Measured electric and magnetic fields from an unusual cloud-to … · 2013-06-02 · Measured...

Measured electric and magnetic fields from an unusual

cloud-to-ground lightning flash containing two positive

strokes followed by four negative strokes

J. E. Jerauld,1,2 M. A. Uman,1 V. A. Rakov,1 K. J. Rambo,1 D. M. Jordan,1

and G. H. Schnetzer1

Received 22 December 2008; revised 29 May 2009; accepted 22 July 2009; published 13 October 2009.

[1] We present electric and magnetic fields measured at multiple stations between about300 and 800 m of a cloud-to-ground ‘‘bipolar’’ lightning flash containing two initialpositive strokes, separated in time by 53 ms and striking ground at two locations separatedby about 800 m, followed by four negative strokes that traversed the same path as thesecond positive stroke. The leader electric field durations for the positive first, positivesecond, and negative third strokes were about 120 ms, 35 ms, and 1 ms, respectively.The first-stroke leader electric field changes measured at five stations ranged from about+16 to +35 kV/m, the second stroke +8 to +13 kV/m, and the third stroke �0.9 to�1.8 kV/m (atmospheric electricity sign convention). The microsecond-scale return strokewaveforms of the first and second (positive) strokes exhibited a similar ‘‘slow-front/fast-transition’’ to those observed for close negative first strokes. The peak rate-of-changeof the positive first stroke electric field normalized to 100 km was about 20 V m�1 ms�1,similar to the values observed for close negative first strokes. The positive secondstroke was followed by a long continuing current of duration at least 400 ms, while thepositive first stroke had a total current duration of only about 1 ms. All four negativestrokes were followed by long continuing current, with durations ranging from about 70 msto about 230 ms. The overall flash duration was about 1.5 s.

Citation: Jerauld, J. E., M. A. Uman, V. A. Rakov, K. J. Rambo, D. M. Jordan, and G. H. Schnetzer (2009), Measured electric and

magnetic fields from an unusual cloud-to-ground lightning flash containing two positive strokes followed by four negative strokes,

J. Geophys. Res., 114, D19115, doi:10.1029/2008JD011660.

1. Introduction

[2] Jerauld et al. [2008] have described the measurementof the close electric and magnetic fields of stepped leadersand first return strokes in 18 cloud-to-ground lightningflashes that lowered negative charge to Earth. The fieldmeasurements were made simultaneously at multiple sta-tions located between 100 m and 1 km from the lightningstrike points, the multiple stations being arrayed over anarea of about 1 km2. In the course of these measurements,one unusual lightning flash, producing two channel termi-nations on ground and containing two strokes that loweredpositive charge followed by four strokes that lowerednegative charge, was observed. That ‘‘bipolar’’ lightningflash is the subject of the present paper which gives the firstwell documented description of a natural downward bipolarlightning flash. Additionally, electric and magnetic fieldmeasurements for the two positive strokes are among the

closest and most detailed that have been made for anypositive strokes.[3] ‘‘Positive lightning,’’ cloud-to-ground lightning that

lowers positive charge to ground, accounts for roughly 10%of all cloud-to-ground lightning worldwide, although thereis significant local and seasonal variability [Rakov andUman, 2003]. Positive discharges comprise the majorityof flashes in some winter storms (e.g., 60% in December inJapan according to Hojo et al. [1989]), while negativelightning is generally dominant in summer thunderstorms.Brook et al. [1982] found that positive flashes accounted forabout 40% of cloud-to-ground flashes in winter storms inJapan. Using U.S. National Lightning Detection Network(NLDN) data from 1992 to 1995, Orville and Silver [1997]reported that the monthly percentage of positive flashesover the contiguous United States ranged from about 3% inAugust 1992 to about 25% in December 1993. In a similarstudy using NLDN data from 1995 to 1997, Orville andHuffines [1999] reported monthly percentages of positiveflashes ranging from about 6% in July 1995 to about 25% inJanuary 1996. There is a tendency for positive lightning tooccur during the dissipating phase of individual thunder-storms [e.g., Fuquay, 1982], regardless of the season, and inthe trailing and final stages of mesoscale storm systems[e.g., Orville et al., 1988].

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, D19115, doi:10.1029/2008JD011660, 2009ClickHere

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1Department of Electrical and Computer Engineering, University ofFlorida, Gainesville, Florida, USA.

2Now at Raytheon Missile Systems, Tucson, Arizona, USA.

Copyright 2009 by the American Geophysical Union.0148-0227/09/2008JD011660$09.00

D19115 1 of 17

http://dx.doi.org/10.1029/2008JD011660

[4] The following are observed properties generallythought to be characteristic of positive lightning discharges[e.g., Rakov and Uman, 2003].[5] 1. Positive flashes are usually composed of a single

stroke (99.6% according to Lyons et al. [1998]), whereasabout 80% of negative flashes contain two or more strokes[Rakov and Huffines, 2003]. Further, Ishii et al. [1998]observed that subsequent strokes in multiple-stroke positiveflashes in winter storms in Japan always created a newtermination on ground.[6] 2. Positive return strokes tend to be followed by

continuing currents that typically have durations of tens tohundreds of millisecond [Rust et al., 1981; Fuquay, 1982],which are likely responsible for the unusually large chargetransfers associated with positive flashes [Brook et al.,1982].[7] 3. Electric field measurements appear to indicate that

positive return strokes are preceded by significant in-cloudactivity lasting, on average, in excess of 100 or 200 ms[Rust et al., 1981; Fuquay, 1982].[8] 4. Positive discharges have been reported [Fuquay,

