A Thunderstorm Cloud Point Charge Localization Method Based on CEEMDAN and SG Filtering

The current thunderstorm monitoring methods ignore the nonlinear and non-stationary characteristics of atmospheric electric field signals, which has a negative effect on the monitoring results. Based on complementary ensemble empirical mode decomposition with adaptive noise and Savitzky-Golay filtering (CEEMDAN-SG), a point charge localization method for the thunderstorm cloud is proposed. After CEEMDAN is used to decompose the electric field signal into a series of intrinsic mode function (IMF) components, the signal is reconstructed after SG filtering of those noise-dominant components. Then, the reconstructed signal is used for point charge localization correction. By changing the signal samples, the decomposition order and SNR of CEEMDAN-SG, CEEMDAN, etc. are compared, and the performance of the method is analyzed. Experiments show that compared to the SNR before reconstruction, the SNR after reconstruction is improved by about 3%. At the same time, the results can match the radar chart well on the time scale. After using the CNN-LSTM network model, it is found that compared with the original signal, the amplitude of the absolute error of the reconstructed signal is larger, so that the signal characteristics can be more displayed. This once again proves the localization effects.

SECTION I. Introduction

Atmospheric electric field intensity is the basic parameter of atmospheric physics and atmospheric electricity [1], [2]. Thunderstorm activities often cause changes in the ground electric field. The ground electric field is small in sunny days, but it will increase significantly during thunderstorms. These changes can be used to invert the formation, development and dissipation of thunderstorm clouds [3]–​[5]. Therefore, studying atmospheric electric field signal is an effective way to analyze thunderstorm activity and realize thunderstorm cloud directional monitoring, which has important significance.

In the 18th century, Europe carried out a series of lightning protection activities, such as lightning rods and other inventions that effectively reduced the economic losses caused by lightning disasters. But these belong to the category of passive lightning protection, so it is impossible to study the characteristics of thunderstorm clouds [6], [7]. As a result, people began to use reliable instruments and technologies to actively protect against lightning, such as atmospheric electric field apparatus, lightning localization technology, etc. [8]–​[11]. In 1950, Malan and Schonland proposed a classic field mill atmospheric electric field apparatus [12]. Subsequently, people made improvements in terms of power consumption, networking, measurement accuracy, etc. [13]–​[15], and used observation data for lightning early warning. An easy-to-implement electric field amplitude threshold method was usually used to give thunderstorm warning signals, but this method had a low probability of successful warning and ignored the inherent physical characteristics of the electric field signals [16]–​[18]. In 2015, Srivastava combined the electric field data under various weather conditions with the Markov model to make the warning probability reach 66.45%. But the false alarm probability at that time also reached 59.7% [19]. In 2016, Lu et al. incorporated modern signal processing methods to provide early warning based on the high-frequency electric field amplitude and its energy ratio. In essence, it is still a kind of method based on electric field amplitude, and it fails to deeply explore the relationship between electric field signal characteristics and thunderstorm activity [20].

In recent years, lightning early warning technology has developed rapidly. In 2019, combining the observation data of atmospheric electric field instrument, weather radar, and lightning locator, Q. Meng et al. established a comprehensive lightning early warning system [21]. But their research only stays on multi-source data fusion and lacks effective data processing algorithms. In 2019, after considering the influence of other meteorological factors such as temperature and humidity, A. Mostajabi et al. used BP neural network to construct a lightning warning model [22]. However, the early warning time of this method is extremely short, and the utilization of atmospheric electric field signals is insufficient. In 2019, Xing et al. used 3D atmospheric electric field components to derive the point charge coordinates of thunderstorm clouds. They proposed a thunderstorm cloud localization algorithm that characterizes the relationship between the electric field signal and the position of the point charge, and has achieved good results [23]. While these studies promote the detection of thunderstorm clouds based on the electric field apparatus, they ignore the nonlinear and non-stationary characteristics of atmospheric electric field signals. Atmospheric electric field is the most direct physical quantity reflecting the change of point charge of thunderstorm cloud. In particular, denoising is the primary issue for studying signal characteristics and point charge localization.

