Initial breakdown pulses in intracloud lightning flashes and their relation to terrestrial gamma ray flashes

1 Introduction

[2] A terrestrial gamma ray flash (TGF) is a burst of gamma rays, typically lasting <1 ms, detected by an Earth-orbiting satellite as coming up from below [Fishman et al., 1994]. TGF production was originally attributed to runaway electrons driven by electrical discharges above thunderstorms [Fishman et al., 1994]. Subsequent research has revealed numerous facts about TGF production. First, TGFs were found to be associated primarily (and maybe exclusively) with the most common type of intracloud (IC) lightning flashes [Cummer et al., 2005; Stanley et al., 2006], namely, those that initiate just above the main negative thundercloud charge, move negative charge upward into the cloud's main positive charge, and move positive charge into the cloud's main negative charge [e.g., Coleman et al., 2003]. Second, most (or perhaps all) TGF production generally occurs during the first 15 ms of development of an IC flash [e.g., Stanley et al., 2006; Shao et al., 2010; Lu et al., 2010]. Third, for the IC flashes that produce TGFs, it has been shown that the TGF is coincident with a very slow magnetic field (B) pulse in the ULF radio band (30–300 Hz) with a typical pulse duration of 2–6 ms and an inferred charge moment change ranging from <10 C km up to 200 C km [Lu et al., 2010, 2011]. Fourth, superimposed on the slow ULF pulse are one or more discrete B pulses, detected in the VLF band, with individual pulse durations of less than 100 µs [e.g., Lu et al., 2011]. For two TGFs studied by Cummer et al. [2011], a few discrete LF-band B pulses with durations of 10–50 µs were coincident (to “within several tens of microseconds”) with each TGF. For the same two TGFs, the source current that caused the LF pulses had a duration of ~150 µs and had “a strong temporal connection” (or correlation) with the TGF gamma ray count rate, leading to the hypothesis that the combination of data “appears to show a distinct radio signature associated with the gamma ray generation itself” [Cummer et al., 2011]. Fifth, many TGFs are coincident (to within 40 µs) with VLF pulses recorded by the World Wide Lightning Location Network (WWLLN) [Connaughton et al., 2010, 2013]. Connaughton et al. [2013] inferred “that the simultaneous VLF discharges are from the relativistic electron avalanches that are responsible for the flash of gamma rays” [see also Dwyer and Cummer, 2013]. Table 1 gives measurement details for the sensors used in the TGF studies cited above.

[3] The above findings show that TGFs are produced during the initial breakdown (IB) stage of IC flashes, defined herein as the first 5–20 ms of a flash [e.g., Villanueva et al., 1994; Shao and Krehbiel, 1996]. The IB stage of IC flashes is characterized by a series of IB pulses (IBPs); these IBPs have been studied with electric field (E) change and B-change data collected in various radio bandwidths [e.g., Kitagawa and Brook, 1960; Weidman and Krider, 1979; Bils et al., 1988; Villanueva et al., 1994; Betz et al., 2008; Nag et al., 2009]. Interferometer data [e.g., Shao and Krehbiel, 1996] and VHF lightning mapping array (LMA) data [e.g., Rison et al., 1999; Coleman et al., 2003] have also contributed to knowledge of the IB stage of IC flashes. The largest IBPs usually occur in the first 5 ms of an IC flash, have typical durations of 10–100 µs, and have characteristic frequencies of 10–100 kHz (in the VLF/LF radio bands). These large-amplitude pulses are now referred to as “classic” IBPs [Nag et al., 2009]. The initial polarity of the E-change of IBPs in IC flashes is positive in the physics definition of E (i.e., an upward, positive E exerts an upward force on a positive charge), which we use herein. IBPs are usually the largest amplitude events in an IC flash [Bils et al., 1988; Villanueva et al., 1994]. Nag et al. [2009] noted that there are many more IBPs with much smaller amplitudes and shorter durations (<4 µs) that they labeled “narrow” IBPs. (We herein call the other IBPs, i.e., those with durations between 4 and 10 µs, “intermediate” IBPs.) Each of the large-amplitude classic IBPs occurs during a slow (on a several millisecond time scale), monotonic E-change; the slow E-change has the same polarity as the peaks of the classic IBP and a magnitude that is “an appreciable fraction of the peak magnitude of the pulse” [Bils et al., 1988]. In 89 IC flashes, Bils et al. [1988] found on average four large-amplitude IBPs per flash. In addition to confirming these findings, Villanueva et al. [1994] speculated that classic IBPs were “likely associated with the initial in-cloud channel formation processes.”

[4] Interferometer measurements of radiation from electrical breakdown indicate that during the IB stage of an IC flash, the breakdown transports negative charge upward from the main negative cloud charge to the upper positive cloud charge, thereby establishing a conducting channel between these two cloud charges [Shao and Krehbiel, 1996]. After the IB stage, the flash develops a horizontal bilevel structure as it spreads through the two cloud charge regions [Shao and Krehbiel, 1996]. LMA data support the Shao and Krehbiel [1996] findings [e.g., Rison et al., 1999; Coleman et al., 2003; Thomas et al., 2004]. We note that to date, the only connection between classic IBPs and the upward negative charge motion in the IB stage seen with interferometers and LMAs is that they both occur during the IB stage. Table 1 includes details for most of the sensors used in the IB studies cited above.

[5] The present study describes new data on IC flashes aimed at causally connecting the large amplitude lightning events occurring at the beginning of IC flashes—classic IBPs and their concurrent, several millisecond duration, monotonic E-changes—with the TGF-associated events described above: the 2–6 ms ULF pulses, the 150 µs source current for the VLF/LF pulses, and the 10–100 µs VLF/LF pulses themselves. It is our hypothesis that classic IBPs along with their slow, monotonic E-change cause TGFs, and we will offer a speculation of how that might occur.

2 Instrumentation and Analysis Techniques

[6] The lightning data in this study were collected during the summers of 2010 and 2011 for flashes occurring over or near the NASA/Kennedy Space Center (KSC) in Florida, USA. The primary instruments include E-change sensors, B-change sensors, and a VHF lightning mapping system. We also used data from the National Lightning Detection Network (NLDN) [e.g., Cummins and Murphy, 2009], plus in 2010, a LINET (Lightning Network) system [Betz et al., 2004; Betz et al., 2007] to detect return strokes and in-cloud current surges. The sensors for this study are included in Table 1.

[7] The E-change sensors have been described in detail in Karunarathne et al. [2013]. They are similar to those used by Stanley et al. [2006] and Shao et al. [2010], but had wider bandwidth and longer triggered capture times (see Table 1). In 2010 we deployed five E-change sensors across a horizontal area approximately 20 km × 40 km centered on KSC [Stolzenburg et al., 2012]. In 2011 we deployed 10 E-change sensors across approximately 70 km × 100 km [Karunarathne et al., 2013]. Sensors for both years recorded continuously at a sampling rate of 10 kilosamples/s (kS/s) and in a triggered mode at 1, 5, or 10 megasamples/s (MS/s) sampling rate with typical record lengths of 500 ms divided into 150/350 ms of pre-/post-trigger data. Herein we display primarily triggered E-change data from 2011 with bandwidth of 0.16 Hz to 2.6 MHz and a sampling frequency of 5 MS/s. Some continuous E-change data from 2010 will also be shown. Table 1 shows that the triggered, 5 MS/s E-change data have sufficient bandwidth to reliably display both the slow monotonic changes described by Bils et al. [1988] and the much faster classic IBPs that occur during the slow changes [e.g., Weidman and Krider, 1979; Bils et al., 1988; Villanueva et al., 1994; Nag et al., 2009].