1982] to involve long horizontal channels, up to 10 km inextent.[9] 5. Time-resolved optical images indicate that positive

leaders appear to move through virgin air either continu-ously or in a stepped fashion, in contrast to negative leaders,which are always optically stepped. Further, distant electricand magnetic fields from positive discharges are less likelyto exhibit clearly identifiable step pulses immediately priorto the return stroke waveform than are first strokes innegative lightning. The average downward speeds of pos-itive leaders are similar to those of negative leaders and bothgenerally increase as the leader nears the ground [Qie andKong, 2007; Saba et al., 2008; Schonland, 1956].[10] ‘‘Bipolar lightning,’’ cloud-to-ground lightning that

sequentially lowers both positive and negative charge toground, has not been as well studied as either negative orpositive lightning. The sparse data on bipolar lightningindicate that the majority of bipolar flashes is initiated byupward leaders from tall objects, events called ‘‘naturalupward lightning’’ [Berger, 1978]. In the data of Berger[1978], obtained between 1963 and 1973 at Mount SanSalvatore in Switzerland, bipolar flashes accounted for 72out of 1196 observed flashes (6%). Rakov [2005], based ona review of literature, states that bipolar flashes may notoccur less often than positive flashes, at least when tallobjects are involved, with bipolar flashes constituting 6 to14% of summer lightning in Europe and the United Statesand 3 to 33% of winter lightning in Japan.[11] All bipolar lightning flashes can be divided into three

categories, based on the characteristics of the currentpolarity reversal [Rakov and Uman, 2003; Rakov, 2003,2005]. Bipolar flashes of Type 1 involve a current andcharge polarity reversal during the initial stage of a naturalupward or a rocket-triggered (rocket trailing a groundedwire) lightning discharge. This initial stage is characterizedby a continuous current flow of the order of 100 A for atime of the order of tenths of a second during and followingthe propagation of an upward-going leader toward and intothe cloud charge. Bipolar flashes of Type 2 involve a changein current and charge polarity between the initial stage of anatural upward or a rocket-triggered lightning discharge and

return strokes that follow the initial stage. Type 3 bipolarflashes involve a polarity reversal between sequential returnstrokes. Type 3 flashes can be grouped into two subcatego-ries, with Type 3a events being natural upward or rocket-triggered lightning discharges, while Type 3b events arenatural downward cloud-to-ground flashes. Thus types 1, 2,and 3a are all associated with natural upward or rocket-triggered lightning discharges, while Type 3b is the onlynatural downward cloud-to-ground bipolar lightning and isthe type of bipolar lightning discussed in the present paper.Events of Type 1 have been reported by McEachron [1939],Davis and Standring [1947], Horii [1982], Hubert et al.[1984], Akiyama et al. [1985], Laroche et al. [1985], andLiu and Zhang [1998], the latter five studies beingconcerned with rocket-triggered lightning discharges.Events of Type 2 have been reported by Berger andVogelsanger [1966], Berger [1978], Nakahori et al.[1982], and Fernandez [1997], the latter study beingconcerned with rocket-triggered lightning discharges.Events of Type 3a have been reported by McEachron[1939], Berger and Vogelsanger [1965], Idone et al.[1987], Schulz and Diendorfer [2003], and Jerauld et al.[2004], the events described by Idone et al. [1987] andJerauld et al. [2004] being rocket-triggered lightning dis-charges. Optical evidence for events of Type 3b showingstrokes of opposite polarity (determined by either close ordistant electric field measurements) following the samechannel to ground in natural downward lightning has beenreported for one flash by Jerauld et al. [2003] (the bipolarflash discussed in the present paper) and for four flashes(about 1% of their observed flashes) by Fleenor et al.[2009]. Evidence for Type 3b events from remote electricfield measurements alone has been given by Nag et al.[2008], while Makela et al. [2008] have questioned whethernatural bipolar cloud-to-ground flashes can even occur.

2. Experiment

[12] The data on the bipolar flash to be presented herewere acquired in Summer 2002 at the International Centerfor Lightning Research and Testing (ICLRT), an outdoorfacility located on the Camp Blanding Army NationalGuard Base in north central Florida. The multiple-stationfield-measuring experiment (MSE) at the ICLRT wasdesigned to acquire electric and magnetic field and fieldderivative waveforms from the five to eight cloud-to-groundlightning flashes expected on average to strike within theroughly 1 km2 of the MSE network per year. Most of theseflashes are expected to lower negative charge to ground.Eighteen negative stepped leaders and the correspondingfirst return strokes acquired by the MSE in 2002 through2004 were analyzed by Jerauld et al. [2008]. The onebipolar lightning discharge recorded by the MSE is dis-cussed here. A sketch of the network is shown in Figure 1,and information about the MSE measurements is presentedin Table 1, with more details being given in Jerauld et al.[2008] and Jerauld [2007]. The 2002–2004 MSE wascomprised of six electric field (E) measurements, twomagnetic field (B) measurements, four electric field deriv-ative (dE/dt) measurements, four magnetic field derivative(dB/dt) measurements, and two optical measurements lo-cated at the sites noted in Figure 1 and Table 1. Photo-

D19115 JERAULD ET AL.: MEASURED ELECTRIC AND MAGNETIC FIELDS

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graphs of the antennas and antenna sites are found inJerauld [2007]. Waveforms from flat-plate antennas (E,dE/dt) and vertical-loop antennas (B, dB/dt) were trans-mitted from the electronics associated with the antennas,via Opticomm MMV-120C fiber optic links, to the elec-tromagnetically shielded Launch Control Trailer (seeFigure 1) where they were appropriately low-pass filteredand digitized. The output of a field mill (measuring the cloudquasistatic electric field at ground level) was monitored by acomputer which automatically armed/disarmed theMSEwhenconditions were conducive/nonconducive to lightning occur-rence. The digitizers in the Launch Control Trailer weretriggered when the output of the two optical sensors, South-West Optical (SWO) and North-East Optical (NEO) inFigure 1 and Table 1, which viewed the MSE at lowaltitudes from opposite corners of the network, simulta-

neously exceeded a threshold, so data were only obtainedfor lightning within or very near the MSE network.

