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On phenomenology of compact intracloud lightning discharges

Amitabh Nag,1 Vladimir A. Rakov,1 Dimitris Tsalikis,1 and John A. Cramer2

Received 4 August 2009; revised 11 March 2010; accepted 23 March 2010; published 29 July 2010.

[1] We examined wideband electric fields, electric and magnetic field derivatives, andnarrowband VHF (36 MHz) radiation bursts produced by 157 compact intraclouddischarges (CIDs). These poorly understood lightning events appear to be the strongestnatural producers of HF‐VHF radiation. All the events transported negative charge upward(or lowered positive charge), 150 were located by the U.S. National Lightning DetectionNetwork (NLDN), and 149 of them were correctly identified as cloud discharges.NLDN‐reported distances from the measurement station were 5–132 km. Three types ofwideband electric field waveforms were observed. About 73% of CIDs occurred inisolation; 24% occurred prior to, during, or following cloud‐to‐ground or “normal” cloudlightning; and 4% occurred in pairs, separated by less than 200 ms (“multiple” CIDs). Fora subset of 48 CIDs, the geometric mean of radiation source height was estimated to be16 km. It appears that some CIDs actually occurred above cloud tops in clear air or inconvective surges (plumes) overshooting the tropopause and penetrating deep into thestratosphere. For the same 48 CIDs, the geometric mean electric field peak normalized to100 km (inclined distance) was as high as 20 V/m, and for 22 events within 10–30 km(horizontal distance), it was 15 V/m, both of which are higher than that for first strokes innegative cloud‐to‐ground lightning. The geometric means of total electric field pulseduration, width of initial half cycle, and ratio of initial peak to opposite polarity overshootwere 23 ms, 5.6 ms, and 5.7, respectively.

Citation: Nag, A., V. A. Rakov, D. Tsalikis, and J. A. Cramer (2010), On phenomenology of compact intracloud lightningdischarges, J. Geophys. Res., 115, D14115, doi:10.1029/2009JD012957.

1. Introduction

[2] Cloud lightning discharges that produce both (1) single,usually solitary bipolar electric field pulses having typicalfull widths of 10–30 ms and (2) intense HF‐VHF radiationbursts (much more intense than those from any other cloud‐to‐ground or “normal” cloud discharge process) are referredto as compact intracloud discharges (CIDs). These dis-charges were first reported by Le Vine [1980] and latercharacterized by Willett et al. [1989] and Smith et al. [1999,2004], among others. Most of the reported electric fieldsignatures of these discharges are produced by distant (tensto hundreds of kilometers) events and hence are essentiallyradiation. The radiation field pulses produced by CIDs arereferred to as narrow bipolar pulses (NBPs). In the follow-ing, we will try to limit the use of term NBP for the fol-lowing reasons. Since any radiation field signature producedby a spatially finite source that turns on and off in a finitetime interval is bipolar [Yaghjian and Hansen, 1996], theadjective “bipolar” appears to be unnecessary. Also, thereare many cloud discharge pulses that are as “narrow” as or

more “narrow” than NPBs [e.g., Nag et al., 2009]. CloseCID waveforms that are dominated by the induction andelectrostatic field components are very rare, with only onebeing previously reported [Eack, 2004]. These, of course,are neither “narrow” nor “bipolar.” Both polarities of theinitial half cycle of the CID radiation field signatures havebeen observed, with negative polarity (atmospheric elec-tricity sign convention, according to which a downward‐directed electric field vector is assumed to be positive) beingmore frequent. The term “CID” was coined by Smith et al.[1999] who inferred that the spatial extent of these dis-charges must be relatively small, 300–1000 m. CIDs tend tooccur at relatively high altitudes, typically more than 10 km[Smith et al., 2004], while Light and Jacobson [2002]reported that CIDs often produced no optical emissionobservable by FORTE satellite. A recent summary ofground‐based and space observations of CIDs is given byHamlin et al. [2009].[3] CIDs have recently attracted considerable attention

because (1) they are likely to be the strongest natural pro-ducers of HF‐VHF radiation [e.g., Thomas et al., 2001],(2) they are considered the prime candidate for proposedsatellite‐based VHF global lightning monitors [e.g., Wienset al., 2008], and (3) it has been suggested that they mayinvolve runaway electron breakdown [e.g., Gurevich andZybin, 2004; Gurevich et al., 2004; Tierney et al., 2005].Possible relation of CIDs to terrestrial gamma‐ray flashes

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

2Vaisala Inc., Tucson, Arizona, USA.

