# A New Approach of 3D Lightning Location Based on Pearson Correlation Combined with Empirical Mode Decomposition

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## Abstract

**:**

## 1. Introduction

## 2. Experiment and Equipment

## 3. Method

_{i}, y

_{i}, z

_{i}) and t

_{i}represent the three-dimensional coordinates of station i and the pulse arrival time, respectively. (x, y, z) and t represent the spatial location and occurrence time of a radiation source, respectively, and c is the propagation speed of electromagnetic waves in the air (3 × 10

^{8}m s

^{−1}). The arrival time of the radiation pulse at station i satisfies Equation (1) as follows:

^{2}, which can be expressed as Equation (2). The minimum chi-square value x

^{2}can be computed using the nonlinear least squares method, which was introduced in [10,12]. First, select at least four stations from all stations to calculate the position of the radiation source, and keep trying different combinations of stations to minimize the chi-square value x

^{2}. The i in Equation (2) represents the i-th station, and N is the number of stations in the lightning detection network. t

^{obs}is the pulse arrival time, and t

^{fit}is the fitted pulse arrival time. ∆t

_{rms}is the time error, which is determined by the performance of the hardware system. Finally, all the positioning points are screened by chi-square value (x

^{2}), under the condition of x

^{2}< 5.

#### 3.1. Data Preprocessing

_{i}(t), the envelopes of the upper and lower extreme points are fitted with a tertiary spline curve. The original signal is subtracted from the average of the two envelopes to obtain c

_{1}. It is judged according to the preset criterion whether c

_{1}is an IMF. If not, X

_{i}(t) is replaced with c

_{1}, and the above steps are repeated until c

_{k}meets the criterion (we assume in advance that this sifting process has been repeated k times).

_{k}is the current relative tolerance of the k-th sifting of an IMF component. We can repeat this sifting process k times and extract an IMF component when the relative tolerance is less than 0.2.

_{n}is the residual component. The residual component r

_{n}usually contains direct current (DC) components, monotonic components, and very low-frequency (VLF) components. Using the EMD method to decompose the original signal X

_{i}(t) into a series of IMF components and the residual component r

_{n}can be expressed as:

_{i}(t) is obtained, and the signal y

_{i}(t) is obtained by normalization. Normalization can be expressed as Equation (6). Among them, max(x

_{i}) is the maximum value of signal x

_{i}(t), and min(x

_{i}) is the minimum value of signal x

_{i}(t). After the normalization process is completed, the difference between the maximum value and the minimum value of each station signal is 2, and the pulse amplitudes between different stations are similar, which is important to achieve pulse matching through Pearson correlation.

#### 3.2. Discharge Electric Pulse Matching

_{A}is the variance of dataset A (a 25 µs time series in this paper). $\overline{A}$ is the average value of dataset A, and $\overline{B}$ is the average value of dataset B.

Conditions (1) ρ_{0} > α |

Conditions (2) ρ_{0} = max(ρ) |

## 4. Results of Data Processing and Pulse Matching

#### 4.1. Results of Data Preprocessing

#### 4.2. Results of Pulse Matching

## 5. Positioning Results and Analysis of Lightning Physical Processes

#### 5.1. Positioning Efficiency of the New Method

#### 5.2. The 3D Location Results of Two Lightning Flashes

#### 5.2.1. IC Flash 001136

^{6}m s

^{−1}and is a typical value of those reported by other researchers [6,37,38]. The whole flash lasted approximately 650 ms.

#### 5.2.2. CG Flash 000241

^{7}–10

^{8}m s

^{−1}[2,36,37,40,41,42]. From the dynamic positioning results of the CG flash, it is found that there were three negative recoil streamers in the positive leader channel. Figure 12 shows the pulses of the second negative recoil streamer and the second K-process pulses of the negative leader channel. The pulses amplitude of the second negative recoil streamer is smaller than the pulses of the second K-process of the negative leader channel, and the duration of the negative recoil streamer is very short (0.2 ms), with a horizontal length of approximately 3 km. The average velocity of the second negative recoil streamer was estimated to be approximately 1.5 × 10

^{7}m s

^{−1}and is typical of those reported by other researchers [2,37,41]. According to the positioning results of the CG lightning flash, after the three negative recoil streamers are finished (approximately 1 ms, 12 ms, and 2 ms), the negative leader channel undergoes a K-process. The negative recoil streamers are not connected to the K-processes. We think that the three negative recoil streamers of the positive leader channel may have triggered the three K-processes of the horizontal negative leader channel of the lightning, respectively.