3. Observations

3.1. General

[13] The MSE network recorded a natural cloud-to-ground bipolar flash (Type 3b) on 4 August 2002, atapproximately 20:05:29 UT. The flash began with twopositive strokes and was followed by four negative strokes.This event, designated MSE0202, is the only natural light-ning flash containing positive return strokes that has beenrecorded on-site by the MSE system from 2002 to thepresent, although numerous positive flashes have beenrecorded within 10 km of the site. The 800 ms YokogawaDL 716 digitizing oscilloscope record, found in Figure 2,

Figure 1. Map of the MSE network showing the estimated locations (each indicated by an ‘‘x’’)of the first positive (bottom left) and five subsequent (one positive and four negative) strokes (shadedcircle in top left) of bipolar flash MSE0202. The first stroke location was determined using the two-dimensional TOA technique, while the general area of the subsequent strokes was estimated from videorecords.

Table 1. Typical MSE Measurement Configuration Settings for the 2002–2004 Experiment

Sensor Stations Amplitude Rangea Sampling Rate Record Length Bandwidth

E-field 2, 4, 5, 6, 9, 10 ±65 kV m�1 10 MHz 0.4, 0.8, or 1.6 s 0.2 Hzb–4 MHzc

B-Field 4, 9 ±80 mT 10 MHz 0.4, 0.8, or 1.6 s 10 Hzd–4 MHzc

dE/dt 1, 4, 8, 9 ±25 kV m�1 ms�1 200 MHz 4 segments, 5 ms each DC-20 MHzc

dB/dt 1, 4, 9 ±120 mT ms�1 200 MHZ 4 segments, 5 ms each 1.6 Hze–20 MHze

Optical NEO, SWO �0.1 to +0.8 V 10 MHz 0.4, 0.8, or 1.6 s DC-1 MHzf

aUsually limited by the oscilloscope settings, that is, the saturation level of fiber optic transmitter and other electronics is typically higher.bLimited by the decay time constant of the integrating circuit.cLimited by the digitizer.dLimited by the active integrator.eLimited by the external active filter.fLimited by the preamplifier.


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shows the electric and magnetic fields of two positiveleader/return-stroke sequences, separated in time by approx-imately 53 ms, followed by a negative leader/return-strokesequence approximately 526 ms later. The atmosphericelectricity sign convention is used. Video (for all strokes)and dE/dt (for the first stroke only) records indicate that thefirst and subsequent stroke ground strike points wereseparated horizontally by about 800 m, as depicted inFigure 1, which shows the well-located first-stroke strikepoint and the less well-determined most probable strikepoint for all of the subsequent strokes as well as the area ofuncertainty for the most probable location (see next para-graph). In addition to the electric fields of the three strokes

recorded by the Yokagawa oscilloscope and shown inFigure 2, the video shows that an additional three strokesfollowed the same channel as the second (positive) and third(negative) strokes. Note that the second positive stroke isreferred to as a subsequent stroke, even though it followed aseparate channel to ground, and thus is probably moresimilar in characteristics to a positive first stroke. Theoverall flash duration was roughly 1.5 s.[14] The first-stroke channel was located with a two-

dimensional difference-in-the-time-of-arrival (hyperbolicpositioning) technique [Jerauld, 2007] which assumes thatthe source is at ground level and, in this case, employs thetime differences in the arrival of the first peak of thedominant dE/dt return-stroke pulse (shown in Figure 13)at 4 stations (stations 1, 4, 8, and 9) in three-station groups.Two of the four three station sets of data provided a singlelocation, while the other two yielded two location solutionseach. Whether the technique yields a one or a two-locationsolution depends on the geometry of the 3 stations relativeto the strike point. The agreement between each of the fourthree-station locations for the common location of the firstpeak in the dE/dt record in Figure 13 is within severalmeters. Location of the two following dE/dt peaks inFigure 13 did not produce such consistent solutions. NodE/dt data were available for the second positive stroke andthe following negative strokes, so estimates of the locationsof these channels were made from video records and wereconsiderably less accurate.[15] The U.S. National Lightning Detection Network

(NLDN), which estimates the locations and peak currentsof cloud-to-ground lightning within the contiguous UnitedStates, reported peak currents of +50.7, +49.9. �14.2,�13.5, �10 kA for the first five strokes (the sixth strokewas not detected by the NLDN). Some comments on thevalidity of these values are found in the Discussion section.Interestingly, four of the five interstroke intervals (the fiveinterstroke intervals are 53, 526, 280, 261, and 300 ms) aresignificantly longer than the typical value of 60 ms given byRakov and Uman [2003] for negative cloud-to-groundlightning, implying that long continuing currents likelyflowed during a portion of these intervals, as verified byvideo records (see later section on Subsequent StrokeCharacteristics).

3.2. First Positive Stroke Characteristics

[16] Figure 3 is a frame from the video showing the firstpositive stroke channel of flash MSE0202, estimated to be680 m from the camera (located in Instrumentation Station1, abbreviated IS1 in Figure 1). As viewed by this onecamera, the channel consisted of an upper horizontal sectionof length about 300 m at an altitude of about 300 m, aseemingly straight-and-vertical section (partially blocked inthe video frame by a structure) extending from ground to aheight of about 40 m, and a middle section leaning at anangle of about 60 degrees from vertical, connecting thevertical and horizontal channel sections.[17] Figures 4 and 5 show portions of overall electric field

waveforms for the first stroke of flash MSE0202 measuredat five stations, the overall waveform at station 9 beingreproduced in Figure 2. Station 10 did not record data. Allof the electric field waveforms consist of a monotonicallyincreasing field change beginning at about 110 ms before

Figure 2. (a) Electric and (b) magnetic fields from bipolarflash MSE0202, displayed on a 800-ms timescale. Time 0indicates the trigger point of the digitizer. The distance tothe first-stoke channel is about 290 m. The distance to thesecond and third stroke channels is on the order of 500 m to1 km. Note that only the east-west component of thehorizontal magnetic field was measured, with the polarityreversal between strokes 1 and 2 (both positive) in B beingdue to the fact that the two strokes were on roughly oppositesides of the loop antenna. In contrast, the polarity reversal inA and B between strokes 2 and 3 (having the same location)is due to the fact that the two strokes transported charge ofopposite polarity (positive and negative, respectively).


