雷暴云电荷结构对闪电放电影响的数值模拟
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摘要
本文的主要工作是在已有的放电参数化方案的基础上,通过改变模式中的初始扰动对四次雷暴进行了多次二维12.5m分辨率放电模拟实验,再现了多种雷暴云电荷结构下的地闪放电现象,就空间电环境特征与地闪接地点之间的相互关系进行了分析,并对三极性雷暴云底部正电荷对闪电放电的影响程度进行了定量估计以及合理性评价；此外,通过建立雷暴云电荷结构模型进行放电模拟实验,分析了雷暴云电荷分布与闪电通道扩展范围的相互关系,并揭示了在具有不同云内电荷浓度分布特征的雷暴云电荷结构下,云闪放电的分形特征以及存在的差异。主要研究成果如下：
(1)三极性雷暴云底部正电荷的大小与分布范围对闪电的放电具有显著影响。在产生负地闪的三极性雷暴云中,底部正电荷缩小至一定量级时,闪电停止发生；而放大一定量级后形成了一种云内反极性放电过程；在产生云闪的三极性雷暴云中,底部正电荷的范围扩大后能产生反极性云闪；在产生正地闪的三极性雷暴云中,底部正电荷对下行正先导具有同性排次作用,其中底部次生正电荷堆电荷量越大和水平分布范围越宽,对下行正先导的抑制作用越明显。
(2)闪电传播的随机性所带来的地闪击地点的不确定范围被限制在3km之内,利用动态聚类法迭代得出的三个击地点位置之间的差为1km左右。负地闪的初始点与击地点的位置差主要分布在0～6km范围内,正、负地闪主要产生于离地面最近的一对电荷堆之间,其起始高度越高,初始点与击地点位置差分布越广；产生于三级性雷暴云电荷结构下的正地闪,其初始于上部的主正电荷堆与中部主负电荷堆之间,其击地点与初始点的距离基本在6km以上。
(3)闪电先导传播范围与电荷堆尺度保持正相关性。云闪通道在穿过电荷累积区中心以前,有较好的分形特征,幂指数约为1.757。云内高密度电荷中心附近电荷浓度变化缓慢,会导致幂指数增加。
This paper use an existing stochastic lightning model and four souding data to perform a2-dimensional thunderstorms numerical simulation experiment which resolution is12.5m. Gives ground flash cases base on different thunderstorm cloud charge structure, and analyzes the relationship between characteristics of electrical environment and ground stroke point. Quantitative estimated the influence of positive charge pile in the bottom of a3-poled thunderstorm on lightning discharge and give rationality evaluated; what's more, makes discharge simulation experiment through establishing space structure model of thunderstorm cloud charge, besides, analysis the relationships between the space charge distribution of thunderstorm and lightning channel extended range, reveals the difference of lightning fractal characteristics under different charge concentration distribution in thunder cloud. The main research results are as follows:
1) Under a3-poled thunderstorm which can generate Negative CG lightning,The size and distribution of positive charge pile in the bottom of a3-poled thunderstorm has significant influence on lightning discharge.; when the bottom positive charge pile is narrowed a certain grade, Lightning will cease; when the bottom positive pile is enlarged a certain magnitude, Reverse polarity of cloud flashes will occur. In a3-poled thunderstorm which can generate IC lightning, when the range of positive charge pile in the bottom is enlarged. Reverse polarity of cloud flashes may occur. In a3-poled thunderstorm which can generate Positive CG lightning, the bottom positive charge pile will exclude the downlink leader, because they have charges of the same polarity. The larger of the quantity and distribution range of charge, The stronger of impact of the bottom positive pile on the downlink leader.
2) Ground strike point uncertainty range is limited to3km because of the lightning propagation randomness, Using dynamic clustering method to iterative three locations which differ about1km. The distance between the initial point and ground strike point of negative CG lightning is mainly distributed in the range of0～6km; CG lightning primarily is produced in a pair of charges which close to ground, the higher of lightning starting height, the larger of range of distance between the initial point and ground strike point; some positive CG lightning which are produced in the three stage of charge structure of thunderstorm cloud is initial between upper part of positive charge pile and mid negative charge pile, the distance between the initial point and ground strike point is basically above6km.
3) The range of Lightning leader propagates keeps positive correlation with the scale of charge in thunderstorm cloud. Before the channel of IC lightning through the charge accumulation centers, lightning The channel of IC lightning have fractal characteristics, the exponent is about1.757, If charge density changes slowly in some place where near the area of high-density charge, exponential will increase.