Copyright 2010 by the American Geophysical Union.0148‐0227/10/2009JD012957

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, D14115, doi:10.1029/2009JD012957, 2010

D14115 1 of 11

http://dx.doi.org/10.1029/2009JD012957

(TGFs) is debated. In this paper we present new experi-mental data that are needed for testing the validity of variousmodels (including those involving runaway breakdown) ofthis phenomenon.

2. Experimental Data and Methodology

[4] We examine wideband electric fields, electric fieldderivatives (dE/dt), magnetic field derivatives (dB/dt), andnarrowband VHF (36 MHz) radiation bursts produced by157 CIDs. The initial polarity of distant (essentially radiation)wideband electric field pulses produced by 156 of theseCIDs was negative (opposite to that of negative returnstrokes). One relatively close waveform did not exhibit theradiation field pulse, with only induction and static fieldcomponents being evident (see Figure 7c). All the 157 eventstransported negative charge upward (or lowered positivecharge). The data were acquired in August–September 2008in Gainesville, FL. Typical measured waveforms for oneCID are shown in Figure 1. We also recorded, over the sametime period, 4 CIDs whose distant electric field waveformshad initial positive polarity. These four transported negativecharge downward (or raised positive charge) and are notfurther considered here.[5] The electric field measuring system included an ele-

vated circular flat‐plate antenna followed by an integratorand a unity‐gain, high‐input‐impedance amplifier. Thesystem had a useful frequency bandwidth of 16 Hz to

10 MHz, the lower and upper limits being determined by thetime constant (about 10 ms) of the integrator and by theamplifier, respectively. The electric field derivative (dE/dt)measuring system included an elevated circular flat‐plateantenna followed by an amplifier. The magnetic fieldderivative (dB/dt) measuring system employed two orthog-onal loop antennas (measuring two orthogonal componentsof dB/dt), each followed by an amplifier. The antennas wereinstalled on the roof of a five‐storey building on theUniversity of Florida campus in Gainesville, FL. The upperfrequency responses of the dE/dt and dB/dt measuring sys-tems were 17 and 15 MHz, respectively. The VHF mea-suring system used a whip antenna, and its center frequencywas 36 MHz with a −3 dB bandwidth of 34–38 MHz. Fiber‐optic links were used to transmit the wideband field andfield derivative signals from the antennas and associatedelectronics to an 8 bit digitizing oscilloscope. In the VHFsystem, a double‐shielded and sleeved coaxial cable wasused for this purpose. The oscilloscope digitized the signalsat 100 MHz. The record length was 500 ms including pre-trigger time of 100 ms. Magnetic field waveforms wereobtained by integration of measured dB/dt waveforms.[6] CIDs were identified by their intense VHF radiation

signature and characteristic wideband field (NBP or, in onecase, its close‐range counterpart) and field derivativewaveforms. Different triggering schemes were employed inacquiring the data analyzed in this paper. For 80 events, thesystem was triggered on VHF only. The trigger threshold

Figure 1. (a) Wideband electric field, (b) electric field derivative (dE/dt), (c) integrated magnetic fieldderivative (dB/dt), and (d) narrowband VHF (36 MHz) radiation burst produced by a CID in Gainesville,FL. From Ez/B� = 2.24 × 108 m/s and r = 17.2 km, the source height h = 15 km.

NAG ET AL.: COMPACT INTRACLOUD DISCHARGES D14115D14115

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was empirically set at a relatively high level so as to mini-mize triggers on cloud‐to‐ground lightning (those were lessthan 6% of all triggers). For 77 events, the system could alsotrigger on wideband electric field, but the VHF thresholdwas always exceeded. Thus, we assume that for all the157 events analyzed here, our measuring system was trig-gered on VHF. The sample of 157 was formed by manuallysearching all our strong VHF records for characteristicwideband field and field derivative CID signatures (seeFigure 1) and accepting only those with electric field peaksgreater than 1.5 times the background noise level. Therewere many strong VHF producers that did not satisfy thelatter criterion, which probably introduced some amplitudebias, as discussed in section 5.[7] GPS timestamps were used to obtain locations esti-

mated by the National Lightning Detection Network(NLDN) for selected events. Out of 157 CIDs, 149 (95%)were correctly identified as cloud discharges and located bythe NLDN. The distances of these events from the mea-surement station ranged from 5 to 132 km. One CID wasmisidentified by the NLDN as a positive cloud‐to‐ground(CG) discharge at 38 km with an estimated peak currentof 24 kA. Seven CIDs were not detected by the NLDN.Table 1 gives the number of located events in different dis-tance ranges.[8] Simultaneous measurements of electric and magnetic

radiation field pulses produced by CIDs and NLDN‐reported horizontal distances to these discharges can be usedto obtain estimates of source heights. For a vertical sourceabove perfectly conducting ground (see Figure 2), the ratioof the vertical component of electric field intensity (Ez) andthe azimuthal component of magnetic flux density (B8) onthe ground surface is given by

