Early phase of lightning currents measured in a short tower associated with direct and nearby lightning strikes

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2010jd014097, 2010 Early phase of lightning currents measured in a short tower associated with direct and nearby lightning strikes Silverio Visacro, 1 Maria Helena Murta Vale, 1 Guilherme Correa, 1 and Andre Teixeira 1 Received 23 February 2010; revised 23 March 2010; accepted 5 April 2010; published 19 August [1] Records of natural lightning currents of negative downward strokes measured at the base of a 60 m high instrumented tower are presented to denote patterns of their early phase. Such patterns in the records of five flashes and two upward unconnected leaders are discussed. Typical profiles of this early phase, comprising the pre return stroke pulses of the current flowing upwards the tower in response to the downward stepped leader approaching the ground, the concavity in the initial rising part of the return stroke waveform, and the abrupt rise around the half peak of the first stroke waveform, are remarked. Statistics are developed for the pre return stroke pulses of current to characterize their amplitude, duration, interval, and risetime for both the first stroke and upward unconnected leaders, which proved to be quite similar. The ratio of the maximum pulse peak to first stroke peak is typically in the range 0.7% to 2.2% of the analyzed currents, different from the value of around 10% found for the distant electric fields radiated by first stroke currents. Citation: Visacro, S., M. H. Murta Vale, G. Correa, and A. Teixeira (2010), Early phase of lightning currents measured in a short tower associated with direct and nearby lightning strikes, J. Geophys. Res., 115,, doi: /2010jd Introduction [2] The knowledge about lightning currents is extremely relevant since they are the main source of lightning effects. Additionally some aspects of the physical processes involved in the lightning discharge formation can be inferred from the patterns of such currents. [3] In most cases the analysis of lightning currents focuses on their impulsive waveform associated with the return stroke, with special interest in the parameters related to the amplitude and front time, such as the peak value and maximum time derivative. Researchers [Visacro, 2004; Berger et al., 1975; Anderson and Eriksson, 1980; Visacro et al., 2004; Rakov and Uman, 2003] consider such aspects in detail. Traditionally, these parameters are obtained from measurements performed at instrumented towers, where a current threshold is usually adopted to trigger the device responsible for recording the current wave. In most cases the record of the current preceding the threshold is lost or has very poor resolution. [4] The early phase of lightning currents comprises the pre return stroke pulses of current flowing along instrumented towers in response to the downward leader that approaches the ground and is associated with the formation of upward leaders, the initial rising part of the return stroke waveform and the abrupt rise of current that leads to the first 1 Lightning Research Center, Federal University of Minas Gerais, Belo Horizonte, Brazil. Copyright 2010 by the American Geophysical Union /10/2010JD peak. This phase is relevant in first strokes and is partially responsible for the great difference in the wavefront of negative first and subsequent stroke currents. Unfortunately, in natural lightning currents this phase is poorly registered. Most of the knowledge about it has been inferred from measurements of electric fields radiated by such currents [Krider and Radda, 1975; Krider et al., 1977; Weidman and Krider, 1978; Willett et al., 1989, 1995, 1998]. Additionally, triggered lightning experiments have provided elements regarding this phase, as presented by Jerauld et al. [2007], in a detailed study of the lightning attachment process based on an unusual triggered lightning stroke. [5] This paper presents original data on the very early phase of currents of natural negative downward strokes measured at Morro do Cachimbo Station, in Brazil. Highquality resolution records corresponding to five flashes and two upward unconnected leaders were chosen for