Statistical Distributions of Lightning Parameters with Emphasis on their Extremely High Values
Abstract
The paper is devoted to the review of the data on the lightning parameters necessary for development and perfection of lightning protection systems. It is shown, that down to present time national and international lightning protection standards are based on the Berger’s data on distribution of lightning amplitudes currents. Experimental data on amplitude of the return-stroke current the received recently in Brazil, Japan, USA (Florida) and Austria are resulted. It is emphasized, that the given data on currents of a lightning are characterized by a wide scatter that specifies necessity of realization of the further researches.
The detailed description of parameters of the return-stroke peak current, including duration of front time, duration of a pulse, a steepness of a current at the front is given. It is emphasized, that median value of amplitude of a current of the first making the return-stroke in 3-4 times is higher than a current of the subsequent components.
The analysis measured median (50%) and severe (1%) values of lighting parameters which are necessary for construction of a curve of distribution in the assumption of its submission lognormal law is carried out. Results of theoretical researches are given according to extreme values of currents of a lightning. It is shown, that, depending on length of the lightning channel (from 4 up to 6 kms), the maximal current can vary from 300 kA up to 500 кА. The minimal value of lightning current is appreciated in 2 кА.
The analysis of results of new direct measurements has shown, that for a lightning of positive polarity the maximal current can reach 340 кА, that appreciably is higher than a settlement maximum for a lightning of negative polarity (200 кА).
Recent theoretical researches have allowed to prove experimentally received lognormal distribution of currents for lightning of negative polarity.
References
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28. Visacro S., Soares A. Jr., Schroeder M. A. O., Cherchiglia L. C. L., de Sousa V. J. Statistical analysis of lightning current parameters: measurements at Morro do Cachimbo Station. – Journal of Geophysical Research, 2004, vol.109, D01105, doi:10.1029/2003JD003662.
29. Visacro S., Silveira F. H. Lightning current waves measured at short instrumented towers: the influence of sensor position. – Geophys. Res. Lett., 2005, vol. 32, pp. L18804-1–5, doi:10.1029/2005GL023255.
30. Takami, J., Okabe S. Observational results of lightning current on transmission towers. – IEEE Trans. Power Delivery, 2007, vol. 22, pp. 547–556.
31. Narita, T., Yamada T., Mochizuki A., Zaima E., Ishii M. Observation of current waveshapes of lightning strokes on transmission towers. – IEEE Trans. Power Delivery, 2000, vol.15, pp. 429–435.
32. Schoene J., Uman M. A., Rakov V. A., et al. Characterization of return-stroke currents in rocket-triggered lightning. – Journal of Geophysical Research, 2009, vol.114, pp. D03106, doi:10.1029/2008JD009873.
33. Schoene, J., Uman M. A., Rakov V. A., Kodali V., Rambo K. J., Schnetzer G. H. Statistical characteristics of the electric and magnetic fields and their time derivatives 15 m and 30 m from triggered lightning. – Journal of Geophysical Research, 2003, vol. 108, pp. 4192, doi:10.1029/2002JD002698.
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35. Cooray V., Rakov V. Engineering lightning return stroke models incorporating current reflection from ground and finitely conducting ground effects. – IEEE Trans. Electromagn. Compat., 2011, vol. 53, pp. 773–781.
36. Diendorfer, G., Pichler H., Mair M. Some parameters of negative upward-initiated lightning to the Gaisberg tower (2000–2007). – IEEE Trans. Electromagn. Compat., 2009, vol. 51, pp. 443–452.
27. Diendorfer G. Review of seasonal variations in occurrence and some current parameters of lightning measured at the Gaisberg Tower. – 4th International Symposium on Winter Lightning (ISWL 2017), 6 pp., 2017.
38. Berger K., Garabagnati E. Lightning current parameters. Results obtained in Switzerland and in Italy. – URSI Conference, Florence, Italy, 1984.
39. Leteinturier C., Hamelin J. H., Eybert-Berard A. Submicrosecond characteristics of lightning return-stroke currents. – IEEE Trans. Electromagn. Compat., 1991, vol. 33, pp. 351–357.
40. Fisher R. J., Schnetzer G. H., Thottappillil R., Rakov V. A., Uman M. A., Goldberg J. D. Parameters of triggered-lightning flashes in Florida and Alabama. – Journal of Geophysical Research, 1993, vol.98, pp.22887–22902.