[8] The 2011 array of E-change sensors can be used to determine the location of IBPs using a time of arrival technique called position by fast antenna or PBFA [Karunarathne et al., 2013]; the PBFA technique is most similar to the three-dimensional location technique used with Los Alamos Sferic Array [Shao et al., 2006]. Weidman and Krider [1979] characterized IBPs as tending to have “two or three fast-rising pulses” (of positive polarity with our E definition) superimposed on the initial deflection of a bipolar waveform. We refer to the fast-rising pulses as “subpulses” in a classic IBP; PBFA locates these subpulses. Since we count the positive peak of the overall bipolar waveform as a subpulse, classic IBPs have at least one subpulse and usually have multiple subpulses. Narrow and intermediate IBPs apparently consist of only one fast-rising subpulse. Examples of classic and narrow IBPs from an IC flash are shown in Nag et al. [2009, Figure 2, with opposite E polarity convention]. Typical PBFA location errors for IBPs of IC flashes within 30 km of KSC are <250 m in horizontal position and <400 m in altitude, with reduced χ² values typically <2 [Karunarathne et al., 2013]. PBFA error estimates are based on Monte Carlo simulations of the timing uncertainty. To obtain a PBFA event location, at least five E-change sensors must have recorded the event with a sufficiently large signal-to-noise ratio and at a 5 or 10 MS/s sampling rate. For these reasons, we are not able to obtain reliable PBFA locations for all subpulses.

[9] The primary B-change sensors used in this study are the same as those used in the TGF investigations cited in section 1 and shown in Table 1 [Lu et al., 2010, 2011; Cummer et al., 2011]. In 2010 we deployed a LINET array around KSC with seven B-change sensors [Stolzenburg et al., 2012]; LINET provided (x, y, z, t) locations of lightning events including IBPs of IC flashes [Betz et al., 2004, 2008].

[10] Data from a VHF lightning mapping system, called LDAR2 (or 4DLSS), are collected and archived by KSC to support its operations. Thomas et al. [2004] describe LDAR2 as a commercial version of the LMA system. For LDAR2 locations within 20 km (40 km) of the LDAR2 origin, horizontal position errors are estimated to be <100 m (<300 m) [Murphy et al., 2008]. Murphy et al. [2008] did not report vertical location errors for LDAR2, but based on analyses in Thomas et al. [2004], we expect the vertical errors to be about 2.4 times the horizontal errors, namely, <240 m (<720 m) at 20 km (40 km) range. We used NLDN data [e.g., Cummins and Murphy, 2009] to select possible TGF events in IC flashes; the events chosen had high peak currents (>20 kA), were not associated with lightning return strokes, and therefore were probably events from IC flashes.

[11] The Cloud to Ground Lightning Surveillance System is another KSC operations support system used in this study; it determines lightning ground strike locations using hardware and software similar to NLDN [Wilson et al., 2009]. These data were used to identify cloud to ground (CG) flashes.

[12] The ULF B-change data can be used to estimate the charge moment change, ∆M, of each slow ULF pulse using the technique described in Cummer et al. [2005] and Lu et al. [2011]. A positive ∆M corresponds to downward motion of positive charge or upward motion of negative charge [Lu et al., 2011]. For this method of determining ∆M, Cummer et al. [2005] estimated “a worst-case absolute error of −33%/+50%.” Note that ∆M = QH, where Q is the charge magnitude of each dipole charge and H is the distance between the two dipole charges.

[13] The E-change data can be used to determine ∆M of the slow monotonic E-changes [e.g., Bils et al., 1988], as follows. The E-changes at the closest four to six sensors to the flash are determined for the duration of the slow monotonic E-change (typically 2–3 ms, essentially the same time as the duration of the slow ULF pulse, as shown below). Then we assume that a simple dipole, with negative charge approximately above positive charge, was produced during the slow monotonic E-change by the initial leader current(s) and that the associated dipole moment change (i.e., ∆M) caused the measured E-changes. The technique for determining the E-change ∆M involved two steps. Step 1 was (a) to use PBFA locations to choose beginning upper (−Q) and lower (+Q) dipole locations (described in more detail in section 3.1.1), (b) to determine the best Q to match the E-changes at the closest sensors, and (c) to calculate a reduced χ² for the solution. Step 2 was to use the result of Step 1 as the beginning of two searches for the best fit values of Q and the (x, y, z) of the lower dipole location using (a) the Levenburg-Marquardt algorithm [e.g., Bevington, 1969; Thomas et al., 2004] and (b) the Trust Region Reflective algorithm [e.g., Coleman and Li, 1996]; the output of Step 2 gave ∆M (=QH), Q, the (x, y, z) of the lower dipole, the distance H between the dipole charges, and the reduced χ² of each solution. Two algorithms are used because the search domain can be more easily restricted in the Trust Region Reflective algorithm, and this proved necessary when the Levenburg-Marquardt algorithm placed the lower charge at an unphysical location.

3 Data

[14] One motivation for this study arose from comparing TGFs recorded by the Gamma-ray Burst Monitor (GBM) on the Fermi Gamma-ray Space Telescope [Briggs et al., 2010] to ULF and LF B-change data and E-change continuous data (10 kS/s sampling). The TGF detection sensitivity of GBM was improved with a new data mode that transmits information on individual photons to the ground for an off-line search [Briggs et al., 2013]. The expanded GBM TGF sample provided nine TGFs within 1000 km of KSC while our E-change sensors were operational. Figure 1 shows one of the nine TGF events along with B-change and E-change data and a LINET (x, y, t) event location; this particular TGF was chosen because it is the only one with a coincident LINET event. (At a distance of 220 km the event was too far from the center of our small LINET array to determine its altitude.) Comparisons between LINET and triggered E-change data in many flashes (not shown) indicate that LINET events at the beginning of IC flashes are large+amplitude, fast-rising subpulses of classic IBPs [see also Betz et al., 2008]. In Figure 1, the LINET event and first large IBP (seen as the first negative-going LF pulse in Figure 1) were coincident to within 3 µs. The LINET event occurred close to the beginning of the TGF, but the relative timing uncertainty between the TGF and the LINET source is probably ±30 µs and is due primarily to event location uncertainties (especially the altitude) and the TGF event time uncertainty.

[15] In Figure 1, the E-change pulses (which are not well-defined in our 10 kS/s continuous data) are roughly coincident with the B-change LF pulses and with the burst of gamma rays. The burst of gammas occurred during the initial half of the slow ULF B-change pulse. Due to the distance to this event, no triggered, wideband E-change data were available to compare to the gamma burst, B-change LF pulses, and slow ULF B-change pulses. The coincidence in Figure 1 prompted us to suspect a possible connection between classic IBPs and the slow ULF pulse and VLF/LF pulses associated with TGFs. Unfortunately, we have not yet found any documented TGF-producing lightning flashes that triggered our E-change sensors.

[23] We chose to search the 14 August 2011 data set for candidate IC Events, since on this day we had several thunderstorms within 50 km of KSC and eight E-change sensors sampling at 5 MS/s. From the LDAR2 and the Cloud to Ground Lightning Surveillance System data, we determined that approximately 1700 CG flashes and 25,500 IC flashes occurred within 75 km of KSC on 14 August 2011. The NLDN search for large amplitude IC pulses found 356 events within 75 km of KSC, so roughly 1.4% of the IC flashes had a large amplitude IC pulse. We then chose two IC flashes, each with two IC Events as defined above, for detailed analysis; these flashes were chosen because they included large ULF B-change ∆Ms, 35 and 77 C km, the latter being the largest ULF B-change ∆M of 14 August 2011. These two flashes are similar in many details, as described below. We also selected seven additional IC flashes with one IC Event each and one event from an IC flash on 14 August that satisfied five of the six IC event criteria (not the NLDN criterion). These eight additional IC flashes share many of the features of the two flashes selected for detailed analysis; the characteristics of all 10 flashes are compared below in tabular form.

