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Establishment and Application of Random Lightning Leader Model
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摘要: 根据地闪先导发展特征，建立了一个闪电先导的二维随机模式，并模拟研究了下行先导与避雷针或地面的连接过程。模拟得到下行先导感应电荷的数量级为10-4 C/m；下行先导出现明显的分叉，且先导接近地面时分叉逐渐增多；模拟的连接过程形态呈现多样性的特点；建筑物上的避雷针在绝大多数情况下可以有效拦截闪电下行先导，但避雷针正上方的下行先导并不是百分之百击中避雷针，远离避雷针的下行先导仍有很大概率被避雷针拦截；在下行先导与避雷针水平距离一定的条件下，建筑物越宽越矮，避雷针有效拦截闪电先导的概率就越小。Abstract: Lightning occurred in the atmosphere is a kind of long-distance discharge phenomenon, and it often causes a variety of disasters which become more serious by the extensive use of electronic devices particularly. With deep understanding on physical processes of lightning occurrence and development, lightning leader model is established based on observational facts to study development of lightning leader and its interaction with structures and provide reference for lightning protection. According to characteristics of CG lightning, a model of random lightning leader is established. The connection process of lightening leader is simulated. The model of lightning leader is developed by simulating ambient potential distribution using an over relaxation method. In the model, the direction of next leader step depends on the probability, and final connection location of downward leader is chosen randomly by the probability formula.The induced charge of downward leader increases with the propagation of downward leader. Simulation results of a random model show that the induced charge of downward leader is about 10-4 C/m. With the development of the downward leader, the branch of downward leader increases. There are diversiform forms in connection process. Downward leader can connect with structure or ground which do not produce upward leader besides upward leader. Downward leader can connect with one of the upward leaders on the ground, and even connect with the ground which does not produce upward leader. Downward leader does not always connect with the tip of upward leader, and it can connect with one branch or middle of the upward leader. Lightning rod may do not produce upward leader and the downward leader above doesn't always connect with the lightning rod, sometimes it connects with structure and ground. The downward leader far away from lightning rod can also connect with the lightning rod. In most conditions, lightning rod can protect the structure from lightning. With fixed distances from downward leader and lightning rod, wider and lower structure is less likely protected by lightning rod.These simulation results are achieved with two-dimensional random lightning leader model within the range of limited space. More simulation and analysis are needed for three-dimensional random lightning leader model within larger spatial extent to find out the behavior characteristics of lightning rod and investigate the protection of lightning rod to buildings. A large number of natural lightning and triggered lightning observations are also needed to further check the reasonableness of the simulation results.
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Key words:
- leader;
- connection process;
- random discharge model
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图 4 先导二维随机模式16种不同情况的模拟结果
Fig. 4 Simulation results of 16 different conditions of 2D random lightning leader model
图 5 2009年8月24日19:08:04(北京时) 广州市1次地闪高速摄像记录
Fig. 5 High-speed video recording of CG lightning at 19:08:04 24 August 2009 in Guangzhou
表 1 先导二维随机模式16种模拟结果的说明
Table 1 Description of 16 simulation results of 2D random lightning leader model
序号 产生上行先导的位置 下行先导的连接位置 避雷针 建筑表面 地面 避雷针产生
的上行先导建筑表面产生
的上行先导地面产生
的上行先导地面 建筑表面 情况1 √ √ 情况2 √ √ 情况3 √ √ √ 情况4 √ √ √ 情况5 √ √ √ 情况6 √ √ √ 情况7 √ √ √ 情况8 √ √ √ 情况9 √ √ √ 情况10 √ √ √ 情况11 √ √ √ 情况12 √ √ √ √ 情况13 √ √ √ √ 情况14 √ √ √ √ 情况15 √ √ √ √ 情况16 √ √ √ √ 
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表 2 先导二维随机模式16种模拟结果的次数统计表
Table 2 Numbers of 16 simulation results of 2D random lightning leader model
下行先导
与避雷针
水平距离/m建筑尺寸
(宽×高)情况
1情况
2情况
3情况
4情况
5情况
6情况
7情况
8情况
9情况
10情况
11情况
12情况
13情况
14情况
15情况
160 40 m×30 m 76 0 17 2 0 0 0 0 0 0 0 0 2 1 1 1 40 m×60 m 90 0 3 2 1 2 1 0 0 0 0 0 1 0 0 0 80 m×30 m 65 0 8 8 1 8 0 0 0 0 0 5 2 2 0 1 50 40 m×30 m 76 0 12 7 1 1 0 0 0 0 0 1 0 1 0 1 40 m×60 m 92 0 3 3 0 1 0 0 0 0 0 0 1 0 0 0 80 m×30 m 68 0 12 6 2 6 0 1 0 0 0 3 0 1 0 1 100 40 m×30 m 81 0 11 3 1 0 1 0 0 0 0 1 0 1 1 0 40 m×60 m 97 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 80 m×30 m 69 0 10 5 3 6 0 0 0 0 0 5 1 1 0 0 150 40 m×30 m 73 0 21 3 2 1 0 0 0 0 0 0 0 0 0 0 40 m×60 m 90 0 7 0 0 2 0 0 0 0 0 0 1 0 0 0 80 m×30 m 73 0 10 6 0 4 0 0 1 1 1 2 2 0 0 0 200 40 m×30 m 68 0 22 7 2 0 0 0 0 0 0 0 0 1 0 0 40 m×60 m 91 0 4 3 0 1 0 0 0 0 0 1 0 0 0 0 80 m×30 m 62 0 15 3 3 6 1 1 0 2 0 5 1 1 0 0 250 40 m×30 m 56 2 25 13 2 0 0 0 0 0 0 1 0 1 0 0 40 m×60 m 75 0 14 7 1 1 0 0 0 0 0 1 0 0 0 1 80 m×30 m 46 1 14 11 1 4 1 0 2 7 0 8 3 2 0 0 总计 1348 3 211 89 20 43 4 2 3 10 1 33 14 12 2 5
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表 3 先导二维随机模式3种类型模拟结果的次数统计表
Table 3 Numbers of three type simulation results of 2D random lightning leader model
下行先导与避
雷针水平距离/m建筑尺寸
(宽×高)类型一
(连接位置：避雷针
产生的上行先导)类型二
(连接位置：建筑或
建筑产生的上行先导)类型三
(连接位置：地面或地面
产生的上行先导)0 40 m×30 m 93 3 4 40 m×60 m 95 2 3 80 m×30 m 86 3 11 50 40 m×30 m 90 1 9 40 m×60 m 96 1 3 80 m×30 m 89 2 9 100 40 m×30 m 93 1 6 40 m×60 m 100 0 0 80 m×30 m 90 1 9 150 40 m×30 m 95 0 5 40 m×60 m 99 1 0 80 m×30 m 89 3 8 200 40 m×30 m 90 0 10 40 m×60 m 97 0 3 80 m×30 m 88 3 9 250 40 m×30 m 82 0 18 40 m×60 m 91 1 8 80 m×30 m 82 6 22 总计 1645 28 137
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