In summary, two practical issues must be taken into account in point charge localization: i) the denoising of the atmospheric electric field signal and its validity verification, and ii) the realization of high-precision point charge localization. With these realistic assumptions, we propose a real-time localization method based on CEEMDAN and SG filtering. In this paper, CEEMDAN is used to decompose the electric field signal into a series of intrinsic mode function (IMF) components, SG filtering is performed on the components whose noise is dominant, and the filtered components and residual components are reconstructed. After using reconstructed signal for point charge localization correction, the effectiveness of the method is studied. Finally, the results are analyzed in combination with the radar chart. In addition, by using the CNN-LSTM network model, the absolute error of the signal sample before and after reconstruction is compared, which further shows the localization effects.

The rest of the paper is organized as follows. Section II gives a particular description of the thunderstorm cloud point charge localization method based on CEEMDAN-SG. Section III qualitatively analyzes the point charge localization performance. Section IV conducts the sunny and thunderstorm weather experiments to validate our method. Finally, concluding remarks are given in section V.

SECTION II. The Thunderstorm Cloud Point Charge Localization Method Based on CEEMDAN-SG

Based on the background of thunderstorm cloud detection, a method which can not only complete the atmospheric electric field signal denoising, but also ensure the threshold warning, polarity reversal and other characteristics of the signal is needed. Therefore, the SG filtering which can meet the above requirements is selected first. Secondly, if the original signal is directly filtered by SG, it is very likely to filter out the useful signal, while CEEMDAN is a powerful method for studying the electric field signal with nonlinear and non-stationary characteristics. This method can be used to decompose the signal, and the obtained signal components of different oscillation scales are convenient for SG filtering according to the autocorrelation characteristics of each component. Finally, the denoised components and the residual modal components can be reconstructed to obtain the denoised signal.

A. CEEMDAN-SG for Atmospheric Electric Field Signals

Firstly, the original atmospheric electric field signal is set to $x(n)$ . After $x(n)$ is added and subtracted from the white noise $\omega (n)$ , the $i-th$ signal is obtained as:\begin{align*} \begin{cases} x_{i}^{+} (n)=x(n)+\omega _{i} (n) \\ x_{i}^{-} (n)=x(n)-\omega _{i} (n) \\ \end{cases}\tag{1}\end{align*}

Among them, $i$ is the number of times that Gaussian white noise is added, and $i=1,2,\ldots,N$ .

After the same steps as the EMD algorithm are used to decompose the signal $x_{i}^{+} (n)$ , $IMF_{ij}^{+} (n)$ are obtained, and their number is $M$ . Similarly, $x_{i}^{-} (n)$ is decomposed into $K\,\,IMF_{ij}^{-} (n)$ . Among them, $IMF_{ij}^{+} (n)$ and $IMF_{ij}^{-} (n)$ respectively represent the $j-th IMF$ obtained by adding and subtracting white noise for the $i-th$ time, and $j=1,2,\ldots,M$ .

The $j-th IMF$ component $IMF_{j} (n)$ after integrated averaging is:\begin{equation*} IMF_{j} (n)=\frac {1}{N}\sum \limits _{i=1}^{N} {\frac {IMF_{ij}^{+} (n)+IMF_{ij}^{-} (n)}{2}}\tag{2}\end{equation*}

The autocorrelation function value $IMF_{j} '(n)$ of each $IMF_{j} (n)$ is calculated separately. According to the autocorrelation characteristics of noise and signal, the mode components $IMF_{1} (n)$ to $IMF_{k} (n)$ dominated by noise are judged. Further, after the SG is used to filter $IMF_{1} (n)$ to $IMF_{k} (n)$ , the denoised components are $IMF_{1} ''(n)$ to $IMF_{k} ''(n)$ .

Finally, the filtered mode components and residual components are used, and the reconstructed electric field signal $x'(n)$ is obtained as:\begin{equation*} x'(n)=\sum \limits _{j=1}^{K} {IMF_{j} ''(n)} +\sum \limits _{j=k}^{M} {IMF_{j} (n)}\tag{3}\end{equation*}

It should be noted that the decomposition process of CEEMDAN is equivalent to the adaptive filtering of signal with narrow band filter. The noise components of the signal are mainly distributed in the high frequency band, that is, mainly concentrated in the first few components. To further determine whether the component belongs to noise, it can be judged according to the autocorrelation analysis.