3.1 Two IC Events in IC Flash A at 2318:27 UT on 14 August 2011

[24] Figure 2 shows an overview of the first 300 ms of E-change versus time for an IC flash (Flash A) that occurred at 2318:27 UT, or 83,907 s after midnight, on 14 August 2011; the flash occurred about 33 km NE of the LDAR2 origin. E-change data from the closest sensor (K14 at a distance of 27.4 km) are shown. Figure 2 also displays (as altitude versus time) LDAR2 data for the entire 300 ms and PBFA data for the first 30 ms of the flash. Most of the PBFA data (17 of 19 events) occurred during the 7 ms of the IB stage (Table 2). This flash was ideal for analysis because most of the subpulses of the IBPs could be located with PBFA. It is easy to see in Figure 2 that the largest fast pulses in Flash A occurred during the IB stage (as typical for IC flashes).

Table 2. IBP Subpulses Located by PBFA for Flashes A and B Listed in Order of Occurrence

Flash Time (Figure)	Identifier	Burst	IBP Type	No. of Subpulses	z (m)	∆z (m)	∆tc (ms)
Overall Altitude Spanned by IBPs = 4220 m (7280 m to 11,500 m)
2318:27 UT (Figure 3a)		A1	intermed.	1	7,280
		A1	classic	1	8,120		0.060
		A1	intermed.	1	7,670		0.190
		A1	classic	2	8,300–8,530	230	0.035
(Figure 4a)	IC Event 1		classic	1	7,760		0.613
(Figure 4b)	IC Event 1	A2	classic	4	8,390–9,050	660	0.502
	IC Event 1	A2	classic	1	10,160		0.010
(Figure 3a)			intermed.	1	11,490		2.403
			classic	1	11,200		0.025
(Figure 5)	IC Event 2	A3	classic	4	10,520–11,500	980	1.967
Overall Altitude Spanned by IBPs = 5610 m (7580 m to 13,190 m)
0030:28 UT (Figure 7a)		B1	classic	2	7,580–8,470	890
		B1	intermed.	1	8,680		0.017
(Figure 8a)	IC Event 3	B2	intermed.b	1	8,710		0.950
	IC Event 3	B2	classic	1	8,770		0.210
	IC Event 3	B2	classic	1	8,790		0.097
	IC Event 3	B2	intermed.	1	8,500		0.034
	IC Event 3	B2	intermed.	1	9,070		0.070
(Figure 8b)	IC Event 3	B2	intermed.	1	9,590		0.042
	IC Event 3	B2	classic	5	8,630–9,660	1030	0.127
(Figure 9a)	IC Event 4		narrowa	1a	9,410		2.772
	IC Event 4		narrowa	1a	8,340		0.100
	IC Event 4		narrowa	1a	8,400		0.040
	IC Event 4		narrowa	1a	8,310		0.058
	IC Event 4		classica	1a	8,210		0.050
(Figure 9b)	IC Event 4	B3	classic	5	10,490–12,270	1780	0.038
			narrowa	1a	9,250		0.000
(Figure 7a)			classic	1	13,190		0.330
			classic	1	12,650		0.220
			classic	1	12,990		0.610

• ^a Abnormal IBP polarity.
• ^b IBP is nearly coincident (<1 µs) with LDAR2 event.
• ^c ∆t is time between the beginning of the IBP and the end of the preceding IBP.

[25] As mentioned in section 1, IC flashes typically move negative charge upward and leave an equivalent positive charge at a lower altitude. During the first 150 ms of Flash A, the overall E-change was positive, i.e., dominated by the upward motion of negative charge. At a range of 27 km, the E-change sensor was beyond the reversal distance [Ogawa and Brook, 1964] (meaning that the upper charge of the dipolar E-change dominated the E-change). Thus, the positive E-change in Flash A fits with upward transport of negative charge.

[26] The LDAR2 data in Figure 2 and Table 3 indicate that after the IB stage, negative polarity breakdown of this IC flash propagated horizontally through the upper positive cloud charge (centered for this flash near 12.5 km altitude) while positive polarity breakdown propagated horizontally through the main negative cloud charge (centered at about 6.9 km), as typical for IC flashes [e.g., Shao and Krehbiel, 1996; Coleman et al., 2003]. We note that the 5.6 km vertical separation distance between the two charge regions is relatively large though not unprecedented [e.g., Koshak et al., 2007]; more typical vertical separation distances are 2–3 km as seen for flashes studied by Shao and Krehbiel [1996] and Coleman et al. [2003].

Table 3. Bursts of IB Pulses for 10 IC Flashes From 14 August 2011

Flash Time (IB stage duration) [Figures]	Bursts in IB Stage	Altitudes Spanned (m)	Burst ∆z (m)	Relative ∆Ea (V m−1)	MNCC Topb (center) Bottom (m)	UPCC Topb (center) Bottom (m)	∆t c (ms)
2318:27 UT	A1	7,280–8,530	1,320	0.9	7,120	13,050	−4.0
(7 ms)	A2	8,390–10,160	1,800	8.4	(6,850)	(12,450)
[Figures 2-5]	A3	10,520–11,500	980	14	6,600	12,040
0030:28 UT	B1	7,580–8,680	1,100	0.6	8,240	13,410	+0.7
(7 ms)	B2	8,630–9,660	1,030	11	(7,190)	(12,910)
[Figures 6-9]	B3	10,490–12,270	1,780	56	5,990	12,040
2050:20 UT	C1	10,070–10,850	780	2.1	8,540	13,950	+47
(2 ms)	C2	10,870–11,330	460	5.4	(8,100)	(12,720)
					7,610	11,110
2055:00 UT	D1	10,440–10,890	450	1.3	8,840	14,590	−0.03
(5 ms)	D2	11,900–14,710	2,810	6.9	(8,150)	(14,330)
					7,640	13,960
2100:16 UT	E1	10,170–10,230	60	0.3	8,700	13,780	−5.0
(7 ms)	E2	11,380–12,980	1,600	13	(7,890)	(12,930)
					7,320	11,770
2102:01 UT	F1	10,890–12,980	2,100	10	9,880	13,870	−8.0
(2 ms)					(9,690)	(13,130)
					9,630	12,730
2135:30 UT	G1	9,800–10,600	800	8.3	8,620	12,840	+3.0
(2 ms)					(8,350)	(11,810)
					8,160	10,970
2257:12 UT	H1	8,730–9,160	430	0.5	8,050	12,910	+0.5
(6 ms)	H2	9,520–10,210	690	1.9	(7,750)	(12,210)
	H3	10,370–11,610	1,240	15	7,360	11,260
2314:17 UT	J1	7,560–7,910	350	2.2	7,440	12,490	−1.3
(4 ms)	J2	7,660–8,700	1,040	5.8	(6,630)	(11,630)
	J3	8,840–10,200	1,360	24	5,550	10,910
2357:27	K1	7,010–8,150	1,140	0.7	7,300	13,730	−2.0
(5 ms)	K2	8,330–8,970	640	6.9	(6,560)	(11,810)
	K3	8,590–11,460	2,870	9.3	5,320	11,060

• ^a Relative ∆E is the calibrated E-change associated with each burst; ∆E data for a particular flash are from the same sensor, but are not range normalized.
• ^b Altitudes of main negative cloud charge (MNCC) and upper positive cloud charge (UPCC) were determined from LDAR2 data after the IB stage.
• ^c ∆t is the time difference between the first IBP of the flash and the first LDAR2 VHF event; negative times mean the IBP occurred before the LDAR2.

[27] During the IB stage PBFA located 17 pulses; 3 of these were intermediate IBPs, and the other 14 were associated with 7 classic IBPs, of which 4 were single subpulse IBPs and 3 were multiple subpulse IBPs. As we show below, the multiple subpulse classic IBPs were associated with the largest charge moment changes. The PBFAs during the IB stage had reduced χ² values ≤1.6; horizontal and vertical location errors were both approximately 200–500 m. Two additional PBFA locations were determined for pulses that occurred 14 ms and 23 ms after the end of the IB stage; the locations of these two pulses were within the upper positive cloud charge as defined by the LDAR2 locations. The last PBFA location is the only one that was time coincident (to within 1 µs) with an LDAR2 source; the arrival time difference between the LDAR2 and PBFA events at the K14 sensor site was 0.7 µs. With LDAR2 location errors of about 200 m in the horizontal and 480 m in the vertical [Murphy et al., 2008], it seems possible that both systems located the same intermediate IBP (7 µs duration, 5 V m⁻¹ E-change at a range of 27 km) since the locations of the two systems differed by only 280 m in the vertical and 750 m in the horizontal.