41. Yang, J., Qie X., Zhang G., et al. Characteristics of channel base currents and close magnetic fields in triggered flashes in SHATLE. – Journal of Geophysical Research, 2010, vol.115, D23102, doi:10.1029/2010JD014420.
42. Cooray V., Rakov V., Theethayi N. The lightning striking distance—revisited. – J. Electrost., 2007, vol. 65, pp. 296–306.
43. Qie X. S., Zhang Q. L., Zhou Y. J., et al. Artificially triggered lightning and its characteristic discharge parameters in two severe thunderstorms. – Sci. China, Ser. D: Earth Sci., 2007, vol. 50, No.8, pp. 1241–1250, doi:10.1007/s11430-007-0064-2.
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46. Thomson E. M., Galib M. A., Uman M. A., Beasley W. H., Master M. J. Some features of stroke occurrence in Florida lightning flashes. – Journal of Geophysical Research, 1984, vol. 89, pp. 4910–4916.
47. Cianos N., Pierce E. T. A ground-lightning environment for engineering usage, Stanford Research Institute Project 1834, Tech. Rep. 1, Stanford Research Institute, Menlo Park, CA, Aug. 1972.
48. Goto Y., Narita K. Electrical characteristics of winter lightning. – J. Atmosph. Terr. Phys., 1995, vol. 12, pp. 57–64.
49. Depasse P. Statistics on artificially triggered-lightning. – Journal of Geophysical Research, 1994, vol. 99, pp. 18515–18522.
50. Krider E. P., Leteinturier C., Willett J. C. Submicrosecond fields radiated during the onset of first return strokes in cloud-to-ground lightning. – Journal of Geophysical Research, 1996, vol. 101, pp. 1589–1597.
51. Willett J., Krider E., Leteinturier C. Submicrosecond field variations during the onset of first return strokes in cloud-to-ground lightning. – Journal of Geophysical Research, 1998, vol. 103, No. D8, pp. 9027–9034.
52. Cooray V., Fernando M., Gomes C., Sorensen T., Scuka V., Pedersen A. The fine structure of positive return stroke radiation fields: A collaborative study between researchers from Sweden and Denmark, in Proc. 24th Int. Conf. Lightning Protection, Birmingham, U.K, 1998, pp. 78–82.
53. Pitts F. L., Perala R. A., Rudolph T. H., Lee L. D. New results for quantification of lightning/aircraft electrodynamics. – Electromagnetics, 1987, vol. 7, pp. 451–485.
54. Willett J. C., Krider E. P. Rise times of impulsive high-current processes in cloud-to-ground lightning. – IEEE Transactions on Antennas and Propagation, 2000, vol. 48, No. 9, pp. 1442–1451.
55. Miyake J., Suzuki T., Shinjou K. Characteristics of winter lightning current on Japan Sea Coast. – IEEE Transactions Power Delivery, 1992, vol. 7, No. 3, pp. 1450–1457.
56. Li J., Cummer S. A., Lyons W. A., Nelson T. E. Coordinated analysis of delayed sprites with high-speed images and remote electromagnetic fields. – Journal of Geophysical Research, 2008, vol. 113, p. D20206 (doi:10.1029/2008JD010008).
57. Lu G., Cummer S. A., Li J., Han F., Blakeslee R. J., Christian H. J. Charge transfer and in-cloud structure of large-charge-moment positive lightning strokes in a mesoscale convective system. – Geophys. Res. Lett., 2009, vol. 36, p. L15805 (doi.10.1029/2009GL038880).
58. Campos L., Saba M. M. F., O. Pinto Jr, Ballarotti M. Waveshapes of continuing currents for properties of M-components in natural negative cloud-to-ground lightning from high-speed video observations. – Atmospheric Research, 2007, vol. 84, pp. 302–310.
59. Kitagawa N., Brook M., Workman E. J. Continuing currents in cloud-to-ground lightning discharges. – Journal of Geophysical Research, 1962, vol. 67, pp. 637–647.
60. Saba M. M. F., O. Pinto Jr., Ballarotti M. G. Relation between lightning return stroke peak current and following continuing current. – Geophys. Res. Lett., 2006, vol. 33, p. L23807, doi:10.1029/2006GL027455.
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#
1. IEC 62305–1. Protection Against Lightning – Part 1: General Principles, 2010.
2. IEEE 1243–1997. IEEE Guide for Improving the Lightning Performance of Transmission Lines, 1997.
3. IEEE 1410–2010. IEEE Guide for Improving the Lightning Performance of Electric Power Overhead Distribution Lines, 2010.
