闪电双向先导理论及观测:极性不对称、不稳定及间歇性

苟学强; 张义军; 李亚珺; 陈明理

doi:10.7498/aps.67.20181079

摘要

闪电双向先导原理的提出及观测验证是闪电物理研究近几十年最重要的进展之一，而正、负先导及流光的极性不对称性及传输的持续、间歇性，是理解闪电各种过程物理机制的关键.本文对闪电双向先导的概念及进展进行了总结和讨论，重点强调了正、负先导流光传输机制特别是门限电场的不对称性，阐述了正先导传输的连续性及其在闪电始发、负先导的空间先导形成、不稳定先导通道中的反冲先导建立等过程中独特的启动作用.

关键词:

A lightning discharge in a thundercloud usually starts with a locally breakdown process (preliminary breakdown) followed by a widely extending leader process. In the early 1960 s, from the view of fundamental electrostatics[Kasemir H W 1960 J. Geophys. Res. 65 1873] suggested that the lightning leader is initiated by an electrodeless discharge with a zero-net-charge conductive channel extending bidirectionally in the ambient electric field of the thundercloud, i.e.the bidirectional leader theory. However, the bidirectional leader theory has just been recognized by lightning researchers since the late 1980 s, when airplane[Mazur V 1989 J. Geophys. Res. 94 3326] and rocket-triggered lightning experiments have proven that the bidirectional leader theory provides the best common physical basis for explaining a variety of lightning processes. Nevertheless, challenges still remain in other properties of the bidirectional leader theory, such as the polarity asymmetry, the sustainability, instability and restrike of a leader channel, which are all the key concerns of lightning researches. In the present paper, we first briefly review the concept and development of the bidirectional leader theory and its appearances in various lightning processes, especially in the negative stepped leader and recoil leader process. By reviewing a variety of field observation data of inception thresholds and propagation properties of long gap spark discharges, we put forward and emphasize an alternative polarity asymmetry of the lightning leader:the polarity asymmetry of continuity, i.e., the continuity of positive leader and the intermittency of negative leader. Based on the detailed discussion, we then argue that the stepwise positive leader may be restrikes due to temporary instability of a continuous positive leader, while the intermittency of negative leader manifests not only a relatively regular stepped leader but also a more erratic negative recoil leader. We further propose that the positive leader-streamer may play a unique role in igniting all kinds of intermittent events in lightning, including the initiation of lightning with the fast positive streamer, the formation of space leader in front of a negative stepped leader with the secondary positive streamer, and the reformation of recoil-leader in an instability leader channel due to its low threshold of inception and propagation. Finally, we discuss the self-adjustable ability of a bidirectional leader, suggesting that the potential drop along the streamer channel in front of the leader tip may be an important factor for stabilizing the bidirectional leader channel.

Keywords:

作者及机构信息

1.
西北师范大学大学物理与电子工程学院, 兰州 730070;

2.
复旦大学大气与海洋科学系大气科学研究院, 上海 200438;

3.
中国科学院寒区旱区环境与工程研究所, 兰州 730000;

4.
香港理工大学屋宇设备工程学系, 香港

通信作者: 苟学强, gxq411@126.com

基金项目: 国家自然科学基金重大研究计划（批准号：91537209）和香港特别行政区研究拨款委员会（批准号：PolyU152139/15E）资助的课题.

Authors and contacts

1.
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China;

2.
Institute of Atmospheric Sciences, Department of Atmospheric and Oceanic Sciences, Fudan University, Shanghai 200438, China;

3.
Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China;

4.
Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China

Corresponding author: Gou Xue-Qiang, gxq411@126.com

Funds: Project supported by the Major Research plan of the National Natural Science Foundation of China (Grant No. 91537209) and the Research Grant Council of the Hong Kong Government, China (Grant No. PolyU 152139/15E).