(1)三极性雷暴云底部正电荷的大小与分布范围对闪电的放电具有显著影响。在产生负地闪的三极性雷暴云中,底部正电荷缩小至一定量级时,闪电停止发生；而放大一定量级后形成了一种云内反极性放电过程；在产生云闪的三极性雷暴云中,底部正电荷的范围扩大后能产生反极性云闪；在产生正地闪的三极性雷暴云中,底部正电荷对下行正先导具有同性排次作用,其中底部次生正电荷堆电荷量越大和水平分布范围越宽,对下行正先导的抑制作用越明显。
(2)闪电传播的随机性所带来的地闪击地点的不确定范围被限制在3km之内,利用动态聚类法迭代得出的三个击地点位置之间的差为1km左右。负地闪的初始点与击地点的位置差主要分布在0～6km范围内,正、负地闪主要产生于离地面最近的一对电荷堆之间,其起始高度越高,初始点与击地点位置差分布越广；产生于三级性雷暴云电荷结构下的正地闪,其初始于上部的主正电荷堆与中部主负电荷堆之间,其击地点与初始点的距离基本在6km以上。
(3)闪电先导传播范围与电荷堆尺度保持正相关性。云闪通道在穿过电荷累积区中心以前,有较好的分形特征,幂指数约为1.757。云内高密度电荷中心附近电荷浓度变化缓慢,会导致幂指数增加。
This paper use an existing stochastic lightning model and four souding data to perform a2-dimensional thunderstorms numerical simulation experiment which resolution is12.5m. Gives ground flash cases base on different thunderstorm cloud charge structure, and analyzes the relationship between characteristics of electrical environment and ground stroke point. Quantitative estimated the influence of positive charge pile in the bottom of a3-poled thunderstorm on lightning discharge and give rationality evaluated; what's more, makes discharge simulation experiment through establishing space structure model of thunderstorm cloud charge, besides, analysis the relationships between the space charge distribution of thunderstorm and lightning channel extended range, reveals the difference of lightning fractal characteristics under different charge concentration distribution in thunder cloud. The main research results are as follows:
1) Under a3-poled thunderstorm which can generate Negative CG lightning,The size and distribution of positive charge pile in the bottom of a3-poled thunderstorm has significant influence on lightning discharge.; when the bottom positive charge pile is narrowed a certain grade, Lightning will cease; when the bottom positive pile is enlarged a certain magnitude, Reverse polarity of cloud flashes will occur. In a3-poled thunderstorm which can generate IC lightning, when the range of positive charge pile in the bottom is enlarged. Reverse polarity of cloud flashes may occur. In a3-poled thunderstorm which can generate Positive CG lightning, the bottom positive charge pile will exclude the downlink leader, because they have charges of the same polarity. The larger of the quantity and distribution range of charge, The stronger of impact of the bottom positive pile on the downlink leader.
2) Ground strike point uncertainty range is limited to3km because of the lightning propagation randomness, Using dynamic clustering method to iterative three locations which differ about1km. The distance between the initial point and ground strike point of negative CG lightning is mainly distributed in the range of0～6km; CG lightning primarily is produced in a pair of charges which close to ground, the higher of lightning starting height, the larger of range of distance between the initial point and ground strike point; some positive CG lightning which are produced in the three stage of charge structure of thunderstorm cloud is initial between upper part of positive charge pile and mid negative charge pile, the distance between the initial point and ground strike point is basically above6km.
3) The range of Lightning leader propagates keeps positive correlation with the scale of charge in thunderstorm cloud. Before the channel of IC lightning through the charge accumulation centers, lightning The channel of IC lightning have fractal characteristics, the exponent is about1.757, If charge density changes slowly in some place where near the area of high-density charge, exponential will increase.
引文
[1]许小峰,郭虎,缪小农等.国外雷电监测预警和预报[M].北京：气象出版社,2003,60-66.
[2]陈渭民.雷电学原理[M].北京：气象出版社,2003,289-318.
[3]肖稳安,张小青.雷电与防护技术基础[M].北京：气象出版社,2006,16-18.
[4]张小青.建筑物内的电子设备的防雷保护[M].北京：电子工业出版社,2000,27-32.
[5]MacGorman D R, Few A A, Teer T L. Layered lightning activity[J]. Geophys Res. 1981,86:9900-9910.
[6]Wilson C T R. On some determinations of the sign and magnitude of electric discharges in lightning flashes[J].1916,A92:555-574.
[7]Wilson C T R. Some thundercloud problems[J].1929, J Franklin Inst,208(1):1-12.
