This paper based on Barrick’s formulations and Wait’s formulations, we analyzed the lightning vertical electric field and it is derivative in the time domain along rough sea surface. Furthermore, we discussed that it effects on Time-of-Arrival (ToA)-based lightning location systems (LLS). We found that the wave-shape and time-delay of the vertical electric field can be significantly affected when propagates along rough the sea surface. The rough sea surface has a few effect on the magnitude of the vertical electric fields. With the observation distance increase, the rise time of the wave-shape becomes long with the increasing of the wind speed. The peaks of the field derivative obviously decrease with the increasing of the wind speed, and the farther observation distance is, the stronger attenuation is. The time-delay of the field derivative increases as the wind speed increases. The observed time-delay resulting from the propagation along rough sea surface might impact the location accuracy of ToA-based LLS.
RubinsteinM.A.TzengY.UmanM.A. et al., An experimental test of a theory of lightning-induced voltages on an overhead wire, IEEE Trans. Electromagn. Comp.31 (1989), 376–383.
2.
MasterM.J. and UmanM.A., Lighting induced voltages on power lines: theory, IEEE Trans. Power. Appl. Syst.103(9) (1984), 2505–2517.
3.
LiX.C. et al., Research on energy coordination between multi-level surge protective devices with the transmission line theory, International Journal of Applied Electromagnetics and Mechanics48 (2015), 345–356.
4.
LiX.C. et al., Propagation and suppression method of lightning wave in coaxial line, International Journal of Applied Electromagnetics and Mechanics49 (2015), 315–325.
5.
YuZ.Q. et al., Simulation calculation and analysis of lightning induced over voltage on power distribution lines, High Voltage Engineering39(2) (2013), 415–422.
6.
RubinsteinM., An approximate formula for the calculation of the horizontal electric field from lightning at close, intermediate, and long range, IEEE Trans. Electromagn. Compat.38 (1996), 531–535.
7.
CoorayV., Propagation effects due to finitely conducting ground on lightning-generated magnetic fields evaluated using Sommerfeld’s integrals, IEEE Trans. Electromagn. Compat.51 (2009), 526–531.
8.
CoorayV.FernandoM.SorensenT. et al., Propagation of lightning generated transient electromagnetic fields over finitely conducting ground, J. Atmospheric Sol.-Terrestrial Phys.62 (2000), 583–600.
9.
DelfinoF.ProcopioR. and RossiM., Lightning return stroke current radiation in presence of a conducting ground: 1. Theory and numerical evaluation of the electromagnetic fields, J. Geophysical Res.: Atmospheres113 (2008), 79–88.
10.
DelfinoF.ProcopioR.RossiM.RachidiF. et al., Lightning return stroke current radiation in presence of a conducting ground: 2. Validity assessment of simplified approaches, J. Geophysical Res.: Atmospheres113 (2008), D05111.
11.
CoorayV., On the accuracy of several approximate theories used in quantifying the propagation effects on lightning generated electromagnetic fields, IEEE Trans. Antennas Propag.56 (2008), 1960–1967.
12.
ShooryA.MoiniR. and RachidiF., Validity of simplified approaches for the evaluation of lightning electromagnetic fields above a horizontally stratified ground, IEEE Trans. Electromagn. Comp.52 (2010), 657–663.
13.
WeidmanC.D. and KriderE.P., Lightning amplitude spectrum in the interval from 100 kHz to 20 MHz, Geophys. Res. Lett.7 (1980), 955–958.
14.
WeidmanC.D.KriderE.P. and UmanM.A., Submicrosecond spectrum of the return stroke waveforms, Geophys. Res. Lett.8 (1981), 931–934.
15.
WillettJ.C.BaileyJ.C.LeteinturierC. et al., Lightning electromagnetic radiation field spectrum in the interval from 0.2 to 20 MHz, J. Geophys. Res.95 (1990), 20367–20387.
16.
MingY. and CoorayV., Propagation effects caused by a rough ocean surface on the electromagnetic fields generated by lightning returns strokes, Radio Sci.29 (1994), 73–85.
17.
ZhangQ.YangJ. and LiD., Propagation effects of a fractal rough ocean surface on the vertical electric field generated by lightning return strokes, Journal of Electrostatics70 (2012), 54–59.
18.
ShooryA.MimouniA.RachidiF. and RubinsteinM., On the accuracy of approximate techniques for the evaluation of lightning electromagnetic fields along a mixed propagation path, Radio Sci.46 (2016), 1–8.
