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 .

In this paper, we have studied the accuracy of field-to-current conversion factors (FCCFs) presented by Baba and Rakov (2007) for currents inferred from electromagnetic field produced by lightning strike to tall objects, considering the perfectly and finitely conducting ground, respectively. For the perfectly conducting ground, the different FCCFs for the initial peak current at the object top, the short-circuit current peak, the largest peak current at the object top, and the peak current at the object bottom have different accuracy ranging from underestimation of 18% to overestimation of 10% for the reflection coefficients at the two ends of object ρ t = À 0.5 and ρ b = 1.0, and from underestimation of 25% to overestimation of 10% for ρ t = À 0.5 and ρ b = 0.7; and their accuracy decreases with the increase of current risetime RT. For the finite conductivity with 0.01 S/m and 0.001 S/m, FCCFs will cause many errors if we do not take into account the propagation effect along the finitely conducting ground, and their errors obviously increase with the decrease of the conductivity. For example, for ρ t = À 0.5 and ρ b = 1.0, the errors are about 20% when the conductivity is 0.01 S/m while the errors are about 55% when the conductivity is 0.001 S/m for lightning strike to the 168 m high object. Therefore, we revised FCCFs by considering the propagation effect of finite conductivity on the electromagnetic field radiated by lightning strike to tall objects and found that our revised FCCFs have much better accuracy for the lossy ground than that presented by Baba and Rakov (2007).

The polarity reversal of the lightning‐generated first sky wave as a function of the observation distance is studied using a novel approach combining the finite‐difference time domain (FDTD) method and the superposition principle of electromagnetic waves. In this method, the sky wave is generated by radiation from the induced current produced by the motion of charged particles driven by the lightning‐radiated electromagnetic waves in the ionosphere. The horizontal and vertical components of the induced current density under the daytime and nighttime ionospheric conditions are evaluated. Their different contributions to the sky wave at different observation distances are analyzed in detail. Furthermore, a physical explanation for the polarity reversal in the time domain is proposed. It is found that, for relatively short observation distances (within ~200 km), the first sky wave is dominated by the component generated by the horizontal equivalent current in the Fresnel zone, while for longer observation distances (larger than ~300 km), the first sky wave is dominated by the component generated by the vertical equivalent current in the Fresnel zone. Since the polarities of the sky wave components generated by the vertical current source and horizontal current source are opposite, the polarity of the sky wave will reverse when increasing the observation distance.

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In this paper we have simulated the far-field waveform characteristic of large bipolar events (LBEs) occurred in winter thunderstorms in Japan and compared the field-to-current conversion factors (FCCFs) of LBEs with that of the lightning cloud-to-ground (CG) return stroke (RS) in summer thunderstorm. As for the physical process of LBEs, Wu et al. (2014) considered that LBEs may be very similar to the typical lightning RS (RS-like process) or caused by an initial continuous current pulse (ICC-like process) in upward lightning flashes. We assume that the lightning channel length of LBEs ranges from 500 m to 1000 m, and the height of tall object struck by LBEs is from 100 m to 300 m. By using the bouncing wave model, we found that only when the injected current waveform of LBEs is characterized with a symmetric Gaussian pulse, the simulated far-field waveform of LBEs both for RS-like process and ICC-like process is similar to that observed by Wu et al. (2014). For striking tall objects with heights from 100 m and 300 m, the FCCFs of LBEs are positively correlated with its channel length and derivatives of injected current waveform, and the FCCF for RS-like process is about similar to that for ICC-like process. However, the FCCFs of LBEs are very different from lightning RS in summer thunderstorm; that is to say, the FCCFs developed for the well-known lightning RS in summer thunderstorm are not suitable for LBEs.

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The equivalent propagation method adopts a variable propagation velocity in lightning location, minimizing the location error caused by various factors in the long-range lightning location network. To verify the feasibility of this method, we establish a long-range lightning location network in China. A new method is used to extract the ground wave peak points of the lightning sferics and is combined with the equivalent propagation velocity method for lightning location. By comparing with the lightning data detected by the lightning locating system called advanced direction and time-of-arrival detecting (ADTD) that has been widely used for tens of years in China, the feasibility of this method is initially verified. Additionally, it is found that the relative detection efficiency of our long-range lightning location network can reach 53%, the average location error is 9.17 km, and the detection range can reach more than 3000 km. The equivalent propagation method can improve the average location accuracy by ~1.16 km, compared with the assumed light speed of lightning-radiated sferic from the lightning stroke point to the observation station. The 50th percentile of the equal propagation velocity is 0.998c, which may be used in the long-range lightning location networks.