this analysis from events measured in the station during the last two years. Such records were obtained after the measuring system of this station was updated and digitized. This allowed the use of a pre trigger function to record the current before the threshold with a very high resolution for both currentamplitude and time scales. To the best of authors knowledge, this is the first time that records of such current phase have been published for natural negative downward lightning strokes. Two records of currents of upward unconnected leaders flowing along the tower complement information provided by the record by Schoene et al. [2008] of the current flowing along a vertical conductor in response to a nearby natural lightning strike to the ground. Since only six to ten flashes are recorded per year, several more years are required to ensure statistical significance to the data of 1of11

2 measurements obtained at the instrumented tower. But to some extent, under a representative approach, the available data allow us to characterize typical patterns of this phase of lightning currents. While data are being acquired, the authors would like to share their results with the lightning research community. 2. Electric Fields Radiate from Distant Natural Lightning Currents [6] As previously mentioned, most patterns of the early phase of lightning currents are inferred from measurements of radiated electric fields. In this respect, the works by Krider and Radda [1975], Krider et al. [1977], and Weidman and Krider [1978] are noteworthy contributions. These scientific contributions denote that the radiated fields produced by first stroke lightning discharges to the ground and measured at distances of several tens of kilometers have structures that are quite similar for different discharges. They also denote the similar structures of electric fields radiated by different subsequent return strokes both in the same discharge and in different ones. Figure 1 illustrates such patterns. [7] In the electric field records, a sequence of small pulses (L pulses) preceding the return strokes are associated with stepped leaders. This is clearly seen in the typical profiles of first stroke fields in Figure 1a. The return stroke begins slowly with a pronounced concavity or front [Krider and Radda, 1975; Krider et al., 1977] that is followed by an abrupt rise that lasts until the first peak. The majority of fronts are concave, although they occasionally appear convex, possibly because a strong pulse (associated with a stepped leader close to the ground) superimposes on the initial rise. [8] Quoting Weidman and Krider [1978], The first stroke begins with an initial portion or front which rises slowly for 2 8 ms to about half of the peak field amplitude. Return strokes subsequent to the first have initial fronts which last ms, on the average, and which rise to about 20% of the peak field. Following the front, both first and subsequent stroke waveforms rise abruptly to peak with 10 90% risetimes of 0.2 ms or less when the field propagation is over seawater. After the initial peak most strokes have a small second peak or shoulder within about 2 ms, and all first strokes have several large subsidiary peaks at intervals of ms following the first peak. [9] According to Weidman and Krider [1978], most field records of subsequent return strokes present no L pulses, depicting a smooth profile before the return stroke current, such as the one in Figure 1b. This occurs when the subsequent stroke is preceded by a dart leader. L pulses are observed in some cases as depicted in Figure 1c, and this has been attributed to subsequent strokes preceded by a dart stepped leader. 2of11 Figure 1. Typical profiles of distant electric field records: (a) first strokes, (b) subsequent strokes preceded by a dart leader, and (c) subsequent strokes preceded by a dartstepped leader. L corresponds to the small pulses characteristic of leader steps. The field amplitudes are normalized to a distance of 100 km. The lower trace in each case shows the field on a time scale of 20 ms/division, and the upper trace is at 5 ms/division. The origin of the time axis is chosen at the peak field in each trace. Adapted from Weidman and Krider [1978].