Ez

B�¼ c cos�

[e.g., Baum, 2008], where c is the speed of light, so that theelevation angle a can be found as

� ¼ cos�1 Ez

cB�

� �:

The source height can be estimated as h = r tan a, where r isthe horizontal distance of the source from the field mea-suring station. This approach is valid for a vertical radiatorand for early‐time field measurements for which Dt � R/c[Baum, 2008], where R is the inclined distance from themeasuring station to the source, this distance being given byR =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ r2

p. For R = 15–30 km, R/c = 50–100 ms, while

Dt (NBP risetime) is typically a few microseconds. In orderto check if our height estimation method is influenced bycalibration of our field measuring systems, we computed

Ez /B� ratios for 43 first return strokes in negative lightningat distances ranging from 8 to 67 km. The return‐strokeinitial field peaks (essentially radiation) are produced bysources near ground (typically within 100 m), so that a ≈ 0and expected ratio Ez /B� ≈ c. We found that the 43 ratioswere within ±16% of the speed of light with the arithmeticmean being 0.99c (essentially equal to the expected value),which gives us confidence in our electric and magnetic fieldmeasurements.[9] For estimating source heights, we selected 48 CIDs

with NLDN‐reported distances ranging from 12 to 89 km,whose electric field peaks were greater than 2.5 times thebackground noise level (in order to reduce the peak‐measurement error). Each of these 48 CIDs was reported by4–22 (11 on average) NLDN sensors with a length of thesemimajor axis of 50% location error ellipse ranging from400 m to 4.9 km (mostly 400 m, so that the median valuewas as small as 400 m).

3. Relation of Compact Intracloud Dischargesto Other Types of Lightning

[10] It is generally thought that CIDs occur in isolation(within several hundred microseconds to a few milliseconds)or at the beginning of ordinary cloud discharges [e.g., Smithet al., 2004]. Krehbiel et al. [2008] reported a CID thatoccurred 800 ms prior to a gigantic jet.[11] The majority (73%) of CIDs examined here appeared

to occur in isolation; that is, there was no other lightningprocess occurring prior to or following the CIDs within the

Table 1. Number of NLDN‐Located Compact Intracloud Discharges in Different Horizontal Distance Ranges

Distance Range (km) 0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–135 0–135

Number of events 5 20 21 24 18 36 13 13 150a

Number of events usedin sections 5 and 6

0 14 8 10 6 3 6 1 48

aOne hundred forty‐nine events were identified by the NLDN as cloud discharges and one event as positive CG. The largest distance in the sample of48 was 89 km.

Figure 2. Geometrical parameters and equations used inestimating radiation source heights. See text for details.


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length of the record (500 ms with a 100 ms pretrigger).About 24% of CIDs were found to occur prior to, during, orfollowing cloud‐to‐ground (CG) or “normal” intracloud(IC) lightning discharges. Specifically, 18% (28 out of 157)of CIDs accompanied ordinary cloud discharges. NLDNlocations were available for 8 IC flashes in all of whichCIDs preceded IC impulsive processes. Five CIDs precededIC impulsive processes by 5.3–67 ms with horizontal sep-aration distances being 1 km or less. Seven CIDs werewithin 10 km of ICs and one beyond 25 km. An example ofwideband electric field and VHF radiation from a CIDfollowed by a cloud (IC) flash is shown in Figure 3. Further,6% (9 out of 157) of the CIDs appeared to occur in asso-ciation with CG flashes. NLDN locations were available for7 CG flashes. In three cases, CIDs were found to precedeCGs by 72–233 ms, while in four cases, they occurredduring or after CGs. In three cases, CIDs were found tooccur within 5 km of CG strokes, and in seven cases, theywere within 20 km. Figure 4a shows the wideband electricfield and VHF radiation from an eight‐stroke CG (onlythe second through seventh strokes were recorded by oursystem), with a CID occurring between the third and fourthstrokes at horizontal distances of 7–8 km from all strokes ofthis flash. Plan view of NLDN locations of this CID and theCG strokes is shown in Figure 4b. Interestingly, locations ofseven out of eight strokes are within less than 1 km of eachother, while one stroke (of order 4), which was immediatelypreceded by the CID, created a new termination on ground,about 3 km away from other strokes of the flash.[12] We also observed three sequences of two CIDs (4%

