JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, D08107, doi: /2010jd014736, 2011

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2010jd014736, 2011 Cloud to ground lightning dipole moment from simultaneous observations by ELF receiver and combined direction finding and time of arrival lightning detection system Zenon Nieckarz, 1 Andrzej Kulak, 2,3 Stanislaw Zieba, 3 and Anna Odzimek 4,5 Received 14 July 2010; revised 25 January 2011; accepted 1 February 2011; published 19 April [1] We present a new method of automatic detection of ELF impulses related to cloud to ground lightning at distances 1 2 Mm from a broadband ELF receiver and also we present a new numerical automated technique for calculating the lightning dipole moment. We have performed the detection for two known data sets of lightning flashes detected by the French lightning detection network Meteorage in southwest Europe over two 48 h periods July and 6 7 September The number of flashes identified in the ELF data compared to the number of flashes detected by Meteorage reach 10 25% when little local activity close to the ELF station is present. The local thunderstorm activity worsens the detection of lightning from larger distances and the efficiency of identification of ELF impulses as lightning can decrease to a few percent. By combining the information on the location of the lightning flashes from Meteorage with the ELF data, lightning dipole moments can be calculated. Our results suggest the dipole moment is linearly correlated with the lightning peak current (p 7.5 I max ) but the dispersion of the dipole moment for a given peak current is significant. One of the reasons of such dispersion is the contribution of the lightning continuing current to the ELF signal. Citation: Nieckarz, Z., A. Kulak, S. Zieba, and A. Odzimek (2011), Cloud to ground lightning dipole moment from simultaneous observations by ELF receiver and combined direction finding and time of arrival lightning detection system, J. Geophys. Res., 116,, doi: /2010jd Introduction [2] This paper concerns the detection of cloud toground (CG) lightning and obtaining the lightning dipole moment using two observation methods working in two different radio frequency ranges. In the first method the electromagnetic (EM) radiation emitted by lightning in very low/high frequency range (VLF/HF) is analyzed; this is used by today s lightning detection networks [MacGorman and Rust, 1998]. The second method analyzes EM waves radiated in the extremely low frequency range (ELF) and recorded by a single ELF station located at a distance of 2000 km from the area of the lightning. [3] The early methods of the measurements of lightning are the measurements of peak current in lightning strokes 1 Institute of Physics, Jagiellonian University, Krakow, Poland. 2 Department of Electronics, Academy of Mining and Metallurgy, Krakow, Poland. 3 Astronomical Observatory, Jagiellonian University, Krakow, Poland. 4 Department of Physics and Astronomy, University of Leicester, Leicester, UK. 5 Now at Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland. Copyright 2011 by the American Geophysical Union /11/2010JD to towers [Berger et al., 1975], multiple point measurements of low frequency electric field [Krehbiel et al., 1979], and direct measurements of the electric current flowing in metal rods injected into thunderclouds using rockets [Hubert et al., 1984]. Those methods typically require measurements in close vicinity of a lightning stroke or at small distances < 100 km. Lightning detection and lightning dipole moment determination have been possible indirectly by methods using the EM radiation emitted by lightning in the ELF/VLF range [Burke and Jones, 1996; Huang et al., 1999; Cummer and Inan, 2000; Cummer and Lyons, 2004]. [4] In this paper we use another method from the second group which is based on the analysis of broadband ELF magnetic signal and enables quick computation of the charge (dipole) moment change related to any lightning stroke, in an automatic way. In this algorithm we define criteria for an automatic identification of lightning related ELF transients in the time domain. We also develop a quantitative analysis of the transients which combined with the information on the distance of the lightning from the ELF receiver allows calculation of the lightning dipole moment. The method is suitable for analysis of lightning occurring in the distance > 100 km up to a few thousand kilometers from an ELF station. This method could be more effective with regard to the number of analyzed 1of9