19.
ZhangQ.LiD.FanY.ZhangY. et al., Examination of the Cooray-Rubinstein (C-R) formula for a mixed propagation path by using FDTD, J. Geophys. Res.117 (2012), D15309.
20.
LiD.RachidiF.RubinsteinM. et al., Propagation effects on lightning magnetic fields over hilly and mountainous terrain, in: IEEE Int. Symp. Electromagn. Compat., Dresden, Germany, 2015, pp. 1436–1440.
21.
LiD.AzadifarM.RachidiF. et al., Analysis of lightning electromagnetic field propagation in mountainous terrain and its effects on ToA-based lightning location systems, J. Geophys. Res. Atmos.121 (2016), 895–911.
22.
LiD.AzadifarM.RachidiF. et al., On lightning electromagnetic field propagation along an irregular terrain, IEEE Transactions on Electromagnetic Compatibility58 (2016), 161–171.
23.
CumminsK.L.MurphyM.J.BardoE.A. et al., A combined TOA/MDF technology upgrade of the US National Lightning Detection Network, Journal of Geophysical Research: Atmospheres (1984–2012)103 (1998), 9035–9044.
24.
CumminsK.L.MurphyM.J. and TuelJ.V., Lightning detection methods and meteorological applications, in: IV International Symposium on Military Meteorology, Malbork, Poland, September, 2000, pp. 25–28.
25.
LewisE.HarveyR. and RasmussenJ., Hyperbolic direction finding with sferics of transatlantic origin, Journal of Geophysical Research65 (1960), 1879–1905.
26.
ThottappillilR.RakovV.A. and UmanM.A., Distribution of charge along the lightning channel: Relation to remote electric and magnetic fields and to return-stroke models, J. Geophys. Res.102 (1997), 6987–7006.
27.
ThottappillilR. and RakovV.A., On different approaches to calculating lightning electric fields, J. Geophys. Res.106 (2001), 14191–14205.
28.
WaitJ.R., Transient fields of a vertical dipole over a homogeneous curved ground, Canadian Journal of Physics34 (1956), 27–35.
29.
WaitJ.R., Recent analytical investigations of electromagnetic ground wave propagation over inhomogeneous earth models, Proceedings of the IEEE62 (1974), 1061–1072.
30.
WaitJ.R., The ancient and modern history of EM ground-wave propagation, IEEE Antennas and Propagation Magazine40 (1998), 7–24.
31.
CoorayV. and De la RosaF., Shapes and amplitudes of the initial peaks of lightning-induced voltage in power lines over finitely conducting Earth: Theory and comparison with experiment, IEEE Trans. Antennas Propag.34 (1986), 88–92.
32.
BarrickD.E., Theory of HF and VHF propagation across the rough sea, 1, the effective surface impedance for a slightly rough highly conducting medium at grazing incidence, Radio Sci.6 (1971), 517–526.
33.
BarrickD.E., Theory of HF and VHF propagation across the rough sea, 2, application to HF and VHF propagation above the sea, Radio Sci.6 (1971), 527–533.
34.
WangY.GuoL. and WuZ., Application of an improved 2D fractal model for electromagnetic scattering from the sea surface, Acta Phys. Sin.55 (2006), 5191–5199 (in Chinese).
35.
RakovV.A. and DulzonA.A., A modified transmission line model for lightning return stroke field calculations, in: Proceedings of the 9th International Symposium on Electromagnetic Compatibility, Switzerland: Zurich, 1991, pp. 229–235.
36.
HeilderF., Traveling current source model for LEMP calculation, in: Proceedings of the 6th International Zurich Symposium on Electromagnetic Compatibility, Switzerland: Zurich, 1985, pp. 157–162.
37.
CaligarisC.DelfinoF. and ProcopioR., Cooray – Rubinstein formula for the evaluation of lightning radial electric fields: Derivation and implementation in the time domain, IEEE Transactions on Electromagnetic Compatibility50 (2008), 194–197.
38.
CoorayV., Effects of propagation on the return stroke radiation fields, Radio Science22 (1987), 757–768.
39.
HonmaN.SuzukiF.MiyakeY. et al., Propagation effect on field waveforms in relation to time-of-arrival technique in lightning location, Journal of Geophysical Research: Atmospheres (1984–2012)103 (1998), 14141–14145.