[8]Simpson S G, Scrase F J. The distribution of electricity in thunderclouds [J]. Proc Roy Soc Lond,1937,161(906):309-352.
[9]Simpson S G, Scrase F J. The distribution of electricity in thunderclouds[J]. Proc Roy Soc Lond,1941,177(970):281-328.
[10]Krider E P.Electric field changes and cloud electric structure[J]. J Geophys Res,1989,94 (D11):13145-13149.
[11]Marshall T C, Rust W D. Electric field soundings Trough thunderstorms[J]. J Geophys Res,1991,96(D12):22,297-22,306.
[12]Vonnegut B, Moore C B, Semonin R G et al. Effect of atmospheric space charge on initial electrification of cumulus clouds[J].J Geophys Res,1962,67:3909-3921.
[13]邵选民,刘欣生.云中闪电及云下部正电荷的初步分析.高原气象[J],1987,6(4)：317-325.
[14]Marshall T C, Rust W D, Winn W P, et al. The electrical structure in two thunderstorm anvil clouds[J]. J Geophys Res,1989,94:2171-2181.
[15]Coleman L M, Marshall T C, Stolzenburg M et al. Effects of charge and electrostatic potential on lightning propagation[J].J Geophys Res,2003, 108:ACL12 1-27.
[16]Macgorman D R, Rust W D. The electrical nature of storms. New York, Oxford University Press,1998.
[17]杨忠江,朱浩,唐宏科等.地面电场仪测量数据的误差来源及分析处理[J].大气科学学报,2010,33(6)：751-756.
[18]孟青,吕伟涛,姚雯等.地面电场资料在雷电预警技术中的应用[J].气象,2005,31(9)：30-33.
[19]Stolzenburg M. An observational study of electrical structure in convective regions of mesoscale convective systems[D].Grad.College, Univ.of Okl,1996.
[20]Rison W, Thomas R J, Krehbiel P R, et al.A GPS-based three-dimensional lightning mapping system:Initial observations in central New Mexico [J]. Geophys Res Lett,1999,26:3573-3576.
[21]Jordan Douglas M, Vincent P. Idone, Richard E. Orville, Vladimir A. Rakov,and Martin A. Uman. Luminosity characteristics of lightning M components[J]. J Geophy Res,1995:25695-25700.
[22]Brook M, Kitagawa N. Radiation from lightning discharges in the frequency range 400-1000 MC/s[J],J Geophy Res,1964,69(12):2431-2434
[23]Krider E P, Weidman C D. The temporal structure of the HF and VHF radiation produced by intracloud lightning discharges[J].J Geophys Res,1979,84(c9),5760-5762.
[24]Proctor D E.VHF radio pictures of cloud flashes. Journal of Geophysical Research, 1981,86:4041-4071.
[25]Proctor D E.Regions where lightning fashes begun. Journal of Geophysical Research,1991.96:5099-5112.
[26]Rison W, Thomas RJ, Krehbiel P R, et al. A GPS-based three-dimensional lightning mapping system:initial observations in Central New Mexico. Geophysical Research Letters 1999,26:3573-3576.
[27]Richard P, Delannoy A, et al.Result of spatial and temporal characterization of the VHF-UHF radiation of lightning. Journal of Geophysical Research,1986,91: 1248-1260.
[28]Rhodes C T, Shao X M, Krehbiel P R, et al. Observations of lightning phenomena using radio interferometry. Journal of Geophysical Research,1994,99: 13,059-13,082.
[29]Shao X M, Krehbiel P R, Thomas R J, et al. Radio interferometric observations of cloud-to-ground lightning phenomena in Florida. Journal of Geophysical Research, 1995,100:2749-2783.
[30]Shao X M, Krehbiel P R, The spatial and temporal development of intracloud lightning[J].J Geophys Res,1996,101:26641-26668.
[31]董万胜,刘欣生等.甚高频闪电辐射源的定位与同步观测试验.自然科学进展：2001,11：955-959.
[32]Ogawa T, and Brook M. The mechanism of the intracloud lightning discharge[J]. J Geophys Res,1964,69:5141-5150.
[33]张义军,Krehbiel P R,刘欣生等.雷暴中的反极性放电和电荷结构[J].科学通报,2002,47(15)：1192-1195.
[34]Zheng D, Zhang Y J, Meng Q. Lightning activity and electrical structure in a thunderstorm that continued for more than 24 h[J]. Atmospheric Research,2010,97:241-256.