3 3.2. Measurement Setup [12] Figure 2 shows a view of Morro do Cachimbo Station, Brazil [Visacro et al., 2004], including its 60 m high freestanding mast. Two Pearson coils installed at the base of the mast measure lightning currents, within a range from 20 A to 200 ka. The current transducers feed an eight channel data acquisition board with a sampling rate of 60 MS/s. Figure 2. View of Morro do Cachimbo Station, Brazil. [10] According to Krider et al. [1977], when referring to the statistics for leader pulses within a 200 ms period before the return stroke, the average pulse interval is 15.9 and 25.3 ms for first stroke and 6.5 and 7.8 ms for subsequent strokes as measured in Florida and Arizona, respectively. The average leader pulse front time (10% to 90%) is 0.2 to 0.3 ms in Florida to distances in the km range and the average width of the leader pulse at half peak signal is in the range ms. The average ratio of the maximum field pulse amplitude to the peak field (return stroke) is 13% in Florida and 7% in Arizona for the first stroke and 9% and 14% for subsequent strokes in Florida and Arizona, respectively. According to the authors such field pulses would be associated with currents in the range 2 8 ka. 3. Early Phase of Natural Lightning Currents Measured at a Short Instrumented Tower 3.1. Introduction [11] Records of currents measured at a short instrumented tower are presented herein to denote details of their early phase. All the records are from negative lightning, presumably downward strokes due to the current patterns at the wavefront and in the pre return stroke period Recent Improvements to the Measuring System [13] Once the station measuring system was updated, the recording capability vastly improved. Presently, 1 s continuous records are stored for each current exceeding 60 A flowing along the tower, with a 33 ns time resolution and a 30 ms pre trigger period. This system may also be configured to store 0.5 s long records with a 17 ns resolution and 15 ms pre trigger period. [14] Figure 3 illustrates the possibility to explore different windows of time and current amplitude to reveal details of measured currents, considering the first stroke of a sevenstroke flash measured in 7 October A full 1 s record was recorded in two current scales, 9 ka and 200 ka. In Figure 3a six of such strokes are seen in a 0.5 s window. In Figures 3b, 3c, and 3d the window of time is decreased to depict details of the impulsive waveform of the first stroke current, including the beginning of the maximum time derivative around the half peak (I P1: first peak current). [15] Figures 3e, 3f, and 3g depict details of the pre returnstroke pulses of current corresponding to the displacement of electrons down the tower in response to the stepped leader approaching the ground. Conventionally, this corresponds to positive pulses of current flowing toward the tower top; however, in this paper the current of such pulses was considered negative in order to make their signal compatible with that of negative return stroke currents, which are responsible for transferring negative charge from cloud to ground. To keep the same approach, the current corresponding to the discharge of upward unconnected leaders was considered positive Typical Profile of First Stroke Currents [16] Two examples of first negative currents with different intensity levels are presented in Figures 4 and 5. In both cases, unipolar pulses of current larger than 20 A are observed from a few milliseconds before the return stroke current, with a few microseconds front time and average duration around 10 ms. [17] The profiles of the pre return stroke pulses of all first currents, with the exception of that mentioned in section 3.6, show quite similar trends, including an interpeak interval around 50 ms in the final 1 ms period. This similarity also applies to the very pronounced concavity at the return stroke wavefront, to the position of the abrupt rise around the half peak and to the presence of several subsidiary peaks or shoulders, being the time elapsed between the first and second peaks typically much shorter than the interval between the other peaks, as commented by Visacro [2004]. In some first stroke waveforms, such as the one shown in Figure 3d, a packet of noise is observed a little before the increase in the time derivative of current. For the time being, the origin of this effect is not clear. 3of11

4 Figure 3. Measured lightning current record shown in different scales of time and amplitude, including the windows A (from Figure 3f) and B (from Figure 3g), as indicated in Figure 3e. [18] The amplitude of pre return stroke pulses seems to be influenced by the amount of charge deposited along the downward leader as depicted in the scatterplot shown later in Figure 9. The integration of the waveforms of the returnstroke currents in Figures 4 and 5 during the first 500 ms after the last pulse provides a rough estimate of the charge they transferred to the ground, around 22 and 7 C, respectively, for the strokes with 153 and 47 ka peak currents. The peak of the highest current pulse exceeds 3 ka for the 153 ka stroke and is superimposed to a continuous current that becomes evident around 300 ms prior to the return stroke current. This uprising current corresponds to the beginning 4of11

