Frequency spectra of various events pertinent to lightning cloud flashes obtained from wavelet transform technique and ratified by narrow band measurement technique

Highlights

• Frequency spectrum of electric field radiated by lightning cloud flashes were obtained.

• The electric fields pertinent to the lightning flashes were recorded by employing both wide-bandwidth and narrow-bandwidth measurement system.

• The cloud flashes have been observed to radiate in the frequency range as low as 3 kHz to a few tens of Mega Hertz(MHz).

• The initial or active stage of cloud flashes are found to radiate in the frequency range of 50 kHz to 5 MHz and predominantly radiate in the range of 500 kHz to 5 MHz.

• The final stages are also found to radiate in the range of 50 kHz to 5 MHz which is comprised of the regular pulse bursts, chaotic pulse trains and Q-streamers (recoil streamers) that radiate in the range of 50 kHz to 10 MHz.

Abstract

In the present study, frequency spectra of the electric field corresponding to the various cloud events, such as, initial breakdown process, regular pulse bursts, chaotic pulse trains and recoil streamers have been analysed. For the purpose, electric field radiated by cloud flashes were obtained simultaneously by a wide bandwidth antenna system and two narrow bandwidth antenna systems tuned at 3 MHz and 30 MHz. The frequency spectra of the broad band electric field signatures were obtained by using the wavelet transform technique and were compared with the magnitudes of the narrow band signals at the given central frequencies. To the best of our knowledge, it is the first study in which frequency spectra is obtained by transforming the time domain signal using wavelet transform technique and ratified by narrow bandwidth system for the cloud flashes. Fifteen cloud flashes pertinent to the Swedish thunderstorms were selected for the purpose. It is found that, the cloud flashes radiate at frequencies as low as 3 kHz to as high as a few tens of Mega Hertz (MHz). Electric field radiation corresponding to the initial breakdown process were found to radiate in the frequency range of 50 kHz to 5 MHz on the average, maximum energy is being radiated in the frequency range of 500 kHz to 5 MHz. Similarly, the final stage corresponding to the regular pulse bursts was found to radiate in the frequency range of 50 kHz to 5 MHz and that corresponding to the chaotic pulse trains was found to be in the range of 100 kHz to 5 MHz. Whereas, the very narrow pulses at the final stage, that can be termed as pulses corresponding recoil streamers (or Q-streamers) were found to radiate in the frequency range of 50 kHz to well above 10 MHz. Q-streamers can be considered as the strongest source of very high frequency and is justified by the simultaneous measurement of the electric fields at very high frequency (30 MHz) narrow bandwidth system. Rectification of the biasness of the conventional wavelet power spectrum has also been performed, however, no significant change in the spectrum was observed. Therefore, this study provides a strong basis for applying the wavelet transform technique without employing large number of narrowband system to acquire frequency domain information of lightning phenomena.

Introduction

Lightning is one of the most common and most fascinating atmospheric phenomena and occurs almost over any region of the globe. Although lightning is believed to be in existence well before the human civilization began on earth, it has not been fully understood to this date. The initiation of lightning within the cloud, exact charge structure of a thundercloud and maximum cloud electric field magnitude, production of x-rays and gamma rays etc., are among the challenges that the scientists have been trying to understand. Lightning can vaguely be categorised into two types, viz. Cloud flashes and cloud to ground flashes. Majority (two third) of the total lightning flashes are believed to be cloud flashes and rest of the one third terminate to the ground and are called cloud to ground flashes or simply ground flashes. The ground flashes, being more spectacular, frightening and deleterious to the lives and structures, are most researched and most understood. Cloud flashes on the other hand, despite their abundance in the atmosphere, are poorly understood. The reason behind is quite obvious. They occur largely inside the cloud obscuring much of their visibility and having less threat on the lives and the structures on the ground. However, with the ever increasing use of electronic gadgets, especially in the avionics and increasing usage of fibre composites in the avionics, the threat of cloud flashes should not be underrated. Moreover, to understand the physics of the lightning, its initiation in the cloud, the knowledge of the features of cloud flashes is of much importance. In order to understand the lightning phenomenology, various techniques have been employed, since the beginning of its scientific research some two hundred and sixty-eight years ago by Benjamin Franklin. Much of the knowledge about the physics of lightning was gained with the help of optical measurement and electric and magnetic field measurement techniques. However, majority of the research was confined to the lightning ground flashes and a very less research has been done on cloud flashes. Recently many researchers have been attracted towards a unique lightning cloud activity called narrow bipolar events (NBEs), or compact intra-cloud discharges (CIDs) or narrow bipolar pulses (NBPs) (e.g. Smith et al., 1999; Jacobson and Heavner 2005; Gurevich and Zybin 2005; Sharma et al., 2008; Nag and Rakov 2009; Nag et al., 2010; Rakov and Rachidi 2009; Wu et al., 2014; Marshall et al., 2013 etc. are some to name) for their uniqueness and probable association with the lightning initiation in the clouds, though none of these studies has been able to resolve the mystery.