of all CIDs analyzed here), with time intervals within thepairs being 43, 66, and 181 ms. These intervals are com-parable to interstroke intervals in CG flashes. The horizontalseparation distances were 16, 24, and 11 km, respectively.The CIDs in the first pair were found to occur successivelyat heights of 18 and 15 km. Electric field record of one of

the “multiple” CID events (the second pair) is shown inFigure 5.[13] The occurrence context of CIDs is summarized in

Figure 6. It is presently not clear how CIDs influence (if atall) the ordinary lightning processes.

4. Different Types of Electric Field Waveforms

[14] The electric field associated with lightning dischargesis often viewed as being composed of the electrostatic,induction, and radiation field components. At larger dis-tances (beyond several tens of kilometers) and at earlytimes, the radiation component is generally the dominantone. As distance decreases, relative contributions of theother two components increase. Most of the CID waveformsfound in the literature are essentially radiation (NBP pulses),with closer waveforms that exhibit both radiation andelectrostatic field components being exceedingly rare. Onlyseven were recorded within 15 km and five within 10 km[Eack, 2004]. Only one waveform [Eack, 2004, Figure 1]dominated by induction and electrostatic field components(no radiation field component is discernible) is found in theliterature.[15] In Figures 7a–7c, we present three types of CID

electric field waveforms recorded in Gainesville, FL. CIDthat produced the essentially radiation field signature, shownin Figure 7a, was located at a horizontal distance of 40 km;for the event shown in Figure 7b, the distance was 9.4 km.In the latter case, note an electrostatic field change of about6 V/m after the radiation pulse (induction field componentmight be significant, too, but is difficult to identify). NLDNdid not detect the CID whose electric field signature isshown in Figure 7c, but its parent thunderstorm wasobserved to be overhead. For this event, the static andinduction components are dominant and the radiationcomponent is indiscernible (negligible). Results presented in

Figure 3. Electric field and VHF (36 MHz) radiation from a CID that was followed by a “normal” IC(from another experiment in Gainesville, FL). Inset shows the CID signature on an expanded (5 ms perdivision) timescale. No NLDN locations are available.


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Figures 7a–7c are consistent with observed [Eack, 2004]and model‐predicted [Watson and Marshall, 2007] wave-forms found in the literature, with the type of waveformshown in Figure 7c being previously recorded, as notedabove, only once.[16] Note that for a short vertical dipole at relatively large

elevation angle a above ground (see Figure 2), the radiationfield peak on the one hand and induction and static fieldchanges on the other hand are expected to have opposite

polarities. Specifically, it follows from equation (A.38) inthe book by Uman [1987, p. 329] for the electric field atperfectly conducting ground due to a differential verticaldipole that the opposite polarities are expected for a >35.3°, which translates to r < 21 km if source height h =15 km.[17] Of the 157 CID signatures examined here, 151

were of type (a), 5 of type (b), and 1 of type (c), where(a), (b), and (c) are the three parts of Figure 7. Unfortu-

Figure 4. (a) Wideband electric field and VHF (36 MHz) radiation from a CID that occurred during aneight‐stroke negative CG, within horizontal distances of 7–8 km of all the CG strokes. Only the secondthrough seventh strokes were recorded by our measurement system. The CID height above ground wasestimated to be about 14 km. Note that the VHF radiation produced by the CID is much larger than thatproduced by the CG strokes (RS2–RS7). Inset shows the CID wideband electric field signature on anexpanded timescale. (b) Plan view of NLDN‐estimated relative positions of the CID (hollow circle)and return strokes (numbered solid circles) of CG flash whose wideband and VHF signatures are shownin Figure 4a. The semimajor axis (SMA) lengths of NLDN‐reported 50% location error ellipses for eachof the return strokes and the CID are also given. Strokes 1–3 occurred before the CID and strokes4–8 occurred after it. Arrows indicate changes in plan‐view location from strokes 1 to 3 to the CID, thento stroke 4 (new termination on ground), and to strokes 5–8.