2 lightning flashes, independent of flash polarity and peak current. 2. Data Sources and Synoptic Situation 2.1. Lightning and ELF Data [5] In our method we use observations of the EM radiation by two different radio observation systems. The first is the lightning detection system operated by the Meteorage which covers France and adjacent area in southwest Europe. The Meteorage company installed the first French lightning detection network and currently operates it on behalf of Meteo France. The network consists of 17 sensors, supported by similar sensors in neighboring countries, built to determine the location and time of positive and negative cloud to ground (CG) strokes occurring over that area. The Meteorage sensors, produced by the American company Global Atmospherics Inc. (GAI, taken over by Vaisala in 2002) use both the direction finding (DF) and time of arrival (TOA) techniques [MacGorman and Rust, 1998, chapter 6] to locate CG lightning. The network provides geographic location, time, stroke multiplicity, and the peak current the first return stroke. The peak current in a DF system is determined from the amplitude of the electric field at a distance, and the quality of this estimate depends on the calibration of the antenna system and assumptions on the speed of the return stroke [MacGorman and Rust, 1998, chapter 5]. The detection efficiency of the network run by Meteorage has been reported to be higher than 90%, the location precision 4 km, time precision 1 ms, and the error of peak current intensity measurements 5% [Bonnet, 2003]. The data we used in our analysis have been obtained from the Meteorage in support of the Eurosprite2005 campaign [Neubert et al., 2008] and the Meteorage data sets contain information about lightning flashes from the area surrounding the observation point at Pic du Midi de Bigorre of 800 km radius (Figure 1) which is only a fraction of the area observed by Hylaty station. [6] The second observation system is a single magnetic ELF station recording continuously two horizontal components of the magnetic field in the frequency range Hz. The station, Hylaty (22.55 E, N), is located in the southeastern corner of Poland, at a remote site in the western Bieszczady mountains [Kulak et al., 2003]. In the presence of lightning in the distance of a few thousand kilometers the magnetic signal contains short field impulses coming from the lightning discharges [Füllekrug and Constable, 2000; Nieckarz et al., 2009]. [7] For our analysis we have selected data from two 48 h periods (two full days): July 2005 and 6 7 September The chosen periods were very active in lightning in the area monitored by the Meteorage and simultaneously there was little activity over the area surrounding the Hylaty station at a few thousand kilometer radius (based on infrared satellite images and satellite Lightning Detection Sensor data, not presented here). Diurnal variations of the number of lightning flashes in the data sets from Meteorage in the two periods are shown in Figure 2. [8] Meteorage detected 16,000 CG lightning strokes on July The stroke closest to Hylaty was at 857 km from Hylaty and the most distant at 2596 km. On 6 7 September 2005 Meteorage detected 515,000 CG lightning strokes, the closest to and the most distant from Hylaty was at 885 km and 2685 km. The mean values of the distance distribution (Figure 3) are 1433 km and 1588 km in July 2005 and 6 7 September 2005, respectively. Both the distance range and mean values of the distance distributions are similar in the two cases. [9] The distributions (normalized to the total number of flashes of the same polarity) of the CG lightning peak current for the two intervals are shown in Figure 4. The group of lightning with the largest peak currents are, for both flash polarities, lightning with peak currents between 5 and 10 ka. Some fraction of the CGs from this group could be intracloud discharges detected by the system as weak cloud to ground lightning but this effect has not been quantified for Meteorage so far (Stephane Pedeboy and Serge Soula, personal communication, 2010). Biagi et al. [2007], who evaluated the performance of the U.S. National Lightning Detection Network (NLDN) estimate that up to 15 ka the majority of small positive events detected by the system may not be CGs. In the present study, the ratio of the number of negative to the number positive flashes is similar and equals 5.7 for July (15% of positive flashes) and 4.8 for 6 7 September (17% of positive flashes) Synoptic Situation [10] The synoptic situation over Europe was different in two situations. On 28 and 29 July 2005, the atmospheric fronts related to the low pressure air in the southwestern part of the British Isles determined the weather conditions over northern and western Europe. The center of this lowpressure area moved slowly toward the northeast from its initial location to the west of the English Channel and created two atmospheric fronts as it crossed central Britain. A warm front was spreading eastward along the 55 parallel from the center of