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time zero (trigger point of the digitizing oscilloscope used),followed by an increase in slope beginning at about �1 ms.The overall positive field change evident in Figure 2 andFigure 4 is presumably due to the downward positive leaderpropagating from cloud-to-ground. The apparent positiveleader duration of over 100 ms (see Figure 2) is significantlylonger than the typical value of about 35 ms observed forstepped leaders of negative first strokes [Rakov and Uman,2003], but consistent with positive leader durations reportedby Heidler and Hopf [1998]. The channel geometry, espe-cially in-cloud and clear-air horizontal and inclined por-tions, is likely at least partly responsible for the shape andlong duration of the positive first leader electric field seen inFigure 2.[18] In Figure 5 at about �40 ms, the electric field of the

positive first stroke leader reaches its peak positive value,after which a ‘‘slow-front/fast-transition’’ associated withthe return stroke is observed, resulting in a reduction of thefield (making it less positive) over a period of about 10 ms.The slow-front duration is about 6–8 ms, followed by thefast transition that abruptly reduces the field in about 2–3 ms. The slow front duration is consistent with themean slow front durations reported by others [Cooray andLundquist, 1982; Hojo et al., 1985; Cooray, 1986a, 1986b;Cooray et al., 1998] for distant positive first return strokeradiation fields, but about a factor of two greater than thosereported for the radiation fields of distant negative firstreturn stroke slow fronts [Weidman and Krider, 1978;Cooray and Lundquist, 1982]. However, the field risetimeof the fast transition (2–3 ms overall) is appreciably largerthan the values reported by others for distant positive returnstrokes [Cooray, 1986a, 1986b; Ishii and Hojo, 1989;Cooray et al., 1998], those being on the order of half a

microsecond or less. This discrepancy is likely related to thefact that there appears to be two sequential fast-transitionsprocesses comprising the overall fast transition to fieldpeak. These two periods of rapid field decrease are sepa-rated by a change in slope (inflection) for about 1 msbetween roughly time �30 ms and �32 ms in the waveformsof Figure 5. At the end of the overall fast transition, betweenroughly time �28 ms and �30 ms in Figure 5, a local peak isobserved in the waveforms, followed by a monotonicdecrease in the field for several milliseconds. The issue ofthere being apparently two separate fast transition periodswill be further discussed later when the dE/dt waveforms(Figures 12 and 13) are considered and in the Discussionsection.[19] Figure 6 is a plot of the leader electric field change

versus distance for the first (positive) stroke of flashMSE0202, along with the best fit power law equation.The best fit curve for the assumed function DEL(r) = Ar�b,, where r is the radial distance from the strike point,decreases as r�0.66 (A = 1.46 � 103), with significant scatterevident in the data of Figure 6. For example, the leader fieldchange value measured at Station 6 (429 m) is approxi-mately +35 kV m�1, greater than the value of about +30 kVm�1 measured at Station 9 (288 m). This variation is likelydue to the complex geometry of the channel (see Figure 3).For a straight vertical channel, a leader field change thatvaries with radial distance from the channel as r�1 isindicative of a more-or-less uniformly charged leader chan-nel, at least in the bottom kilometer or so for relatively closefield measurements such as ours [Rubinstein et al., 1995].Jerauld et al. [2008] present data similar to those found inFigure 6 for 14 individual negative-stepped leader fieldchanges. With these field changes as a function of distancealso approximated as DEL(r) = Ar�b, the values of ‘‘b’’range from 0.34 to 1.60 and the values of ‘‘A’’ from 1.04 �103 to 2.66 � 105; and there were several negative-steppedleader field changes similar in magnitude versus rangecharacteristics to that for the present first positive leaderfield change.[20] Some parameters of the first positive stroke electric

field waveforms, including the overall leader field changeand the values of the initial return stroke peaks and thecorresponding 30–90% risetimes, are given in Table 2 (theStation 2 waveform illustrating the measured parameters isgiven in Figure 7). Overall, the return stroke electric fieldwaveforms of Figure 5 are not dissimilar, except for polarity,from those associated with negative return strokes at similardistances measured by Jerauld et al. [2008, Figure 5].[21] Using the current (I)-velocity (v)-electric field (E)

relation of the single-wave transmission line model [e.g.,Jerauld et al., 2007; Uman and McLain, 1969]

E tð Þ ¼ m0v

2p rI t � r=cð Þ ð1Þ

where m0 is the permeability of free space, we estimated thepeak return stroke current at ground from the local peak atthe end of the overall fast transition of each of the electricfield waveforms measured at different distances (Figure 5).For equation (1) to be valid, the electric field peak at the endof the fast transition must be pure radiation field, the returnstroke speed v must be constant, the ground must be

Figure 3. Frame of video (inverted gray scale) showingthe first (positive) stroke channel (thick black line), whichwas located approximately 680 m from the camera. The leftportion of the image is obscured by a rain shield placed overthe window. The bottom vertical portion of the channel ispartially obscured by the ‘‘Test house structure,’’ which islocated about 60 m from the camera, and is barely visible inthe image. Although the channel appears to terminate on thestructure, it does not, as the channel and structure areseparated by about 600 m. The camera was facingapproximately southwest. IS1 = Instrumentation Station 1,where the camera was located.