参考文献

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[2]	Kasemir H W 1960 J. Geophys. Res. 65 1873
[3]	Mazur V 1989 J. Geophys. Res. 94 3311
[4]	Mazur V 1989 J. Geophys. Res. 94 3326
[5]	Castellani A, Bondiou-Clergerie A, Lalande P, Bonany A, Gallimberti I 1998 IEE. Proc. Sci. Meas. Technol. 145 193
[6]	Chen M, Watanabe T, Takagi N, Du Y, Wang D, Liu X 2003 J. Geophys. Res. 108 4240
[7]	van der Velde O, Montanya J 2013 J. Geophys. Res. 118 13504
[8]	Shao X, Krehbiel P 1996 J. Geophys. Res. 101 26641
[9]	Thomas R J, Krehbiel P R, Rison W, Hamlin T, Harlin J, Shown D 2001 Geophys. Res. Lett. 28 143
[10]	Warner T A, Saba M M F, Schumann C, Helsdon J H, Orville R E 2016 J. Geophys. Res. Atmos. 121 9251
[11]	Montany J, van der Velde O, Williams E R 2015 Sci. Rep. 5 15180
[12]	Rison W, Krehbiel P R, Stock M G, Edens H E, Shao X M, Thomas R J, Stanley M A, Zhang Y 2016 Nat. Commun. 7 10721
[13]	Biagi C J, Uman M A, Hill J D, Jordan D M 2014 J. Geophys. Res. Atmos. 119 8160
[14]	Wang Z, Qie X, Jiang R, Wang C, Lu G, Sun Z, Liu M, Pu Y 2016 J. Geophys. Res. Atmos. 121 14307
[15]	Jiang R, Qie X, Zhang H, Liu M, Sun Z, Lu G, Wang Z, Wang Y 2017 Sci. Rep. 7 3457
[16]	Saba M M F, Cummins K L, Warner T A, Krider E P, Campos L Z S, Ballarotti M G, Pinto J O, Fleenor S A 2008 Geophys. Res. Lett. 35 L07802
[17]	Mazur V, Ruhnke L H, Warner T A, Orville R E 2013 J. Electrostat. 71 763
[18]	Qie X, Pu Y, Jiang R, Sun Z, Liu M, Zhang H, Li X, Lu G, Tian Y 2017 J. Geophys. Res. Atmos. 122 586
[19]	Wang D, Takagi N, Gamerota W R, Uman M A, Jordan D M 2015 J. Geophys. Res. Atmos. 120 10637
[20]	Hill J D, Uman M A, Jordan D M, Ngin T, Gamerota W R, Pilkey J, Caicedo J 2016 J. Geophys. Res. Atmos. 121 853
[21]	Stock M G, Akita M, Krehbiel P R, Rison W, Edens H E, Kawasaki Z, Stanley M A 2014 J. Geophys. Res. Atmos. 119 3134
[22]	Stock M G, Krehbiel P R, Lapierre J, Wu T, Stanley M A, Edens H E 2017 J. Geophys. Res. Atmos. 122 8135
[23]	Lu W, Chen L, Ma Y, Rakov V A, Gao Y, Zhang Y, Yin Q, Zhang Y 2013 Geophys. Res. Lett. 40 5531
[24]	Jiang R, Qie X, Wang C, Yang J 2013 Atmos Res. 129 90
[25]	Lu G, Jiang R, Qie X, Zhang H, Sun Z, Liu M, Wang Z, Liu K 2014 Geophys. Res. Lett. 41 9174
[26]	Zhang Y, Krehbiel P R, Zhang Y, Lu W, Zheng D, Xu L, Huang Z 2017 Geophys. Res. Lett. 44 4332
[27]	Pu Y, Jiang R, Qie X, Liu M, Zhang H, Fan Y, Wu X 2017 Geophys. Res. Lett. 44 7029
[28]	Qi Q, Lu W, Ma Y, Chen L, Zhang Y, Rakov V A 2016 Atmos. Res. 178 260
[29]	Zhang Y, Lu W, Li J, Dong W, Zheng D, Chen S 2009 Atmos. Res. 91 326
[30]	Wang C X, Qie X S, Jiang R B, Yang J 2012 Acta Phys. Sin. 61 039203 (in Chinese)[王彩霞, 郄秀书, 蒋如斌, 杨静 2012 物理学报 61 039203]
[31]	Wang X J, Yuan P, Cen J Y, Zhang T L, Xue S M, Zhao J C, Xu H 2013 Acta Phys. Sin. 62 109201 (in Chinese)[王雪娟, 袁萍, 岑建勇, 张廷龙, 薛思敏, 赵金翠, 许鹤 2013 物理学报 62 109201]
[32]	Mazur V, Ruhnke L H 1998 J. Geophys. Res. 103 23299
[33]	Iudin D I, Rakov V A, Mareev E A, Iudin F D, Syssoev A A, Davydenko S S 2017 J. Geophys. Res. Atmos. 122 6416
[34]	Tan Y B, Liang Z W, Shi Z, Zhu J, Guo X 2014 Sci. China: Earth Sci. 57 2125
[35]	Krehbiel P R, Riousset J A, Pasko V P, Thomas R J, Rison W, Stanley M A, Edens H E 2008 Nat. Geosci. 1 233
[36]	Riousset J A, Pasko V P, Krehbiel P R, Rison W, Stanley M A 2010 J. Geophys. Res. 115 A00E10
[37]	Mazur V, Runke L H 1993 J. Geophys. Res. 98 12913
[38]	Mazur V 2016 Principles of Lightning Physics (Bristol: IOP Publishing) pp1-183