[35]Akita M, Satoru Y, Nakamure Y, et al. Effects of Charge Distribution in Thunderstorms on Lightning Propagation Paths in Darwin, Australia[J].Journal of the atmospheric sciences.2011,68:719-726.
[36]Takeuti T, Nakano M, Brook M, et al. The anomalous winter thunderstorms of the Hokuriku coast[J], J Geophys Res,1978,83:2385-2394.
[37]Carey L D, Rutledge S A. Electrical and multi-parameter radar observations of a severe hailstorm[J].J Geophys Res,1998,103:13,979-14,000.
[38]Clarence N D, Malan D J. Preliminary discharge processes in lightning flashes to ground[J]. Q J R Meteorol Soc,1957,83(356):161-172.
[39]Jayaratne E R, Saunders C P R. The "rain gush", lightning, and the lower positive charge in thunderstorms[J]. J Geophys Res,1984,89(D7):11816-11818
[40]Rawlins F, A numerical study of thunderstorm electrification using a three-dimensional model incorporating the ice phase[J].Q J R Meteorol Soc, 1982,108:779-800.
[41]Baker M B, Christian H J and Latham J, A computational study of the relationships linking lightning frequency and other thundercloud parameters [J], Quarterly Journal of the Royal Meteorological Society,1995,121:1525-548.
[42]Kasemir H W., A contribution to the electrostatic theory of a lightning discharge[J]. J Geophys Res,1960,65(2):1873-1878.
[43]Helsdon J H, Wu Jr G, Farley R D, An intracloud lightning parameterization scheme for a storm electrification model[J]. J Geophys Res,1992,97:5865-5884.
[44]Mazur V, Ruhnke L H. Model of electric charges in thunderstorms and associated lightning.J Geophys Res,1998,103:23299-23308.
[45]Mansell E R, MacGorman D, Ziegler C L et al. Simulated three dimensional branched lightning in a numerical thunderstorm model[J], Journal of Geophysical Research.2002,107(D9):4075,doi:10.1029/2000JD000244.
[46]Tan Y B, Tao S C, et. al. Fine-resolution simulation of the channel structures and propagation features of intracloud lightning [J], Geophysical Research Letters, 2006, No.33.
[47]Tan Y b, Tao S C, et al., Numerical simulations of the bi-level and branched structure of intracloud lightning flashes, Science in China Ser. D Earth Sciences, 2006, No.49
[48]Tao S C, Tan Y B, Zhu B Y, et al. Fine-resolution simulation of cloud-to-ground lightning and thundercloud charge transfer [J]. Atmospheric Research,2009,91, 360-370.
[49]Gardiner B, Lamb D, Pitter R L, et al.Measurements of initial potential gradient and particle charges in a montana summer thunderstorm [J]. J Geophys Res,1985,90(D4):6079-6086.
[50]Marshall T C, McCarthy M P, Rust W D. Electric field magnitudes and lightning initiation in thunderstorms [J]. J Geophys Res,1995,100(D4):7097-7103.
[51]Solomon R, Schroeder V, Baker M B, Lightning initiation-conventional and runaway-breakdown hypotheses, Q J Roy Meteoro Soc.2001,127:2683-704.
[52]郄秀书,张广庶,孔祥贞等.青藏高原东北部地区夏季雷电特征的观测研究[J].高原气象,2002,22(3)：209-215.
[53]李荣,王才伟,卢贵武.不同电结构中雷暴的特征.地球物理学报[J].1999,42(增刊)：57-64.
[54]Nag A and Rakov V A. Some inferences on the role of lower positive charge region in facilitating different types of lightning [J]. Geophysical research letters,2009,36, doi:10.1029/2008GL036783.
[55]Ulanski, Garstang. The role of surface divergence and vorticity in the life cycle of convective rainfall. Part I. Observations and analysis[J]. J Atoms Sci,.197835 (6): 1047-1062.
[56]Horvath T. Computation of the lighting stroke probability and the effectiveness of the air termination [J]. Journal of Electrostatic,1989,23(2):305-332.
[57]Horvath T. Computation of lighting protection.England:Research Studies Press,1991.
[58]Erikssion A J. Lightning striking distances-an analytical study. Proceeding of 6th International Conference on Gas Discharge and Its Application. Edinburgh, UK:IEE Press,1980,143-146.
[59]Eriksson A J. The incidence of lightning strikes to power lines. IEEE Trans, on Power Delivery,1986,2(3):859-886.