Although, the cloud discharges can be viewed as being composed of an early (or active) stage and a late (or final stage) (Rakov and Uman, 2003), they are more complex as compared to the cloud to ground flashes. In general, the upper and the lower boundaries of a negative charge region, where the electric fields are highest, are the most likely places for a cloud flash to begin (Rakov and Uman, 2003). Further, it is thought that cloud flashes often bridge the main negative and upper positive charge regions (Rakov and Uman, 2003). The other possibility is to bridge the lower boundary of the negative charge region and the lower positive charge region. According to Nag and Rakov (2009), the downward propagating negative charge might be converted into a cloud flash if the strength of the lower positive charge region (LPCR) is comparable to that of the main negative charge region.

Moreover, the cloud discharges are of much interest to the scientific community in order to understand the initiation of lightning within the cloud. The HF and VHF radiation (f ≥ 1 MHz) is of more interest as the radiation field of micro discharges lie in this range of frequency (Hayakawa et al., 2008). This radiation contains very important information on discharge processes inside a thundercloud. Apparently, elementary micro discharges with the front duration t_f ~10 ns and complete duration t ~1μs are the elementary emitters in the VHF/UHF band (Hayakawa et al., 2008).

The present work is aimed to study the features of electric field produced by the cloud flashes in frequency domain. Attempts have been made to investigate the frequency of radiation by cloud flashes at different stages. The frequency spectra of different lightning events have been analysed by many researchers in the past. The word ‘spectrum’ is generally used in the literature on lightning in the frequency range to mean the magnitude of the Fourier transform of the electric field radiated during the discharge (LeVine 1987). The measurement of the frequency spectrum in a lightning flash have been made either by monitoring the power received at individual frequencies using a narrow bandwidth recording device or by recording the transient radiation with wide bandwidth device and then Fourier transforming the waveform to obtain a spectrum (Le Vine, 1987; Nanevicz et al., 1987). The measurements of first type were extensively used in 1950's and 1960's however, that of second type were mainly used after 1980 (Le Vine 1987). The frequency spectra, obtained from either ways, were found to be similar. The Fourier transform approach, widely used after Serhan et al. (1980), has an advantage that a spectrum can be associated with a particular lightning process with the shape of the waveform (Willett et al., 1990). Serhan et al. (1980), Willett et al., (1998) analyzing the Fourier transformation of the first and subsequent return strokes, reported that the frequency spectrum falls off nearly as 1/f between the 5 kHz–100 kHz. They have further reported that the trend for the subsequent return strokes is also same but with somewhat low amplitude. Weidman et al. (1981), analyzing the spectra of first return strokes, measurement being carried out almost over the salt water to minimize the propagation effect, reported that 1/f trend can be extended up to 2 MHz, however, the trend changes as 1/f² between 2 MHz and 10 MHz and as 1/f⁵ above 10 MHz. Weidman et al. (1981) further reported that spectra of the fast rising portion of leader steps, the initial fast transition in return strokes and transition in positively intra cloud pulses to be surprisingly similar.

Weidman and Krider (1986), analyzing the amplitude spectra of the fast rising, initial portion of fields produced by return strokes, leader steps and cloud pulses in the range of 1 MHz–20 MHz, reported that the spectrum amplitude varies as 1/f from 1 MHz to 6 MHz and it varies as 1/f² from 6 MHz to 20 MHz. They further reported that the spectral amplitudes of leader steps just before return strokes and the fast portion of cloud pulses that triggered the recording system tend to lie 5–10 dB below the amplitudes of first return strokes over the entire frequency interval.

Analyzing, the electromagnetic field spectra in the interval of 0.2–20 MHz, from first and subsequent return strokes, stepped, dart and chaotic leaders; and characteristic pulses, Willett et al. (1990) concluded that the return strokes are the strongest sources of radiation from cloud-to-ground lightning in the above frequency range. They further reported that the spectra of first and subsequent return strokes are identical in that range of frequency. Moreover, the spectra of stepped and dart stepped leader are nearly identical and are very similar to that of characteristic pulses. The spectral amplitude has been reported to decrease somewhat faster than 1/f in the interval of 0.2–20 MHz, and the energy spectral density as 1/f² up to about 5 MHz. Above 12 MHz, the spectral amplitude is reported to decrease as 1/f⁵.