[28] As seen in Figure 2, the PBFA findings support and confirm the findings of Shao and Krehbiel [1996] and others that the initial breakdown processes of an IC flash move upward from the main negative cloud charge to the upper positive cloud charge and create a conducting path between these charge regions. A new finding from Figure 2 is that IBPs appear to be directly related to the initial breakdown and its upward motion; this connection is shown in more detail below. As will be seen, the initial polarity of the IBPs and their subpulses was positive, indicating that they transported negative charge upward [e.g., Weidman and Krider, 1979]. Additionally, these PBFA findings show that the classic IBPs seem to be directly involved with establishing the conducting path between the main negative and upper positive cloud charges. We therefore agree with the speculation of Villanueva et al. [1994] that the classic IBPs are “likely associated with the initial in-cloud channel formation processes.” Below, we speculate that the initial in-cloud channel formation is caused by an “initial leader” that is different from the stepped leaders propagating horizontally through the main negative and upper positive cloud charges during later stages of the flash.

[29] Figure 3a shows 12 ms of the Figure 2 data with the addition of the ULF and LF B-change data; the figure is focused on the 7 ms IB stage of Flash A. There are two classic IBPs that qualify as IC events based on the criteria listed above. IC Event #1 had 2.8 ms duration; IC Event #2 lasted 3 ms. (The exact begin and end times of the candidate events are based primarily on the timing of the two significant ULF pulses). IC Event #1 is coincident with the second multiple subpulse classic IBP in the E-change data; its more precise beginning time was chosen to start after the end of the first multiple subpulse classic IBP. Figures 3b and 3c provide plan views of the PBFA and LDAR2 locations at two scales and show that the event locations moved NE, then N, across a horizontal area about 1 km × 1 km.

[30] Before discussing the individual IC Events, we note that Figure 3a shows that most of the upward transport of negative charge during the IB stage occurred during the time of the three bursts seen in the PBFA data of the IBPs. There was one multiple subpulse IBP in each burst of IBPs. The first burst of Flash A (Burst A1) began at the beginning of the IB stage and lasted about 200 µs. It included the first three IBPs (each with a single fast pulse) and a two subpulse classic IBP (Figure 3a and Table 2). This burst spanned 1200 m in altitude (7.3 km to 8.5 km) and had a slow, monotonic E-change of ~0.9 V m⁻¹ (at a range of 27 km) over a 1 ms period that included the two subpulse classic IBP. As seen in Figure 4 and Table 2, Burst A2 began about 1.1 ms later, lasted about 200 µs, and included a four-subpulse classic pulse followed, only 10 µs later, by a single subpulse classic IBP. Together these two classic IBPs extended the initial leader another 1700 m upward to 10.2 km altitude; the lowest IBP locations of Burst A2 were slightly below the upper altitude reached in Burst A1. There was also a significant slow monotonic E-change associated with Burst A2 that is described in more detail in the next section. About 2.4 ms after the second burst, there were two small-amplitude, single pulse IBPs near 11.5 km altitude separated in time by 35 µs. About 2.0 ms after these two IBPs, the third and final burst, A3, was associated with just one IBP, a four-subpulse classic IBP (see Figure 5). Burst A3 lasted about 600 µs, spanned the altitude range of 10.5 km to 11.5 km, and had an even larger slow, monotonic E-change than the previous bursts. The lowest subpulse in Burst A3 was only a few hundred meters above the highest subpulse in Burst A2.

[31] In addition to showing that the upward progression of the initial leader occurred with three short bursts separated by 1–4 ms, the above data also reveal that the amplitudes of the slow, monotonic E-changes that accompanied the three multiple subpulse classic IBPs in this flash were successively larger. A similar amplitude increase was found in all eight of the IC flashes with multiple bursts (Table 3). As we will show below, the amplitude of the slow, monotonic E-changes is directly related to the amount of charge moved upward by the initial leader (i.e., its dipole moment change). Thus, the successively larger amplitudes indicate that successively higher-altitude bursts move successively larger charges upward.

[32] In summary, the upward progression of IBP locations spanned ~4 km in altitude in three bursts, with times between IBP bursts of 1–4 ms and burst distances of 1000–1700 m. Thus, one hypothesis about the classic IBPs in Flash A is that they are a manifestation of the initial leader that is different from a stepped leader and that establishes a conductive channel between the main negative and the upper positive charge regions of the cloud. The subpulses of the IBPs are the largest pulses in the flash, and as shown below, they and the initial leader develop in a vertical in situ (or ambient) cloud electric field that is close to the threshold for relativistic runaway electron avalanche events. The (upward) progression of IBPs does not resemble a typical (downward) negative stepped leader seen in optical data of cloud-to-ground (CG) flashes, i.e., with interstep time intervals of 15–50 µs and step distances of 5–50 m [e.g., Schonland, 1956; Hill et al., 2011]. On the other hand, the progression of IBPs is more similar to a horizontal negative stepped leader in an IC flash studied by Winn et al. [2011]; that leader had interstep times of 0.5–7 ms, step distances of 50–600 m, and developed in a horizontal electric field of 10 kV m⁻¹. Thus, an alternative hypothesis of leader development in the IB stage is that the leader channel is established by a stepped leader and that IBPs are a manifestation of the stepped leader.

[33] However, if there was also a stepped leader associated with the initial upward leader extension, we did not see clear evidence of it in our data. Stepped leaders are typically observed with VHF lightning mapping arrays, and the LDAR2 system is such an array. There are very few LDAR2 events during the IB stages of the 10 flashes studied herein (Table 3), and Figure 3 is a typical example. Figure 3 shows that only four LDAR2 sources were located during the IB stage of Flash A versus 17 subpulses of IBPs (Table 2); only two of the LDAR2 sources were coincident with an IBP subpulse. For Flash A, as for the other flashes studied herein, most (three of four) of the LDAR2 sources occurred during the bursts of IBPs and at the altitudes and horizontal positions of the IBPs of a particular burst (rather than spread more uniformly across the entire vertical gap between the main negative cloud charge and the upper positive cloud charge as would be expected for a typical stepped leader). Perhaps, the LDAR2 sources are showing only a few of the leader steps of the sort described by Winn et al. [2011]. The sparse LDAR2 sources located as the initial leader spans the vertical gap and the large vertical distance spanned by each IBP burst make us think that no stepped leader occurred during the IB stage.

[34] Additional support for the idea that no stepped leader occurred at the beginning of Flash A is found in two other recent studies. First, Betz et al. [2008] found that many flashes, both IC and CG, begin either with a pulse detected at VLF/LF frequencies but not at VHF frequencies or with a pulse that is time coincident (to less than 200 µs) at both frequencies. The initial VLF/LF pulse was detected with a LINET system, so the pulse was almost certainly an early, classic IBP. Betz et al. [2008] argued that only a relatively long discharge—hundreds of meters in length rather than tens of meters for a typical stepped leader—would be detected at VLF/LF frequencies. Based on this argument and on the fact that the first IBP detection occurred before or concurrent with the first VHF source location, Betz et al. [2008] concluded that the first detected pulse (an IBP) occurred without being preceded by a stepped leader and proposed that the pulse was caused by an avalanche of relativistic runaway electrons. For comparison with the Betz et al. [2008] data, Table 3 includes the time difference, ∆t, between the first IBP and the first LDAR2 source for the group of 10 flashes, with negative times indicating that the IBP occurred earlier. In particular for Flash A, the first IBP preceded the first LDAR2 source by about 4 ms. Overall in Table 3, the first IBP preceded the first LDAR2 event by more than 1 ms for five flashes, while the IBP and LDAR2 source were coincident (to within 1 ms) for three flashes, and for two flashes the LDAR2 source preceded the IBP by more than 1 ms.