The autocorrelation characteristic of signal refers to the correlation degree of signal at two different time points $t_{1} $ and $t_{2} $ . For any random signal $x(t)$ , its autocorrelation function is:\begin{equation*} R_{x} (t_{1},t_{2})=E(x(t_{1})x(t_{2}))\tag{4}\end{equation*} In order to get the correlation degree of the signal at some time points accurately, the normalized autocorrelation function is used as follows:\begin{equation*} \rho _{x} (\tau)=\frac {R_{x} (\tau)}{R_{x} (0)}\tag{5}\end{equation*}

Among them, $\tau =t_{1} -t_{2} $ , and $\tau $ is the time difference.

On the one hand, the autocorrelation function amplitude of random noise is the largest at zero point, but it decreases rapidly to a very small at non-zero point, which is due to the randomness and weak correlation of noise at all times. For ideal Gaussian white noise, its normalized autocorrelation function is 1 at zero point and zero at other points. On the other hand, the autocorrelation function amplitude of the sinusoidal signal synthesized at different frequencies is the largest at zero. However, at the non-zero point, the autocorrelation function does not decrease rapidly to a very small value, but changes with the time difference, which is due to the correlation in the signal. This is obviously different from the autocorrelation function of noise [24], [25].

Based on this, according to the autocorrelation characteristics of IMF, the above method of using autocorrelation function is introduced to select useful signal components and noise components. For the components dominated by noise, there are few useful components. At this time, after using SG filtering to denoise these components, the denoising components and residual mode components are reconstructed to get the denoising electric field signal.

In fact, SG filtering is mainly to fit a polynomial by taking a fixed number of points near point $x_{i} $ of the IMF data, and get a smooth value $g_{i} $ ($g_{i} \in matrixG$ ) from the value of the polynomial in point $x_{i} $ [26], [27]. $n_{l} $ and $n_{r} $ represent the number of points on the left and right of $x_{i} $ respectively. $p_{i} (x)$ is an $M$ -power polynomial relative to point $x_{i}$ , which is used to fit the $n_{l} +n_{r} +1$ points in the sense of least squares. Therefore, it can be obtained that:\begin{equation*} g_{i} =\sum \limits _{k=0}^{M} {b_{k} \left({\frac {x-x_{i}}{\Delta x}}\right)} k\tag{6}\end{equation*}

According to the IMF data $y_{i} $ , the $M$ -power polynomial $p_{i} (x)$ fitting is performed:\begin{equation*} p_{i} (x)=\sum \limits _{k=0}^{M} {b_{k} \left({\frac {x-x_{i} }{\Delta x}}\right)} k\tag{7}\end{equation*}

Assuming that the abscissa $x_{i} $ has a uniform spacing of $x_{i+1} -x_{i} =\Delta x$ , in order to fit the test data with $p_{i} (x)$ in the sense of least squares, the coefficient $b_{k} $ must be determined so that:\begin{equation*} min\sum \limits _{j=i-n_{l}}^{i+n_{r}} [p_{i} (x_{j}) -y_{j}]^{2}\tag{8}\end{equation*}

The matrix $A$ , $B$ and $Y$ are defined respectively:\begin{align*} A=&\left [{ {{\begin{array}{cccc} {(-n_{_{l}}^{M})} & {\cdot \cdot \cdot } & {-n_{l}} & 1 \\ {-(n_{l} -1)^{M}} & & {-(n_{l} -1)} & \vdots \\ \vdots & & \vdots & \vdots \\ 0 & & 0 & 1 \\ \vdots & & \vdots & \vdots \\ {n_{r}^{M}} & {\cdot \cdot \cdot } & {n_{r}} & 1 \\ \end{array}}} }\right] \\&\qquad \qquad \in R^{(n_{l} +n_{r} +1)\times (M+1)} \tag{9}\\ B=&\left [{ {{\begin{array}{cc} {b_{M}} \\ \vdots \\ {b_{1}} \\ {b_{0}} \\ \end{array}}} }\right]\in R^{(M+1)} \tag{10}\\ Y=&\left [{ {{\begin{array}{cc} {y_{j-n_{l}}} \\ {y_{j-n_{l} +1}} \\ \vdots \\ {y_{j}} \\ \vdots \\ {y_{j+n_{r}}} \\ \end{array}}} }\right]\in R^{(n_{l} +n_{r} +1)}\tag{11}\end{align*}