[60]Dellera L and Garbagnati E "Lightning Stroke Simulation by Means of the Leader Progression Model".IEEE Trans. PD,1990,Vol.5:2009-2029,
[61]Petrov N, Petrova G, Alessandro F D, Quantification of the probability of lightning strikes to structures using a fractal approach, IEEE Trans. Dielectr.Electr. Insul. 2003,10 (4):641-654.
[62]张小青,高结构体雷击率计算[J],高电压技术,2003,29(3)：3-5.
[63]康春华,基于引雷空间的建筑物累计特性研究[D].硕士学位论文,北京交通大学,2007
[64]任晓毓,张义军,吕伟涛.雷击建筑物的先导连接过程模拟[J].应用气象学报.2010.21(4)：450-457
[65]Tan Y B, Tao S C,Zhu B Y, et al. Numerical simulations of the bi-level and branched structure of intracloud lightning flashes[J]. Science in China (Ser. D), 2006,46(6):661-672
[66]Davis S M. Properties of lightning discharges from multiple-station wideband electric field measures, [Ph. D. thesis]:University of Florida,1999
[67]Thomas R J, Krehbiel P R, Digon W, et al. Observations of VHF source powers radiated by lightning[J].J Geophys Res,2001,28:143-146
[68]Takeuti T, Nakano M, Brook M, et al. The anomalous winter thunderstorms of the Hokuriku coast[J]. J Geophys Res,1978,83:2385-2394.
[69]Marshall T C, Rust W D. Two types of vertical electrical structures in the stratiform precipitation regions of mesoscale convective systems[J]. Bull. Am. Meteorol. Soc, 1993,74:2159-2170.
[70]吴诚鸥,秦伟良等.近代实用多元统计分析[M].气象出版社,2007,52-56.
[71]Wilson C T R, The electric field of a thundercloud and some of its effects [J]. Proc Phys Soc,1925,37:32-37.
[72]Vonnegut B, Possible mechanism for the formation of thunderstorm electricity, paper presented at the Conference on Atmospheric Electricity, Wentworth NH, 1955.
[73]Kasemir H W.The thundercloud, in Problems of Atmospheric and Space Electricity, edited by S. Coroniti, Elsevier, New York,1965,215-231.
[74]Williams E, The tripoles tructureo f thunderstorm[J].J Geophys Res.1989,94: 13,151-13,167.
[75]Krehbiel P, The electrical structure of thunderstorms, in The Earth's Electrical Environment, Nat'l. Academy Press, Washington, D.C.,1986,90-113.
[76]Chiu Chinshan. Numerical study of cloud electrification in an axisym-metric, time-dependent cloud model [J]. J Geophys Ras,1978,83:5025-5049.
[77]言穆弘,刘欣生,安学敏等.雷暴非感应起电机制的模拟研究.Ⅰ.云内因子影响[J].高原气象,1996,15(4)：425-437.
[78]言穆弘,刘欣生,安学敏等. 雷暴非感应起电机制的模拟研究.Ⅱ.环境因子影响[J].高原气象,1996,15(4)：438-447.
[79]Kuettner J P, Zev Levin, J D Sartor. Thunderstorm electrification-inductive or non-inductive [J]. J Atmos Sei,1982,38:2470-2484.
[80]孙安平,言穆弘,张义军,等.2002a.三维强风暴动力-电耦合数值模拟研究Ⅰ：模式 及其电过程参数化方案.气象学报,60(6)：722-731.
[81]孙安平,言穆弘,张义军,等.2002b.三维强风暴动力-电耦合数值模拟研究Ⅱ：电结构形成机制[J].气象学报,60(6)：732-739.
[82]郭凤霞,张义军,郄秀书,等.2003.雷暴云不同空间电荷结构数值模拟研究[J].高原气象,22(3)：268-274.
[83]周志敏,郭学良.强雷暴云中电荷多层分布与形成过程的三维数值模拟研究[J].大气科学,33(3),600-620
[84]Niemeyer L, Piotronero L, Weismann H J. Fractal Dimension of Dielectric Breakdown[J]. Phys Rev Letts,1984,52:1033-1036.
[85]谭涌波,陶善昌,祝宝友.雷暴云内闪电双层、分枝结构的数值模拟[J].中国科学,2006,36(5)：486-496
[2]陈渭民.雷电学原理[M].北京：气象出版社,2003,289-318.
[3]肖稳安,张小青.雷电与防护技术基础[M].北京：气象出版社,2006,16-18.
[4]张小青.建筑物内的电子设备的防雷保护[M].北京：电子工业出版社,2000,27-32.