[39]	Bazelyan E, Raizer Y 2000 Lightning Physics and Lightning Protection (Bristol: IOP Publishing, London) pp27-221
[40]	Williams E R 2006 Plasma Sources Sci. Technol. 15 S91
[41]	Gou X, Chen M, Du Y, Dong W 2010 Geophys. Res. Lett. 37 L11808
[42]	Gou X, Chen M, Zhang G 2018 J. Geophys. Res. Atmos. 123 1351
[43]	Huo Y L, Zhang G S, L S H, Yuan P 2013 Acta Phys. Sin. 62 059201 (in Chinese)[火元莲, 张广庶, 吕世华, 袁萍 2013 物理学报 62 059201]
[44]	Sun K Y, Zhao X Y, Zhang G L, Zang H M 2014 Acta Phys. Sin. 63 029204 (in Chinese)[孙柯岩, 赵小莹, 张功磊, 臧洪明 2014 物理学报 63 029204]
[45]	Gallimberti I, Bacchiega G, Bondiou-Clergerie A, Lalande P 2002 C. R. Phys. 3 1335
[46]	da Silva C L, Pasko V P 2013 J. Geophys. Res. 118 13561
[47]	Williams E, Heckman S 2012 J. Aerospace Lab. 5 1
[48]	Rison B 2014 Colorado Lightning Mapping Array (LMA) Data. Version 10 UCAR/NCAR-Earth Observing Laboratory. https://data.eol.ucar.edu/dataset/353.209. Accessed 28 September, 2018
[49]	Kulikovsky A A 2000 J. Phys. D: Appl. Phys. 33 1514
[50]	van der Velde O A, Montany J, Soula S, Pineda N, Mlynarczyk J 2014 J. Geophys. Res. Atmos. 119 12755
[51]	Lapierre J L, Sonnenfeld R G, Stock M, Krehbiel P R, Edens H E, Jensen D 2017 J. Geophys. Res. Atmos. 122 4150
[52]	Becerra M, Cooray V A 2006 IEEE Trans. Power Delivery 21 897
[53]	Gallimberti I 1979 J. Phys. Colloq. 40 193
[54]	Les Renardieres Group 1977 Electra 53 31
[55]	Domens P, Gilbert A, Dupuy J, Hutzler B 1991 J. Phys. D: Appl. Phys. 24 1748
[56]	Chen S, Zeng R, Zhuang C, Zhou X, Ding Y 2016 Plasma Sci. Technol. 18 305
[57]	Kostinskiy A Y, Syssoev V S, Bogatov N A, Mareev E A, Andreev M G, Bulatov M U, Sukharevsky D I, Rakov V A 2018 J. Geophys. Res. Atmos 123 5360
[58]	Bazelyan E M, Raizer Y P, Aleksandrov N L 2007 J. Phys. D: Appl. Phys. 40 4133
[59]	Raizer Y P 1991 Gas Discharge Physics (New York: Springer-Verlag) pp222-223
[60]	Popov N A 2009 Plasma Phys. Rep. 35 785
[61]	Lalande P, Bondiou-Clergerie A, Bacchiega G, Gallimberti I 2002 C. R. Phys. 3 1375
[62]	Wang D, Takagi N 2011 J. Geophys. Res. 116 D10205
[63]	Visacro S, Guimaraes M, Murta Vale M H 2017 J. Geophys. Res. Atmos. 122 12786
[64]	Douglas-Hamilton D H, Mani S A 1974 J. Appl. Phys. 45 4406
[65]	Sigmond R S 1984 J. Appl. Phys. 56 1355
[66]	Luque A, Stenbaek-Nielsen H C, McHarg M G, Haaland R K 2016 J. Geophys. Res. Space 121 2431
[67]	Phelps C T 1974 J. Atmos. Sol-Terr. Phys. 36 103
[68]	Schonland B F J, Malan D J, Collens H 1935 Proc. Roy. Soc. A 152 595
[69]	Gorin B N, Levitov V I, Shkilev A V 1976 IEE Conf. Publ. 143 274
[70]	Les Renardieres Group 1981 Electra 74 67
[71]	Kochkin P, Lehtinen N, van Deursen A P J, stgaard N 2016 J. Phys. D: Appl. Phys. 49 425203
[72]	Chen M, Takagi N, Watanabe T, Wang D, Kawasaki Z I, Liu X 1999 J. Geophys. Res. 104 27573
[73]	Wang D, Takagi N, Uman M A, Jordan D M 2016 J. Geophys. Res. Atmos. 121 14612
[74]	Hill J D, Uman M A, Jordan D M 2011 J. Geophys. Res. 116 D16117
[75]	Biagi C J, Uman M A, Hill J D, Jordan D M, Rakov V A, Dwyer J R 2010 J. Geophys. Res. 115 D23215
[76]	Lapierre J L 2015 Ph. D. Dissertation (New Mexico: Institute of Mining and Technology)
[77]	Cooray V, Arevalo L 2017 Atmosphere 8 245
[78]	Warner T A, Cummins K L, Orville R E 2012 J. Geophys. Res. 117 D19109
[79]	Heckman S 1992 Ph. D. Dissertation (Cambridge: Massachusetts Institute of Technology)
[80]	Mazur V, Ruhnke L H 2014 J. Geophys. Res. 119 2786
[81]	Agop M, Nica P, Niculescu O, Dimitriu D G 2012 J. Phys. Soc. Jpn. 81 064502
[82]	Chen M L, Gou X Q, Du Y P 2013 Atmos. Res. 125 76