5 Smooth current profile: Second stroke, 31 Octo- Figure 6. ber Figure 4. Current of an intense first negative stroke: Singleflash, 1 February of the concavity at the return stroke current wavefront. It is believed that the pulses before this uprising current are caused mainly by an inducing effect associated with the charge displaced to the downward leader extremity at each step. The larger pulses superimposed to the uprising current are expected to be associated with the formation of upward leaders. The same profile is observed for the 48 ka stroke, though the amplitude of the current pulses is much lower, around 400 A. The peak of the highest pulse is around 2% of the return current peak for the intense currents and around 1% for moderate currents, much smaller than the value of around 10% found for electric fields (13% and 7 % according to Weidman and Krider [1978]). Figure 5. Current of a moderate first negative stroke: Multiple flash, 31 October Figure 7. Unusual smooth profile of a first stroke current: two scales, 24 February of11

6 3.5. Typical Profile of Subsequent Stroke Currents [19] No current of subsequent strokes measured at the base of the tower showed the field record patterns of Figure 1c. The typical profile of the early stage of the measured lightning currents in subsequent strokes is shown in Figure 6. Basically, no pulses with amplitude larger than 10 A (corresponding to the noise level) were observed in the measured subsequent strokes. Only in two records was a set of pulses observed in the last 50 ms prior to the return stroke current, superimposed to an uprising continuous current, with a very short interpeak interval, around 10 ms. It is not clear whether the lack of L pulses is due to the charging of the lightning channel by a dart leader or if the L pulses caused by a dart stepped leader are not observed due to the noise level. [20] It is known from radiated electric field signatures that, in some cases, subsequent currents present L pulses. In such cases, the charging of channel before the return stroke is attributed to dart stepped leaders. It seems likely that at least part of the electric field pulses attributed to dartstepped leaders are in fact due to subsequent strokes that create new channel terminations to the ground, since the construction of such terminations involves a process similar to the evolution of stepped leaders of first strokes that are expected to radiate pre return stroke pulses. Figure 8. Measured current profile of two upward unconnected leaders, measured in (a) 30 March 2009 and (b) 31 October Unusual Profile for a First Stroke Current [21] The current waveform of a first stroke of a multiple flash measured on 24 February (2008) and depicted in Figure 7 has an unusual aspect. The current profile in the early phase is very smooth, and no pre return stroke pulses are observed. This suggests that no stepped leaders occurred during the channel formation. [22] Apparently, the reason for this unusual profile was explained later, when the authors correlated the stroke event with the data from the lightning location system installed in the state of Minas Gerais, whose location accuracy is estimated to be about 500 m at the tower proximities. Though the event was the current of a first stroke to the tower, it was indeed the second stroke of a multiple flash (four stroke flash) whose first stroke occurred nearby the tower. The solution given by the location system for the time correlated first stroke is approximately 300 m distant from the tower. Therefore, the record had naturally the typical profile of a subsequent stroke current. Table 1. Recorded Currents: First Strokes and Upward Unconnected Leaders Date Type of Event First Pulse Detection (ms) Before Return Stroke Peak Current (ka) Return Stroke Ratio I P mp /I P rc (%) a 1 Feb First One stroke flash Feb First Four stroke flash b Oct First Nine stroke flash Mar First Three stroke flash Oct First Six stroke flash Before Upward Leader Collapse Discharge After the Upward Leader Collapse 31 Oct Upward unconnected leader Three stroke flash c March 2009 Upward unconnected leader One stroke flash d a I P mp, largest peak of the pre return stroke pulses of current; I P rc, return stroke peak current. b This event was a first stroke to the tower but was the second stroke of a four stroke flash. c Distance of lightning strike to ground: few hundreds meters. d Distance of lightning strike to ground: around 2 km. 6of11