By using equations (9) to (11), (8) is rewritten into the following matrix form:\begin{equation*} min\left \|{ {AB-Y} }\right \|_{2}\tag{12}\end{equation*}

In order to optimize (12), $AB=Y$ needs to be satisfied, namely:\begin{equation*} A^{T}AB=A^{T}Y\tag{13}\end{equation*}

Because $A^{T}~A$ is a positive definite matrix, its inverse matrix exists. According to (13), it can be obtained that:\begin{equation*}B=(A^{T}A)^{-1}A^{T}Y\tag{14}\end{equation*}

Therefore, the matrix ${ }\mathop {Y}\limits ^{\wedge } =A(A^{T}A)^{-1}A^{T}Y$ is obtained, and the smooth value $G=A(A^{T}A)^{-1}A^{T}$ . In addition, considering the denoising effect, the fitting order, data window and smoothing time of SG filtering are set to 3, 7 and 2 respectively.

B. Method of the Point Charge Localization for the Thunderstorm Cloud

Based on the electrostatic field theory, the 3D atmospheric electric field measurement model shown in Fig. 1 is used to locate the point charge of the thunderstorm cloud [16], [23].

FIGURE 1.

3D atmospheric electric field measurement model.

FIGURE 2.

The flow chart of the point charge localization method.

In Fig. 1, a 3D coordinate system is established with a point $N$ as the origin of the coordinates. $S(x,y,z)$ is the position of the point charge of the thunderstorm cloud, and $N(0,0,0)$ is the position of the electric field apparatus. $h$ represents the sum of the altitude of the apparatus itself and the elevation where it is located. The horizontal and elevation angles of the point charge are $\alpha $ and $\beta $ respectively. $r$ is the distance from $S$ to $N$ . The electric field signal of $S$ measured at $N$ is $x(n)$ , and the electric field components in the directions $x$ , $y$ , and $z$ are $E_{x} $ , $E_{y} $ , and $E_{z} $ respectively.

Furthermore, the spherical coordinates $(r,\alpha,\beta)$ and rectangular coordinates $(x,y,z)$ of the point charge are as follows:\begin{align*}&\begin{cases} r=\sqrt [{4}]{\dfrac {A^{2}(1-B)^{2}}{E_{x}^{2}+E_{y}^{2}+E_{z}^{2}}} \\ \alpha =arctan\frac {E_{y}}{E_{x}} \\ \beta =arctan\frac {\varepsilon _{1} E_{z}}{\varepsilon _{2} \sqrt {E_{x} ^{2}+E_{y}^{2}}} \\ \end{cases} \tag{15}\\&\begin{cases} x=rcos\alpha cos\beta \\ y=rsin\alpha cos\beta \\ z=rsin\beta \\ \end{cases}\tag{16}\end{align*}

Among them, $A=-\frac {q}{4\pi \varepsilon _{1}}$ , $B=\frac {\varepsilon _{2} -\varepsilon _{1}}{\varepsilon _{2} +\varepsilon _{1}}$ .

After the correlation between the electric field component and the point charge position is considered, the point charge localization is corrected. We define that $E_{x} $ in the true north direction is greater than 0, and $E_{y} $ in the true east direction is greater than 0. The corrected point charge spherical coordinates $(r',\alpha ',\beta ')$ and rectangular coordinates $(x',y',z')$ are:\begin{align*}&\begin{cases} r'=\sqrt [{4}]{\frac {A^{2}(1-B)^{2}}{E_{x}^{2}+E_{y}^{2}+E_{z}^{2}}} \\ \alpha '=\begin{cases} arctan\dfrac {E_{y}}{E_{x}},&when~~ E_{x} {>0} \\ arctan\dfrac {E_{y}}{E_{x}}+180^{\circ },&when~~ E_{x} {< 0 }~and ~E_{y} {>0} \\ arctan\dfrac {E_{y}}{E_{x}}-180^{\circ },&when ~~E_{x} {< 0 }~and~ E_{y} {< 0} \\ \end{cases}\\ \beta '=arctan\dfrac {\varepsilon _{1} \left |{ {E_{z}} }\right |}{\varepsilon _{2} \sqrt {E_{x}^{2}+E_{y}^{2}}} \\ \end{cases} \\ \tag{17}\\&\begin{cases} x'=r'cos\alpha 'cos\beta ' \\ y'=r'sin\alpha 'cos\beta ' \\ z'=r'sin\beta ' \\ \end{cases}\tag{18}\end{align*}