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nately, no source heights could be estimated for waveformsof types (b) and (c).

5. Source Heights

[18] Smith et al. [2004] used two methods to estimate CIDheights above ground. One was based on measuring delays ofionosphere and ground‐ionosphere reflections with respect

to direct‐path wave in VLF/LF ground‐based (Los AlamosSferic Array) field records. The other one employed FORTEsatellite VHF records showing direct‐path and ground‐reflection signals. The ground‐based estimates were onaverage 1 km higher than the satellite estimates, the latterbeing considered by Smith et al. as more accurate.[19] The distribution of source heights for 48 CIDs

inferred here, using the method described in section 2, is

Figure 5. (top) Wideband electric field record showing two CIDs that occurred 66 ms apart at a hori-zontal distance of 24 km from each other. The height of CID 2 above ground was estimated to be about17 km, while the height of CID 1 is unknown. (bottom) Individual CID signatures displayed on expanded(10 and 5 ms per division for CID 1 and CID 2, respectively) time scales.

Figure 6. Occurrence context of CIDs. Percentages of CIDs occurring in different context do not add to100% because of rounding.


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shown in Figure 8. The minimum and maximum sourceheights were 8.8 and 29 km, respectively. The geometricmean was 16 km and median was 15 km, the latter beingsimilar to the median source height of 13 km reported for thesame NBP initial polarity by Smith et al. [2004].[20] Note that the heights larger than 15–20 km are likely

to be above the upper cloud boundary and therefore appear

unrealistic. Thus, it is necessary to evaluate errors in heightestimates before attempting their interpretation and dis-cussing their significance. There are two primary sources oferror in our estimated source height: elevation angle errorand horizontal distance error. The angle error is due toinaccuracies in the measurements of the electric and mag-netic field peaks. The distance error can be estimated usingNLDN‐reported 50% location error ellipses. Detailed anal-ysis of errors in source heights is presented in Appendix A.As seen in Figures A1 and A2, 42 of 48 events had heighterrors less than 30% and 39 had errors less than 25%. Theoverall error range is 4.7%–95% with a mean of 17%. Ifevents with height errors greater than 25% were excluded,the geometric mean height would be equal to that for theoriginal sample of 48. Thus, the apparently unrealisticsource heights cannot be explained by their estimation errors(assuming that there are no additional, presently unknownerror sources). There are nine CIDs in our data set for whichheights were estimated to be greater than 20 km, with errorsranging from 6% to 23%. We found them unremarkable inall respects, except for their height. All nine were isolated,occurred at horizontal distances ranging from 32 to 63 km,and had cosa ranging from 0.75 to 0.94 (mean = 0.87).[21] Jacobson and Heavner [2005] found that a few

thousands (about 20%) of their 20,993 CIDs observed inFlorida occurred above 15 km and a few occurred above20 km (see their Figure 8), with the height distribution peakbeing at 13–14 km. Their altitude measurement uncertaintieswere less than 2 km, and they specifically stated that it islikely that at least some of their events were truly occurringabove the nominal tropopause (that is, above cloud tops),whose altitude they estimated to be about 15 km. In our dataset, 17 (about 35%) out of 48 CIDs appeared to occur atheights ranging from 15 to 20 km, which is a larger per-centage than that (about 20%) in the study of Jacobson and

Figure 7. Three types of CID electric field waveformsexhibiting: (a) only radiation, (b) radiation and static fieldcomponents (induction component is not apparent), and(c) only induction and static field components. Note thatfor the geometry shown in Figure 2, the radiation fieldpeak on the one hand and induction and static field changeson the other are expected to have opposite polarities whena > 35.3°. Assuming a source height of 15 km and usingNLDN‐estimated distances, we found a = 21° and 58° forFigures 7a and 7b, respectively. Of 157 CID signatures,151 were of type (a), 5 of type (b), and 1 of type (c).

Figure 8. Histograms of radiation source heights for48 CIDs.