[35] Second, the findings in Stolzenburg et al. [2013] also support the idea that no stepped leader occurred during the IB stage of Flash A. Stolzenburg et al. [2013] studied IBPs of CG flashes with a high-speed video camera (operated at 50,000 frames/s) and the same E-change sensor array at KSC used in this study. Through direct visual observation of the IB stage of several CG flashes, they found that the initial leaders are the first luminous events in CG flashes, are hundreds of meters long, and occur before the stepped leader begins. Stolzenburg et al. [2013] showed that individual classic IBPs in the E-change data are coincident with individual extensions of the visually observed initial leader in CG flashes, thereby proving that each classic IBP is radiated by the physical extension of the initial leader. Stolzenburg et al. [2013] also obtained video records of IBPs for a few IC flashes. For the IC flashes, the initial leaders were not in the camera's field of view, but scattered light from the initial leaders was detected and showed that IBPs were coincident with the first luminous events in those flashes, thereby supporting the suggestion above that the first IBPs occur immediately after flash initiation and before a stepped leader develops.

3.1.1 IC Event #1

[36] IC Event #1 (Figure 3) satisfied the ‘Event’ criteria as follows: It occurred during the IB stage, the B-change data had a slow ULF pulse with a 15 C km charge moment change, there were multiple LF B-change pulses during the slow ULF pulse, and the NLDN pulse had an estimated peak current of 43 kA. Figure 4a shows the 2.8 ms of IC Event #1 defined by the duration of the ULF pulse. Burst A2 of IBPs (discussed above) occurred during this IC event. The E-change data in Figure 4a show three classic IB pulses superimposed on a slow, monotonic E-change of 8.4 V m⁻¹ over the 2.8 ms period; about 40% of the monotonic change (3.5 V m⁻¹) occurred during the ~170 µs duration of the four-subpulse classic IBP. In other words, 60% of the slow, monotonic E-change happened “very” slowly over 2.8 ms while the other 40% occurred “faster” during the 170 µs of the classic IBP. As found by Bils et al. [1988], the amplitudes of the subpulses within the classic IB pulse were larger than the slow, monotonic E-change. However, the exact contribution of the subpulses to the total E-change is not clear. We hypothesize that the slow monotonic E-change (of several millisecond duration) is caused by the upward current of negative charge in the developing initial leader of this flash and that this current is also responsible for the slow ULF B-change pulse (of 2–6 ms according to Lu et al. [2011]). The peak of the ULF pulse lags the four-subpulse classic IB pulse by about 0.5 ms so that the ULF pulse peak occurs near the middle of the overall monotonic E-change for the entire 2.8 ms time period. What is uncertain about the slow change is whether it is caused by current flow in nonextending leader or slow, upward extension of that leader.

[37] For easier comparison of the slow E-change associated with this IC Event and others given below, we range-normalized the E-change to a distance of 30 km. For IC Event #1, the range-normalized E-change was 7.4 V m⁻¹. The slow E-change may be too slow to produce a significant radiation field component so that it will not be seen at distant sensors; it at least includes induction and electrostatic field contributions at closer sensors [Uman et al., 1975].

[38] If we compare Figure 4a to Figure 1 (with a known TGF occurrence), we see that these two figures are quite similar in terms of the B-change data, with the LF pulses (and the gamma ray burst in Figure 1) occurring during the first half of the ULF pulse. It is also clear that the triggered E-change data in Figure 4a are much more similar to the LF and ULF B-change pulses than those revealed in the low-frequency continuous E-change data in Figure 1.

[39] Figure 4b shows 500 µs of the Figure 4a data including the 170 µs of the four-subpulse classic IBP and the single subpulse classic IBP that occurred 10 µs later (together these 5 PBFAs make up Burst A2). The LF B-change pulses have a different shape from the subpulses of the IBP for at least two reasons. First, the sign of the azimuthal B-change is opposite to that of the E-change (as expected for B and E radiation components of the general field equations of Uman et al. [1975]), and second, the LF sensor's relatively short (160 µs) decay time acts to differentiate the B signal with respect to time [Cummer et al., 2011]. Nevertheless, the similarities in the absolute occurrence times of the pulses (and therefore in the interpulse intervals) make it seem likely that the same physical event(s) caused both the subpulses and the LF pulses. The physical event(s) are some form of source current(s) [Cummer et al., 2011]. (Later we speculate that a relativistic electron avalanche developing just above the initial leader may have been the source current of each IBP subpulse and LF pulse pair.) We note that both the classic IBP duration and the overall duration the LF pulses was ~170 µs, which is in reasonable agreement with the 150 µs LF source current durations determined by Cummer et al. [2011] for two other documented TGFs. Such a source current might also account for the 3.5 V m⁻¹ monotonic E-change that occurred during the IBP. The 170 µs duration of this classic IBP is quite long compared to typical IBP durations. For 137 classic IBPs, Weidman and Krider [1979] found a mean duration of 63 µs with a standard deviation of 39 µs; only 12 of their IBPs had durations longer than 100 µs and the 4 longest were 170–230 µs.

[40] We note that the timing of the LF pulses in Figure 4b was 6–10 µs ahead of the E-change subpulses. We attribute the time difference primarily to the uncertainty in the PBFA locations relative to both the E-change sensor and the B-change sensor. However, another source of the time difference is the fact that the IB pulse locations change as the leader moves (Figure 3c), but we can only shift the arrival times by a fixed amount (appropriate for at least one PBFA location, but not for the other PBFA locations).

[41] From the slow ULF B-change pulse, a ∆M of 15 C km was determined using the technique described in Cummer et al. [2005] and Lu et al. [2011]. As outlined in section 2, the E-change data at the four closest sensors were used to determine ∆M of the coincident, slow, monotonic E-change. For the upper dipole charge location, we used either the highest PBFA location of the four-subpulse classic IBP (Figure 4b) or the higher location of the single subpulse classic IBP (Figure 4b). For the lower dipole, we used three possible locations: (1) the lowest altitude PBFA location (7.3 km) during the entire IB stage of the flash, (2) the highest PBFA location (8.5 km) of the previous IBP burst (A1), and (3) the lowest PBFA location (8.4 km) of the four-subpulse classic IBP of the IC event. We tested the six different pairs of upper and lower dipole locations as starting values of both the Levenburg-Marquardt (L-M) and the Trust Region Reflective (TRR) algorithms to determine a best fit to the E-change data. Five of the pairs gave ∆M = 12 C km with the dipole spanning some or all of the altitude range of Burst A2, namely, 8.4 km to 10.2 km, rather than moving charge from the starting altitude (7.3 km) of the upward developing initial leader. The (Q, H) values ranged from (7 C, 1.7 km) to (20 C, 0.6 km). Note that ∆M determines the ∆E measured at the different sensor sites, so different combinations of Q and H that give the same ∆M (=QH) will fit the ∆E data. (The sixth pair was rejected because both algorithms resulted in the wrong sign of Q and ∆M.) For the pairs with ∆M = 12 C km, the reduced χ² values were ≤0.02 and the percent differences between the measured E-changes and calculated dipole E-changes at the 4 sensors were <1%. The agreement between the E-change estimate and the ULF B-change estimate (15 C km) is reasonable, especially considering the possible errors in both. The estimate of ∆M using the E-change data has the advantage of fitting the ∆E measured at several different E-change sensor sites. Thus, we conclude that the slow ULF B-change pulse and the slow, monotonic E-change occurring over the same 2.8 ms time period were caused by the same current(s) moving negative charge upward. The E-change calculation of ∆M assumes that the dipolar charge is due to a current that moved charge in an established conducting channel to two fixed locations rather than a current that was progressing upward with time.