The flow chart of the localization method of the thunderstorm cloud point charge based on CEEMDAN-SG is as follows:

SECTION III. Performance Analysis of the Point Charge Localization Method

A. Analysis of CEEMDAN-SG in Localization

The vertical electric field component signal from 0:00 to 0:10 on April 14, 2017 are taken as samples, and the sample number is 600. The effects of CEEMDAN-SG are analyzed, and the results are as follows:

From Fig. 3, the vertical component signals are mainly composed of mode components $IMF_{1} (n)$ to $IMF_{9} (n)$ . After calculate the normalized autocorrelation function of each component, we get $IMF_{1} '(n)$ to $IMF_{9} '(n)$ . The results are shown in Fig. 4.

FIGURE 3.

The decomposition of the vertical electric field component.

FIGURE 4.

The normalized autocorrelation function of each mode component.

In Fig. 4, the autocorrelation characteristics of the previous 4th-order mode components are similar to noise. Therefore, SG filtering is performed on $IMF_{1} (n)$ to $IMF_{4} (n)$ , and then the filtered components $IMF_{1} ''(n)$ to $IMF_{4} ''(n)$ and the remaining components $IMF_{5} (n)$ to $IMF_{9} (n)$ are reconstructed. The results are shown in Fig. 5.

FIGURE 5.

Results before and after denoising using SG.

From 0:00 to 0:30 on April 14, 2017, the vertical electrical field component data are used, and 600, 800, and 1000 samples are selected respectively. At the same time, the noise with a SNR of 10dB is added for comparative analysis with CEEMD, EEMD and EMD. Table 1 shows the results.

TABLE 1 Validation of CEEMDAN-SG

In Table 1, compared to EMD and EEMD, the SNR based on CEEMDAD is higher. After SG filtering, the SNR of the signal further increases, indicating that CEEMDAN-SG has a better denoising effect. At the same time, as the number of samples increases, the SNR gradually decreases. In addition, CEEMDAN algorithm keeps balancing the SNR in the decomposition process, so its decomposition order is relatively large. In general, there is no obvious difference in the order of decomposition between the three algorithms.

B. Analysis of Ranging and Direction Finding Error in Localization

According to the electric charge distribution in the air and the charge structure principle of thunderstorm clouds [16], [23], the point charge localization performance is studied. Let the permittivity $\varepsilon _{1} $ and $\varepsilon _{2} $ of the air and the surface of the electric field apparatus be 1 and 5 respectively, and let the charge $q$ be $5C$ .

By using (17), the measurement errors $\sigma _{r} $ , $\sigma _{\alpha } $ , $\sigma _{\beta } $ of distance $r$ , horizontal angle $\alpha $ , and elevation angle $\beta $ caused by electric field component measurement error $\sigma _{Ei} $ are obtained by (17):\begin{align*} \begin{cases} \sigma _{r} =\dfrac {6}{5}\pi ^{\frac {3}{2}}r^{3}\sigma _{E_{i}} \\[8pt] \sigma _{\alpha } =\dfrac {12}{5}\pi r^{2}\sqrt {1+25tan^{2}\beta } \sigma _{E_{i}} \\[8pt] \sigma _{\beta } =\dfrac {12}{25}\pi r^{2}cos\beta \sqrt {(1+24sin^{2}\beta)(1+25tan^{2}\beta)} \sigma _{E_{i}} \end{cases}\tag{19}\end{align*}

It can be seen from (19) that electric field error $\sigma _{Ei} $ is the main factor affecting the localization accuracy. The smaller the error $\sigma _{Ei} $ and distance $r$ are, the smaller the ranging and direction finding error will be. The errors of 600, 800 and 1000 samples measured by CEEMDAN-SG are reduced by 0.0223kV/m, 0.0190kV/m and 0.0189kV/m, respectively. After assuming that the error $\sigma _{Ei} $ before denoising is 0.05kV/m, the relationship between $\sigma _{Ei} $ and the localization performance is further analyzed.

(19) is used to study the relationship between distance $r$ , measurement error $\sigma _{Ei} $ and ranging error $\sigma _{r} $ . The results are shown in Fig. 6.

FIGURE 6.

