In this paper we have studied the effect of strike to a cone-shaped mountain surrounded by two chains of hills on the lightning vertical electric field and azimuthal magnetic field at different distances, by using two-dimensional finite-difference time-domain (2-D FDTD) method in cylindrical coordinate systems. In order to analyze the electrostatic shielding effect of strike to a cone-shaped mountain surrounded by two chains of hills on the lightning, we chose three mountains, and the left one is stroke by lightning, and the right one is near the obervation site, and the middle one with the top heights increasing from 0 to 2 km is between them. For the observed point, the electrostatic shielding effect of the right one on the lightning vertical electric field is the most serious, and the electric field is much less than that for strike to flat ground level; compared with the electric field, the shielding effect of the right one on the lightning azimuthal magnetic field becomes less, for most cases, the lightning magnetic field at the observed site is larger than that for flat ground cases mainly due to that of the increment caused by strike to the right mountain. With the increase of distance (e.g., 20 km from the lightning strike point), the shielding effect of the right mountain on the lightning field becomes less, because the reflected wave from the right mountain bottom plays a more important role over intermediate ranges, and the far radiation electromagnetic field peak value becomes larger due to such a reflecting wave. Therefore, in the lightning detecting technique, we should pay more attention to the effect caused by chains of hills on the lightning location and the estimation of lightning current peak.
References
[1]
Uman, M.A., McLain, D.K. and Krider, E.P. (1975) The Electromagnetic Radiation from a Finite Antenna. American Journal of Physics, 43, 33-38. https://doi.org/10.1119/1.10027
[2]
Rakov, V. and Uman, M.A. (1998) Review and Evaluation of Lightning Return Stroke Models Including Some Aspects of Their Application. IEEE Transactions on Electromagnetic Compatibility, 40, 403-426. https://doi.org/10.1109/15.736202
[3]
Rachidi, F., Bermudez, J.L., Rubinstein, M. and Rakov, V.A. (2004) On the Estimation of Lightning Peak Currents from Measured Fields Using Lightning Location Systems. Journal of Electrostatics, 60, 121-129. https://doi.org/10.1016/j.elstat.2004.01.010
[4]
Azadifar, M., Rachidi, F., Rubinstein, M., et al. (2016) Evaluation of the Performance Characteristics of the European Lightning Detection Network EUCLID in the Alps Region for Upward Negative Flashes Using Direct Measurements at the Instrumented Säntis Tower. Journal of Geophysical Research: Atmospheres, 121, 595-606. https://doi.org/10.1002/2015JD024259
[5]
Li, D., et al. (2016) On Lightning Electromagnetic Field Propagation along an Irregular Terrain. IEEE Transactions on Electromagnetic Compatibility, 58, 161-171. https://doi.org/10.1109/TEMC.2015.2483018
[6]
Motoyama, H., Janischewskyj, W., Hussein, A.M., Rusan, R., Chisholm, W.A. and Chang, J.S. (1996) Electromagnetic Field Radiation Model for Lightning Strokes to Tall Structures. IEEE Transactions on Power Delivery, 11, 1624-1632. https://doi.org/10.1109/61.517526
[7]
Rachidi, F., Janischewskyj, W., Hussein, A.M., Nucci, C.A., Guerrieri, S., Kordi, B. and Chang, J.S. (2001) Current and Electromagnetic Field Associated with Lightning-Return Strokes to Tall Objects. IEEE Transactions on Electromagnetic Compatibility, 43, 356-367. https://doi.org/10.1109/15.942607
[8]
Baba, Y. and Rakov, V.A. (2005) Lightning Electromagnetic Environment in the Presence of a Tall Grounded Strike Object. Journal of Geophysical Research: Atmospheres, 110. https://doi.org/10.1029/2004JD005505
[9]
Baba, Y. and Rakov, V.A. (2007) Lightning Strikes to Tall Objects: Currents Inferred from Far Electromagnetic Fields versus Directly Measured Currents. Geophysical Research Letters, 34, L19810. https://doi.org/10.1029/2007GL030870
[10]
Hussein, A.M., Milewski, M. and Janischewskyj, W. (2008) Correlating the Characteristics of the CN Tower Lightning Return-Stroke Current with Those of Its Generated Electromagnetic Pulse. IEEE Transactions on Electromagnetic Compatibility, 50, 642-650. https://doi.org/10.1109/TEMC.2008.924398
[11]
Pavanello, D., Rachidi, F., Janischewskyj, W., Rubinstein, M., Shostak, V.O., Nucci, C.A., Cummins, K.L., Hussein, A.M. and Chang, J.-S. (2009) On the Current Peak Estimates Provided by Lightning Detection Networks for Lightning Return Strokes to Tall Objects. IEEE Transactions on Electromagnetic Compatibility, 51, 453-458. https://doi.org/10.1109/TEMC.2009.2025913
[12]
Bermudez, J.L., Rachidi, F., Janischewskyj, W., Shostak, V., Rubinstein, M., Pavanello, D., Hussein, A.M., Chang, J.S., Nucci, C.A. and Paolone, M. (2005) Far-Field-Current Relationship Based on the TL Model for Lightning Return Strokes to Elevated Strike Objects. IEEE Transactions on Electromagnetic Compatibility, 47, 146-159. https://doi.org/10.1109/TEMC.2004.842102
[13]
Bermudez, J.L., Rachidi, F., Janischewskyj, W., Shostak, V., Rubinstein, M., Pavanello, D., Hussein, A.M., Chang, J.S. and Paolone, M. (2007) Determination of Lightning Currents from Far Electromagnetic Fields: Effect of a Strike Object. Journal of Electrostatics, 56, 289-295. https://doi.org/10.1016/j.elstat.2006.09.007
[14]
Rachidi, F. (2007) Modeling Lightning Return Strokes to Tall Structures: A Review. Journal of Lightning Research, 1, 16-31.