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perfectly conducting, and the return stroke channel must bestraight and vertical at radial distance r. Equation (1) hasbeen tested by Willett et al. [1988, 1989, 2008] and found tobe substantially accurate for negative strokes in triggeredlightning (which are similar to subsequent strokes in naturalnegative lightning) when fields are observed at about 5 km,but its applicability to positive first strokes has never beenverified. The peak current was calculated from equation (1)for three assumed return stroke speeds: 1 � 108, 2 � 108,and 3 � 108 m s�1, and is given in Table 2. The corres-ponding mean estimated peak currents (averaged over thefive electric field waveforms) were about +137, +69, and+45 kA, respectively. These are probably overestimatessince the field peak at the end of the fast transition likelycontains additional field components besides the radiationfield, as further expounded upon in the Discussion section.As noted earlier, the NLDN estimated first strokepeak current (derived from distant field measurements)was 50.7 kA.[22] Figures 8 and 9 show electric and magnetic field

waveforms, both measured at Stations 4 and 9, for the first(positive) stroke of flash MSE0202. The magnetic field

waveforms in Figure 8 indicate that the duration of the firststroke current was on the order of 1 ms (the decay timeconstant of the B-field measurements was about 15 ms). It isinteresting to note that neither the field nor the video recordsindicate the presence of continuing currents after the first(positive) stroke. As noted in the Introduction, the presenceof continuing currents, transferring large amounts of charge,are characteristic of positive return strokes. The electric andmagnetic field waveforms both exhibit a slow-front/fast-transition combination. As is evident from Figure 9, duringthe slow front and fast transition, the shapes of E andB-field waveforms are very similar at both Stations 4and 9, especially at Station 4.[23] Figure 10 shows the electric field waveform (dis-

played on three times scales) measured at a distance of45 km for the first (positive) stroke. The waveform wasmeasured at the Gainesville station of the Los AlamosSferics Array (LASA), which was operated by Los AlamosNational Laboratories [Smith et al., 2002]. The samplinginterval for these data was 1 ms and the amplitude of thewaveform was not calibrated in electric field units. Inter-estingly, while no clear evidence of leader stepping is

Figure 4. First positive stroke electric field waveforms on a 5-ms timescale. Time 0 indicates the triggerpoint of the digitizer. Station 10 was not functioning.


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present in either the close fields or the close field derivativesrecorded by the MSE network, there does appear to be somepulse activity in the distant waveforms during the 2 msbefore the return stroke. Further, pulses are observed duringthe first millisecond after the return stroke.[24] Figure 11 shows the LASA distant electric field

waveform overlaid on the magnetic field waveform mea-sured at Station 9 (288 m). The close and distant waveformsare remarkably similar during the slow front and the fasttransition, up to the time of the peak, perhaps indicating thatthey are both primarily radiation field for that time period,although in the Discussion section we present an argumentto suggest that the slow front of the close magnetic fieldshould contain a significant induction field component.[25] Figure 12 shows dE/dt waveforms measured at four

stations for the first (positive) stroke, and Figure 13 gives anexpanded version of the latter part of the station 9 wave-form. The dominant dE/dt pulse occurring at about �30 msat station 9 in Figures 12 and 13 is to be associated with thesecond portion of the fast transition to peak in Figure 5 atstation 9 at about �30 ms. The dE/dt waveform of Figure 12is composed of a slow front (associated with the electricfield slow front in Figure 5) followed by a fast transition

(associated with the rapid field decrease in Figure 5).However, most of the slow front in the electric field shownin Figure 5 precedes the dE/dt waveforms in Figure 12. Theinitial part of the dE/dt waveform, at the beginning of

Figure 5. First positive stroke electric field waveforms on a 40-ms timescale. Station 10 was notfunctioning.

Figure 6. Leader electric field changes plotted versusdistance for the first positive stroke. Also plotted is the bestfit power law equation of the form DEL(r) = Arb.


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Figure 12, is composed of three individual pulses that occurnear the end of the slow front in the electric field shown inFigure 5 (at about �33 ms at station 9). Slow front pulseshave been reported by Murray et al. [2005] in distant(radiation field) dE/dt waveforms from negative firststrokes, as well as from observations of close negative firststroke dE/dt waveforms recorded by the MSE system[Jerauld et al., 2007, 2008]. This first group of three pulsesin Figure 12, when integrated, leads to the rapid rising firstpart of the fast-transition (before the inflection) in theelectric field waveforms of Figure 5. It follows that it isarguable whether the first group of pulses is to be calledslow front pulses or referred to as fast transition pulses.More comments are found in the Discussion section.[26] A burst of pulses is observed in the dE/dt waveforms,

beginning about 10 ms after the peak and hence not evidentin Figure 12 or 13, and having a duration of some tens ofmicroseconds. Similar pulses have been observed in theclose negative first stroke field derivative waveforms mea-sured by the MSE system [Jerauld, 2007].[27] Table 3 gives some parameters of the first (positive)

stroke dE/dt waveforms. The ‘‘peak value’’ in Table 3 isobtained using a theoretical calibration of the dE/dt antennagain. The ‘‘scaled peak value’’ is determined by comparingthe numerically integrated dE/dt with the colocated mea-sured electric field on the assumption that the electric fieldmeasurement is the better calibrated of the two [Jerauld etal., 2008]. The scaling factors changed from storm day tostorm day, the possible reasons being discussed by Jerauldet al. [2008]. Only stations 4 and 9 had colocated E-fieldand dE/dt antennas, so only the dE/dt measurements at 4and 9 could be scaled to colocated electric fields. For station4 the unscaled peak was multiplied by 1.55 to obtain thescaled peak; for station 9 the scaling factor was 1.9.[28] The dB/dt waveforms for the first (positive) stroke

are shown on a 10 ms timescale in Figure 14. Both the east-west and north-south components of the magnetic fieldderivative were measured at Station 1, but only the east-west component is discernible, as the north-south compo-nent is apparently below the noise level of the measurement.This is likely because the relative azimuth angle betweenthe lightning channel and the plane of the east-west orientedloop sensor (which measured the north-south component ofthe field) was almost 90 degrees. It follows that the east-west component measured at Station 1 likely represents thetotal azimuthal field. No data were recorded at Station 9 dueto a problem with the fiber optic link. The dE/dt waveformsmeasured at Stations 1 and 4 (Figure 12) are essentially

identical in shape to the corresponding measured dB/dtwaveforms. Similar results were found for the dE/dt anddB/dt waveforms of negative first strokes [Jerauld et al.,2008]. The similarity between the dE/dt and dB/dt wave-shapes is likely indicative of the waveforms being primarilycomposed of the radiation field component. The ratio of theelectric and magnetic field derivative peaks should be equalto the speed of light, a general result for pure radiation fieldspropagating along a perfectly conducting plane. The ratiosat Station 1 (616 m) and Station 4 (825 m) (at Station 4 dE/dtwas scaled to the colocated measured electric field) werefound to be about 3.6 � 108 m s�1 and 2.8 � 108 m s�1,respectively. The ratios given above are reasonably closeto the speed of light (3.0 � 108 m s�1), given theuncertainty of about 10% in the calibration of each ofthe electric and magnetic field antennas, and the fact thatthe dE/dt calibration at station 1 was theoretical and notscaled to a colocated electric field measurement, as wasthe case at station 4.