the low pressure area to the west of the Baltic Sea. Over the whole period, this front moved slightly northward and affected southern Sweden. The second front spread more or less due southward from the low pressure center toward the coast of northwestern Africa. Over the whole period, this front maintained a north south shape and moved from the western Iberian Peninsula to eastern France accompanied by thunderstorms and lightning recorded by the Meteorage system. At the same time, high pressure air over western Ukraine affected the weather in central and eastern Europe. On 28 July, southeastern Poland, including the Hylaty station, was under the influence of a high pressure system centered in the Ukraine. The type of circulation was southern anticyclonal with the advection of subtropical air creating a kind of hot and humid tropical conditions that tend to increase the likelihood of convection thunderstorms. This is indeed what happened during the afternoons of 28 and 29 July in central and eastern Poland and western Ukraine and Belarus. [11] On 6 7 September 2005, the initial locations of the centers of low and high pressure systems over Europe were similar to those in July, but the front positioning, air masses and development of the situation were different. The lowpressure air centered west of the English Channel was moving southward and weakening, splitting into a few 2of9

3 Figure 1. Map of cloud to ground lightning flashes detected by Meteorage over two 48 h periods: (top) July 2005 and (bottom) 6 7 September The gray area indicates approximately the range of lightning locations provided by Meteorage during the Eurosprite2005 campaign. Pluses and minuses are locations of positive and negative flashes detected during the analyzed periods. Hylaty station is marked by the open black square. smaller fronts creating an area of low pressure in western Europe without a deep low pressure center. It did not create fronts that would spread deep into central and eastern Europe. It was only toward the evening hours on 7 September that a cold front moved southward from over the Baltic Sea into Poland, while an Adriatic Sea front was created with a precipitation zone. The weather in southeast Poland, including at Hylaty, was affected by high pressure air over Ukraine. The advection of polar continental air masses from the south took place on 6 September. On the following day, the polar continental air masses continued into southern Poland with the only change being a change of anticyclonic advection from southern to southwestern anticyclonic. Central and southern Poland was free from thunderstorm activity. 3. ELF Impulse Selection [12] Due to the variety of electromagnetic phenomena observed in the frequency range from a fraction of hertz to several tens of Hz, the sources of which are in the Earth s crust (magnetostriction of rocks in the crust) [Nagata, 1970; Mazzarella and Palumbo, 1988], in the Earth s atmosphere (lightning activity) [Greenberg et al., 2007; Nieckarz et al., 2009], and in the ionosphere and magnetosphere (ionospheric Alfven resonances, magnetospheric pulsations) 3of9

4 Figure 2. Hourly variations of the number of lightning flashes detected by Meteorage in two 48 h periods: (left) July 2005 and (right) 6 7 September [Belyaev et al., 1989] the waveform of the signal detected at the ground, such as in the Hylaty station records, is complicated and stochastic rather than harmonic. For example, in the signal s background short impulses occur which come from the atmospheric cloud to ground (CG) lightning discharges occurring at a distance from the station. Some of the signals come from the lightning occurring in the region where the Meteorage is operated. A one to one identification of the CGs and ELF impulses is required for further analysis of the CG related impulses. First the amplitude of each impulse in the ELF records is estimated. The time of an ELF impulse t i ELF coming from any lightning flash is delayed by dt i from the exact moment of the occurrence of the lightning as determined by Meteorage. Each impulse is delayed by a different dt due to different distances from the Hylaty station. The relation between the times is t ELF i ¼ t MET i þ dt i ; ð1þ where t i ELF is the (UTC) time of the recording of the ith impulse by the Hylaty system, t i MET is the (UTC) time of the stroke determined by the Meteorage and dt i is the delay due to signal propagation from the signal source to Hylaty. For Hylaty and Meteorage the delays due to the propagation of ELF waves at those distances are 3 to 9 ms. As the Hylaty station samples the signal at the frequency of f s 175 Hz (1/f s 6 ms) and the lightning strokes occur randomly, the signal delay in the ELF time series is equivalent to 0 to 2 signal samples. Therefore it cannot be guaranteed that