The relationships between the distance, electric field component measurement error and ranging error.

In Fig. 6, the ranging error $\sigma _{r} $ before and after SG filtering increases with the increase of distance $r$ . In particular, the change of $\sigma _{r} $ before filtering is the most obvious, reaching a maximum of 0.3340km. If the distance $r$ is increased, the error $\sigma _{r} $ of 600 samples after SG filtering will increase the slowest, and the maximum is only 0.1850km. The error $\sigma _{r} $ changes of 800 and 1000 samples after SG filtering are similar, and the maximum error reaches 0.2071km and 0.2077km respectively. In general, CEEMDAN-SG can be used to reduce the ranging error, which has achieved good results.

Similarly, (19) is used to study the relationship between elevation angle $\beta $ , electric field measurement error $\sigma _{Ei} $ and measurement error $\sigma _{\alpha } $ of horizontal angle. The results are shown in Fig. 7.

FIGURE 7.

The relationships between the elevation angle, electric field component measurement error and horizontal angle measurement error.

In Fig. 7, when the elevation angle $\beta $ is less than 80 degrees, the horizontal angle error $\sigma _{\alpha } $ almost does not change with $\beta $ . However, when $\beta $ is greater than 80 degrees, the error $\sigma _{\alpha } $ rises sharply with the increase of $\beta $ , and this trend is more obvious without SG filtering. After using SG filtering, with the increase of $\beta $ , the variations of the error $\sigma _{\alpha } $ based on 800 and 1000 samples are almost the same, but the variation of 600 samples is relatively small. In conclusion, the introduction of CEEMDAN-SG can reduce the horizontal angle error $\sigma _{\alpha } $ . In addition, the analysis of elevation angle error $\sigma _{\beta } $ is similar to that here, so it will not be repeated. It is worth noting that the large measurement error caused by the extreme elevation angle needs to be further studied.

SECTION IV. Experimental Results and Analyses

As a test point, the 3D atmospheric electric field apparatus is installed on the roof of the School of Electronics and Information Engineering, Nanjing University of Information Science and Technology (Nuist), as shown in Fig. 8. The positive X-axis of the coordinate system where the apparatus is located is defined as north, and the positive Y-axis is east. After reconstructing the electric field signal measured by the apparatus, the results of the localization are obtained and compared with the radar chart.

FIGURE 8.

The installation environment of the 3D atmospheric electric field apparatus.

A. Experiments on a Sunny Weather

The atmospheric electric field signals from 14:00 to 14:20 on August 4, 2019 are selected. Since the horizontal electric field components $E_{x} $ and $E_{y} $ in sunny days have little variation, only the vertical electric field component $E_{z} $ is selected for analysis. The results after processing with CEEMDAN-SG are shown in Fig. 9.

FIGURE 9.

The signal reconstruction results from 14:00 to 14:20 on August 4, 2019.

In Fig. 9, the signal $E_{z} '$ obtained after denoising is almost the same as the original signal $E_{z} $ , and $E_{z} $ contains less noise. At the same time, the change of $E_{z} $ is relatively stable, corresponding to the sunny environment. Since there is no point charge over the electric field apparatus, there is no need to conduct localization research. Table 2 lists the statistical results of the electric field data shown in Fig. 9.

TABLE 2 The Statistical Results of the Electric Field Signals in Sunny Days

In Table 2, the average value and standard deviation of the vertical electric field component of the original signal are 0.1059kV/m and 1.2548 respectively, and so are the results processed by CEEMDAN-SG. Among them, the average value is slightly lower than that measured by conventional electric field apparatus in [28]. However, compared with the standard deviation of 0.073 measured in this reference, the standard deviation measured here is larger, reaching 1.2548. The instability of electric field during this period may be influenced by distant thunderstorm activity.

B. Experiments in Thunderstorm Weather

Fig. 10 shows a time series diagram of the electric field data observed between 16:30 and 16:50 on August 4, 2019.

FIGURE 10.

The atmospheric electric field signal from 16:30 to 16:50 on August 4, 2019.

As shown in Fig. 10, during the thunderstorm, the fluctuation range of $E_{x} $ , $E_{y} $ , and $E_{z} $ is significantly larger than that of sunny days. It can be clearly seen that the variation trend of the 3D electric field components is basically the same during this period. However, the change of $E_{z} $ is much larger than that of $E_{x} $ and $E_{y} $ . It is worth noting that the first polarity reversal occurred in the electric field around 16:38 and several polarity reversals occurred in the following time, which may be caused by the discharge activity in the thunderstorm.

