An improved ray theory and transfer matrix method‐based model for lightning electromagnetic pulses propagating in Earth‐ionosphere waveguide and its applications

Abstract

An improved ray theory and transfer matrix method‐based model for a lightning electromagnetic pulse (LEMP) propagating in Earth‐ionosphere waveguide (EIWG) is proposed and tested. The model involves the presentation of a lightning source, parameterization of the lower ionosphere, derivation of a transfer function representing all effects of EIWG on LEMP sky wave, and determination of attenuation mode of the LEMP ground wave. The lightning source is simplified as an electric point dipole standing on Earth surface with finite conductance. The transfer function for the sky wave is derived based on ray theory and transfer matrix method. The attenuation mode for the ground wave is solved from Fock's diffraction equations. The model is then applied to several lightning sferics observed in central China during day and night times within 1000 km. The results show that the model can precisely predict the time domain sky wave for all these observed lightning sferics. Both simulations and observations show that the lightning sferics in nighttime has a more complicated waveform than in daytime. Particularly, when a LEMP propagates from east to west (Φ = 270°) and in nighttime, its sky wave tends to be a double‐peak waveform (dispersed sky wave) rather than a single peak one. Such a dispersed sky wave in nighttime may be attributed to the magneto‐ionic splitting phenomenon in the lower ionosphere. The model provides us an efficient way for retrieving the electron density profile of the lower ionosphere and hence to monitor its spatial and temporal variations via lightning sferics.

FDTD Modeling of LEMP Propagation in the Earth‐Ionosphere Waveguide With Emphasis on Realistic Representation of Lightning Source

“…For nighttime conditions, β is set to 0.8 km −1 and h ′ is set to 84 km, while for daytime conditions β is set to 0.3 km −1 and h ′ is set to 70 km. The adopted values of h ′ and β are the same as those used by Qin et al () (see their Table ) in computing the field waveforms shown in their Figures 4 and 5. Equation overestimates the ionospheric conductivity at h > 90 km or so, but this does not influence any of our results, which remain essentially the same when the conductivity is capped at 1 S/m for h > 90 km.…”

“…In other words, the entire computational domain above ground is assumed to be lossy and nonuniform, but isotropic and linear. In section 4, we will test the validity of our simplified approach against measurements presented by Qin et al () and show that it is justified, at least for daytime conditions.…”

“…In this section, for testing the validity of our simplified model, we attempted to reproduce the vertical electric field waveforms (including sky waves) measured at different distances and directions of propagation (angles ϕ between the direction to the source and direction of Earth's magnetic field; for example, ϕ = 0 corresponds to propagation direction from north to south) by Qin et al ().…”

“…Qin et al () developed a new version of the ray‐theory model for simulating propagation of LEMP in the EIWG (in the frequency band of 3 kHz to 150 kHz, which is similar to that in the model of Jacobson et al (, )). The lightning source was represented by a point dipole placed on the surface of finitely conducting (lossy) ground.…”

“…The presented results show that the model reasonably reproduces the observed first sky wave waveforms. Qin et al () concluded that their model is adequate for predicting lightning sky waves in VLF/LF bands at distances up to 1,000 km.…”