## 6. Conclusions

- (1)
- The lightning electric field signal is decomposed by the EMD method and then partially synthesized, which removes the low-frequency components from the original signal and facilitates subsequent pulse seeking and pulse matching. Normalizing the decomposed and resynthesized signals can make the pulse amplitudes of the same radiation source at different stations more consistent.
- (2)
- After the signal is processed by the MED method, Pearson correlation is applied to match lightning electric field pulses. This paper uses the new method to locate the lightning channels of an IC lightning flash and a CG lightning flash and analyzes the location results for the two lightning flash. Compared with a previous method, the results show that the new method has good performance in lightning location and has significantly improved the accuracy of pulse matching and the mapping quality of lightning discharges.
- (3)
- According to the positioning result of a CG lightning flash, after the three negative recoil streamers were finished (approximately 1 ms, 12 ms, and 2 ms), the negative leader channel underwent a K-process. The negative recoil streamers were not connected to the K-processes. The three negative recoil streamers of the positive leader channel may have triggered the three K-processes of the horizontal negative leader channel of the lightning, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Zhu, Y.; Stock, M.; Bitzer, P. A new approach to map lightning channels based on low-frequency interferometry. Atmos. Res.
**2020**, 247, 105139. [Google Scholar] [CrossRef] - Rison, W.; Thomas, R.J.; Krehbiel, P.R.; Hamlin, T.; Harlin, J. A GPS-based three-dimensional lightning mapping system: Initial observations in central new mexico. Geophys. Res. Lett.
**1999**, 26, 3573–3576. [Google Scholar] [CrossRef] [Green Version] - Krehbiel, P.R.; Riousset, J.A.; Pasko, V.P.; Thomas, R.J. Upward electrical discharges from thunderstorms. Natu. Geosci.
**2008**, 1, 233–237. [Google Scholar] [CrossRef] - Thomas, J.R.; Krehbiel, P.R.; Rison, W.; Hunyady, S.J.; Winn, W.P. Accuracy of the Lightning Mapping Array. J. Geophys. Res.-Atmos.
**2004**, 109, D14207. [Google Scholar] [CrossRef] [Green Version] - Edens, H.E.; Eack, K.B.; Eastvedt, E.M. VHF lightning mapping observations of a triggered lightning flash. Geophys. Res. Lett.
**2012**, 39, L19807. [Google Scholar] [CrossRef] - Sun, Z.; Qie, X.; Liu, M. Characteristics of a Negative Cloud-to-Ground Lightning Discharge Based on Locations of VHF Radiation Sources. Atmos. Ocean. Sci. Lett.
**2014**, 7, 248–253. [Google Scholar] - Chen, Z.; Zhang, Y.; Zheng, D.; Zhang, Y.; Fan, X.; Fan, Y. A Method of Three-Dimensional Location for LFEDA Combining the Time of Arrival Method and the Time Reversal Technique. J. Geophys. Res.-Atmos.
**2019**, 124, 6484–6500. [Google Scholar] [CrossRef] - Fan, X.; Zhang, Y.; Zheng, D.; Zhang, Y.; Lyu, W.; Liu, H.; Xu, L. A New Method of Three-Dimensional Location for Low-frequency Electric Field Detection Array. J. Geophys. Res.-Atmos.
**2018**, 123, 8792–8812. [Google Scholar] [CrossRef] - Fan, X.; Zhang, Y.; Krehbiel, P.R.; Zhang, Y.; Zheng, D.; Yao, W. Application of Ensemble Empirical Mode Decomposition in Low-Frequency Lightning Electric Field Signal Analysis and Lightning Location. IEEE Trans. Geosci. Remote. Sens.
**2021**, 59, 86–100. [Google Scholar] [CrossRef] - Ma, Z.; Jiang, R.; Qie, X.; Xing, H.; Liu, M.; Sun, Z. A low frequency 3D lightning mapping network in north China. Atmos. Res.
**2021**, 249, 105314. [Google Scholar] [CrossRef] - Lyu, F.; Cummer, S.A.; Lu, G.; Zhou, X.; Weinert, J. Imaging lightning intracloud initial stepped leaders by low-frequency interferometric lightning mapping array. Geophys. Res. Lett.