Furthermore, CEEMDAN-SG is used to reconstruct the electric field signal, and the localization method is introduced to study the development process of thunderstorm cloud. The results are shown in figures 11, 12 and Table 3. It should be noted that the color change from red to green in Fig. 12 corresponds to the sequence of time.

TABLE 3 The Statistical Results of the Electric Field Signals in Thunderstorm Weather

FIGURE 11.

The signal reconstruction results from 16:30 to 16:50 on August 4, 2019.

FIGURE 12.

The localization results of the point charge in thunderstorm weather.

In Fig. 11, the atmospheric electric field signal obtained after denoising is different from the original signal shown in Fig. 10. The signal contains a certain amount of noise whose amplitude is large especially when the signal changes dramatically. In order to directly reflect the difference before and after reconstruction, the average value and standard deviation of electric field data shown in Table 3 are also given. In Table 3, the average value of electric field signal in thunderstorm weather is obviously larger than that in sunny day shown in Table 2. In addition, the standard deviations of electric field components $E_{x} $ , $E_{y} $ and $E_{z} $ are large, and the maximum value reaches 5.3120kV/m. On the whole, the standard deviation after reconstruction is slightly less than that before reconstruction, which shows that the method has good denoising effect.

Fig. 12 shows the final results of the localization method. The blue dotted line in Fig. 12 shows the general trend of the point charge motion. It can be seen from Fig. 12(a) that at 16:30, the point charge occurs at 26.10 degrees north by west and 1.054 km away from the electric field apparatus. As time goes by, the thunderstorm cloud moves to the southeast and gets closer to the apparatus. Combined with Fig. 12(d), from about 16:38, the point charge gradually moves from northwest to northeast. At about 16:43, the point charge reaches the upper area in the northeast direction of the apparatus. At this point, the elevation angle reaches 74.31 degrees, almost perpendicular to the Z-axis of the coordinate system where the apparatus is located. Meanwhile, Fig. 12(d) shows that the elevation angle around 16:43 is about 70 degrees. Therefore, it can be further determined that there is a thunderstorm cloud above the apparatus at that time. During the period of 16:43 to 16:50, the amplitude of electric field signal decreases in the intense movement, and the activity of thunderstorm cloud gradually weakens. These are also reflected in figures 12 (b) and (c). Finally, it can be seen from Fig. 12(d) that the horizontal angle changes from positive to negative at 16:38. This is caused by the polarity reversal of the horizontal electric field components, which also corresponds to the analysis results in Fig. 10.

To further verify the effectiveness of the method, the real-time radar chart as shown in Fig. 13 is selected for comparative analysis. In addition, the blue cross marked in the figures is the position of the electric field apparatus at NUIST station.

FIGURE 13.

The radar chart of Nanjing radar station from 16:24 to 16:52, August 4, 2019.

In Fig. 13, the core area of the thunderstorm cloud at 16:24 is located in the northwest of the electric field apparatus. From 16:24 to 16:41, the thunderstorm cloud moves from northwest to northeast, which is likely to have a polarity reversal of the horizontal angle. From 16:41 to 16:47, the thunderstorm area reaches above the NUIST station. At this time, the radar echo intensity is as high as 45dBZ. During this period, the large angle fluctuations shown in Fig. 12(d) may be caused by the intense charge activity in the cloud. From 16:47 to 16:52, the radar echo intensity drops to about 30dBZ, indicating that the thunderstorm activity is gradually weakening. The results of the point charge localization match the radar chart well.

C. Verification Experiments Combined with CNN-LSTM

The network model combining CNN and LSTM [29], [30] is used to mainly predict the vertical electric field signals before and after reconstruction. The 1200 samples in thunderstorm weather experiment are divided into training set and test set at a ratio of 8:2, and the results are shown in figures 14 and 15, respectively. At the same time, Table 4 shows the determination coefficients of the prediction results.

TABLE 4 The Determination Coefficients of the Prediction Results Before and After Reconstruction

FIGURE 14.

The prediction results of the vertical electric field signal in thunderstorm weather.

FIGURE 15.