[5]MacGorman D R, Few A A, Teer T L. Layered lightning activity[J]. Geophys Res. 1981,86:9900-9910.
[6]Wilson C T R. On some determinations of the sign and magnitude of electric discharges in lightning flashes[J].1916,A92:555-574.
[7]Wilson C T R. Some thundercloud problems[J].1929, J Franklin Inst,208(1):1-12.
[8]Simpson S G, Scrase F J. The distribution of electricity in thunderclouds [J]. Proc Roy Soc Lond,1937,161(906):309-352.
[9]Simpson S G, Scrase F J. The distribution of electricity in thunderclouds[J]. Proc Roy Soc Lond,1941,177(970):281-328.
[10]Krider E P.Electric field changes and cloud electric structure[J]. J Geophys Res,1989,94 (D11):13145-13149.
[11]Marshall T C, Rust W D. Electric field soundings Trough thunderstorms[J]. J Geophys Res,1991,96(D12):22,297-22,306.
[12]Vonnegut B, Moore C B, Semonin R G et al. Effect of atmospheric space charge on initial electrification of cumulus clouds[J].J Geophys Res,1962,67:3909-3921.
[13]邵选民,刘欣生.云中闪电及云下部正电荷的初步分析.高原气象[J],1987,6(4)：317-325.
[14]Marshall T C, Rust W D, Winn W P, et al. The electrical structure in two thunderstorm anvil clouds[J]. J Geophys Res,1989,94:2171-2181.
[15]Coleman L M, Marshall T C, Stolzenburg M et al. Effects of charge and electrostatic potential on lightning propagation[J].J Geophys Res,2003, 108:ACL12 1-27.
[16]Macgorman D R, Rust W D. The electrical nature of storms. New York, Oxford University Press,1998.
[17]杨忠江,朱浩,唐宏科等.地面电场仪测量数据的误差来源及分析处理[J].大气科学学报,2010,33(6)：751-756.
[18]孟青,吕伟涛,姚雯等.地面电场资料在雷电预警技术中的应用[J].气象,2005,31(9)：30-33.
[19]Stolzenburg M. An observational study of electrical structure in convective regions of mesoscale convective systems[D].Grad.College, Univ.of Okl,1996.
[20]Rison W, Thomas R J, Krehbiel P R, et al.A GPS-based three-dimensional lightning mapping system:Initial observations in central New Mexico [J]. Geophys Res Lett,1999,26:3573-3576.
[21]Jordan Douglas M, Vincent P. Idone, Richard E. Orville, Vladimir A. Rakov,and Martin A. Uman. Luminosity characteristics of lightning M components[J]. J Geophy Res,1995:25695-25700.
[22]Brook M, Kitagawa N. Radiation from lightning discharges in the frequency range 400-1000 MC/s[J],J Geophy Res,1964,69(12):2431-2434
[23]Krider E P, Weidman C D. The temporal structure of the HF and VHF radiation produced by intracloud lightning discharges[J].J Geophys Res,1979,84(c9),5760-5762.
[24]Proctor D E.VHF radio pictures of cloud flashes. Journal of Geophysical Research, 1981,86:4041-4071.
[25]Proctor D E.Regions where lightning fashes begun. Journal of Geophysical Research,1991.96:5099-5112.
[26]Rison W, Thomas RJ, Krehbiel P R, et al. A GPS-based three-dimensional lightning mapping system:initial observations in Central New Mexico. Geophysical Research Letters 1999,26:3573-3576.
[27]Richard P, Delannoy A, et al.Result of spatial and temporal characterization of the VHF-UHF radiation of lightning. Journal of Geophysical Research,1986,91: 1248-1260.
[28]Rhodes C T, Shao X M, Krehbiel P R, et al. Observations of lightning phenomena using radio interferometry. Journal of Geophysical Research,1994,99: 13,059-13,082.
[29]Shao X M, Krehbiel P R, Thomas R J, et al. Radio interferometric observations of cloud-to-ground lightning phenomena in Florida. Journal of Geophysical Research, 1995,100:2749-2783.
[30]Shao X M, Krehbiel P R, The spatial and temporal development of intracloud lightning[J].J Geophys Res,1996,101:26641-26668.
[31]董万胜,刘欣生等.甚高频闪电辐射源的定位与同步观测试验.自然科学进展：2001,11：955-959.
[32]Ogawa T, and Brook M. The mechanism of the intracloud lightning discharge[J]. J Geophys Res,1964,69:5141-5150.