**2016**, 43, 5516–5523. [Google Scholar] [CrossRef] - Bitzer, P.M.; Christian, H.J.; Stewart, M.; Burchfield, J.; Podgorny, S.; Corredor, D. Characterization and applications of VLF/LF source locations from lightning using the Huntsville Alabama Marx Meter Array. J. Geophys. Res.-Atmos.
**2013**, 118, 3120–3138. [Google Scholar] [CrossRef] - Karunarathne, S.; Marshall, T.C.; Stolzenburg, M.; Karunarathna, N.; Vickers, L.E.; Warner, T.A. Locating initial breakdown pulses using electric field change network. J. Geophys. Res.-Atmos.
**2013**, 118, 7129–7141. [Google Scholar] [CrossRef] - Yoshida, S.; Wu, T.; Ushio, T.; Kusunoki, K.; Nakamura, Y. Initial results of LF sensor network for lightning observation and characteristics of lightning emission in LF band. J. Geophys. Res.-Atmos.
**2014**, 119, 12034–12051. [Google Scholar] [CrossRef] - Qiu, S.; Yang, B.; Dong, W.S.; Gao, T.C. Application of correlation time delay estimation in broadband interferometry for lightning detection. Sci. Meteorol. Sin.
**2009**, 29, 92–96. (In Chinese) [Google Scholar] - Cao, D.; Qie, X.; Duan, S.; Xuan, Y.; Wang, D. Lightning discharge process based on shortbaseline lightning VHF radiation source locating system. Acta Phys. Sin.
**2012**, 61, 510–522. [Google Scholar] - Sun, Z.; Qie, X.; Liu, M.; Cao, D.; Wang, D. Lightning VHF radiation location system based on short-baseline TDOA technique—Validation in rocket-triggered lightning. Atmos. Res.
**2013**, 129–130, 58–66. [Google Scholar] [CrossRef] - Sun, Z.; Qie, X.; Jiang, R.; Wu, X.; Wang, Z.; Lu, G. Characteristics of a rocket-triggered lightning flash with large stroke number and the associated leader propagation. J. Geophys. Res.-Atmos.
**2014**, 119, 13388–13399. [Google Scholar] [CrossRef] - Sun, Z.; Qie, X.; Liu, M.; Jiang, R.; Wang, Z.; Zhang, H. Characteristics of a negative lightning with multiple-ground terminations observed by a VHF lightning location system. J. Geophys. Res.-Atmos.
**2016**, 121, 413–426. [Google Scholar] [CrossRef] [Green Version] - Zhang, G.; Li, Y.; Wang, Y.; Zhang, T.; Wu, B.; Liu, Y. Experimental study on location accuracy of a 3D VHF lightning-radiation-source locating network. Sci. China Ser. D-Earth Sci.
**2015**, 58, 2034–2048. [Google Scholar] [CrossRef] - Li, Y.; Zhang, G.; Wen, J.; Wang, D.; Wang, Y.; Zhang, T.; Fan, X. Electrical structure of a Qinghai–Tibet Plateau thunderstorm based on three-dimensional lightning mapping. Atmos. Res.
**2013**, 134, 137–149. [Google Scholar] [CrossRef] - Li, Y.; Zhang, G.; Wang, Y.; Wu, B. Observation and analysis of electrical structure change and diversity in thunderstorms on the Qinghai-Tibet Plateau. Atmos. Res.
**2017**, 194, 130–141. [Google Scholar] [CrossRef] - Li, Y.; Zhang, G.; Zhang, Y. Evolution of the charge structure and lightning discharge characteristics of a Qinghai-Tibet Plateau thunderstorm dominated by negative cloud-to-ground flashes. J. Geophys. Res.-Atmos.
**2020**, 125, e2019JD031129. [Google Scholar] [CrossRef] - Shi, D.; Zheng, D.; Zhang, Y.; Zhang, Y.; Huang, Z.; Lu, W. Low-frequency E-field Detection Array (LFEDA)—Construction and preliminary results. Sci. China Earth Sci.
**2017**, 60, 1896–1908. [Google Scholar] [CrossRef] - Zhang, Y.; Dong, W.; Zhao, Y.; Zhang, G.; Zhang, H.; Chen, C. Study of charge structure and radiation characteristic of intracloud discharge in thunderstorms of Qinghai-Tibet Plateau. Sci. China Ser. D-Earth Sci.
**2004**, 47, 108–114. [Google Scholar] - Qie, X.; Kong, X.; Zhang, G.; Zhang, T.; Yuan, T.; Zhou, Y. The possible charge structure of thunderstorm and lightning discharges in northeastern verge of Qinghai–Tibetan Plateau. Atmos. Res.