The prediction results of the reconstructed signal of vertical electric field in thunderstorm weather.

Figures 14(a) and 15(a) show the prediction results of the electric field signals, and it can be preliminarily seen that the results have a good fitting degree. First, combined with Table 4, there is almost no difference in the determination coefficients between the training set and the test set before and after the reconstruction, indicating the validity of the model. Secondly, in figures 14(b) and 15(b), as the signal before reconstruction is disturbed by noise, the electric field signal features are not obvious, resulting in relatively small absolute error. After the reconstruction, the sample noise is reduced, which makes the characteristics of electric field signal more obvious. Therefore, the absolute error amplitude of the latter is larger. This also demonstrates the effectiveness of CEEMDAN-SG. From the 800th sample point corresponding to 16:43, it is found that the absolute error of the reconstructed sample data rises sharply. In combination with Fig. 10, the point charge at this time point is above the electric field apparatus, and soon after, a second polarity reversal occurs, as well as a dramatic change in the electric field. These once again verify the effectiveness of the method.

D. Contrast Experiments

In order to further verify the effectiveness of the method, it is compared with references [23], [31]. Because the proposed method and references [23], [31] are based on the 3D atmospheric electric field apparatus, it is feasible to use the electric field signal data measured by the apparatus shown in Fig. 8 for comparative analysis.

In order to explore the relationship between the electric field signal and the point charge localization performance, only thunderstorm weather experiments in references [23], [31] are selected for analysis. Among them, signal preprocessing method, performance improvement and validity verification results are mainly compared. The results are shown in Table 5.

TABLE 5 Contrast Experimental Results

As can be seen from Table 5, in [31], EEMD and extreme gradient boosting (XGBoost) are combined to classify and reconstruct the atmospheric electric field signal. In fact, denoising is the primary problem of thunderstorm cloud physical characteristics and early warning. Although they have carried out the thunderstorm warning experiment, it is difficult to meet the requirement of false alarm rate because of no denoising. At the same time, in [23], the point charge is located directly by using the signal data, which has the same denoising problem as in [31]. In general, this paper uses the signal processed by CEEMDAN-SG to complete the point charge localization.

Both Xing et al. [23] and Xu et al. [31] improve the thunderstorm warning performance. On the one hand, based on the indirect measurement error, Xing et al. [23] qualitatively analyze the ranging and direction-finding error, which can show the effectiveness of the method. On the other hand, compared with the ordinary voting decision-making method, Xu et al. improve the detection probability by 4.8%, and decrease the false alarm probability by 5.2% to 6.4%. It can be found that the former only stays at the theoretical level, while the latter may not reach this level due to the lack of denoising. In contrast, the proposed method not only improves the performance theoretically, but also increases the SNR by about 3%, thus achieving a better localization effect.

Finally, [23] and [31] only use radar chart and lightning location system respectively to carry out the validity verification experiment. In this paper, four different ways are used to verify the effectiveness. The first way is similar to that of [23], which is described in Section III. By analyzing figures 6 and 7, it is found that the introduction of CEEMDAN-SG can effectively reduce the localization error. The second and third ways are radar chart and CNN-LSTM, respectively. It is worth noting that CNN-LSTM is not limited to amplify the electric field signal characteristics, but also can be applied in the next thunderstorm development prediction. The final way is the comparison experiment here with the latest relevant methods.

SECTION V. Conclusion and Future Work

The CEEMDAN-SG algorithm can be used to preprocess the 3D atmospheric electric field signal. This can not only effectively reduce the measurement errors of the atmospheric electric field components, but also more accurately grasp the electric field changes at different times. The atmospheric electric field measurement model is established, and the thunderstorm cloud point charge localization method is introduced after using SG filtering to reconstruct the signal. This can track the movement path of the point charge in real time, making it possible to visualize thunderstorm activity. Finally, combining the radar chart and CNN-LSTM network model, the experiments verify that the method has a better localization effect. It provides a new way of thinking for thunderstorm warning. Of course, there are many problems with thunderstorm detection technology. In this paper, atmospheric electric field signals are denoised by SG filtering. Further research and analysis are needed on how to design a better denoising method based on the inherent physical characteristics of thunderstorm clouds to reduce the localization errors from the source. The next step of our work will focus on thunderstorm prediction and early warning based on deep learning.