4. Berger K., Anderson R. B., Kroninger H. Parameters of lightning flashes. – Electra, 1975, No. 41, pp. 23–37.
5. Berger К. Methods and results of the lightning research on the Monte San Salvatore near Lugano in the years 1963-1971. – Bull. SEV 63, 1972, No. 24, pp. 1403–1422.
6. Cooray V., Rakov V. On the upper and lower limits of peak current of first return strokes in negative lightning flashes. – Atmospheric Research, 2012, vol.117, pp.12–17.
7. Zhu Y., Rakov V. A., Tran M. D., Nag A. A study of National Lightning Detection Network responses to natural lightning based on ground-truth data acquired at LOG with emphasis on cloud discharge activity. – J. Geophys. Res. Atmos., 2016, vol. 121, No. 24, pp.14651–14660.
8. Jerauld J., Rakov V. A., Uman M. A., et al. An evaluation of the performance characteristics of the U.S. National Lightning Detection Network in Florida using rocket-triggered lightning. – J. Geophys. Res., 2005, vol. 110, D19106, pp.1–6, doi:10.1029/2005JD005924.
9. Mallick S., Rakov V. A., Hill J. D., et al. Performance characteristics of the NLDN for return strokes and pulses superimposed on steady currents, based on rocket-triggered lightning data acquired in Florida in 2004–2012. – J. Geophys. Res. Atmos., 2014, vol. 119, pp. 3825–3856, doi:10.1002/2013JD021401.
10. Nag A., Mallick S., Rakov V. A., et al. Evaluation of U.S. National Lightning Detection Network performance characteristics using rocket-triggered lightning data acquired in 2004–2009. – J. Geophys. Res., 2011, vol.116, D02123, pp.1–8, doi:10.1029/2010JD014929.
11. Rakov V. A. On estimating the lightning peak current distribution parameters taking into account the lower measurement limit. – Elektrichestvo, 1985, No. 2, pp.57–59.
12. Rakov V. A. A review of the interaction of lightning with tall objects. Recent Res. Devel. Geophysics, 2003, No. 5, pp.57–71, Research Signpost, India.
13. Sargent M. A. The frequency distribution of current magnitudes of lightning strokes to tall structures. – IEEE Trans. Power Appar. Syst., 1972, vol. 91, pp. 2224–2229.
14. Borghetti A., Nucci C. A., Paolone M. Estimation of the statistical distributions of lightning current parameters at ground level from the data recorded by instrumented towers. – IEEE Trans. Power Delivery, 2004, vol.19, No.3, pp. 1400–1409, doi:10.1109/TPWRD.2004.829116.
15. Mata C. T., Rakov V. A. Evaluation of lightning incidence to elements of a complex structure: a Monte Carlo approach. – In Proceedings of the 3rd International Conference on Lightning Physics and Effects (LPE) and GROUND’ 2008, Florianopolis, Brazil, 2008, November, pp. 351–354.
16. CIGRE TF 33.01.03, Report 118. Lightning exposure of structures and interception efficiency of air terminals, October 1997, 86 p.
17. Popolansky F. Lightning current measurement on high objects in Czechoslovakia. 20th Int. Conf. on Lightning Protection (ICLP), Interlaken/Switzerland, 1990, Proc. report 1.3.
18. Anderson R. B., Eriksson A. J. Lightning parameters for engineering application. – Electra, 1980, vol. 69, pp. 65–102.
19. CIGRE WG 33.01, Report 63. Guide to Procedures for Estimating the Lightning Performance of Transmission Lines, 1991, 61 p.
20. Hileman A. R. Insulation Coordination for Power Systems. New York, NY: Marcel Dekker, 1999, 767 p.
21. Popolansky F. Frequency distribution of amplitudes of lightning currents. –Electra, 1972, No. 22, pp. 139–147.
22. Gamerota W. R., Elisme´ J. O., Uman M. A., Rakov V. A. Current waveforms for lightning simulation. IEEE Trans. Electromagn. Compat. 2012, vol. 54, pp. 880–888, DOI: 10.1109/TEMC.2011.2176131.
23. Eriksson A. J., Meal D. V. The incidence of direct lightning strikes to structures and overhead lines. In Lightning and Power Systems, London: IEE Conference Publication, 1984, No. 236, pp. 67–71.