3.3. Subsequent Stroke Characteristics

[29] Figures 15 and 16 show portions of the electric fieldwaveforms of Figure 2 from the second (positive) stroke offlash MSE0202, and Figure 17 shows electric field wave-forms from the third (negative) stroke, also evident at theend of the waveform of Figure 2. Video records indicate thatboth the second and third strokes (as well as strokes 4–6)followed the same channel to ground, with these channels

Table 2. Parameters of the Measured Electric Field Waveforms for the First (Positive) Stroke of Bipolar Flash

MSE0202

Parameter

Station

Units 2 4 5 6 9 Mean

Distance m 749 825 646 429 288Leader field change kV m�1 20.6 16.7 16.0 34.9 30.4Return-stroke initial peak value kV m�1 �3.4 �2.6 �3.5 �9.0 �10.3Initial peak 30–90% risetime ms 2.1 2.1 2.1 2.0 1.9TLM Ip, v = 1 � 10�8 m s�1 kA +127 +107 +112 +192 +148 +137TLM Ip, v = 2 � 10�8 m s�1 kA +63.3 +53.3 +56.2 +96.0 +73.7 +68.5TLM Ip, v = 3 � 10�8 m s�1 kA +42.3 +35.7 +37.6 +64.2 +49.3 +45.7

Figure 7. Return stroke electric field waveform measuredat Station 2, for the first positive stroke at a distance of 749m. Several waveform parameters are labeled.


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Figure 9. First positive stroke electric and magnetic field waveforms, both measured at Stations 4 and9, on a 40-ms timescale. Only the east-west component of the magnetic fields was measured.

Figure 8. First positive stroke electric and magnetic field waveforms, both measured at Stations 4 and 9,on a 3-ms timescale. Only the east-west component of the magnetic fields was measured.


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possibly including horizontal and inclined sections, similarto that of the first stroke channel. The video records wererelatively poor in quality, and hence we have not includedthem here. While we cannot determine the location of thesubsequent stroke channels with any precision, videorecords place them in the northwest area of the site, andour best estimates of the location and of the area ofuncertainty are shown in Figure 1, upper left corner.[30] The duration of the second downward positive leader

is about 35 ms, which is very close to the typical valuesobserved for negative downward stepped leaders. The

leader electric field changes at the five measurement sta-tions ranged from about +16 to +13 kV m�1. The finestructure of the microsecond-scale return stroke electricfield waveforms (Figure 16) is similar to that observed forthe first (positive) stroke (e.g., Figure 5), although the slowfront portion of the latter is more pronounced relative to thatof the former. However, both first and second positivestroke waveforms exhibit an inflection in the electric field(at about 53.06 ms in Figure 16) during the fast transition aswell as a local peak at the end of the fast transition. Electricfield and video records indicate that the second positivestroke was followed by a long continuing current that had aduration of at least 400 ms, consistent with the character-istics of positive lightning discharges noted in the Introduc-tion, that positive return strokes tend to be followed bycontinuing currents that typically last for tens to hundreds ofmillisecond.[31] The duration of the third (negative) leader is about

1 ms, consistent with the typical duration of a negativedescending dart leader [Rakov and Uman, 2003]. The leaderelectric field changes at the five stations ranged from about�0.9 to �1.8 kV m�1, these values being consistent withthose measured for negative dart leaders at distances on theorder of 1 km. The signature of two M components areobserved superimposed on the electric field waveforms atabout 0.6 and 3 ms after the return stroke. M componentsare current pulses, superimposed on the continuing currentof some tens to hundreds of amperes, that typically haveamplitudes of hundreds of amperes and risetimes of somehundreds of microseconds [Rakov et al., 2001]. Videorecords indicate that the third (negative) stroke was fol-lowed by a long continuing current having a duration ofabout 165 ms, comparable to the total interstroke intervalduration of 280 ms, while the next three negative strokesexhibited optically observable continuing currents of 230 ms(interstroke interval duration 260 ms), 70 ms (interstrokeinterval duration about 300 ms), and 100 ms. A flashcontaining four negative strokes, each followed by a long

Figure 10. Electric field of the first positive strokemeasured at a distance of 45 km by the Los Alamos SfericsArray (LASA). The waveform is displayed on (a) 2-ms,(b) 1.5-ms, and (c) 500-ms timescales. The amplitude of thewaveform has been normalized to its initial peak. Time zerocorresponds to the beginning of the fast transition. Dataprovided courtesy of Los Alamos National Laboratories(LANL).

Figure 11. Magnetic field measured at 288 m, overlayedwith the electric field measured a distance of 45 km fromthe first positive stroke. Time zero corresponds to thebeginning of the fast transition. The distant field wasmeasured by the Los Alamos Sferics Array (LASA) and isprovided courtesy of Los Alamos National Laboratories(LANL).