[15]
Mosaddeghi, A., Shoory, A., Rachidi, F., Diendorfer, G., Pichler, H., Pavanello, D., Rubinstein, M., Zweiacker, P. and Nyffeler, M. (2010) Lightning Electromagnetic Fields at Very Close Distances Associated with Lightning Strikes to the Gaisberg Tower. Journal of Geophysical Research, 115, D17101. https://doi.org/10.1029/2009JD013754
[16]
Zhang, Q., He, L., Ji, T. and Hou, W. (2014) On the Field-to-Current Conversion Factors for Lightning Strike to Tall Objects Considering the Finitely Conducting Ground. Journal of Geophysical Research, 119, 8189-8200. https://doi.org/10.1002/2014JD021496
[17]
Zhang Q., Hou W., Ji T., He, L. and Su J. (2014) Validation and Revision of Far-Field-Current Relationship for the Lightning Strike to Electrically Short Objects. Journal of Atmospheric and Solar-Terrestrial Physics, 120, 41-50. https://doi.org/10.1016/j.jastp.2014.08.015
[18]
Soto, E., Perez, E. and Herrera, J. (2014) Electromagnetic Field Due to Lightning Striking on Top of a Cone-Shaped Mountain Using the FDTD. IEEE Transactions on Electromagnetic Compatibility, 56, 1112-1120. https://doi.org/10.1109/TEMC.2014.2301138
[19]
Soto, E., Perez, E. and Younes, C. (2014) Influence of Non-Flat Terrain on Lightning Induced Voltages on Distribution Networks. Electric Power Systems Research, 113, 115-120. https://doi.org/10.1016/j.epsr.2014.02.034
[20]
Paknahad, J., Sheshyekani, K., Hamzeh, M. and Rachidi, F. (2014) Lightning Electromagnetic Fields and Their Induced Voltages on Overhead Lines: The Effect of a Non-Flat Lossy Ground. In: Proceedings of 32nd International Conference on Lightning Protection, Shanghai, 591-594. https://doi.org/10.1109/ICLP.2014.6973193
[21]
Khosravi, R., Sadeghi, S.H.H. and Moini, R. (2016) Electromagnetic Field Due to Lightning Strike to a Tall Tower Sitting on a Mountainous Terrain. IEEE Transactions on Electromagnetic Compatibility, 58, 1090-1099. https://doi.org/10.1109/TEMC.2016.2551301
[22]
Yee, K.S. (1966) Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media. IEEE Transactions on Antennas and Propagation, AP-14, 302-307. https://doi.org/10.1109/TAP.1966.1138693
[23]
Yang, C. and Zhou, B. (2004) Calculation Methods of Electromagnetic Fields Very Close to Lightning. IEEE Transactions on Electromagnetic Compatibility, 46, 133-141. https://doi.org/10.1109/TEMC.2004.823626
[24]
Roden, J.A. and Gedney, S.D. (2000) Convolution PML (CPML): An Efficient FDTD Implementation of the CFS-PML for Arbitrary Media. Microwave and Optical Technology Letters, 27, 334-339. https://doi.org/10.1002/1098-2760(20001205)27:5<334::AID-MOP14>3.0.CO;2-A
[25]
Baba, Y. and Rakov, V.A. (2005) On the Use of Lumped Sources in Lightning Return Stroke Models. Journal of Geophysical Research, 110, D03101. https://doi.org/10.1029/2004JD005202
[26]
Jurgens, T.G., Taflove, A., Umashankar, K. and Moore, T.G. (1992) Finite-Difference Time-Domain Modeling of Curved Surfaces. IEEE Transactions on Antennas and Propagation, 40, 357-366. https://doi.org/10.1109/8.138836
[27]
Yu, W. and Mittra, R. (2001) A Conformal Finite Difference Time Domain Technique for Modeling Curved Dielectric Surfaces. IEEE Microwave and Wireless Components Letters, 11, 25-27. https://doi.org/10.1109/7260.905957
[28]
Heidler, F., Cvetic, J. and Stanic, B.V. (1999) Calculation of Lightning Current Parameters. IEEE Transactions on Electromagnetic Compatibility, 14, 399-404. https://doi.org/10.1109/61.754080
[29]
Nucci, C.A., Mazzetti, C., Rachidi, F. and Ianoz, M. (1988) On Lightning Return Stroke Models for LEMP Calculations. Presented at the 19th International Conference Lightning Protection, Graz, Austria.
[30]
Rachidi, F. and Nucci, C.A. (1990) On the Master, Uman, Lin, Standler and the Modified Transmission Line Lightning Return Stroke Current Models. Journal of Geophysical Research: Atmospheres, 95, 20389-20393. https://doi.org/10.1029/JD095iD12p20389