3.1.2 IC Event #2

[42] IC Event #2 is shown in Figure 5, which is an expanded portion of Figure 3. The IC event criteria were satisfied as follows: The event occurred during the IB stage, the B-change data had a 3 ms slow ULF pulse with a 35 C km charge moment change, and there were four LF B-change pulses during the slow ULF pulse. Burst A3 occurred during IC Event #2 and included only one IBP, a four-subpulse classic IBP. The E-change data of Figure 5 show a slow, monotonic E-change of 14.2 V m⁻¹ over the 3 ms period with about 35% happening very slowly and 65% of the monotonic change (9.1 V m⁻¹) happening faster during the ~600 µs duration of the four subpulse classic IBP. For IC Event #2, the range-normalized E-change was 14 V m⁻¹. As for IC Event #1 (Figure 4b) the LF B-change pulses and the subpulses of the IBP have similar absolute occurrence times, so they also have similar interpulse intervals.

[43] The ULF slow B pulse gave a ∆M of 35 C km. The E-change calculation of ∆M, using the four closest sensors over the 3 ms duration of IC Event #2, was based on only three pairs of beginning dipole locations since the highest PBFA of the four-subpulse classic IBP was also the highest PBFA of the IC Event. The TRR algorithm gave ∆M = 23 C km with reduced χ² values ≤0.4 and percent differences between the measured and calculated dipole E-changes at the four sensors <2%. The (Q, H) values ranged from (6.7 C, 3.4 km) to (8.5 C, 2.7 km). (We rejected the L-M algorithm results because the lower dipole positions were too far from the PBFA and LDAR2 locations to be believable.) As for IC Event #1, the best fit upper and lower dipole locations indicated that IC Event #2 moved charge along most or all of the altitude range spanned by Burst A3. The agreement between the E-change estimate (23 C km) and the ULF B-change estimate (35 C km) is again reasonable. As in IC Event #1, the E-change calculation of ∆M in IC Event #2 assumes a current that moved charge in an established conducting channel between two fixed locations.

[44] Comparing the B-change and E-change data in Figure 5 as done for IC Event #1, we again conclude that the same physical events are likely producing the features seen in both the B-change and the E-change data of IC Event #2. The very long 600 µs duration of this four-subpulse classic IBP is a surprising feature of these data; its duration was more than 2.5 times the longest duration of the 137 classic IBPs studied by Weidman and Krider [1979].

3.2 Two IC Events in Flash B at 0030:28 UT on 14 August 2011

[45] Another pair of IC events, similar to those just discussed from Flash A, were found in IC Flash B, which occurred at 0030:28 UT (roughly 23 h before Flash A) about 43 km SSW of the LDAR2 origin. Figure 6 shows an overview of Flash B for the first 200 ms of E-change data and LDAR2 plus PBFA data for the IB stage of the flash. As in Flash A, the largest fast pulses in Flash B occurred during the IB stage (though a few later pulses in Flash B were almost as large as the largest IBPs). The overall E-change of the flash was positive, as for Flash A and as expected for a normal IC flash with upward transport of negative charge. However, in Flash B, almost 90% of the positive E-change was associated with the IB stage; in Flash A, the IB stage contributed only 20% of the positive E-change. Based on the LDAR2 data, the upper positive and main negative cloud charges for Flash B were centered at approximately 12.9 km and 7.2 km, respectively (Table 3). As discussed above, the 5.7 km vertical separation of these charge regions is larger than usual for IC flashes.

[46] Figure 7a shows 12 ms of the Figure 6 data with the addition of the ULF and LF B-change data; Figure 7 is focused on the IB stage of Flash B. During the IB stage (which lasted 7 ms), PBFA located 28 pulses: 3 narrow, 7 intermediate, and 18 subpulses in 9 classic IBPs having 1–5 subpulses (Table 2). Unlike any other IBPs in Flashes A and B and in the eight additional flashes with IC Events, six IBPs had an initial negative (downward) deflection, i.e., opposite in polarity to all other IBPs; we discuss these six abnormal IBPs later. The 28 PBFAs had reduced χ² values ≤1.1, and horizontal locations errors averaged 210 m with a range of 160–430 m. However, the possible vertical location errors were larger than usual with an average of 1360 m and a range of 920–1900 m. These possible errors were relatively large because, as seen in Figure 7b, there were only two sensors (FLT and K24) within 40 km of the located pulses (since BCC was not operating) [Karunarathne et al., 2013]. However, comparing the PBFA and LDAR2 locations for the only IBP of Flash B that was time coincident (to within 1 µs) in both systems gives us reason to think the PBFA vertical errors are not so large. This coincident event was an intermediate IBP with an 8 µs duration and a 3 V m⁻¹ E-change at a range of 51 km. (In Figure 8a, the LDAR2 point is barely visible behind the leftmost PBFA location.) The small differences between the PBFA and LDAR2 locations (120 m, 60 m, 50 m, 0.6 µs) indicate these locations are in good agreement.

[47] Regarding bursts of IBPs, Flash B was quite similar to Flash A. Figure 7a shows that most of the upward progression during the IB stage of Flash B occurred in three bursts of IBPs. Burst B1 began at the beginning of the IB stage and lasted about 100 µs. It included a two-subpulse classic IBP and an intermediate IBP, spanned 1100 m in altitude, and had a slow, monotonic E-change of ~0.6 V m⁻¹ (at the FLT sensor at a range of 22 km, not shown) over a 1 ms period. As seen in Figure 8 and Table 2, Burst B2 began about 1.6 ms later, lasted about 700 µs, and included four intermediate IBPs, two single subpulse classic IBPs, and ended with a five-subpulse classic pulse. Burst B2 extended the initial leader another 900 m upward and had a slow monotonic E-change of 11 V m⁻¹ (at the FLT sensor). The lowest IBP locations of Burst B2 were slightly below the upper altitude reached in Burst B1. Burst B3 occurred about 3.1 ms after Burst B2, was associated with a single subpulse classic IBP and a five-subpulse classic IBP (see Figure 9). Burst B3 lasted about 740 µs, spanned the altitude range of 1800 m, and had a slow, monotonic E-change of 56 V m⁻¹. If we ignore the opposite polarity IBPs that occurred close to the time of Burst B3, then the lowest IBP locations of Burst B3 were 2 km above the upper altitude reached in Burst B2.

[48] Figure 7 also shows that only five LDAR2 sources were located during the IB stage of Flash B versus 28 IBP subpulses. Only two of the LDAR2 sources were coincident with an IBP subpulse. As in Flash A, most LDAR2 sources (four of five) occurred during the bursts of IBPs and at the altitudes of the IBPs of a particular burst. These data lead us to think that between bursts of IBPs, charge transport occurred mainly in the previously established leader channel and that leader extension occurred mainly during the bursts.

[49] Based on the slow ULF pulse in Figures 7 and 8, the first IC event in Flash B, called IC Event #3, had a 2.0 ms duration and included the time of IBP Burst B2. The E-change data of Figure 8a (from K14 sensor at a range of 51 km) show a slow, monotonic E-change of 1.4 V m⁻¹ over the duration of IC Event #3, with about 65% happening very slowly and 35% (0.5 V m⁻¹) happening faster during the five-subpulse classic IB pulse. For IC Event #3, the range-normalized E-change was 6.3 V m⁻¹. The ULF estimate of ∆M = 18 C km. The E-change estimates for both algorithms (L-M and TRR) were ∆M = 12 C km with reduced χ² values ≤0.01 and percent differences between the measured and calculated dipole E-changes at four sensors <1%. The (Q, H) values ranged from (18 C, 0.66 km) to (20 C, 0.6 km). The agreement between the E-change and B-change ∆Ms was reasonable. The upper dipole location was chosen as the highest PBFA location of the five-subpulse classic IBP of IC Event #3 (Figure 8). The two algorithms yielded the lower dipole location only 100–200 m above and 50 m horizontally from the lowest PBFA of the five-subpulse classic IBP. Thus, the dipole charge locations associated with charge transfer during IC Event #3 and Burst B2 were essentially defined by the upper and lower PBFA locations of the five-subpulse classic IBP.