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continuing current, is a relative rare event in itself. Valineand Krider [2002] found 2 of 251 multiple-stroke negativeflashes and Saba et al. [2006a] found none of 186 multiple-stroke negative flashes with four or more strokes followedby long continuing current. It has been shown that continu-ing current is preferentially initiated by negative returnstrokes with peak currents roughly equal to or smaller thanthe typical (as inferred from the measured electric fields[Shindo and Uman, 1989; Rakov and Uman, 1990; Saba etal., 2006b]), a finding not inconsistent with the NLDNinferred peak currents of �14.2, �13.5, and �10 kA forthree of the negative strokes of the bipolar flash, values nearthe median subsequent stroke value of �12 kA reported byBerger et al. [1975].

4. Discussion

[32] The geometry of the first positive stroke shown inFigure 3 does not appear to satisfy the requirement of thetransmission line model that the channel be straight andvertical, leading to equation (1), unless the slow front/fasttransition fields emanate from the bottom 40 m or so of thechannel above ground, that portion of the channel appar-ently being more-or-less straight and vertical. The fact thatthe locations given by the four dE/dt time-of-arrival three-station solutions (computed assuming the source was atground level) for the first part of the dominant dE/dt pulse(associated with the second portion of the electric field fasttransition) agree to within a few meters suggests that thesecond part of the fast transition was indeed radiated fromcurrent in that bottom 40 m channel portion. Thus it is

certainly possible that the initial peak of the electric fieldwas also radiated from that straight, vertical bottom channelportion, leading to the reasonable results that are obtainedfrom the use of equation (1), as discussed below. As part ofthe following discussion, we also provide an argument forthe reasonableness of NLDN’s values for the peak currentsof the two positive return strokes.[33] The NLDN peak current values calculated for the

first five strokes of the bipolar flash, +50.7, +49.9, �14.2,�13.5, �10 kA, are each assumed in the NLDN calculationto be proportional to the associated NLDN-measured distant

Figure 12. First positive stroke dE/dt waveforms on a 10-ms timescale.

Figure 13. Latter portion of the dE/dt waveform measuredat Station 9 from the first positive stroke on a 4-mstimescale.


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peak electric and magnetic fields (radiation fields), with theproportionality constant having been determined from acomparison of direct current measurements on negativestrokes in rocket-triggered lightning and the measureddistant radiation fields of the rocket-triggered strokes,account having been taken of rf signal attenuation due topropagation effects [Cummins et al., 1998; Jerauld et al.,2005; J. A. Cramer et al., Recent upgrades to the U.S.national lightning detection network, paper presented at the18th International Lightning Detection Conference, Vaisala,Inc., Helsinki, Finland, 7–9 June, 2004]. Rocket-triggeredstrokes are thought to be very similar to subsequent strokes innatural negative flashes. Currently, there are no positivereturn stroke peak current measurements that have beencompared with the corresponding NLDN-reported values toconfirm that the negative triggered-lightning (negative sub-sequent stroke) calibration is valid for positive first strokes.Possibly related to this issue is the fact that the NLDN-reported return stroke currents for the first two positive

strokes, both near 50 kA, are higher than the median valueof +35 kA reported by Berger et al. [1975] for positive firststrokes measured on towers in Switzerland, while the NLDN-reported peak currents of the three negative subsequentstrokes, �14, �14, �10 kA, are consistent with the medianvalue of �12 kA reported by Berger et al. [1975] andAnderson and Eriksson [1980] from direct tower measure-ments for negative subsequent strokes.[34] The electric field measured at close range in our

experiments can be considered to be composed of three fieldcomponents: radiation, induction, and electrostatic [e.g.,Jerauld et al., 2007]. For a hypothetical electric fieldwaveform composed of a single frequency, the magnitudesof the radiation field component, induction field component,and the electrostatic field component of the total electricfield are equal at a distance r = l/2p where l is thewavelength associated with that single frequency (l = c/f,where c is the speed of light [e.g., Stratton, 1941, p. 435]).At distances closer than l/2p the electrostatic field domi-nates. At greater distances, the radiation field dominates. Areturn stroke slow front electric field having a duration of,for example, 5.0 ms can be considered more or lessequivalent to one quarter of a sine wave of period 20 ms,representing an effective frequency of 50 kHz and aneffective wavelength of 6 km. The magnitude of the threefield components of the slow front, to the extent that theslow front can be approximated by a single frequency sinewave, would thus be equal near 1 km, two or three timesgreater than the distances at which our measurements weremade. Our slow fronts (Figure 5) are 6 to 8 ms, increasing

Figure 14. First positive stroke dB/dt waveforms on a 10-ms timescale. Note that both the east-west(EW) and north-south (NS) components of the field were measured and calculated at Station 1, whileonly the east-west component was measured at Station 4. Station 9 was not functioning.

Table 3. Parameters of the Measured dE/dt Waveforms for the

First (Positive) Stroke of Bipolar Flash MSE0202

Parameter

Station

Units 1 4 8 9

Distance m 616 825 601 288Peak value kV m�1 ms�1 �3.6 �1.7 �3.0 �5.3Scaled peak value kV m�1 ms�1 – �2.6 – �10.130–90% risetime ms 0.36 0.33 0.40 0.29Half-peak width ms 0.41 0.35 0.36 0.35


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somewhat the distance at which the three field componentsare equal, by the argument above. It follows that the slowfronts contain a sizable, perhaps dominant, electrostaticcomponent. The fast transition following the slow front,leading to the sharp local peak in the electric field wave-forms of Figure 5, consists of two rapidly rising sectionsthat contain much higher frequency components than theslow front and thus are likely to be mostly radiation field atour measurement distances.[35] If we assume that the peak values of the sharp local

peaks are pure radiation field when they actually containadditional field components (and assume that there is nosignificant attenuation of the peaks due to propagationeffects), we should obtain from equation (1) an overestima-tion of the peak current. The value of +45 kA in Table 2,corresponding to a return stroke speed of 3 � 108 m s�1 (thespeed of light), is closest to the NLDN-reported value ofabout +50 kA. The +45 kA value can also be obtained fromequation (1) if both (1) the speed is lower than the speed oflight and (2) potential electrostatic and induction fieldcomponents are subtracted from the total measured field,