7 Figure 9. Scatterplot of the maximum pulse peak and the return stroke peak current of measured first strokes Current Profile of Upward Unconnected Leaders [23] Another interesting experimental result obtained by the authors refers to the current of upward unconnected leaders. Figure 8 shows two nice and detailed records associated with the current of such events that correspond to the onset and development of upward leaders that fail to connect to the downward leader. [24] In both cases the profile of current is quite similar to that of regular first strokes before the return stroke. The short unipolar pulses corresponding to the response to the stepped leader approaching the ground follow the same patterns, including the interpeak interval around 50 ms. However, while in the first strokes the current experiences a continuous and consistent increase from a few hundreds of microseconds before the return stroke, in both upward unconnected leaders the current rises but retains a certain value, without evolving, until the process collapses. The positive charge deposited at the structure extremity and along the upward leader is then discharged to the ground, causing the flow of a relatively intense current. In the presented cases, after a short time (less than 10 ms) the discharge current reaches a peak estimated to be around 800 A in the first record and around 400 A in the second one. The highest positive peak pulses have intensity around 250 A in both cases and occurred just prior to the collapse of the deposited charge. 4. Quantitative Evaluations for the Recorded Currents 4.1. General Considerations [25] Although only five flashes and two upward unconnected leaders are available for analysis, the authors believe it would be instructive to have statistics on the corresponding data. Table 1 indicates the recorded events, and Figures 9 14 characterize some of their parameters. Particularly, Figure 9 shows a scatterplot of the maximum pulse peak and the return stroke peak current for the measured first strokes. [26] The plot suggests a significant influence of the amount of charge deposited along the downward leader on the amplitude of the pre return stroke current pulses. Figure 10. The amplitude of pre return stroke pulses of current: first strokes (a) 153 ka current included and (b) excluded; (c) upward unconnected leaders. 7of11

8 [28] The histograms of Figure 10a indicate that the median pulse peak is 263 A for connecting leader pulses in the case of a first stroke in a negative flash, when all records are considered. Because the large charge of the 153 ka stroke greatly influences this value, another mean was calculated excluding the pulses of such current, Figure 10b. In this case, the mean pulse peak was decreased to 79 A, less than one third of the previous mean. [29] The pulses of the two upward unconnected leaders are quite similar to those of the first strokes. Per Figure 10c, the mean peak value of the pulses in upward unconnected leaders is 86 A. Differences are observed only during the last 300 ms before the onset of the return stroke current. In this interval, as in the first strokes, the pulse peaks exceed 100 A and are superimposed to a continuous current. However, this current remains stable, and the pulse peaks do not evolve but remain limited to less than 200 A until the process collapses. Figure 11. The interpulse interval: (a) first strokes and (b) upward unconnected leaders The Amplitude of the Pre Return Stroke Pulses of Current [27] In the analyzed cases of first strokes, unipolar prereturn stroke pulses of current were observed from a few milliseconds before the return stroke current ( ms), with typical amplitude ranging from a few tens to a few hundreds of amperes. The pulses begin with low amplitudes, around 20 A, and most of them remain lower than 50 A before a time threshold, around 300 ms prior to the returnstroke current. Only after that do the pulse peaks exceed 100 A and are superimposed to an uprising continuous current. However, in this final period the amplitude of such pulses may reach very high values, from a few hundred to a few thousand amperes. It is clear that the charge accumulated in the downward leader influences the amplitude of the pulses, but only in this final phase. In the record of the unusual 153 ka first negative stroke, several pulse peaks were higher than 1 ka, and one of them exceeded 3 ka. Figure 12. The duration of pre return stroke pulses of current (full width at half peak): (a) first strokes and (b) upward unconnected leaders. 8of11