施引文献

[1]	Schonland B F J 1938 Proc. Roy. Soc. A 164 132
[2]	Kasemir H W 1960 J. Geophys. Res. 65 1873
[3]	Mazur V 1989 J. Geophys. Res. 94 3311
[4]	Mazur V 1989 J. Geophys. Res. 94 3326
[5]	Castellani A, Bondiou-Clergerie A, Lalande P, Bonany A, Gallimberti I 1998 IEE. Proc. Sci. Meas. Technol. 145 193
[6]	Chen M, Watanabe T, Takagi N, Du Y, Wang D, Liu X 2003 J. Geophys. Res. 108 4240
[7]	van der Velde O, Montanya J 2013 J. Geophys. Res. 118 13504
[8]	Shao X, Krehbiel P 1996 J. Geophys. Res. 101 26641
[9]	Thomas R J, Krehbiel P R, Rison W, Hamlin T, Harlin J, Shown D 2001 Geophys. Res. Lett. 28 143
[10]	Warner T A, Saba M M F, Schumann C, Helsdon J H, Orville R E 2016 J. Geophys. Res. Atmos. 121 9251
[11]	Montany J, van der Velde O, Williams E R 2015 Sci. Rep. 5 15180
[12]	Rison W, Krehbiel P R, Stock M G, Edens H E, Shao X M, Thomas R J, Stanley M A, Zhang Y 2016 Nat. Commun. 7 10721
[13]	Biagi C J, Uman M A, Hill J D, Jordan D M 2014 J. Geophys. Res. Atmos. 119 8160
[14]	Wang Z, Qie X, Jiang R, Wang C, Lu G, Sun Z, Liu M, Pu Y 2016 J. Geophys. Res. Atmos. 121 14307
[15]	Jiang R, Qie X, Zhang H, Liu M, Sun Z, Lu G, Wang Z, Wang Y 2017 Sci. Rep. 7 3457
[16]	Saba M M F, Cummins K L, Warner T A, Krider E P, Campos L Z S, Ballarotti M G, Pinto J O, Fleenor S A 2008 Geophys. Res. Lett. 35 L07802
[17]	Mazur V, Ruhnke L H, Warner T A, Orville R E 2013 J. Electrostat. 71 763
[18]	Qie X, Pu Y, Jiang R, Sun Z, Liu M, Zhang H, Li X, Lu G, Tian Y 2017 J. Geophys. Res. Atmos. 122 586
[19]	Wang D, Takagi N, Gamerota W R, Uman M A, Jordan D M 2015 J. Geophys. Res. Atmos. 120 10637
[20]	Hill J D, Uman M A, Jordan D M, Ngin T, Gamerota W R, Pilkey J, Caicedo J 2016 J. Geophys. Res. Atmos. 121 853
[21]	Stock M G, Akita M, Krehbiel P R, Rison W, Edens H E, Kawasaki Z, Stanley M A 2014 J. Geophys. Res. Atmos. 119 3134
[22]	Stock M G, Krehbiel P R, Lapierre J, Wu T, Stanley M A, Edens H E 2017 J. Geophys. Res. Atmos. 122 8135
[23]	Lu W, Chen L, Ma Y, Rakov V A, Gao Y, Zhang Y, Yin Q, Zhang Y 2013 Geophys. Res. Lett. 40 5531
[24]	Jiang R, Qie X, Wang C, Yang J 2013 Atmos Res. 129 90
[25]	Lu G, Jiang R, Qie X, Zhang H, Sun Z, Liu M, Wang Z, Liu K 2014 Geophys. Res. Lett. 41 9174
[26]	Zhang Y, Krehbiel P R, Zhang Y, Lu W, Zheng D, Xu L, Huang Z 2017 Geophys. Res. Lett. 44 4332