[33]张义军,Krehbiel P R,刘欣生等.雷暴中的反极性放电和电荷结构[J].科学通报,2002,47(15)：1192-1195.
[34]Zheng D, Zhang Y J, Meng Q. Lightning activity and electrical structure in a thunderstorm that continued for more than 24 h[J]. Atmospheric Research,2010,97:241-256.
[35]Akita M, Satoru Y, Nakamure Y, et al. Effects of Charge Distribution in Thunderstorms on Lightning Propagation Paths in Darwin, Australia[J].Journal of the atmospheric sciences.2011,68:719-726.
[36]Takeuti T, Nakano M, Brook M, et al. The anomalous winter thunderstorms of the Hokuriku coast[J], J Geophys Res,1978,83:2385-2394.
[37]Carey L D, Rutledge S A. Electrical and multi-parameter radar observations of a severe hailstorm[J].J Geophys Res,1998,103:13,979-14,000.
[38]Clarence N D, Malan D J. Preliminary discharge processes in lightning flashes to ground[J]. Q J R Meteorol Soc,1957,83(356):161-172.
[39]Jayaratne E R, Saunders C P R. The "rain gush", lightning, and the lower positive charge in thunderstorms[J]. J Geophys Res,1984,89(D7):11816-11818
[40]Rawlins F, A numerical study of thunderstorm electrification using a three-dimensional model incorporating the ice phase[J].Q J R Meteorol Soc, 1982,108:779-800.
[41]Baker M B, Christian H J and Latham J, A computational study of the relationships linking lightning frequency and other thundercloud parameters [J], Quarterly Journal of the Royal Meteorological Society,1995,121:1525-548.
[42]Kasemir H W., A contribution to the electrostatic theory of a lightning discharge[J]. J Geophys Res,1960,65(2):1873-1878.
[43]Helsdon J H, Wu Jr G, Farley R D, An intracloud lightning parameterization scheme for a storm electrification model[J]. J Geophys Res,1992,97:5865-5884.
[44]Mazur V, Ruhnke L H. Model of electric charges in thunderstorms and associated lightning.J Geophys Res,1998,103:23299-23308.
[45]Mansell E R, MacGorman D, Ziegler C L et al. Simulated three dimensional branched lightning in a numerical thunderstorm model[J], Journal of Geophysical Research.2002,107(D9):4075,doi:10.1029/2000JD000244.
[46]Tan Y B, Tao S C, et. al. Fine-resolution simulation of the channel structures and propagation features of intracloud lightning [J], Geophysical Research Letters, 2006, No.33.
[47]Tan Y b, Tao S C, et al., Numerical simulations of the bi-level and branched structure of intracloud lightning flashes, Science in China Ser. D Earth Sciences, 2006, No.49
[48]Tao S C, Tan Y B, Zhu B Y, et al. Fine-resolution simulation of cloud-to-ground lightning and thundercloud charge transfer [J]. Atmospheric Research,2009,91, 360-370.
[49]Gardiner B, Lamb D, Pitter R L, et al.Measurements of initial potential gradient and particle charges in a montana summer thunderstorm [J]. J Geophys Res,1985,90(D4):6079-6086.
[50]Marshall T C, McCarthy M P, Rust W D. Electric field magnitudes and lightning initiation in thunderstorms [J]. J Geophys Res,1995,100(D4):7097-7103.
[51]Solomon R, Schroeder V, Baker M B, Lightning initiation-conventional and runaway-breakdown hypotheses, Q J Roy Meteoro Soc.2001,127:2683-704.
[52]郄秀书,张广庶,孔祥贞等.青藏高原东北部地区夏季雷电特征的观测研究[J].高原气象,2002,22(3)：209-215.
[53]李荣,王才伟,卢贵武.不同电结构中雷暴的特征.地球物理学报[J].1999,42(增刊)：57-64.
[54]Nag A and Rakov V A. Some inferences on the role of lower positive charge region in facilitating different types of lightning [J]. Geophysical research letters,2009,36, doi:10.1029/2008GL036783.
[55]Ulanski, Garstang. The role of surface divergence and vorticity in the life cycle of convective rainfall. Part I. Observations and analysis[J]. J Atoms Sci,.197835 (6): 1047-1062.
[56]Horvath T. Computation of the lighting stroke probability and the effectiveness of the air termination [J]. Journal of Electrostatic,1989,23(2):305-332.
[57]Horvath T. Computation of lighting protection.England:Research Studies Press,1991.
[58]Erikssion A J. Lightning striking distances-an analytical study. Proceeding of 6th International Conference on Gas Discharge and Its Application. Edinburgh, UK:IEE Press,1980,143-146.