**2005**, 76, 231–246. [Google Scholar] [CrossRef] - Qie, X.; Zhang, T.; Chen, C.; Zhang, G.; Zhang, T.; Wei, W. The lower positive charge center and its effect on lightning discharges on the Tibetan-Plateau. Geophys. Res. Lett.
**2005**, 32, L05814. [Google Scholar] [CrossRef] [Green Version] - Zhang, G.; Zhao, Y.; Qie, X.; Zhang, T.; Wang, Y.; Chen, C. Observation and study on the whole process of cloud-to-ground lightning using narrowband radio interferometer. Sci. China Ser. D-Earth Sci.
**2008**, 51, 694–708. [Google Scholar] [CrossRef] - Qie, X.; Zhang, T.; Zhang, G.; Zhang, T.; Kong, X. Electrical characteristics of thunderstorms in different plateau regions of China. Atmos. Res.
**2009**, 91, 244–249. [Google Scholar] [CrossRef] - Zhang, T.; Qie, X.; Yuan, T.; Zhang, G.; Zhang, T.; Zhao, Y. Charge source of cloud-to-ground lightning and charge structure of a typical thunderstorm in the Chinese Inland Plateau. Atmos. Res.
**2009**, 92, 475–480. [Google Scholar] [CrossRef] - Li, Y.; Zhang, G.; Wen, J.; Wang, Y.; Zhang, T.; Fan, X.; Wu, B. Spatial and temporal evolution of a multi-cell thunderstorm charge structure in coastal areas. Chin. J. Geophys.
**2012**, 55, 498–508. [Google Scholar] [CrossRef] - Fan, X.; Zhang, G.; Wang, Y.; Li, Y.; Zhang, T.; Wu, B. Analyzing the transmission structures of long continuing current processes from negative ground flashes on the Qinghai-Tibetan Plateau. J. Geophys. Res.-Atmos.
**2014**, 119, 2050–2063. [Google Scholar] [CrossRef] [Green Version] - Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis. Proc. Mathematical. Phys. Eng. Sci.
**1998**, 454, 903–995. [Google Scholar] [CrossRef] - Thomas, R.J.; Krehbiel, P.R.; Rison, W.; Hamlin, T.; Harlin, J.; Shown, D. Observations of VHF source powers radiated by lightning. Geophys. Res. Lett.
**2001**, 28, 143–146. [Google Scholar] [CrossRef] [Green Version] - Zhang, G.; Wang, Y.; Qie, X.; Zhang, T.; Zhao, Y.; Li, Y. Using lightning locating system based on time-ofarrival technique to study three-dimensional lightning discharge processes. Sci. China Ser. D-Earth Sci.
**2010**, 53, 591–602. [Google Scholar] [CrossRef] - Li, S.; Qiu, S.; Shi, L.; Li, Y. Broadband VHF observations of two natural positive cloud-to-ground lightning flashes. Geophys. Res. Lett.
**2020**, 47, e2019GL086915. [Google Scholar] [CrossRef] - Akita, M.; Nakamura, Y.; Yoshida, S.; Morimoto, T.; Ushio, T.; Kawasaki, Z. What occurs in K process of cloud flashes. J. Geophys. Res.-Atmos.
**2010**, 115, D07106. [Google Scholar] [CrossRef] - Winn, W.P.; Aulich, G.D.; Hunyady, S.J.; Eack, K.B.; Edens, H.E.; Krehbiel, P.R. Lightning leader stepping, K changes, and other observations near an intracloud flash. J. Geophys. Res.-Atmos.
**2011**, 116, D23115. [Google Scholar] [CrossRef] [Green Version] - Hare, B.M.; Scholten, O.; Dwyer, J.; Trinh, T.N.G.; Buitink, S. Needle-like structures discovered on positively charged lightning branches. Nature
**2019**, 568, 360–363. [Google Scholar] [CrossRef] - Mazur, V. Triggered lightning strikes to aircraft and natural intracloud discharges. J. Geophys. Res.-Atmos.
**1989**, 94, 3311–3325. [Google Scholar] [CrossRef] - Mazur, V.; Williams, E.; Boldi, R.; Maier, L.; Proctor, D.E. Initial comparison of lightning mapping with operational Time-of-Arrival and Interferometric system. J. Geophys. Res.-Atmos.
**1997**, 102, 11071–11085. [Google Scholar] [CrossRef] - Shao, X.M.; Krehbiel, P.R. The spatial and temporal development of intracloud lightning. J. Geophys. Res.-Atmos.
**1996**, 101, 26641–26668. [Google Scholar] [CrossRef]