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Heavner [2005]. The discrepancy could be due to our rel-atively small sample size. Further, Smith et al. [2004], whoexamined 115,537 CIDs (mostly in the vicinity of Florida),reported hundreds of them occurring above 20 km, up to ashigh as 30 km (see their Figure 5). In fact, the median heightfor their CIDs with negative (physics sign convention) ini-tial polarity radiation field signature was as high as 18 km;that is, 50% of those CIDs were located above 18 km, whichis higher than 33% in our study. Observations of Smith et al.[2004] are supported by more recent data reported bySuszcynsky and Lay [2009]. Additionally, Betz et al. [2009],who used the 3‐D VLF/LF time‐of‐arrival (TOA) method,observed many (apparently hundreds) of lightning sources atheights greater than 20 km (see their p. 130, Figure 5.12a).In summary, very large (>20 km) source heights have beenobserved using three different methods: ionospheric andground reflections [Smith et al., 2004; Suszcynsky and Lay,2009], 3‐D VLF/LF TOA [Betz et al., 2009], and Ez/B� ratio(present study).[22] It is possible that some of the CIDs observed at

heights greater than 15 km or so were associated withconvective surges overshooting the tropopause and pene-trating deep into the stratosphere [e.g., Romps and Kuang,2009]. Darrah [1978] observed tropopause overshoots upto 5 km in severe storms. As of today, there is no expla-nation for the occurrence of CIDs above 20 km (in clear air).One of the reviewers stated that, if the source heights greaterthan 20 km are correct, “some of our fundamental assump-tions about atmospheric electricity are incorrect.” Wewonder if at least some of the CIDs inferred to occur wellabove the cloud top (in the stratosphere) could be associatedwith gigantic jets. Krehbiel et al. [2008] described giganticjets as resembling negative upward leaders exhibiting

impulsive rebrightening and extending from cloud tops tothe ionosphere.

6. Electric Field Waveform Characteristics

[23] For the subset of 48 CIDs, we estimated electric fieldpeaks normalized, assuming inverse distance dependence, toR = 100 km and to a = 0° as

EN ¼ ER

100

� �cos 0o

cos�:

Normalization to a = 0° corresponds to h = 0, but at 100 km,the result is essentially the same for median h = 15 km. Thedistribution of normalized electric field peaks is shown inFigure 9. The geometric mean is 20 V/m, which is consid-erably larger than the initial electric field peak at 100 km fornegative first return strokes (6 V/m in Florida [Rakov andUman, 2003]). We found that the normalized electric fieldpeak tends to increase with horizontal distance (determina-tion coefficient = 0.59). This suggests that our sample isbiased toward larger peaks, with the bias increasing withincreasing distance. Indeed, the geometric mean normalizedelectric field peak for horizontal distance ranges of 10–30,30–50, and 50–70 km were found to be 15 V/m (n = 22),23 V/m (n = 16), and 31 V/m (n = 9), respectively. One CIDthat occurred at 89 km had a normalized electric field peakof 35 V/m. This amplitude bias was apparently introducedby the requirement to have sufficiently pronounced fieldsignatures for estimating source heights. Note that evenfor the smallest distances, 10–30 km, the source strength(15 V/m) is considerably higher than that for first returnstrokes in negative CGs (6 V/m).[24] Willett et al. [1989] reported an arithmetic mean

distance‐normalized NBP initial peak of 8.0 ± 5.3 V/m at100 km for 18 Florida CIDs that occurred in a storm at adistance of 45 km (no distances for individual events wereavailable). Further, Smith et al. [1999] found a mean of9.5 ± 3.6 V/m at 100 km for 24 CIDs at horizontal distancesranging from 82 to 454 km (there might have been signif-icant propagation effects) in New Mexico and West Texas.Our arithmetic mean (±standard division) is 21 ± 8.9 V/m at100 km for all the 48 events and 15 ± 3.4 V/m for 22 eventswithin 10–30 km.[25] Figures 10a and 10b show distributions of the total

pulse duration (including the opposite polarity overshoot)and the total width of the initial half cycle, respectively, forthe 48 CIDs. The total durations range from 9.6 to 38 mswith arithmetic and geometric means of 24 and 23 ms,respectively. The total width of the initial half cycle rangesfrom 2.8 to 13 ms with arithmetic and geometric meansbeing 6.1 and 5.7 ms, respectively. Smith et al. [1999] foundthe arithmetic mean total pulse duration to be 26 ± 4.9 ms,which is similar to our estimate.[26] Figure 10c shows the distribution of the ratio of ini-

tial electric field peak to opposite polarity overshoot for the48 CIDs. The ratio ranges from 3.5 to 17 with arithmetic andgeometric means being 6.1 and 5.7, respectively. Willettet al. [1989] reported the arithmetic mean ratio to be 8.8 ±5.2 for 18 events and 9.1 ± 2.0 for 6 events in two differentstorms in Florida, while Smith et al. [1999] found thearithmetic mean ratio to be 2.7 for 24 CIDs in New Mexico

Figure 9. Histograms of electric fields peaks normalized toR = 100 km and a = 0° for 48 CIDs.