[27]	Pu Y, Jiang R, Qie X, Liu M, Zhang H, Fan Y, Wu X 2017 Geophys. Res. Lett. 44 7029
[28]	Qi Q, Lu W, Ma Y, Chen L, Zhang Y, Rakov V A 2016 Atmos. Res. 178 260
[29]	Zhang Y, Lu W, Li J, Dong W, Zheng D, Chen S 2009 Atmos. Res. 91 326
[30]	Wang C X, Qie X S, Jiang R B, Yang J 2012 Acta Phys. Sin. 61 039203 (in Chinese)[王彩霞, 郄秀书, 蒋如斌, 杨静 2012 物理学报 61 039203]
[31]	Wang X J, Yuan P, Cen J Y, Zhang T L, Xue S M, Zhao J C, Xu H 2013 Acta Phys. Sin. 62 109201 (in Chinese)[王雪娟, 袁萍, 岑建勇, 张廷龙, 薛思敏, 赵金翠, 许鹤 2013 物理学报 62 109201]
[32]	Mazur V, Ruhnke L H 1998 J. Geophys. Res. 103 23299
[33]	Iudin D I, Rakov V A, Mareev E A, Iudin F D, Syssoev A A, Davydenko S S 2017 J. Geophys. Res. Atmos. 122 6416
[34]	Tan Y B, Liang Z W, Shi Z, Zhu J, Guo X 2014 Sci. China: Earth Sci. 57 2125
[35]	Krehbiel P R, Riousset J A, Pasko V P, Thomas R J, Rison W, Stanley M A, Edens H E 2008 Nat. Geosci. 1 233
[36]	Riousset J A, Pasko V P, Krehbiel P R, Rison W, Stanley M A 2010 J. Geophys. Res. 115 A00E10
[37]	Mazur V, Runke L H 1993 J. Geophys. Res. 98 12913
[38]	Mazur V 2016 Principles of Lightning Physics (Bristol: IOP Publishing) pp1-183
[39]	Bazelyan E, Raizer Y 2000 Lightning Physics and Lightning Protection (Bristol: IOP Publishing, London) pp27-221
[40]	Williams E R 2006 Plasma Sources Sci. Technol. 15 S91
[41]	Gou X, Chen M, Du Y, Dong W 2010 Geophys. Res. Lett. 37 L11808
[42]	Gou X, Chen M, Zhang G 2018 J. Geophys. Res. Atmos. 123 1351
[43]	Huo Y L, Zhang G S, L S H, Yuan P 2013 Acta Phys. Sin. 62 059201 (in Chinese)[火元莲, 张广庶, 吕世华, 袁萍 2013 物理学报 62 059201]
[44]	Sun K Y, Zhao X Y, Zhang G L, Zang H M 2014 Acta Phys. Sin. 63 029204 (in Chinese)[孙柯岩, 赵小莹, 张功磊, 臧洪明 2014 物理学报 63 029204]
[45]	Gallimberti I, Bacchiega G, Bondiou-Clergerie A, Lalande P 2002 C. R. Phys. 3 1335
[46]	da Silva C L, Pasko V P 2013 J. Geophys. Res. 118 13561
[47]	Williams E, Heckman S 2012 J. Aerospace Lab. 5 1
[48]	Rison B 2014 Colorado Lightning Mapping Array (LMA) Data. Version 10 UCAR/NCAR-Earth Observing Laboratory. https://data.eol.ucar.edu/dataset/353.209. Accessed 28 September, 2018
[49]	Kulikovsky A A 2000 J. Phys. D: Appl. Phys. 33 1514
[50]	van der Velde O A, Montany J, Soula S, Pineda N, Mlynarczyk J 2014 J. Geophys. Res. Atmos. 119 12755
[51]	Lapierre J L, Sonnenfeld R G, Stock M, Krehbiel P R, Edens H E, Jensen D 2017 J. Geophys. Res. Atmos. 122 4150
