The Multi-scale Entropy Feature of the Chaotic Leader in the Cloud-ground Lightning

Li Chan; Zhang Yang; Lü Weitao; Zheng Dong; Tan Yongbo

Vol.25, NO.3, 2014

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Li Chan, Zhang Yang, Lü Weitao, et al. The multi-scale entropy feature of the chaotic leader in the cloud-ground lightning. J Appl Meteor Sci, 2014, 25(3): 347-353.

Citation:

Li Chan, Zhang Yang, Lü Weitao, et al. The multi-scale entropy feature of the chaotic leader in the cloud-ground lightning. J Appl Meteor Sci, 2014, 25(3): 347-353.

Li Chan, Zhang Yang, Lü Weitao, et al. The multi-scale entropy feature of the chaotic leader in the cloud-ground lightning. J Appl Meteor Sci, 2014, 25(3): 347-353.

Citation:

Li Chan, Zhang Yang, Lü Weitao, et al. The multi-scale entropy feature of the chaotic leader in the cloud-ground lightning. J Appl Meteor Sci, 2014, 25(3): 347-353.

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The Multi-scale Entropy Feature of the Chaotic Leader in the Cloud-ground Lightning

Li Chan^1,2,
Zhang Yang²,
Lü Weitao^2,3,
Zheng Dong²,
Tan Yongbo^{1,3
,
,}

1.
College of Atmospheric Physics, Nanjing University of Information Science & Technology, Nanjing 210044
2.
Laboratory of Lightning Physics and Protection Engineering, State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081
3.
Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science & Technology, Nanjing 210044

Received Date: 2013-07-02
Rev Recd Date: 2013-12-03
Publish Date: 2014-05-31

Abstract

Abstract

The chaotic leader is different from stepped leader and dart leader with distinctive features. It has many narrow pulses, causing strong high-frequency radiation. The pulse occurs right at the position of preceding stepped leader and dart leader, but its structure, width and interval all show significant irregularities. The chaotic leader is a new and special one with no exact definition of its pulse characterization so far.Multi-scale entropy is applied to the analysis of chaotic leader, and some key parameters applying in the lightning irregular pulse signal analysis are given after detailed analysis. Dart leader signal, stepped leader signal and the chaotic leader signal are analyzed with the given method and the results are compared, and case studies of the three-leader multi-scale entropy features prove the feasibility of this method. It's found out through statistical analysis that 3 leaders are different in entropy value especially when the scale is greater than 3, and thus they can be clearly distinguished by entropy values. Entropy value greater than 1.5 may indicate chaotic leader, and entropy value less than 1.5 is classified as stepped leader or dart leader. Furthermore chaotic leader and dart leader entropy value both increase with scales first and then stabilize but stepped leader entropy value doesn't change much. Characteristic entropy values for the chaotic leader are given: The average is about 2.0—2.1, the maximum is 2.6—2.8, and the minimum is 1.51—1.59. Based on the analysis of multi-scale entropy characteristics of 3 leaders, the physical meaning of the irregularity is also discussed. The irregularity degree of chaotic electric field pulse can be reflected by the entropy value: The greater the entropy value is, the greater the degree of irregularity. The characteristics of the electric field pulse in the waveform is directly related with the development of the discharge process. For the dart leader or stepped leader, the smaller entropy value illustrates that its discharge is regular. The chaotic leader in small scale with larger entropy directly demonstrates that in this range scale its discharge, polarity and intensity are irregular. It shows the electric discontinuity somewhere in the leader development channel during a certain period before the occurrence of subsequent stroke.
- sample entropy;
- multi-scale entropy;
- dart leader;
- stepped leader;
- chaotic leader

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References(25)

Figures and Tables

Fig. 1 Random signal (a) and sinusoidal signal (b)

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Fig. 2 The entropy of random signal and sinusoidal signal with different scales

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Fig. 3 The fast electric field change waveforms of dart leader (a), stepped leader (b) and chaotic leader (c)

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Fig. 4 Multi-scale entropy comparison between stepped leader and the chaotic leader

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Fig. 5 Multi-scale entropy statistical analysis and comparison between dart leader, stepped leader and the chaotic leader

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Table 1 E_SP(m, 0.15D_S, N) of the chaotic leader

m	样本1				样本2				样本3
m	N=500	N=3000	N=5000	变化率/%	N=500	N=3000	N=5000	变化率/%	N=500	N=3000	N=5000	变化率/%
1	0.99	0.99	0.90	8	1.18	1.40	1.23	4	0.77	0.70	0.69	10
2	0.82	0.82	0.77	5	0.89	1.06	0.90	1	0.61	0.59	0.58	6
3	0.81	0.80	0.73	9	0.82	0.98	0.80	2	0.60	0.53	0.52	14
4	0.75	0.77	0.70	7	0.85	0.91	0.74	13	0.52	0.50	0.48	7
注：变化率指N=5000时相对于N=500时的样本熵的变化。下同。

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Table 2 E_SP(2, r, N) of the chaotic leader

r	样本1				样本2				样本3
r	N=500	N=3000	N=5000	变化率/%	N=500	N=3000	N=5000	变化率/%	N=500	N=3000	N=5000	变化率/%
0.1D_S	1.06	1.12	1.07	2	1.17	1.36	1.17	0.1	0.74	0.74	0.74	0.4
0.15D_S	0.82	0.83	0.78	5	0.89	1.06	0.91	1	0.62	0.59	0.58	6
0.2D_S	0.67	0.66	0.60	10	0.72	0.88	0.75	4	0.53	0.49	0.47	11
0.25D_S	0.55	0.55	0.49	12	0.62	0.76	0.64	5	0.46	0.41	0.40	13

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Table 3 Entropy features of dart leader stepped leader and the chaotic leader

尺度	直窜先导			梯级先导			不规则先导
尺度	平均值	最大值	最小值	平均值	最大值	最小值	平均值	最大值	最小值
1	0.1202	0.5203	0.0072	0.7060	1.2214	0.4309	1.2021	2.3356	0.7126
2	0.1985	0.7521	0.0128	0.7498	1.2929	0.3849	1.7055	2.3379	1.1297
3	0.2599	0.7803	0.0172	0.7616	1.2814	0.3734	1.9150	2.4108	1.3624
4	0.3145	0.8307	0.0221	0.7875	1.2425	0.4075	2.0139	2.6005	1.5211
5	0.3557	0.8551	0.0268	0.8111	1.2231	0.4215	2.0532	2.5217	1.5161
6	0.4122	0.8711	0.0311	0.8549	1.3519	0.4513	2.0956	2.8274	1.5393
7	0.4440	0.8821	0.0354	0.8822	1.3135	0.4853	2.0894	2.5642	1.5600
8	0.4732	0.8930	0.0394	0.9156	1.4629	0.4929	2.0826	2.6472	1.5700
9	0.5027	0.9218	0.0432	0.9645	1.4789	0.5245	2.0175	2.6232	1.5284
10	0.5138	0.9852	0.0463	0.9620	1.4390	0.5381	2.0728	2.8824	1.5192

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