24. Bazelyan E. M., Aleksandrov N. L., Carpenter R. B., Raizer Yu. P. Reverse discharges near grounded objects during the return stroke of branched lightning flashes. In Proceedings of the 28th International Conference on Lightning Protection, Kanazawa, Japan, 2006, pp. 187–92.
25. Melander B. G. Effects of tower characteristics on lightning arc measurements. In Proceedings of the 1984 International Conference on Lightning and Static Electricity, Orlando, FL, 1984, pp. 34/1–34/12.
26. Eriksson A. J., Penman C. L., Meal C. L. A review of five years’ lightning research on an 11 kV test-line. In Lightning and Power Systems. London: IEE Conference Publication, 1984, No. 236, pp. 62–66.
27. CIGRE Technical Brochure 549 “Lightning Parameters for Engineering Applications”. Working Group С4.407, August 2013, 117 p.
28. Visacro S., Soares A. Jr., Schroeder M. A. O., Cherchiglia L. C. L., de Sousa V. J. Statistical analysis of lightning current parameters: measurements at Morro do Cachimbo Station. – Journal of Geophysical Research, 2004, vol.109, D01105, doi:10.1029/2003JD003662.
29. Visacro S., Silveira F. H. Lightning current waves measured at short instrumented towers: the influence of sensor position. – Geophys. Res. Lett., 2005, vol. 32, pp. L18804-1–5, doi:10.1029/2005GL023255.
30. Takami, J., Okabe S. Observational results of lightning current on transmission towers. – IEEE Trans. Power Delivery, 2007, vol. 22, pp. 547–556.
31. Narita, T., Yamada T., Mochizuki A., Zaima E., Ishii M. Observation of current waveshapes of lightning strokes on transmission towers. – IEEE Trans. Power Delivery, 2000, vol.15, pp. 429–435.
32. Schoene J., Uman M. A., Rakov V. A., et al. Characterization of return-stroke currents in rocket-triggered lightning. – Journal of Geophysical Research, 2009, vol.114, pp. D03106, doi:10.1029/2008JD009873.
33. Schoene, J., Uman M. A., Rakov V. A., Kodali V., Rambo K. J., Schnetzer G. H. Statistical characteristics of the electric and magnetic fields and their time derivatives 15 m and 30 m from triggered lightning. – Journal of Geophysical Research, 2003, vol. 108, pp. 4192, doi:10.1029/2002JD002698.
34. Rakov, V. A., Uman M. A., Rambo K. J. et al. New insights into lightning processes gained from triggered-lightning experiments in Florida and Alabama. – Journal of Geophysical Research, 1998, vol.103, 14117–14130.
35. Cooray V., Rakov V. Engineering lightning return stroke models incorporating current reflection from ground and finitely conducting ground effects. – IEEE Trans. Electromagn. Compat., 2011, vol. 53, pp. 773–781.
36. Diendorfer, G., Pichler H., Mair M. Some parameters of negative upward-initiated lightning to the Gaisberg tower (2000–2007). – IEEE Trans. Electromagn. Compat., 2009, vol. 51, pp. 443–452.
27. Diendorfer G. Review of seasonal variations in occurrence and some current parameters of lightning measured at the Gaisberg Tower. – 4th International Symposium on Winter Lightning (ISWL 2017), 6 pp., 2017.
38. Berger K., Garabagnati E. Lightning current parameters. Results obtained in Switzerland and in Italy. – URSI Conference, Florence, Italy, 1984.
39. Leteinturier C., Hamelin J. H., Eybert-Berard A. Submicrosecond characteristics of lightning return-stroke currents. – IEEE Trans. Electromagn. Compat., 1991, vol. 33, pp. 351–357.
40. Fisher R. J., Schnetzer G. H., Thottappillil R., Rakov V. A., Uman M. A., Goldberg J. D. Parameters of triggered-lightning flashes in Florida and Alabama. – Journal of Geophysical Research, 1993, vol.98, pp.22887–22902.
41. Yang, J., Qie X., Zhang G., et al. Characteristics of channel base currents and close magnetic fields in triggered flashes in SHATLE. – Journal of Geophysical Research, 2010, vol.115, D23102, doi:10.1029/2010JD014420.
42. Cooray V., Rakov V., Theethayi N. The lightning striking distance—revisited. – J. Electrost., 2007, vol. 65, pp. 296–306.