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and West Texas. Our estimate is between the previouslyreported values.

7. Summary

[27] We examined wideband electric fields, electric andmagnetic field derivatives, and narrowband VHF (36 MHz)radiation bursts produced by 157 CIDs. These lightningevents appear to be the strongest natural producers ofHF‐VHF radiation. The initial polarity of distant widebandelectric field pulses produced by these CIDs was negative(opposite to that of negative return strokes). NLDN located150 of the 157 CIDs at distances ranging from 5 to 132 kmfrom the measurement station and correctly identified149 (95%) of them as cloud discharges. Different types ofelectric field waveforms are presented and discussed. Themajority (about 73%) of CIDs appeared to occur in isolationfrom any other lightning process, while about 24% werefound to occur prior to, during, or following CG or “normal”IC lightning. About 18% were associated with cloud flashesand 6% with ground ones. In three cases, two CIDs occurredwithin 43, 66, and 181 ms of each other (the first docu-mented “multiple” CIDs), with a total of 4% of CIDsoccurring in pairs. For 48 CIDs, the geometric means ofsource height (estimated from measured electric to magneticfield ratio and horizontal distance reported by the NLDN)and the electric field peak normalized to 100 km, and zeroelevation angle were estimated to be 16 km and 20 V/m,respectively. It appears that some CIDs actually occurredabove cloud tops in clear air or in convective surges(plumes) overshooting the tropopause and penetrating deepinto the stratosphere. For nine CIDs, estimated heights weregreater than 20 km, with errors ranging from 6% to 23%. Asof today, there is no explanation for the occurrence of CIDsabove 20 km (in clear air). The geometric means of totalelectric field pulse duration, width of initial half cycle, andratio of initial peak to opposite polarity overshoot were23 ms, 5.6 ms, and 5.7, respectively.

Appendix A: Analysis of Errors in CID Heights

[28] In section 5, we estimated CID heights assuming thatthe CID channel is vertical. In this Appendix, we firstexamine errors in height for this most likely geometry andthen consider the case when the CID channel deviates fromthe vertical.

A1. Vertical CID Channel

[29] The errors in source height were estimated in thefollowing manner [Taylor, 1997]. The total height error wasfound by combining in quadrature (the square root of thesum of squares) the error components due to the error inhorizontal distance r and the error in field ratio Ez/CB�,which were assumed to be random and independent of eachother. Each of the error components was found using thederivative method of evaluation of error in function, h = rtan (cos−1x), from errors in its variables (r and x).[30] Errors in Ez and B8 were estimated as quantization

errors of 8 bit digitizers used to measure the fields. TheRMS value of quantization error for an 8 bit digitizer is1/256/√12 = 0.113% [Santina and Stubberud, 2005]. This

Figure 10. (a) Total pulse duration including overshoot,(b) total width of initial half cycle, and (c) ratio of initialelectric field peak to opposite polarity overshoot for48 CIDs.


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error and the field peaks were used to compute quantizationerrors for individual events. For magnetic field waveforms,the derivative method was additionally employed to accountfor the error due to combining the north‐south (NS) andeast‐west (EW) field components to compute the totalmagnetic field, and it was found that the error in magneticfield may be increased relative to the quantization errorgiven above by up to 20% (depending on the ratio of the NSand EW components). In order to simplify calculations, weapplied an average increase of 10% to all the events. Theresultant range of errors in Ez was 1.1%–3.0% (AM = 2.1%),and for B�, it was 0.34%–1.6% (AM = 0.73%). These twoerrors were combined in quadrature to yield a range of errorsin the field ratio of 1.2%–3.4% (AM = 2.3%).[31] The error in h due to error in x is given by Dhx =@h

