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  • View in gallery

    The power spectrum of the ELF magnetic field recorded on 1 Jan 2005 (1500–1600 UT) at Hylaty (NS antenna), calculated for a 1-h time period of observations. Points indicate the observed spectrum, and the solid line indicates the fitting analytical function [Eq. (2)].

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    The monthly run of the 1-h mean of lightning activity calculated from observations made in January 2006: (top) NS and (bottom) EW antennas. The bottom axis is consistently numbered, as in Fig. 6.

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    The location of Hylaty station in southeastern Poland (49°11′37″N, 22°33′18″E) and great circles indicating from which source regions the signals are received by NS and EW antennas.

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    The monthly average values of the 24-h variations of It (1-h mean value) calculated from signals observed by the NS (solid line) and EW (dashed line) antennas at Hylaty (data from January 2006).

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    The relative periodograms of the lightning activity indices , , and showing (a) the periodograms calculated after removing sine curves with annual and semiannual periods from the original time series and (b) the periodogram after removing the four sine curves with periods 353, 169, 45, and 17.6 days. The dashed lines show the FAP significance level.

  • View in gallery

    Maps of DPS of daily IRS indices calculated for the three world thunderstorm centers: (top) the Maritime Continent, (middle) Africa, and (bottom) America. (left) Periods between 2 and 15 days (calculated from Scargle–Lomb periodograms, using a 60-day sliding window) and (right) periods between 10 and 30 days (calculated from Scargle–Lomb periodograms, using a 90-day sliding window). The largest amplitudes (in arbitrary units) are shown in black, and zero amplitudes are shown in white.

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Study of the Periodicities of Lightning Activity in Three Main Thunderstorm Centers Based on Schumann Resonance Measurements

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  • 1 Institute of Geography and Spatial Management, Jagiellonian University, Krakow, Poland
  • | 2 Astronomical Observatory, Jagiellonian University, Krakow, Poland
  • | 3 Astronomical Observatory, Jagiellonian University, and Department of Electronics, Academy of Mining and Metallurgy, Krakow, Poland
  • | 4 Astronomical Observatory, Jagiellonian University, Krakow, Poland
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Abstract

Time variations of lightning activity in the three main tropical thunderstorm centers located in the Maritime Continent (Pakistan, India, Southeast Asia, Indonesia, and Australia), Africa, and the Americas are analyzed using a lightning activity index IRS, which is calculated from the resonances of magnetic field in the extremely low frequency range—the Schumann resonances—which were observed at Hylaty station (Poland) in the time interval July 2005–May 2006. Power spectrum analysis of the IRS series is carried out for this time interval. The annual and semiannual variations are shown in all of the series together with the following characteristic periodicities: 45 (Madden–Julian oscillation), 17.6, 13.5, and 4.8 days, seen mainly in the series describing the lightning activity of the Maritime Continent. In addition, maps of the dynamical power spectrum are constructed. They present variability both in the values of characteristic periods 26–30, 17–22, 12–14, 9–10, and 5–7 days and in their duration. During the studied time interval, according to these indices, the African center was the most active, whereas the American and Maritime Continent centers showed a similar level of activity. The largest differences among the centers were observed in the summer months in the Northern Hemisphere.

Corresponding author address: Zenon Nieckarz, Institute of Geography and Spatial Management, Jagiellonian University, Gronostajowa 7, 30-387 Krakow, Poland. Email: zenon.nieckarz@uj.edu.pl

Abstract

Time variations of lightning activity in the three main tropical thunderstorm centers located in the Maritime Continent (Pakistan, India, Southeast Asia, Indonesia, and Australia), Africa, and the Americas are analyzed using a lightning activity index IRS, which is calculated from the resonances of magnetic field in the extremely low frequency range—the Schumann resonances—which were observed at Hylaty station (Poland) in the time interval July 2005–May 2006. Power spectrum analysis of the IRS series is carried out for this time interval. The annual and semiannual variations are shown in all of the series together with the following characteristic periodicities: 45 (Madden–Julian oscillation), 17.6, 13.5, and 4.8 days, seen mainly in the series describing the lightning activity of the Maritime Continent. In addition, maps of the dynamical power spectrum are constructed. They present variability both in the values of characteristic periods 26–30, 17–22, 12–14, 9–10, and 5–7 days and in their duration. During the studied time interval, according to these indices, the African center was the most active, whereas the American and Maritime Continent centers showed a similar level of activity. The largest differences among the centers were observed in the summer months in the Northern Hemisphere.

Corresponding author address: Zenon Nieckarz, Institute of Geography and Spatial Management, Jagiellonian University, Gronostajowa 7, 30-387 Krakow, Poland. Email: zenon.nieckarz@uj.edu.pl

1. Introduction

The Schumann resonances (SR; Schumann 1952) have been discovered to be related to global lightning activity and have been linked with the possibility of monitoring global climate change; Williams (1992) showed correlation between the amplitude of the first SR mode and relative changes in tropical surface temperature, and Price (2000) studied the link between global lightning activity calculated from SR measurements and the content of water vapor in the upper troposphere.

a. The Schumann resonances

The SR are resonances of the electromagnetic field inside the cavity formed by the earth’s surface and ionosphere. The frequencies of the power spectrum maxima are defined for each resonance mode by the equation predicted theoretically by Schumann (1952),
i1520-0493-137-12-4401-e1
where n = 1, 2, 3, … ; c is the velocity of electromagnetic waves in the earth–ionosphere cavity; and a is the earth’s radius. The fundamental SR mode (n = 1) is observed at ∼8 Hz, and the subsequent modes are observed at ∼14, 20, 26, 33, 39, and 45 Hz. The cavity is excited by lightning discharges produced by about 2000 thunderstorm cells active at any time over the globe and located mainly in three tropical areas in the Maritime Continent, Africa, and the Americas, which are called the Maritime, African, and American thunderstorm activity centers, respectively. These centers together produce approximately 40–60 lightning discharges per second (Christian et al. 2003).

b. Studies on the variations of SR and lightning activity

Balser and Wagner (1960) related the diurnal variation of SR amplitudes and resonance frequencies to changes in global lightning activity. From this time, various authors exploited SR as an indicator of global lightning activity. Estimation of lightning activity is usually done by tracking the parameters (mainly intensities and peak frequencies) of the SR modes, which are determined by fitting symmetric Lorentzian curves to observed SR spectra (Williams 1992; Sentman 1995; Sátori and Zieger 1996; Price 2000) or by computing cumulative intensity of the first three or more SR modes (Sentman and Fraser 1991, Heckman et al. 1998, Nickolaenko et al. 1998; Nickolaenko and Hayakawa 2002). However, some influence of the solar activity on the parameters of the earth–ionosphere resonance cavity, and hence on SR, according to Schlegel and Füllekrug (1999), Kułak et al. (2003), and Sátori et al. (2005), is not negligible and affects both the resonance frequencies fn and spectral width of resonance modes Γn.

Periodicities in lightning activity were studied earlier by Williams (1994), Sátori and Zieger (1996), Füllekrug and Fraser-Smith (1997), Nickolaenko et al. (1999), Anyamba et al. (2000), Williams et al. (2000), Sátori and Zieger (2003), and Williams (2005). Various oscillation periodicities have been discovered: periods of one year, half a year, one-third of a year, and over 10 days. Patel (2001) and Williams et al. (2001) showed 5-day modulation of global lightning activity.

In this paper, we study temporal variations of global lightning activity in the three main world thunderstorm centers. The lightning activity is estimated from observations of SR at Hylaty observation station in July 2005–May 2006 conducted by the Schumann Resonance Laboratory from Krakow. The Krakow SR observations began in 1992 (Kułak et al. 2003), but until 2005 they were carried on sporadically. In June 2005 a new observation station, Hylaty, located in southeast Poland (49°11′37″N, 22°33′18″E), started continuous measurements. At this new station an observation system is located in a special underground cavity and consists of two magnetic antennas, a microprocessor acquisition system, and independent power supply. The antennas are directed horizontally along the north–south (NS) and east–west (EW) directions. The magnetic field components BNS and BEW are recorded with an amplitude resolution of ∼3.8 nT per 16 bits (58 fT) and at the sampling frequency of 178 Hz. The analog part of the system, through filtering processes, transmits signals in the frequency range from 0.01 to 55 Hz.

In our method of calculating lightning activity from SR observations, we apply asymmetric resonance curves, called Breit–Wigner curves (Micek et al. 2004; Kułak et al. 2006), to describe observed SR power spectra and to calculate a lightning activity index IRS via a resonance curve-fitting algorithm. Next, we attempt to analyze periodicities in lightning activity using the Scargle–Lomb periodograms (Scargle 1982).

2. Method

a. Calculation of the lightning activity index IRS

The electromagnetic waves propagating and superposing in the earth–ionosphere cavity create resonance fields and fields of waves running out from sources, with both transmitting energy from lightning discharges to the earth–ionosphere cavity. As a result, asymmetry of the resonance spectral lines is observed (Kułak et al. 2006). The fact that the observed SR spectral lines differ from the theoretical Lorentzian functions was noticed by Price and Melnikov (2004). Mushtak and Williams (2002) stated that the justification for the selection of Lorentzian function is as much physical as mathematical, and Williams et al. (2006) discussed simplifications that allow replacement of the theoretical electric spectrum obtained via the zonal harmonic series (Nickolaenko and Hayakawa 2002) as a sum of individual Lorentzians. According to our understanding of the Schumann Resonance phenomenon, using the Lorentzian functions to describe the spectral response of the earth–ionosphere cavity is too broad a simplification. Our approach explores the concept that the observed extremely low frequency (ELF) spectrum (4–60 Hz) can be depicted by an asymmetric function given by Eq. (2), which decomposes the measured ELF field components BNS and BEW into resonance fields and running wave fields (Kułak et al. 2006):
i1520-0493-137-12-4401-e2
The fitting function describing the shape of each nth peak from the N = 7 observed includes the following parameters: the amplitude an (in mathematical meaning, but in the physical sense it is intensity), the asymmetry en, the peak frequency fn, and the width Γn. In the case of the lack of asymmetry (i.e., when en = 0), the shape of the nth observed peak has the form of a Lorentzian resonance curve and the parameters have the classical meaning (Γn is the width between half power points).

In the first step, signals from the NS and EW antennas are analyzed separately to calculate corresponding power spectra. The adjustment of the fit of the observed power spectrum to the model function (2) is done with an interactive multiple least squares fitting program. In the result, for each resonance mode the parameters an, en, fn, and Γn are determined independently from the BNS and BEW field components. Figure 1 shows a power spectrum computed from a signal detected by the NS antenna and the fitting function described by Eq. (2).

Next, having the amplitudes (intensities) of the first six resonance modes for both components (Nieckarz et al. 2009), we calculate and indices according to
i1520-0493-137-12-4401-e3
These indices represent the estimate of lightning activity at a moment t. By fitting the asymmetric resonance curves, we eliminate, at least partly, the influence of running waves on the spectra that disturb resonance parameters (Kułak et al. 2006). The sum of amplitudes an is set to be the measure of lightning activity—our IRS index—because it seems to be the power-related parameter least susceptible to any changes caused by errors in the fitting procedure and thus the most reliable. Figure 2 shows a 1-month series of 1-h mean lightning activity indices and . Diurnal variations, as well as a few-day oscillation periods, are clearly visible, and this indicates that some oscillation periods appear in the data.

b. Study of variations of lightning activity in tropical areas

Our measuring station, Hylaty, is globally located north of the African center, west of the Maritime Continent, and east of the tropical Americas (great circle paths), as shown in Fig. 3. This localization gives the possibility to separate out the lightning activity from different source regions by using independently NS and EW magnetic components at different times during the day. Even though the NS antenna is sensitive to both the American and Maritime Continent centers, the lightning activity peaks from these centers appear mainly at specific time intervals (Whipple 1929; WMO 1956; Blakeslee et al. 1999; Christian et al. 2003; Greenberg and Price 2007): around 0800 UTC for the Maritime center and around 2000 UTC for the American center. The lightning activity peak of the African center is easily observed at 1400 UTC using the EW magnetic component. The previously mentioned time intervals are visible in the 24-h run of daily indices INS and IEW presented in Fig. 4. Taking into account both the intervals of the active hours of each center and the sensitivity of the antennas for different tropical regions, we construct the daily indices , , and using
i1520-0493-137-12-4401-e4
i1520-0493-137-12-4401-e5
i1520-0493-137-12-4401-e6
The time intervals (the active hours) chosen for obtaining daily indices for the three centers are 0000–1200 (Maritime), 1000–2200 (Africa), and 1200–0000 UTC (Americas). We assume that the daily IRS index calculated for a given tropical thunderstorm center is proportional to its mean daily lightning activity and applied to all types of contributing discharges.

We begin the search for periodicities in the three discussed time series , , and by calculating Scargle–Lomb periodograms (Scargle 1982) for all the investigated time intervals. Using this periodograms and an iterative technique of fitting and subtracting sinusoids in the time domain (Delache and Scherrer 1983; Horne and Baliunas 1986; Zięba et al. 2001), it is possible to find all the periodicities hidden in the data for series with gaps. This approach allows us to also diagnose the periods longer than the length of the data, although with a large uncertainty. Table 1 presents periods of the strongest sinusoids hidden in the data. We mark their statistical significance level giving the false-alarm probability (FAP), which is the probability that the sinusoid can be generated by noise (Bai and Cliver 1990). Figure 5 shows periodograms recalculated for these series after removing from the original time series the sinusoids with periods whose FAP values are smaller than 5%. The phase and amplitude of this sinusoidal oscillation are fitted from the original time series using the least squares method. Because of the nonstationary nature of the lightning activity, we examine also how the short-term “dynamical” behavior of the data changes from time interval to time interval during July 2005–May 2006. For this purpose, the maps of dynamical power spectrum (DPS), shown in Fig. 6, are produced for each of the analyzed time series by calculating Scargle–Lomb periodograms for shorter intervals (smaller subsets) of data chosen by a sliding window. The position of a window is changed along the time axis every 1 day. We applied two different windows of 60 and 90 days in length. The first one was used to detect short periods between 2 and 15 days, and the second was used to reveal oscillations of periods between 10 and 30 days.

3. Results and discussion

Statistical parameters characterizing the calculated series of the three indices , and are shown in Table 2. Both the mean and median values of IRS indicate that Africa is the most active center during all the considered seasons, except the summer (the season names are for the Northern Hemisphere), when America dominated. The percentile values display the same picture; they are clearly shifted into higher values for the Africa center. The highest values of almost all the statistical parameters observed in the America center during the summer months are probably caused by an additional lightning activity received by the NS antenna from the West Africa region. The accepted method of the IRS calculation assigns this activity to the Americas. This makes values in some days very large, which in consequence results in high values of the standard deviation and the interpercentile range. In the remaining seasons, the statistical parameters of and show that the Maritime Continent and American centers are similar. The prominence of the African center in the global lightning activity was noted by Christian et al. (2003) and Williams and Sátori (2004).

However, this should be treated with care for at least two reasons. The first one is connected with the day–night asymmetry (Sentman and Fraser 1991; Melnikov et al. 2004; Sátori et al. 2007), which is not considered in our approach and can modify the SR amplitudes by about 15%–20%. This effect introduces a low bias to the American center rather than to the Maritime one, because the active hours for the American center often occur during night hours at Hylaty. As in our method, the SR measurements from the NS antenna are used for calculation of both and indices, daytime flashes from Southeast Asia can mix with nighttime flashes from the Americas (and vice versa). This of course changes the mutual relation among our indices. The next reason that influences the relations among indices is connected with the given location of the receiving station and the global distribution of the thunderstorm centers. This results in unequal detection of signals from all three discussed regions. However, all these limits are unimportant when the indices are used for following the changes of lightning activity in each of the centers independently and without doing comparison among them. They also do not influence our study of periodic variations longer than one day.

From Table 1, it is evident that the annual and semiannual periods are present in all the analyzed series. Additionally, the two statistically significant periodicities of 45 and 17.6 days are discovered in the lightning activity of the Maritime Continent. The 17.6-day oscillation is seen also in the American center but not in Africa. Figure 5 shows a multiple structure in the periodogram for the Americas that spreads from 13 to about 20 days. The complex structures at about 3, 5, 8, 10, 13.5, and 20 days are seen in the periodogram for the Maritime Continent and at about 6 and 9 days in the periodogram for Africa. Their significance levels are very low, indicating that these oscillations are weak and irrelevant or that they are real but present in shorter time intervals. Additionally, their periodicity can fluctuate in some range of periods decreasing the significance level of the main sinusoid.

With the aim to clarify this point, the maps of DPS of the daily IRS index for each of the centers were constructed for periods less than 30 days. Figure 6 shows the maps of DPS of the daily IRS index calculated for the three centers. The periods between 2 and 15 days obtained with the 60-day window are shown in the left panel of Fig. 6, whereas those between 10 and 30 days obtained with the 90-day window are in the right panel of Fig. 6. During summer, an oscillation with a period of 5–6 days is present in all the centers. It disappears in midautumn for the Maritime Continent and American centers, where a 9–10 days oscillation becomes prominent in midwinter. In the African center, the ∼6-day oscillation is present all the year, but the oscillation period changes and varies within a 5–7-day range. The 12–14-day oscillation is present in all the centers at most times of the year. The structures of period changes around 14 and 10 days beginning near day 360 for both the Maritime Continent and the Americas look very similar to each other. It is possible that they are caused by a day and a night lightning activity in one of these centers. In this case, our method shows this activity in both above-mentioned centers. Other oscillations of increasing period, from 17 days in the summer of 2005 to 26 days in the spring of 2006, are observed. The period of these oscillations increases systematically and its changes are most clearly visible in the American center. In the case of the Africa center, the oscillation fluctuates between 14 and 18 days and additionally in the winter of 2006 between 22 and 28 days. In the Maritime Continent, there are two time intervals when the periodicity of 17–22 days is clearly visible: the first comprises the summer days and the second includes days from the end of autumn to the end of winter (the boreal summer). From the end of autumn until the spring of 2006, the periodicity of 28–30 days is also presented in the Maritime Continent center, whereas in the African center this oscillation can be noticed only during the short time interval in the middle of the winter. The oscillations hidden in , data have the largest significance level in comparison to those presented in the indices of the other centers. This denotes the period stability of the Maritime Continent center oscillations in longer time intervals, which is confirmed by the parallelism of black structures representing the oscillation periods to the time axis in Fig. 6.

The positive correlation between global lightning activity and surface air temperature on the annual and semiannual time scale were announced by Williams (1994). Then, the lightning variation on these scales were explored in papers (Sátori and Zieger 1996; Füllekrug and Fraser-Smith 1997; Heckman et al. 1998; Williams 1999; Williams et al. 2000). The intraseasonal periodicities (10–60 days) found in the analyzed time series of our daily indices IRS are observed in various meteorological parameters such as wind, humidity, sea surface temperature (SST), and latent heat flux (LHF) oscillation (Singh et al. 2002). They are connected with the Madden–Julian oscillation (MJO) in deep convection (Madden and Julian 1971, 1994). The relations between MJO and SR have been studied by Anyamba et al. (2000). At present, diversity of opinion exists on the modeling of the MJO/intraseasonal oscillation (ISO; 20–30- and 40–60-day modes; Hayashi and Golder 1993), but generally the ocean–atmosphere interaction plays an important role in modulating these modes (Sengupta et al. 2001; Nanjundiah and Krishnamurti 2007; Pegion and Kritman 2008). The periodicities of 9–10, 12–14, and 17–22 days can relate to the quasi-biweekly mode (QBM; also called 10–20-day mode). The QBM is known to have a major influence in determining the active and break conditions of monsoons (Chatterjee and Goswami 2004; Han et al. 2006; Rahman and Simon 2006). The shortest 5–7-day periodicity is also recognized in observations of various climatological and geophysical parameters (Grodsky and Carton 2001; Londhe et al. 2005; Chronis et al. 2007). They can probably all be linked with planetary-scale equatorial waves (5-day Rossby and 6-day Kelvin) in the low-latitude mesosphere and lower thermosphere (MLT) region (Pancheva et al. 2008). The cited papers are only some examples of a rich literature. They show that the periodicities observed in our daily indices of lightning activity are present in various climatological data.

4. Conclusions

This study exploited the potential linkage between the global thunderstorm activity and the measurements of two magnetic components of Schumann resonance carried out in a single station for the construction of lightning activity indices IRS for three main world thunderstorm centers located in the tropical regions of the Maritime (Pakistan, India, Southeast Asia, and Australia), African, and American continents. The careful analysis of the three time series consisting of the daily indices , , and allow the formulation of the following conclusions:

  • (i) The annual, semiannual, and intraseasonal periodicities (43–47, 26–30, 17–22, 12–14, and 9–10 days) as well as the short-period oscillations (5–7 days) are clearly visible.

  • (ii) Using the maps of DPS of the lightning activity indices, we are able to analyze changes in the oscillation periods and the observed time intervals of their occurrences. This could not be possible by calculating periodograms on the basis of all the data series.

  • (iii) According to our daily indices, in all of the seasons except the Northern Hemisphere summer, the African center dominated the global lightning activity, whereas the indices of Maritime and America centers show similar activity. However, the direct comparison of different centers can be burdened with errors, which are unimportant when the lightning activity of a given center is traced in different time intervals.

  • (iv) The agreement of the periodicities found in our indices with those known from various climate studies indicates that the presented method of the investigation of the global lightning activity can be useful.

Acknowledgments

We are grateful to Dr. Earle Williams and two anonymous reviewers for valuable comments and suggestions, which have been very helpful to the improvement of the original manuscript. This research was funded by the Polish Ministry of Science and Higher Education Grant N30705032/2568.

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Fig. 1.
Fig. 1.

The power spectrum of the ELF magnetic field recorded on 1 Jan 2005 (1500–1600 UT) at Hylaty (NS antenna), calculated for a 1-h time period of observations. Points indicate the observed spectrum, and the solid line indicates the fitting analytical function [Eq. (2)].

Citation: Monthly Weather Review 137, 12; 10.1175/2009MWR2920.1

Fig. 2.
Fig. 2.

The monthly run of the 1-h mean of lightning activity calculated from observations made in January 2006: (top) NS and (bottom) EW antennas. The bottom axis is consistently numbered, as in Fig. 6.

Citation: Monthly Weather Review 137, 12; 10.1175/2009MWR2920.1

Fig. 3.
Fig. 3.

The location of Hylaty station in southeastern Poland (49°11′37″N, 22°33′18″E) and great circles indicating from which source regions the signals are received by NS and EW antennas.

Citation: Monthly Weather Review 137, 12; 10.1175/2009MWR2920.1

Fig. 4.
Fig. 4.

The monthly average values of the 24-h variations of It (1-h mean value) calculated from signals observed by the NS (solid line) and EW (dashed line) antennas at Hylaty (data from January 2006).

Citation: Monthly Weather Review 137, 12; 10.1175/2009MWR2920.1

Fig. 5.
Fig. 5.

The relative periodograms of the lightning activity indices , , and showing (a) the periodograms calculated after removing sine curves with annual and semiannual periods from the original time series and (b) the periodogram after removing the four sine curves with periods 353, 169, 45, and 17.6 days. The dashed lines show the FAP significance level.

Citation: Monthly Weather Review 137, 12; 10.1175/2009MWR2920.1

Fig. 6.
Fig. 6.

Maps of DPS of daily IRS indices calculated for the three world thunderstorm centers: (top) the Maritime Continent, (middle) Africa, and (bottom) America. (left) Periods between 2 and 15 days (calculated from Scargle–Lomb periodograms, using a 60-day sliding window) and (right) periods between 10 and 30 days (calculated from Scargle–Lomb periodograms, using a 90-day sliding window). The largest amplitudes (in arbitrary units) are shown in black, and zero amplitudes are shown in white.

Citation: Monthly Weather Review 137, 12; 10.1175/2009MWR2920.1

Table 1.

The periodicities found in all the investigated series. FAP estimates the probability that the given periodicity can be generated by noise. The FAP value of each given periodicity computed according to the procedure described by Bai and Cliver (1990). The term ΔP denotes the uncertainty in periodicity resulting from the length of the time series T = 321 days.

Table 1.
Table 2.

The statistical parameters characterizing the time series of the three indices of lightning activity , , and calculated for four seasons and for the entire time interval July 2005–May 2006.

Table 2.
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