9 Figure 13. The risetime of pre return stroke pulses of current: (a) first strokes and (b) upward unconnected leaders. [30] It is important to emphasize the difference in the ratio of the maximum pulse peak to the peak of the measured return stroke current in relation to the corresponding ratio of electric fields records. The average value of this ratio is 13% and 7% for electric fields of first strokes in Florida and Arizona, respectively, according to Krider et al. [1977]. The measured data indicated this ratio to be lower than 1% for most of the measured currents, reaching 2.25% only in the unusual case of the 153 ka current. This difference is explained by the fact that the measured peak fields are in fact directly associated with the pulses of discharge current of the downward stepped leader and not to the low amplitude pulses of upward currents induced in the tower in response to this downward leader. This result suggests that, in most cases, the pulses of current in the ground are expected to be much lower than the 2 8 ka predicted by Krider et al. [1977] for the leader step current near the ground The Interpulse Interval [31] The interpeak intervals of the pre return stroke pulses in the individual first stroke and also in the upward unconnected leaders are similar for all currents, with a typical average value around 50 ms during the last 1 ms prior to the return stroke current. [32] The histograms in Figure 11 show the distribution of the interpulse interval, here defined as the time elapsed between the end of the preceding pulse and the beginning of the next one. Typically this interval is shorter than 50 ms for both first strokes and upward unconnected leaders. However, before the last 1 ms prior to the return stroke current, the interval of the first pulses is usually long (hundreds of microseconds in some cases), and this affects significantly the mean value of this interval, displacing it to around 62 and 69 ms for the first strokes and upward unconnected leaders respectively The Duration of the Pre Return Stroke Pulses of Current [33] The pulse duration is here defined as the full width of the pulse at half peak. The histograms depicted in Figure 12 indicate similar mean durations for the pulses of first strokes and upward unconnected leaders, around 7.5 and 8.0 ms, respectively. The difference is attributed to the limited number of samples analyzed. The majority of the pulses last less than 12.5 ms and only in very few cases exceed 20 ms The Risetime of the Pre Return Stroke Pulses of Current [34] The majority of the low amplitude pre return stroke pulses of first strokes and upward unconnected leaders have waveforms that are almost symmetrical in relation to the peak time, as depicted in Figures 3f and 3g, though the decay time tends to be larger than the risetime. This trend appears to be different for the high amplitude pulses (larger than 100 A), where the risetime appears to be much shorter than the decay time. [35] The histograms of Figure 13 indicate median values for the risetime of the pulses of first strokes and upward unconnected leaders of around 4 and 4.9 ms, respectively, the same order of magnitude of return stroke current risetime in first strokes. This typical range of risetimes observed in the individual records are quite different from the typical ms risetimes observed in the pulses of electric field records [Krider et al., 1977] Comments on Parameters of the Pre Return Stroke Current Pulses in Subsequent Strokes [36] The measured records of subsequent strokes do not include the current of any dart stepped leaders. Pulses are observed only at the very last moment before the returnstroke current. Nonetheless, the authors believe it is pertinent to present a brief comment on such pulses. The basic profile presented in Figure 14 was observed in subsequentstroke records. [37] Around 100 ms prior to the return stroke current, short A pulses begin to be observed with peak intervals of about 10 ms. Around 50 ms later, an uprising continuous current superimposes such pulses. In this phase the pulses amplitude substantially increased to more than 100 A, and the peak intervals appear to decrease slowly until the return 9of11

10 Figure 14. Illustrative record of pre return stroke pulses of a subsequent current: second stroke in a three stroke flash, 24 March stroke current is established. The duration and the risetime of such larger pulses are typically short. Most pulses last less than 7 ms and have risetimes shorter than 2 ms. 5. Summary and Conclusions [38] Some rare experimental results corresponding to the records of five negative lightning flashes and two upward unconnected leaders measured at a short instrumented tower were presented and analyzed in different windows of time and current amplitude to reveal their main patterns. To the best of the authors knowledge, this is the first time this early phase of natural lightning currents has been published in such details. The results are considered a contribution to complement information about such patterns, which have been basically inferred from radiated fields or from triggered lightning experiments as commented by Rakov et al. [1998]. [39] For the analyzed cases, typical profiles of currents of first strokes, of subsequent strokes preceded by a dart leader, and of upward unconnected leaders were presented, and they seemed all consistent with profiles predicted from distant electric fields radiated