@x

�� Dx; for r, it is Dhr =

@h

@r

�� Dr [Taylor, 1997]. Note that

Dx and Dr are in absolute units with the corresponding

errors in relative units being ðDh

hÞx ¼

Dx

xð1� x2Þ and

ðDh

hÞr ¼

Dr

r. Errors in r were estimated using NLDN‐

reported 50% location error ellipses. The resulting range oferrors in h due to errors in x is 3.3%–95% (AM = 17%), andfor r, it is 0.63%–21% (AM = 2.1%). Note that, except forone event, errors in h due to errors in r are less than 5%.[32] Finally, we combined in quadrature the two compo-

nents of the error in h with the resultant error range being4.7%–95% (AM = 17%), almost the same as that due toerrors in x alone, which implies that the error componentdue to error in r is negligible.[33] Errors in h versus cos a = x and height value are

shown in Figures A1 and A2, respectively. Note that (a) theerror in source height is a sensitive function of the ratio x =cos a only when this ratio exceeds 0.95 (a < 18°) or so (seeFigure A1) and (b) the largest heights estimated in our studyare associated with relatively small errors. In fact, twoevents with the largest height errors were estimated to occurat heights of 10 km or less as seen in Figure A2. As notedin section 5, the overwhelming majority of the events(42 of 48) had height errors less than 30% and 39 had errors

less than 25%. If the events with height errors greater than25% or 30% were excluded, the geometric mean heightwould be the same in both cases and equal to that for theoriginal sample of 48.

A2. Nonvertical CID Channel

[34] Heidler and Hopf [1998] give an equation for Ez/B�

ratio in terms of both elevation angle a and polarizationangle b (the angle between the incident electric field vectorand the plane of incidence):

Ez

B�¼ c

cos�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffitan2 � sin2 �þ 1

p :

This equation reduces to our equation for the field ratio,Ez/B� = c cos a, when b = 0 (the incident electric fieldvector is in the plane of incidence, which constitutes theso‐called parallel polarization). For b = 90°, the incidentelectric field vector is perpendicular to the plane of inci-dence, which constitutes the so‐called perpendicular polar-ization, and the total electric field at the ground reflectionpoint vanishes. This corresponds to a horizontally orientedradiator. We computed the field ratio for b = 5° and b = 10°for the entire range of elevation angles (from 0° to 90°) andfound that it differs by less than 2% from the ratio for b = 0°.Even for b = 20°, the maximum error is as small as 6%. Notethat, as the error in h due to errors in the field ratio increaseswith decreasing the elevation angle, the error due to radiatordeviation from the vertical decreases with decreasing thisangle. In summary, errors due to CID channel being slightlyoff the vertical are expected to be smaller than those due toerrors in the field ratio discussed in the previous section.

[35] Acknowledgments. This research was supported in part byNational Science Foundation grants ATM‐0346164 and ATM‐0852869and by Defense Advanced Research Projects Agency. The authors thankY. Baba and anonymous reviewers for their comments on the paper.

ReferencesBaum, C. E. (2008), Measurement of closure position between downwardand upward leaders: return‐stroke initiation position, in Proceedings ofXXIX General Assembly of the International Union of Radio Science,edited by D. Erricolo, URSI, Chicago, USA.

Figure A1. Errors in CID height versus cos a = EzcB�

.

Figure A2. Errors in CID height versus height value.


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Betz, H.‐D., K. Schmidt, and W. P. Oettinger (2009), LINET: An interna-tional VLF/LF lightning detection network in Europe, in Lightning: Prin-ciples, Instruments and Applications: Review of Modern LightningResearch, edited H.‐D. Betz, U. Schumann, and P. Laroche, Springer,New York.

Darrah, R. P. (1978), On the relationship of severe weather to radar tops,Mon. Weather Rev., 106, 1332–1339.

Eack, K. B. (2004), Electrical characteristics of narrow bipolar events,Geophys. Res. Lett., 31, L20102, doi:10.1029/2004GL021117.

Gurevich, A. V., and K. P. Zybin (2004), High energy cosmic ray particlesand the most powerful discharges in thunderstorm atmosphere, Phys.Lett. A, 329, 341–347.

Gurevich, A.V., Y. V. Medvedev, and K. P. Zybin (2004), New typedischarge generated in thunderclouds by joint action of runaway break-down and extensive atmospheric shower, Phys. Lett. A, 329, 348–361.

Hamlin, T., K. C. Wiens, A. R. Jacobson, T. E. L. Light, and K. B. Eack(2009), Space‐ and ground‐based studies of lightning signatures, inLightning: Principles, Instruments and Applications, edited by H. D.Betz, U. Schumann, and P. Laroche, pp. 287–307, Springer, New York.

Heidler, F., and C. Hopf (1998), Measurement results of the electric fieldsin cloud‐to‐ground lightning in nearby Munich, Germany, IEEE Trans.EMC, 40(4), 436–443.

Jacobson, A. R., and M. J. