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
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
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).
b. Study of variations of lightning activity in tropical areas
We begin the search for periodicities in the three discussed time series
3. Results and discussion
Statistical parameters characterizing the calculated series of the three indices
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
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
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
(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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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
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
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
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
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
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
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
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
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
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
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
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
The relative periodograms of the lightning activity indices 
Citation: Monthly Weather Review 137, 12; 10.1175/2009MWR2920.1
The relative periodograms of the lightning activity indices
Citation: Monthly Weather Review 137, 12; 10.1175/2009MWR2920.1
The relative periodograms of the lightning activity indices
Citation: Monthly Weather Review 137, 12; 10.1175/2009MWR2920.1
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
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
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
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.
The statistical parameters characterizing the time series of the three indices of lightning activity 