by lightning currents. For the first strokes, this includes the pre return stroke pulses, the very pronounced concavity at the current wavefront, the abrupt rise around the half peak, and the subsidiary peaks along the current wave. Double peaks were observed in the measured first stroke currents, though the time elapsed between them was always longer than 4 ms, different from the typical value around 2 ms in the electric field signatures mentioned by Weidman and Krider [1978]. [40] Some characteristics of the unipolar pulses before the return stroke current and before the current collapse in upward unconnected leaders were analyzed. [41] In first strokes, their amplitude is typically in the range of A before a time threshold of about 300 ms prior to the return stroke current. Following these observations, some pulses exceeding 100 A are observed in most records, and, specifically in the 153 ka current, several pulses exceed 1 ka. It seems that the charge deposited along the stepped leader influences the amplitude of such pulse peaks in the final period, around 300 ms, prior to the return stroke. The mean pulse peak of about 80 A, obtained for a sample that excludes the pulses of the 153 ka return stroke, is increased to 260 A when the pulses of this stroke are included in the sample. The ratio of the maximum pulse peak to the peak of the measured return stroke current is lower than 1% for all measured currents, except for the 153 ka current (2.25%). Such values are much lower than the average ratio around 10% of the maximum pulse peak to peak electric field radiated by the current of distant first strokes [Krider et al., 1977]. Similar amplitudes were found for the peak of the upward unconnected leaders pulses, with a median value of 86 A. [42] The interpeak intervals for the pulses of individual first strokes and also of the upward unconnected leaders are similar for all currents, typically around 50 ms during the last 1 ms prior to the return stroke current. In subsequent stroke currents, pulses are observed only during the last 100 ms prior to the return stroke with a reduced interpeak interval, around 10 ms. The durations of the pulses in first strokes and upward unconnected leaders are short and similar, with mean values around 13 and 19 ms respectively. The risetimes are similar for pulses in first stroke and upward unconnected leader currents, with mean values in the range of 4 to 5 ms. [43] The parameters of the measured currents (pulse interval, duration, and risetime) are all considerably larger than the corresponding parameters of distant electric field records mentioned by Krider et al. [1977]. [44] In the first strokes, an uprising continuous current begins about ms prior to the return stroke current and is responsible for the pronounced concavity in the wavefront. In subsequent strokes this continuous current starts later, nearly 50 ms prior to the return stroke current. In both cases this current is superimposed to pulses exceeding 100 A, but their interpeak interval is shorter in subsequent strokes, nearly 10 ms, compared to 50 ms in first strokes. [45] Acknowledgment. This work was supported in part by CNPq grant / References Anderson, R. B., and A. J. Eriksson (1980), Lightning parameters for engineering application, Electra, 69, Berger, K., R. B. Anderson, and H. Kröninger (1975), Parameters of lightning flashes, Electra, 41, Krider, E. P., and G. J. 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DeCarlo (2008), Lightning induced currents in a buried loop conductor and a grounded vertical conductor, IEEE Trans. EMC (50), no. 1, pp of 11

11 Visacro, S. (2004), A representative curve for lightning current waveshape of first negative stroke, Geophys. Res. Lett., 31, L07112, doi: / 2004GL Visacro, S., A. Soares Jr., and M. A. O. Schroeder et al. (2004), Statistical analysis of lightning current parameters: Measurements at Morro do Cachimbo station, J. Geophys. Res., 109, D01105, doi: / 2003JD Weidman, C. D., and E. P. Krider (1978), The fine structure of lightning return stroke wave forms, J. Geophys. Res., 83(C12), doi: / JC083iC12p Willett, J. C., J. C. Bailey, V. P. Idone, A. Eybert Berard, and L. Barret (1989), Submicrosecond intercomparison of radiation fields and currents in triggered lightning return strokes based on the transmission line model, J. Geophys. Res., 94(D11), doi: /jd094id11p Willett, J. C., D. M. Le Vine, and V. P. Idone (1995), Lightning channel morphology revealed by return stroke radiation field waveforms, J. Geophys. Res., 100(D2), doi: /94jd Willett, J. C., E. P. Krider, and C. Leteinturier (1998), Submicrosecond field variations during the onset of first return strokes in cloud to ground lightning, J. Geophys. Res., 103(D8), doi: /98jd G.Correa,M.H.MurtaVale,A.Teixeira,andS.Visacro,Lightning Research Center, Federal University of Minas Gerais, Av. Antonio Carlos 6627, Pampulha, , Belo Horizonte, Brazil. (Lrc@cpdee. ufmg.br) 11 of 11