[59]Eriksson A J. The incidence of lightning strikes to power lines. IEEE Trans, on Power Delivery,1986,2(3):859-886.
[60]Dellera L and Garbagnati E "Lightning Stroke Simulation by Means of the Leader Progression Model".IEEE Trans. PD,1990,Vol.5:2009-2029,
[61]Petrov N, Petrova G, Alessandro F D, Quantification of the probability of lightning strikes to structures using a fractal approach, IEEE Trans. Dielectr.Electr. Insul. 2003,10 (4):641-654.
[62]张小青,高结构体雷击率计算[J],高电压技术,2003,29(3)：3-5.
[63]康春华,基于引雷空间的建筑物累计特性研究[D].硕士学位论文,北京交通大学,2007
[64]任晓毓,张义军,吕伟涛.雷击建筑物的先导连接过程模拟[J].应用气象学报.2010.21(4)：450-457
[65]Tan Y B, Tao S C,Zhu B Y, et al. Numerical simulations of the bi-level and branched structure of intracloud lightning flashes[J]. Science in China (Ser. D), 2006,46(6):661-672
[66]Davis S M. Properties of lightning discharges from multiple-station wideband electric field measures, [Ph. D. thesis]:University of Florida,1999
[67]Thomas R J, Krehbiel P R, Digon W, et al. Observations of VHF source powers radiated by lightning[J].J Geophys Res,2001,28:143-146
[68]Takeuti T, Nakano M, Brook M, et al. The anomalous winter thunderstorms of the Hokuriku coast[J]. J Geophys Res,1978,83:2385-2394.
[69]Marshall T C, Rust W D. Two types of vertical electrical structures in the stratiform precipitation regions of mesoscale convective systems[J]. Bull. Am. Meteorol. Soc, 1993,74:2159-2170.
[70]吴诚鸥,秦伟良等.近代实用多元统计分析[M].气象出版社,2007,52-56.
[71]Wilson C T R, The electric field of a thundercloud and some of its effects [J]. Proc Phys Soc,1925,37:32-37.
[72]Vonnegut B, Possible mechanism for the formation of thunderstorm electricity, paper presented at the Conference on Atmospheric Electricity, Wentworth NH, 1955.
[73]Kasemir H W.The thundercloud, in Problems of Atmospheric and Space Electricity, edited by S. Coroniti, Elsevier, New York,1965,215-231.
[74]Williams E, The tripoles tructureo f thunderstorm[J].J Geophys Res.1989,94: 13,151-13,167.
[75]Krehbiel P, The electrical structure of thunderstorms, in The Earth's Electrical Environment, Nat'l. Academy Press, Washington, D.C.,1986,90-113.
[76]Chiu Chinshan. Numerical study of cloud electrification in an axisym-metric, time-dependent cloud model [J]. J Geophys Ras,1978,83:5025-5049.
[77]言穆弘,刘欣生,安学敏等.雷暴非感应起电机制的模拟研究.Ⅰ.云内因子影响[J].高原气象,1996,15(4)：425-437.
[78]言穆弘,刘欣生,安学敏等. 雷暴非感应起电机制的模拟研究.Ⅱ.环境因子影响[J].高原气象,1996,15(4)：438-447.
[79]Kuettner J P, Zev Levin, J D Sartor. Thunderstorm electrification-inductive or non-inductive [J]. J Atmos Sei,1982,38:2470-2484.
[80]孙安平,言穆弘,张义军,等.2002a.三维强风暴动力-电耦合数值模拟研究Ⅰ：模式 及其电过程参数化方案.气象学报,60(6)：722-731.
[81]孙安平,言穆弘,张义军,等.2002b.三维强风暴动力-电耦合数值模拟研究Ⅱ：电结构形成机制[J].气象学报,60(6)：732-739.
[82]郭凤霞,张义军,郄秀书,等.2003.雷暴云不同空间电荷结构数值模拟研究[J].高原气象,22(3)：268-274.
[83]周志敏,郭学良.强雷暴云中电荷多层分布与形成过程的三维数值模拟研究[J].大气科学,33(3),600-620
[84]Niemeyer L, Piotronero L, Weismann H J. Fractal Dimension of Dielectric Breakdown[J]. Phys Rev Letts,1984,52:1033-1036.
[85]谭涌波,陶善昌,祝宝友.雷暴云内闪电双层、分枝结构的数值模拟[J].中国科学,2006,36(5)：486-496