**Figure 1.**The seven stations of the 3D lightning radiation source location system in the Datong region of Qinghai Province, China.

**Figure 3.**Different components of station MD obtained by the EMD decomposition method for IC flash 001136.

**Figure 5.**Part of the normalized electric field waveform of IC flash 001136 detected by the station MD and these 93 extracted pulses.

**Figure 7.**The height of the radiation sources corresponding to the pulses in Figure 5.

**Figure 8.**Location results for IC flash 001136 using the algorithm of the 3D lightning radiation source location system [20,21,22,23]. In the figure, (

**a**) the height of the radiation source changes with time, (

**b**) the vertical projection of the east-west direction, (

**c**) the number of radiation sources changes with the height, (

**d**) the horizontal projection, and (

**e**) the vertical projection of the north-south direction.

**Figure 9.**Location results for IC flash 001136 using the new method. In the figure, (

**a**) the height of the radiation source changes with time, (

**b**) the vertical projection of the east-west direction, (

**c**) the number of radiation sources changes with the height, (

**d**) the horizontal projection, and (

**e**) the vertical projection of the north-south direction.

**Figure 10.**The 45° angle top view to the horizontal of IC flash 001136 from east to west. (

**a**) Height-time plots and (

**b**) the 45° top view from east to west.

**Figure 11.**The VHF radiation sources of CG flash 000241. The different panels show (

**a**) the height of the radiation source changes with time, (

**b**) the vertical projection of the east-west direction, (

**c**) the number of radiation sources changes with the height, (

**d**) the horizontal projection, and (

**e**) the vertical projection of the north-south direction.

**Figure 12.**The pulses of the second negative recoil streamer and the second K-process pulses of the negative leader channel.

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**MDPI and ACS Style**

Wang, Y.; Min, Y.; Liu, Y.; Zhao, G.
A New Approach of 3D Lightning Location Based on Pearson Correlation Combined with Empirical Mode Decomposition. *Remote Sens.* **2021**, *13*, 3883.
https://doi.org/10.3390/rs13193883

**AMA Style**

Wang Y, Min Y, Liu Y, Zhao G.
A New Approach of 3D Lightning Location Based on Pearson Correlation Combined with Empirical Mode Decomposition. *Remote Sensing*. 2021; 13(19):3883.
https://doi.org/10.3390/rs13193883

**Chicago/Turabian Style**

Wang, Yanhui, Yingchang Min, Yali Liu, and Guo Zhao.
2021. "A New Approach of 3D Lightning Location Based on Pearson Correlation Combined with Empirical Mode Decomposition" *Remote Sensing* 13, no. 19: 3883.
https://doi.org/10.3390/rs13193883