[50] Based on the slow ULF pulse in Figures 7 and 9, IC Event #4 (the second in Flash B) had a duration of almost 3.0 ms, which included the time of IBP Burst B3. Burst B3 included only a five-subpulse classic IBP. The E-change data in Figure 9a (from the K14 sensor at a range of 51 km) show a slow, monotonic E-change of 9.1 V m⁻¹ over this duration, with about 30% happening very slowly and 70% (6.4 V m⁻¹) of the monotonic change happening faster during the five-subpulse classic IBP. For IC Event #4 the range-normalized E-change was 46 V m⁻¹. The ULF estimate of ∆M was 77 C km (the largest ∆M in the data of 14 August 2011). With the E-change data, both the TRR and L-M algorithms gave ∆M = 81 C km, with reduced χ² between 4.5 and 4.9. The (Q, H) values ranged from (37 C, 2.2 km) to (150 C, 0.54 km). The agreement between the E-change and B-change ∆Ms was good. As before, the upper dipole location was chosen as the highest PBFA location of the five-subpulse classic IBP of IC Event #4 (Figure 9a), and different versions of the algorithms yielded the lower dipole location at varying altitudes in the range spanned by the five-subpulse classic IBP. In spite of the relatively poor reduced χ² values, the percent differences between the measured E-changes and calculated dipole E-changes at the four closest sensors ranged from only 0.01% to 4.5%. For Flash B (as for Flash A), the largest ∆M was associated with an exceptionally long-duration (740 µs) multiple subpulse classic IBP.

[51] The six single-subpulse IBPs with opposite polarity are best seen in Figure 9b. They have the lowest PBFA altitudes, and (with one exception) they have short durations (3–6 µs) and small amplitudes (~1 V m⁻¹ in Figure 9b). The other IBP of these six was a single subpulse classic IBP with a 15 µs duration and a 5 V m⁻¹ amplitude in Figure 9b. We omitted the opposite polarity IBPs from Burst B3 because their altitudes were so much lower than the five-subpulse classic IBP of Burst B3 and because we have not seen a similar series of opposite polarity IBPs of other IC flashes. The opposite polarity (initial negative deflection) indicates either downward transport of negative charge or upward transport of positive charge. As yet we have no explanation of these opposite polarity IBPs, so we do not know if they are significant, but it seems clear that they do not occur during the initial development of most IC flashes. In spite of their relatively small amplitudes, they were easily seen at five or six E-change sensors, thereby allowing their PBFA locations to be determined.

4 Discussion and Speculations

[56] In this section we combine our findings with other facts and present some speculations about how initial leader development in IC flashes may be related to gamma ray production. We assume that relativistic electrons cause the gamma rays of TGFs [e.g., Carlson et al., 2009, 2010; Celestin and Pasko, 2011; Celestin et al., 2012; Xu et al., 2012; Dwyer, 2012]. Carlson et al. [2009, 2010] suggested that cold electrons might be accelerated to relativistic speeds in the large E fields found near the tips of leaders; they assumed that the total E seen by the electrons would be the sum of E due to charge on the leader and the ambient E due to the cloud charges. Celestin and Pasko [2011] suggested that cold electrons are accelerated to relativistic speeds in the large E at the tips of streamers associated with stepped leaders; these relativistic electrons would be further accelerated by the larger-scale E due to the charged tip of the stepped leader. Dwyer [2012] proposed a relativistic feedback mechanism in which “the charge moment change from lightning may drive the system over the feedback threshold, resulting in a self-sustained production of runaway electrons and a very rapid burst of gamma rays”. Our data give an estimate of the charge moment change of individual IBP bursts and their associated slow, monotonic E-change. As shown below, from these data we can obtain a rough estimate of E due to charge at the upper, negative tip of the initial leader; combining that E value with typical ambient E values provides an estimate of the total E.

[57] We found that IBPs span the gap between a storm's main negative and upper positive cloud charges. The ambient E in this gap is large and is often close to the relativistic electron avalanche threshold of 280 kV m⁻¹ at sea level [Symbalisty et al., 1998; Dwyer, 2003]. An example (see Figure 10) of this fact is shown in a balloon sounding of the ambient E in an active thunderstorm in Oklahoma [Stolzenburg et al., 2007]; the gap between the top of the main negative cloud charge (at about 8.5 km altitude) and the bottom of the upper positive cloud charge (at 13 km altitude) is about 4.5 km and thus is similar to the gaps in Flashes A and B discussed above. Across the gap, the ambient E is equivalent to a sea level value of 180–200 kV m⁻¹. Thus, if the negative charge at the tip of an initial leader is large enough, a relativistic electron avalanche would be possible above the leader tip at almost any altitude within the gap due to the superposition of the ambient E and the E due to the charge at the tip of the initial leader. Since IBPs occur in this gap and since IBPs are recognized to be the largest-amplitude events in IC lightning flashes, it seems plausible that relativistic electron avalanches are involved in causing IBPs.

[58] We found that the IC events were 2–3 ms in duration and were associated with a burst of IBPs including one multiple subpulse IBP. In the discussions of Flashes A and B above, we identified the upward sloping E-changes as “slow, monotonic E-changes” [after Bils et al., 1988] composed of two contributions: (i) “very slow” E-changes that occurred during the few milliseconds of a IC Event and (ii) a faster E-change associated with the multiple subpulse classic IBP within the IC event.

[59] Two possible scenarios for the “very slow” monotonic E-change are as follows. In scenario A, stepped leader extension of the initial leader could explain the very slow E-change if induced negative charge developed quickly at tip of a slowly extending leader. In this scenario the leader channel would need a relatively high conductivity. Carlson et al. [2010] have a careful discussion of leader charging in an ambient E and a good model of the development of E due to a conducting leader immersed in an ambient E. In scenario B, no leader extension occurs, the very slow change is due to slow inductive charging of the leader tip in a weakly conductive leader channel. The ambient E again drives the charge rearrangement (“inductive charging”) on the initial leader, but this rearrangement occurs more slowly because of the low conductivity of the nascent leader channel. The lack of any clear evidence of a stepped leader motivated the second scenario.

[60] Two scenarios could also explain the change from very slow to faster monotonic E-change. In scenario C, faster stepped leader extension could explain the faster E-change if either the extra channel length and/or an increasingly conductive channel leads to faster growth of induced negative charge at the leader tip. In scenario D, no leader extension occurs; instead, faster inductive charging of the leader tip occurs due to an increasingly conductive leader channel. In scenario D, the multiple subpulse classic IBP that occurs during the faster monotonic E-change extends the initial leader upward, thereby making a new leader section that is weakly conductive.

[61] Two scenarios could explain the subpulses in classic IBPs. Scenario E is based on Weidman and Krider [1979], who suggested that the subpulses “are probably associated with the formation of the discharge channel in some stepped fashion”. Their suggestion was based on the facts that subpulses and stepped leaders and dart-stepped leaders near the ground have similar rise times (0.3 µs), widths (0.5 µs), and intersubpulse intervals (16 and 7 µs, respectively). We agree with Weidman and Krider [1979] concerning the rise times of subpulses, but for the IC Events investigated above, we find many subpulses have widths and intersubpulse intervals much longer than those quoted. For example, the four IBP subpulses in Figure 5 have widths of 5–10 µs and intersubpulse intervals of 120, 130, and 140 µs (see also Figures 4b, 8b, and 9b). Thus, if the subpulses of classic IBPs are stepped leader pulses, the steps are different from those of negative stepped leaders near the ground. Relativistic electron avalanche events caused by such steps might produce TGFs [e.g., Carlson et al., 2010], or the steps may produce an avalanche of thermal electrons that produce TGFs [e.g., Celestin and Pasko, 2011]. In scenario F, each subpulse in the multiple subpulse classic IBP is a relativistic electron avalanche event, and these events cause extensions of the initial leader. This scenario seems like a good candidate mechanism since the ambient E plus E due to charge in the leader tip could easily exceed the relativistic electron avalanche threshold. The motivation for scenario F is that (1) the largest amplitude E-changes of IC flashes are IBPs and (2) IBPs only occur during when the initial leader is developing in the region with the largest ambient E magnitudes. These facts make us suspect that a mechanism other than leader stepping is needed to explain both the subpulses of classic IBPs and gamma ray production. More precise time comparisons between TGF production and IBP subpulse occurrence are needed to test these scenarios.

[62] A key detail in scenario F concerns the dipole charge distribution developed by the very slow monotonic E-change (scenario B): Is it large enough to make the net electric field exceed the relativistic electron avalanche threshold (280 kV m⁻¹ at sea level pressure) over several hundred meters (e.g., at least 500 m) to allow for sufficient e-folding in the avalanche development? As indicated in Figure 10, the ambient E magnitude may be about 50 kV m⁻¹ at 10 km altitude. In IC Event #1, discussed in section 3.1.1, the magnitudes of the ±Q and H values of the ∆M calculation ranged from 7 C with a charge separation distance of 1700 m or (±7 C, 1700 m) to (±20 C, 600 m) for a total ∆M of 12 C km. As noted in section 3.1.1, the very slow change caused about 60% of ∆M, and roughly half of the slow E-change occurred before the burst of IBPs discussed in scenario F. Thus, for the (±7 C, 1700 m) final dipole, a rough estimate of the vertical dipole before the burst of IBPs is (±2.1 C, 1700 m). If we assume that the upper leader tip (with −2.1 C) is located at 9.5 km altitude, then E due to the dipole at a distance of 500 m above the leader tip (i.e., at 10 km altitude) is 72 kV m⁻¹ pointing downward. Superposing this E with the downward pointing 50 kV m⁻¹ ambient E gives a total E = 122 kV m⁻¹ at 10 km altitude, which is 1.4 times the avalanche threshold value of 86 kV m⁻¹ at 10 km. A similar calculation with the (±20 C, 600 m) dipole gives a total E of 221 kV m⁻¹ at 10 km or 2.5 times the avalanche threshold. IC Event #1 (along with Event #3) had the smallest ∆M of the four IC events. A similar calculation for IC Event #4 (with the largest ∆M, 81 C km) is of interest. The E-change of IC Event #4 was fit with dipoles ranging from (±37 C, 2200 m) to (±150 C, 540 m). Only 30% of the total E-change was caused by the very slow E-change, and we again assume that half of this occurred before the IBP burst, so the dipole values before the IBP burst of IC Event #4 were (±5.6 C, 2200 m) and (22.5 C, 540 m). The dipole E values at 500 m above the dipoles are 193 and 623 kV m⁻¹, respectively; after including the ambient E, they are 2.8 and 7.8 times the relativistic avalanche threshold. The point of these simple calculations is to indicate how large the charges of the IC events were. Another indication of their great magnitude is seen in the fact that the smallest dipole (±7 C, 1700 m; IC Event #1) caused an 8.4 V m⁻¹ E-change at the K14 sensor located 27,000 m away. The calculations above are consistent with the dipole charges determined to fit the overall E-changes of the four IC events. Using the methods of Carlson et al. [2010], Celestin et al. [2012], or Dwyer [2012], one might construct a more sophisticated model of the initial leader currents, including charges distributed along the leader rather than the dipole point charges used herein. Such a model should provide more accurate estimates of the E-change associated with the very slow charge motion and hence better examinations of scenario F. We note that these models will also need to match the E-changes at the various sensor sites, as done herein.

[63] Scenarios B, D, and F assume that the initial leader (i.e., the leader during the IB stage of the IC flash) is not a stepped leader; instead, the leader extension occurs via relativistic electron avalanche events. As discussed earlier, support for this hypothesis comes from Betz et al. [2008] and from Stolzenburg et al. [2013]. Betz et al. [2008] showed that the first IBP of a flash often occurred before any channel preparation by a stepped leader; they therefore hypothesized that a relativistic electron avalanche event caused the first IBP. Stolzenburg et al. [2013] observed the initial leaders of CG flashes and showed that the initial leader extension was very different from a typical stepped leader, that each extension was coincident with an IBP, and that the first luminous events in a flash were initial leader extensions. Stolzenburg et al. [2013] also concluded that the typical negative stepped leader in a CG flash begins after the IB stage ends. For IC flashes, we hypothesize a similar leader development, namely, an initial leader during the IB stage that changes to a typical stepped leader (as described by Winn et al. [2011]) after the IB stage is completed. It may be that the initial leader in both CG and IC flashes is needed to make a sufficiently conductive channel to allow typical stepping to occur.

[64] We favor scenarios B, D, and F above, primarily because they seem to fit better with our findings about IBP locations and development and with the apparent lack of a stepped leader. However, scenarios A, C, and E or others not envisioned herein may prove correct when more data are available. Since many IC flashes seem to have large-amplitude pulses during their IB stage, our hypothesis suggests that gamma ray production may be common for IC flashes. Of course, not all of these gammas will reach satellite altitudes; the higher in altitude the gamma rays are produced, the more likely it is that they will reach an orbiting satellite and be recorded as a TGF [e.g., Dwyer and Smith, 2005].

[65] Rison et al. [1999] used LMA data in New Mexico to show that some IC flashes begin with a “narrow positive bipolar” pulse (NPBP) of the sort previously studied by Willett et al. [1989] and others; these NPBPs are similar to a single subpulse classic IBP with an especially large amplitude. Unlike the multiple subpulse classic IBPs with their associated slow, monotonic E-changes, NPBPs have only one positive subpulse [Willett et al., 1989]. NPBPs sometimes have additional oscillations on the falling side of the positive subpulse that are rarely (if ever) seen in classic IBPs. These oscillations have been attributed to current reflections in the NPBP's short conducting channel [e.g., Hamlin et al., 2007; Nag and Rakov, 2010]. None of the events studied herein are NPBPs at the beginning of IC flashes.

[66] Finally, we note that our data show no evidence of positive leaders developing simultaneously with the initial negative leaders. This does not mean that there were no positive leaders present.

5 Conclusions

[67] This study has focused on the initial breakdown (IB) stage of IC flashes, in particular, IC flashes that may have produced the upward bursts of gamma rays called TGFs. Our conclusions are based on comparisons of wideband E-change data, multiband B-change data, and LDAR2 (VHF lightning mapping) data from 10 IC flashes, two of which were described in detail. With the E-change data, we were able to find the (x, y, z, t) locations of fast IB pulses (IBPs) using a time-of-arrival technique that we call PBFA; the PBFA data allow us to see how the IBPs fit into the overall development of an IC flash.

[68] It is important to note that with one exception, no gamma ray detecting satellites passed within range of KSC during the lightning observations on 14 August 2011, so no correlated TGF data were available for the 10 IC flashes studied herein. The exception is that the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite [e.g., Smith et al., 2005] was located 790 km horizontally from the last flash in Table 3, but did not detect a TGF (T. Gjesteland and N. Ostgaard, personal communication, 2012). The lack of a TGF detection for this flash is not surprising because TGF detections are exceedingly rare at a range of 790 km [e.g., Collier et al., 2011; Briggs et al., 2013]. Thus, the connection of our data to TGFs is based on the similarity of the multiband B-change data to the same data recorded with known TGFs [e.g., Lu et al., 2010, 2011; Cummer et al., 2011]. Figure 1 shows a TGF detection along with nontriggered E-change data and the multiband B-change data for comparison to Figures 3 and 7, which show the IB stage of the two IC flashes investigated in detail. Nine of the 10 flashes studied included “IC events”, meaning that they satisfied criteria based on previous studies of flashes associated with recorded TGFs. The original group of 356 IC events occurred on average about once in 70 IC flashes. The IC events in Flashes A and B, which were studied in detail, had especially large charge moment changes in the group of 356; we estimate that such IC events only occur once in 1000 IC flashes.