[52]	Becerra M, Cooray V A 2006 IEEE Trans. Power Delivery 21 897
[53]	Gallimberti I 1979 J. Phys. Colloq. 40 193
[54]	Les Renardieres Group 1977 Electra 53 31
[55]	Domens P, Gilbert A, Dupuy J, Hutzler B 1991 J. Phys. D: Appl. Phys. 24 1748
[56]	Chen S, Zeng R, Zhuang C, Zhou X, Ding Y 2016 Plasma Sci. Technol. 18 305
[57]	Kostinskiy A Y, Syssoev V S, Bogatov N A, Mareev E A, Andreev M G, Bulatov M U, Sukharevsky D I, Rakov V A 2018 J. Geophys. Res. Atmos 123 5360
[58]	Bazelyan E M, Raizer Y P, Aleksandrov N L 2007 J. Phys. D: Appl. Phys. 40 4133
[59]	Raizer Y P 1991 Gas Discharge Physics (New York: Springer-Verlag) pp222-223
[60]	Popov N A 2009 Plasma Phys. Rep. 35 785
[61]	Lalande P, Bondiou-Clergerie A, Bacchiega G, Gallimberti I 2002 C. R. Phys. 3 1375
[62]	Wang D, Takagi N 2011 J. Geophys. Res. 116 D10205
[63]	Visacro S, Guimaraes M, Murta Vale M H 2017 J. Geophys. Res. Atmos. 122 12786
[64]	Douglas-Hamilton D H, Mani S A 1974 J. Appl. Phys. 45 4406
[65]	Sigmond R S 1984 J. Appl. Phys. 56 1355
[66]	Luque A, Stenbaek-Nielsen H C, McHarg M G, Haaland R K 2016 J. Geophys. Res. Space 121 2431
[67]	Phelps C T 1974 J. Atmos. Sol-Terr. Phys. 36 103
[68]	Schonland B F J, Malan D J, Collens H 1935 Proc. Roy. Soc. A 152 595
[69]	Gorin B N, Levitov V I, Shkilev A V 1976 IEE Conf. Publ. 143 274
[70]	Les Renardieres Group 1981 Electra 74 67
[71]	Kochkin P, Lehtinen N, van Deursen A P J, stgaard N 2016 J. Phys. D: Appl. Phys. 49 425203
[72]	Chen M, Takagi N, Watanabe T, Wang D, Kawasaki Z I, Liu X 1999 J. Geophys. Res. 104 27573
[73]	Wang D, Takagi N, Uman M A, Jordan D M 2016 J. Geophys. Res. Atmos. 121 14612
[74]	Hill J D, Uman M A, Jordan D M 2011 J. Geophys. Res. 116 D16117
[75]	Biagi C J, Uman M A, Hill J D, Jordan D M, Rakov V A, Dwyer J R 2010 J. Geophys. Res. 115 D23215
[76]	Lapierre J L 2015 Ph. D. Dissertation (New Mexico: Institute of Mining and Technology)
[77]	Cooray V, Arevalo L 2017 Atmosphere 8 245
[78]	Warner T A, Cummins K L, Orville R E 2012 J. Geophys. Res. 117 D19109
[79]	Heckman S 1992 Ph. D. Dissertation (Cambridge: Massachusetts Institute of Technology)
[80]	Mazur V, Ruhnke L H 2014 J. Geophys. Res. 119 2786
[81]	Agop M, Nica P, Niculescu O, Dimitriu D G 2012 J. Phys. Soc. Jpn. 81 064502
[82]	Chen M L, Gou X Q, Du Y P 2013 Atmos. Res. 125 76

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