lightning-radiated electromagnetic field propagation over complex mountainous terrain. The gain in the CPU time can be as high as a factor of 4 to 5, while the accuracy remains unchanged with respect to the conventional FDTD.

In this article, the effect of a mountain located on the propagation path of lightning-radiated electromagnetic fields was systematically studied by using the two-dimensional finite-difference time-domain method (2-D FDTD), considering the influence of the return stroke (RS) type, the ground conductivity, the mountain height and the width at the base, its position, and the observation distance. The field peak reduction and the wave arrival time delay, compared with those for the perfectly conducting flat ground, are analyzed in detail. The results show that, with an increase in the mountain height, the field peak reduces and the wave arrival time delay increases. The wave arrival time is insensitive to the change of mountain widths. The terrain envelope method can be used to estimate the additional time delay introduced by the mountain. For a mountain lower than 1 km or so, the additional attenuation effect of the mountain on the field peak can be ignored for most practical purposes. Furthermore, the propagation process of the lightning-radiated electromagnetic wave over the mountain was studied by analyzing the spatiotemporal evolution characteristics of the field. The analysis shows that the electromagnetic wave propagates to the back of the mountain through the diffraction process at the mountaintop.

This paper presents the computed lightning-radiated vertical electric field and azimuthal magnetic field at the ground level at observing distances ranging from 0.3 to 50 km from the lightning channel for striking the cone-shaped mountain top, by using the two-dimensional finite-difference time-domain method in cylindrical coordinate systems. It is found that the mountain height and the inclination angle have a significant effect on the lightning-radiated electromagnetic field both for the close and far observing distances. For the lightning-radiated vertical electric field, the enhancement of the far field beyond several kilometers (mainly radiation field component) is due to the reflection process in the transition between the mountain terrain and the flat ground, but the reduction of close field near the mountain terrain (mainly quasi-electrostatic field component) is due to the shadowing effect, but not due to such reflection. For the lightning-radiated azimuthal magnetic field, the field values for different mountain terrains, including the mountain height and inclination angle, increase both for close and far observing distances.

A new approximate method for lightning-radiated extremely low-frequency (ELF) and very low-frequency (VLF) ground wave propagation over intermediate ranges is presented in this paper. In our approximate method, the original field attenuation function is divided into two factors in frequency domain representing the propagation effect of the ground conductivity and Earth’s curvature, and both of them have clearer formulations and can more easily be calculated rather than solving a complex differential equation related to Airy functions. The comparison results show that our new approximate method can predict the lightning-radiated field peak value over the intermediate range with a satisfactory accuracy within maximum errors of 0.0%, −3.3%, and −8.7% for the earth conductivity of 4 S/m, 0.01 S/m, and 0.001 S/m, respectively. We also find that Earth’s curvature has much more effect on the field propagation at the intermediate ranges than the finite ground conductivity, and the lightning-radiated ELF/VLF electric field peak value (V/m) at the intermediate ranges yields a propagation distance d (km) dependence of d−1.32.