theoretically predicted sample related to t i ELF from equation (1) will be the signal s local maximum. The position of the maximum in the recorded signal can occur at a different time than predicted by equation (1) because the signal is a superposition of any EM signals occurring at the same time (e.g., signal from other lightning strokes, other terrestrial signals and signals coming from space), the noise from the electronics and antennas, as well as changes of the propagation speed in the Earth ionosphere cavity caused by the day night asymmetry [e.g., Pechony et al., 2007]. Therefore, for an automatic identification of CG related impulses in the ELF signal, we applied the following algorithm. Our main assumption is that both the times and locations of the strokes are known. This information in our case was known from the Meteorage records and is considered as accurate. [13] In the first step, for each Meteorage flash time, the closest ELF sample was found in both N S and E W antenna signals and the signals have been analyzed in the time neighborhood of ±5 samples. The signal mean averages are calculated, independently for N S and E W components. Next, an 11 point departure from the mean is calculated for the two components (B i NS, B i EW ) and the departure for the total field B i. The maximum of the departures over the 11 samples is further considered as Figure 3. The number of lightning flashes detected by Meteorage on (left) July 2005 and (right) 6 7 September 2005 as a function of the distance flash Hylaty receiver. 4of9

5 directions and sources located in various parts of the globe. In addition to natural sources the noise generated by humanmade sources and by electronics is also recorded. As a result, the recorded signal at the predicted time related to the time occurrence of a CG stroke is complicated to such extent that it is difficult to relate a sample to a signal peak generated by the CG. In preliminary analysis of our ELF data we established that if db i is less than 30% of B i and if da i,real is less than da i then we can observe a peak in the ELF signal. Therefore we adopt this as the criterion for the detection of a CG related ELF transient. This completes the automatic selection (identification) of CG related ELF impulses. Impulses which do not fulfill the above criterion are not considered as identified as CG related ELF impulses. Figure 4. Distribution of the peak current of the lightning flashes detected by Meteorage in two 48 h periods: July 2005 and 6 7 September the amplitude of a CG related signal in the ELF measurements. The local average signal level, for each of the 11 samples, is calculated as the arithmetic mean over ±10 signal samples (excluding the central sample). [14] Next, from the signal amplitudes B EW i and B NS i and the field modulus B i the azimuth A i to the signal s source is calculated as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jb i j¼ ð B NS i Þ 2 þ B EW i ð Þ 2 jb i;angle j¼arctan BEW i B NS i ð2þ ð3þ 4. Calculation of Lightning Dipole Moment From ELF Impulses [16] Kulak et al. [2010] analyze the effect of the spectral characteristics of cloud to ground lightning and the contribution of the return stroke and continuing current to these characteristics in relation to magnetic ELF signal generated by lightning. They also consider the role of anti alias filter and the bandwidth of the receiver on the amplitude of the signal recorded by an ELF receiver. The field amplitude B pulse can be expressed as follows [Kulak et al., 2010]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B pulse Df Z jhr; ð f ÞgðfÞj 2 df ; ð5þ 0 where r is the distance between the source and observer, f is the frequency of an EM wave, m 0 is the magnetic permeability of free space, g( f ) is the spectral characteristics of the ELF receiver, Df the equivalent energetic spectrum of the receiver [Kraus, 1966, p. 244], H(r, f ) is the spectrum amplitude of the magnetic component of the EM wave, c is a dimensionless receiver parameter [Kulak et al., 2010, equation (19)], and Df is A i ¼ B i;angle 90 ; A i ¼ B i;angle þ 90 ; for CG for þ CG; ð4þ R 0 Df ¼ jgðfþjdf 2 R 0 jgðf : ð6þ Þj2 df where B i,angle is the angle (clockwise) between the North and the B vector, and B i NS and B i EW are the N S and E W components of B, respectively. Errors of B i NS and B i EW, db i EW, db i NS are their standard errors calculated from the same range of points as the average local signal level described above. The errors for B i and A i, db i and da i, have been calculated using the error propagation. It is important in our method that the determination of the real azimuth A i,real to the source is possible knowing the geographic coordinates of the source (a CG stroke) and the ELF station. Because the error of each CG location in the Meteorage data set compared to the distance of the CG activity area to Hylaty result in relatively small errors of the calculated real azimuth, we further consider the azimuth A i,real calculated for each stroke as certainty. We define the difference between the azimuth derived from the ELF signal da i and the real azimuth A i,real as da i,real. [15] As previously underlined the ELF signal is a superposition of signals coming to the receiving point from all [17] The spectrum amplitude of the magnetic component of the EM wave H(r, f ) in the far field zone (i.e., where the distance source receiver is larger than the height of the ionosphere, r h) produced by a CG lightning stroke can be described as p f Hr; ð f Þ ¼ 2 hðfþðf Þ ðf ÞH 2 1 ð Þ 2rf ðf Þ e rðf Þ ; where H 1 (2) is the second kind Hankel function of the first order, r is the distance, f is frequency, u is the group velocity of an EM wave in the Earth ionosphere waveguide which is frequency dependent, h is the frequency dependent ionospheric height, a is a frequency dependent damping coefficient, p is the source dipole moment and ( f ) is the source spectrum. [18] We use the Kirillov et al. [1997] formula for the height of the ionosphere h( f ), Ishaq and Jones [1977] formula for ð7þ 5of9

6 Table 1. Number of ELF Pulses Identified as Cloud to Ground Lightning Which Were Also Detected by Meteorage in Two 48 h Periods, July 2005 and 6 7 September 2005, and the Effectiveness Parameter EI Polarity the group velocity u( f ) and an expression from Jones and Knott [1999] for the damping coefficient a( f ) ðf Þ ¼ July September 2005 Number EI(%) Number EI(%) CG , CG All , hðfþ ¼ 9: lnð0:01f Þ ½mŠ ð8þ ðf Þ ¼ 7: f 0:64 ½1=mŠ ð9þ c 1:64 0:1759 ln f þ 0:0179ðln f Þ 2 m=s ½ Š; ð10þ where c is the speed of light and f frequency. Equations (8) (10) are empirical fits where the frequency f should be a number in Hz and the speed of light in m/s. The dimension of each result is given in the square bracket at the end of each equation. [19] Since the ionospheric height h 10 2 km and the distance from Hylaty to the lightning flashes detected by Meteorage is 10 3 km (equation (7)) for the field in the far zone should be used. By combining equations (7), (8), (9), (10) and (5) we obtain the following expression for the lightning dipole moment p, B pulse p ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð11þ 2 Df 2 R H ð2þ 2rf u e ðf Þ rðf Þ gðfþ ðf Þ t 2 0 hðfþðf Þ df [20] Equation (11) is the formula for calculations of the dipole moment of the lightning flashes detected by our automatic algorithm described in section 3, taking into account the characteristics of the Hylaty receiver: c = 1 (for the case of a receiver with Chebyshev anti alias filters [Kulak et al., 2010]), Df = 66.1 Hz, and g( f ) = 1 for f 66.1 Hz and g( f ) = 0 for f > 66.1 Hz. We also assume that the spectral characteristics of the lightning source is flat in this frequency range, i.e., ( f ) 1[Jones, 1970; Burke and Jones, 1996]. Thus the dipole moment can be calculated knowing the field amplitudes B pulse in the ELF signal, the ELF receiver characteristics (c, g( f )), and the distance from the lightning to the receiver r (here calculated from the geographic coordinates from the Meteorage data sets). 5. Results [21] We present here the results of the identification of ELF transients in Hylaty data related to the CGs detected by Meteorage over the two selected thunderstorms in July and 6 7 September 2005 (as described in section 3). Table 1 presents the number of negative and positive flashes and the total number of the identified lightning flashes. Next to the these numbers is the percentage of the flashes identified in ELF data to the number of CG lightning detected by Meteorage, called EI, a parameter of the effectiveness of the method. [22] Below we analyze the effectiveness parameter EI in more detail. Figure 5 shows the time variation of this parameter in the two considered periods. The parameter significantly decreased in the evening hours of 28 and 29 July 2005 and night hours at the end of 7 September Those are periods where thunderstorm activity was also present near the Hylaty station (up to a few hundreds km from Hylaty). It is clear though from this plot that when no local thunderstorm activity is present EI rises above 10% and stays between 10 and 25%. [23] The difference between the EI in the two periods (Table 1 and Figure 5; EI is approximately twice as high on 6 7 September as on July) could be again related to the thunderstorm activity near Hylaty which decreases the efficiency of the identification. Analyzing the dependence of EI on the lightning distance from Hylaty we observe that EI slightly decreases in the distance range from 1200 to 2400 km (Figure 6). The larger variations of the EI at small (<1200 km) and large distances (>2400 km) are statistical fluctuations of the EI due to a small number of lightning events in these distance ranges (Figure 3). [24] Another histogram (normalized to the total number of flashes) in Figure 7 shows how the EI changes with the flash peak current I max (5 ka bins). Different levels of EI in the two cases seems to be again mainly due to local thunderstorm activity which enables identification of CG related ELF impulses with sufficiently accurate determination of their amplitude. In both cases, independently of the stroke polarization, the EI tends to saturate, with I max increasing by 20% and 60%. Therefore a 100% EI cannot be expected even in favorable observation conditions and even with very high values of I max. [25] The flashes identified in the ELF data in this analysis are a subset of flashes detected by Meteorage. Means and medians of the peak current have been calculated for the Figure 5. Time variation of the effectiveness parameter EI of the CG detection in ELF Hylaty data in two 48 h periods July 2005 and 6 7 September of9

7 Table 2. Main Statistical Parameters (Mean and Median) of the Peak Current I max Determined by the Meteorage in Two 48 h Periods, July 2005 and 6 7 September 2005, for the ELF Impulses Identified as the CG Lightning (ELF) and All Discharges Detected by Meteorage (MET) Polarity Peak Current (ka) July September 2005 Mean Median Mean Median CG (MET) CG (ELF) CG (MET) CG (ELF) Figure 6. Changes of the effectiveness parameter EI with the distance from the lightning to the ELF Hylaty receiver for the two 48 h periods July 2005 and 6 7 September subset of the ELF detected flashes and the total of flashes from Meteorage, and are shown in Table 2. The mean values are almost identical for ELF detected +CGs and CGs. The ratio of the average peak current for the ELF detected flashes to the mean peak current of CGs from the Meteorage data set is 2.2 and 1.5 for the positive CGs and negative CGs, respectively. This implies that flashes with higher peak currents are more likely to be identified in ELF data, as expected. However, the higher ratio for +CGs requires more consideration. [26] Having identified the lightning flashes in our ELF data in the next step we calculate the lightning dipole moment for each lightning stroke according to equation (11). The results are presented in Figure 8. [27] The largest group of identified flashes have the dipole moment in the range of Ckm, independently of the flash polarization. Basic statistics of the distributions are listed in Table 3. [28] The ratio of the mean dipole moment of the positive strokes to the mean dipole moment of the negative strokes is similar in these two cases and equal to 2.03 in the July case and 1.96 in September. [29] In Figure 9 we show the dipole moment p as the function of the return stroke current I max. The technique that we applied to calculate the dipole moment gives similar distributions of the lightning dipole moment (versus the peak current) and average values as in previous studies [Füllekrug and Constable, 2000; Hu et al., 2002; Cummer and Lyons, 2005; Neubert et al., 2005]. [30] In addition, for each of the two periods we found a linear dependency of the lightning dipole moment on the lightning peak current and the correlation coefficient (with the significance level less than ), 28 19; Jul; 2005 p ¼ 7:44ð0:07ÞI max þ 1:6ð2:0Þ; R ¼ 0:78 6 7; Sep 2005 p ¼ 7:53ð0:03ÞI max þ 6:7ð1:0Þ; R ¼ 0:67; ð12þ Figure 7. Cloud to ground lightning detection effectiveness EI as a function of the peak current of the lightning flashes detected by Meteorage in two 48 h periods, July 2005 and 6 7 September 2005, and identified as impulses in Hylaty ELF data. Figure 8. Distribution of the lightning dipole moment for lightning flashes detected by Meteorage in two 48 h periods, July 2005 and 6 7 September 2005, and identified in Hylaty ELF data. 7of9

8 Table 3. Main Statistical Parameters (Mean, Standard Deviation, and Maximum) of the Lightning Dipole Moment Calculated From the ELF Impulses Identified as CG Lightning in Two 48 h Periods, July 2005 and 6 7 September 2005 Polarity Dipole Moment (Ckm) July September 2005 Mean SD Max Mean SD Max CG CG where the peak current I max is expressed in kiloamps and the dipole moment in coulomb kilometers. The coefficients of the linear regression are equal within the error limits which implies an average relation between the dipole moment and the peak current is the same in the two periods and equals 7.5. The offset coefficient in the regression analysis, which in theory should be zero, is positive in both cases. In addition, the larger value of the offset the smaller the correlation coefficient R becomes, and therefore the offset could be used as a relative error estimate. Despite a welldefined dependency between I max and p we observe significant dispersion of the dipole moment. There are a few reasons leading to such dispersion. First, only signals which the amplitude error db i is less than 30% of B i have been considered in the analysis; this explains less than half of the dispersion. Secondly, the method assumes the lightning current can be described in quasi static approximation and does not take into account the lightning continuing current (which affects B pulse [Kulak et al., 2010]) or multistrokes [Rakov and Uman, 1994; Heavner et al., 2002] or strokes occurring simultaneously at a different location. 