Sonnadara et al. (2006), analysed the frequency spectrum of lightning cloud flashes in the range of 20 kHz to 20 MHz, for the first 10 ms time window and reported that the frequency spectrum follows 1/f from 20 kHz to 2 MHz and 1/f² above 2 MHz. Unlike the other researchers, Sonnadara et al. (2006) used Fourier transform technique to obtain the frequency spectrum for the whole electric field during the first 10 ms of the cloud flash. Further, the spectra obtained, by Sonnadara et al. (2006), for the individual cloud pulses were not found to follow the trend obtained previously by Weidman et al. (1981). However, the effect of the high pass filter with a pass band at 5 kHz on magnitude of the spectra in the lower frequency region is not clear.

Although, the Fourier transform technique, that is straight forward to obtain the frequency spectra of each individual specific events such as return strokes, subsequent return strokes and cloud pulses has advantages over the narrowband techniques that give the composite spectra of the whole events (LeVine, 1987), it has its limitations too. The Fourier transform technique requires wide bandwidth recordings and large dynamic range because the power at high frequencies tends to decrease rapidly. Furthermore, when a time domain signal is Fourier transformed to frequency domain signal, the time information is lost. This issue is not important while dealing with the stationary signals but while dealing with the transient signals, as that of lightning electromagnetic fields, it becomes significant (Torrence and Compo, 1998). It is therefore wavelet transform technique has been used in the present study. The wavelet transform technique used in this study has already been used by a few authors in the field of lightning electromagnetics (e.g. Miranda 2008; Sharma et al., 2011 etc.). In the study carried out by Sharma et al. (2011), frequency spectra for different lightning events such as negative return strokes, stepped leaders, subsequent return strokes, positive return strokes and narrow bipolar pulses were calculated.

According, Sharma et al. (2011), the range of frequency in which maximum energy is radiated for PB pulses was 51–739 kHz and that for leaders was 87–720 kHz. Whereas, the range of frequency in which the maximum energy was radiated for the negative return strokes was 2.8–40 kHz, that for the first subsequent strokes was 4.5–55 kHz and, for the positive return strokes was 5.5–81 kHz. They also observed that the range of frequency of radiation by Narrow Bipolar Pulses (NBPs) (58–714 kHz) was similar to the range of frequency radiated by PB pulses. More recently, Esa, 2014, Esa et al., 2014 used the wavelet transform technique to obtain the frequency range of first electric pulse leading to the negative ground flash, IC flash, positive ground flash and Isolated breakdown (IB) pulses and report that the first pulses leading to negative ground flash and cloud flash radiate at much higher frequency range as compared to those leading to the positive ground flash and IB pulses.

Since, the wavelet transform technique has already been used by many of the researchers, (Torrence and Compo 1998; Miranda 2008; Sharma et al., 2011), the details of the wavelet technique will not be discussed and for more details reader is referred to those papers and the references therein. The wavelet transform computation was carried out using the algorithm, used by the Torrence and Compo (1998). The power spectrum obtained by this technique is an average sense, the transform coefficient squared divided by the scale it associates, however, it causes bias in the power spectrum if the integration ranges are different for different scales (Liu et al., 2007). This biased power spectrum can easily be rectified, by dividing each energy value with scale it corresponds to (Liu et al., 2007). More recently, same technique was adopted by Veleda et al. (2012) to rectify the biasness, in the computation of cross wavelet transform (XWT). It has been reported by both Liu et al. (2007) and Veleda et al. (2012), that there is a significant improvement in the power spectra after performing the rectification.

In the present study, the frequency domain features pertinent to the, largely ignored, cloud flashes were analysed by applying the wavelet transform technique. Frequency domain information pertinent to the lightning cloud flashes is very rare in the literature. The electromagnetic radiation by the cloud flashes have been recorded by employing two techniques. One of the techniques is being employing the narrow band filters tuned at certain frequency to sense the electric field radiated by the lightning discharge at that frequency. And the other technique employed is being sensing the electric field by lightning discharge with the help of wide bandwidth antenna system and wavelet transforming the time domain signal so obtained. However, the data collected by later technique were used for the wavelet transform whereas the data recorded by the former technique were used just for comparison.

We believe that the information about the frequency spectra corresponding to the various lightning events is very important for the scientists for the better understanding of the physical processes of the electrical discharges inside the cloud and design engineers for efficient protective measures.