43. Qie X. S., Zhang Q. L., Zhou Y. J., et al. Artificially triggered lightning and its characteristic discharge parameters in two severe thunderstorms. – Sci. China, Ser. D: Earth Sci., 2007, vol. 50, No.8, pp. 1241–1250, doi:10.1007/s11430-007-0064-2.
44. Schoene J., Uman M. A., Rakov V. A. Return stroke peak current versus charge transfer in rocket-triggered lightning. – Journal of Geophysical Research, 2010, vol. 115: D12107, doi:10.1029/2009JD013066.
45. Uman M. A. The Lightning Discharge. Orlando (Fla): Academic Press, 1987, 391 p.
46. Thomson E. M., Galib M. A., Uman M. A., Beasley W. H., Master M. J. Some features of stroke occurrence in Florida lightning flashes. – Journal of Geophysical Research, 1984, vol. 89, pp. 4910–4916.
47. Cianos N., Pierce E. T. A ground-lightning environment for engineering usage, Stanford Research Institute Project 1834, Tech. Rep. 1, Stanford Research Institute, Menlo Park, CA, Aug. 1972.
48. Goto Y., Narita K. Electrical characteristics of winter lightning. – J. Atmosph. Terr. Phys., 1995, vol. 12, pp. 57–64.
49. Depasse P. Statistics on artificially triggered-lightning. – Journal of Geophysical Research, 1994, vol. 99, pp. 18515–18522.
50. Krider E. P., Leteinturier C., Willett J. C. Submicrosecond fields radiated during the onset of first return strokes in cloud-to-ground lightning. – Journal of Geophysical Research, 1996, vol. 101, pp. 1589–1597.
51. Willett J., Krider E., Leteinturier C. Submicrosecond field variations during the onset of first return strokes in cloud-to-ground lightning. – Journal of Geophysical Research, 1998, vol. 103, No. D8, pp. 9027–9034.
52. Cooray V., Fernando M., Gomes C., Sorensen T., Scuka V., Pedersen A. The fine structure of positive return stroke radiation fields: A collaborative study between researchers from Sweden and Denmark, in Proc. 24th Int. Conf. Lightning Protection, Birmingham, U.K, 1998, pp. 78–82.
53. Pitts F. L., Perala R. A., Rudolph T. H., Lee L. D. New results for quantification of lightning/aircraft electrodynamics. – Electromagnetics, 1987, vol. 7, pp. 451–485.
54. Willett J. C., Krider E. P. Rise times of impulsive high-current processes in cloud-to-ground lightning. – IEEE Transactions on Antennas and Propagation, 2000, vol. 48, No. 9, pp. 1442–1451.
55. Miyake J., Suzuki T., Shinjou K. Characteristics of winter lightning current on Japan Sea Coast. – IEEE Transactions Power Delivery, 1992, vol. 7, No. 3, pp. 1450–1457.
56. Li J., Cummer S. A., Lyons W. A., Nelson T. E. Coordinated analysis of delayed sprites with high-speed images and remote electromagnetic fields. – Journal of Geophysical Research, 2008, vol. 113, p. D20206 (doi:10.1029/2008JD010008).
57. Lu G., Cummer S. A., Li J., Han F., Blakeslee R. J., Christian H. J. Charge transfer and in-cloud structure of large-charge-moment positive lightning strokes in a mesoscale convective system. – Geophys. Res. Lett., 2009, vol. 36, p. L15805 (doi.10.1029/2009GL038880).
58. Campos L., Saba M. M. F., O. Pinto Jr, Ballarotti M. Waveshapes of continuing currents for properties of M-components in natural negative cloud-to-ground lightning from high-speed video observations. – Atmospheric Research, 2007, vol. 84, pp. 302–310.
59. Kitagawa N., Brook M., Workman E. J. Continuing currents in cloud-to-ground lightning discharges. – Journal of Geophysical Research, 1962, vol. 67, pp. 637–647.
60. Saba M. M. F., O. Pinto Jr., Ballarotti M. G. Relation between lightning return stroke peak current and following continuing current. – Geophys. Res. Lett., 2006, vol. 33, p. L23807, doi:10.1029/2006GL027455.
61. Rakov V. A., Uman M. A. Lightning: Physics and Effects. New York: Cambridge Univ. Press, 2003, 687 p.
62. Toland R.B., Vonnegut B. Measurement of maximum electric field intensities over water during thunderstorms. – Journal of Geophysical Research, 1977, vol. 82, pp.438–440.
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