6. Summary [31] Observations by the lightning detection network Meteorage and single station magnetic ELF measurements at Hylaty have been used. Due to the frequent occurrence of the pressure systems described in section 2.2 and due to the relatively frequent occurrence of the scenario of the development and travel of atmospheric fronts across Europe (with their accompanying thunderstorms [van Delden, 2001; Bielec Bakowska, 2003]) the ELF measurements performed in the Bieszczady Mountains seem to present themselves as a natural complement and an enhancement of measurement results obtained by lightning detection systems in western Europe. [32] A numerical automatic technique of identification of lightning flashes as ELF impulses and a method of calculation of the lighting dipole moment have been developed and applied to the observational data. The method takes into account various factors affecting the measured magnetic impulse generated by cloud to ground lightning such as the bandwidth of the ELF receiver and it uses the correct wave solutions for EM field in the Earth ionosphere waveguide reducing the effect of the distance between the source and the receiver on the recorded signal. [33] Main advantages of the analysis and the method are as follows. (1) Identification of CG related ELF impulses is based on simple and quick algorithm. This creates a possibility of determination of the lightning dipole moment in addition to other data from conventional lightning detection systems. (2) Errors defined in the method can be used to estimate the reliability of the impulse identification process. (3) ELF receivers are low cost and a single station is sufficient to use such a method with a conventional VLF system, located in the distance of > 1000 km. (4) Lightning dipole moment of cloud to ground lightning can be obtained via a new method. [34] Main disadvantages of the method are as follows. (1) The identification efficiency parameter (EI) on average does not exceed 25%. (2) EI is strongly dependent on the lightning peak current I max (increases with higher peak currents) and does not exceed 60% even for I max >= 100 ka. (3) Local thunderstorm activity (near the ELF receiver) decreases the identification efficiency. [35] Using the method presented here we calculated the lightning dipole moment for 70,000 lightning flashes in a thunderstorm system. Average values and distribution of the dipole moment as a function of the lightning peak current are consistent with results obtained using different methods. The relation between the dipole moment and the peak current in equation (12) can potentially be applied in the studies Figure 9. Lightning dipole moment p as a function of the peak current I max of the CG lightning identified in Hylaty ELF data from two 48 h periods: (left) July 2005 and (right) 6 7 September of9

9 of the cloud electricity and global atmospheric circuit studies [Rycroft and Odzimek, 2010]. In addition, by comparing the azimuth angle to lightning strokes obtained from ELF observations by the method described in section 3 and the azimuth calculated from the strokes coordinates, some physical properties of the Earth ionosphere waveguide can be investigated [Füllekrug et al., 1996; Füllekrug and Sukhorukov, 1999]. [36] Acknowledgments. This work has been supported by the Polish Ministry of Science and Higher Education grant N /2568. We thank Torsten Neubert and the National Space Institute, Technical University of Denmark, and the Meteorage company for access to lightning data. A. Odzimek acknowledges support from the European Commission, grant PERG GA , 7th European Community Framework Programme (FP7). References Belyaev, P. P., S. V. Polyakov, V. O. Rapoport, and V. Y. 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Kulak, Department of Electronics, Academy of Mining and Metallurgy, Al. Mickiewicza 30, Krakow, Poland. (radiol1@wp.pl) Z. Nieckarz, Institute of Physics, Jagiellonian University, Reymonta 4, Krakow, Poland. (zenon.nieckarz@uj.edu.pl) A. Odzimek, Institute of Geophysics, Polish Academy of Sciences, Ksiecia Janusza 64, Warsaw, Poland. (aodzimek@igf.edu.pl) S. Zieba, Astronomical Observatory, Jagiellonian University, Orla 171, Krakow, Poland. (ulaistan@wp.pl) 9of9