leaving only the radiation field component. If, for example,we assume that the NLDN-reported peak current of +50 kAis correct and that our return stroke electric field peaksare composed of about 60% radiation field, the returnstroke speed calculated from equation (1) would be near2 � 108 m s�1; if the field peaks are only 30% radiationfield, the calculated speed would be near 1 � 108 ms �1.Mach and Rust [1993], Idone et al. [1987], and Jerauld etal. [2004] (the latter two are for rare positive subsequentstrokes in rocket-triggered lightning), all reported positivereturn stroke speeds near 1 � 108 m s�1, while Nakano etal. [1987] reported a positive return stroke speed of 2 �108 m s�1. We can conclude that there is reasonableconsistency between the NLDN-reported peak current valueand the peak current for the first positive stroke that wecalculate from equation (1) using close measured electricfield peaks (taking account of the fact that the close fields arenot pure radiation fields) and assuming reasonable return-stroke speeds.[36] While the exact distances from the second positive

stroke to the measurement stations are not known, they are

Figure 15. Second (positive) stroke electric field waveforms on a 55-ms timescale. Station 10 was notfunctioning.


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in the same general range as for the first positive stroke, asis evident from Figure 1. Additionally, the initial field peakvalues for the second positive stroke, shown in Figure 16,are similar to those shown in Figure 5 for the first positivestroke. Thus it is reasonable that the NLDN-reported peakcurrent value for the second stroke, about 50 kA, isessentially the same as for the first stroke, since they areboth derived from apparently more or less equal distantradiation field values.[37] Averaging the normalized (to 100 km using an

inverse distance relationship) positive first stroke dE/dt peakwaveforms measured at Stations 1, 4, 8 and 9, we find thatour mean dE/dt peak value is about 20 V m�1 ms�1. Thisvalue is very similar to the normalized mean value of 22 Vm�1 ms�1 reported by Cooray et al. [1998] for 22 positivedE/dt waveforms that propagated over tens to hundreds ofkilometers of seawater. This value is also very similar to thatobtained for the close negative first return strokes reportedby Jerauld et al. [2008], and about half the value reportedby Krider et al. [1996] for negative first strokes propagatingover seawater. In contrast Heidler and Hopf [1998] reported

(for lightning over land in Germany) that the mean dE/dtpeak for positive strokes was appreciably higher than fornegative strokes.[38] For the measured dE/dt peak values, assumed to be

pure radiation field, and with an assumed return strokespeed of about 2 � 108 m s�1, the TL model (equation (1))predicts the peak dI/dt value of the first (positive) stroketo be roughly +50 kA ms�1. For an assumed speed of 1 �108 m s�1, the TL model predicts a peak dI/dt value is+100 kA ms�1. Krider et al. [1996] calculated a mean peakdI/dt value of 115 kA ms�1 for negative first strokes frommeasurements of 63 negative first stroke dE/dt waveformsthat propagated over tens to hundreds of kilometers ofseawater and application of equation (1) with an assumedspeed of 2 � 108 m s�1.[39] Figure 12 shows the overall dE/dt waveform mea-

sured at Station 9, 288 m from the first positive stroke. Boththe initial broad pulse (around �32 ms at Station 9) and thedominant pulse (around �30 ms at Station 9 and shownexpanded in Figure 13) exhibit multiple peaks. The gapbetween the two main pulse groups in Figure 12 is consis-

Figure 16. Second (positive) stroke electric field waveforms on a 37-ms timescale. Station 10 was notfunctioning.


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tent with the inflection point (brief change in slope)observed in the corresponding electric and magnetic fieldwaveforms (Figures 5 and 9). Clearly both dE/dt pulsegroups contribute to the two-step fast transition observedin the electric field waveforms (Figure 5), although onecould argue from the literature on negative first stroke fields[e.g., Jerauld et al., 2008] that the initial dE/dt pulse groupand the corresponding initial rapid E-field rise to theinflection point in the first part of the overall fast transition(around �32 ms at Station 9 in Figure 5) is to be associatedwith the slow front. The matter appears to be one ofterminology rather than of physics. From a physical pointof view, all of the dE/dt pulses evident in Figure 12 arelikely associated with common processes. As noted byMurray et al. [2005] and by Jerauld et al. [2008] fornegative first return strokes, when viewed on an expandedtimescale, the slow front and fast transition in both electricfield and dE/dt often appear to be one continuous process(that is, there is no clear transition point between the slowfront and the fast transition). Thus it may well be that thelatter part of the attachment process, involving the connec-tion of upward (from ground) and downward leaders and

the formation of the return stroke, is indeed a continuousprocess involving multiply-connected upward and down-ward leaders that are characterized by the multiple dE/dtpulses seen in Figure 12, culminating in the final dE/dtpulse associated with the final rise of the return strokecurrent to peak value. Thus from a physical point of view, inboth negative and positive first strokes, the dE/dt pulses thatoccur during the slow front (often called slow front pulses)may well have a common generation mechanism as thedominant (usually final) dE/dt pulse (called the fast transi-tion pulse) in the sequence of dE/dt pulses that represent thephysical processes associated with return stroke initiation.

[40] Acknowledgments. This work was supported in part by U.S.DOT (FAA) grant 99-G-043 and NSF grants ATM-0003994 and ATM-0346164. We thank X.M. Shao for providing the Los Alamos Sferics Arraydata shown in Figures 10 and 11.

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Figure 17. Third (negative) stroke electric field waveforms on a 2-ms timescale. Station 10 was notfunctioning.


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��J. E. Jerauld, Raytheon Missile Systems, 1151 East Hermans Road M/S

T9, Tucson, AZ 85756, USA.D. M. Jordan, V. A. Rakov, K. J. Rambo, G. H. Schnetzer, and

M. A. Uman, Department of Electrical and Computer Engineering,University of Florida, 311 Larsen Hall, P.O. Box 116200, Gainesville, FL32611, USA. ([email protected])


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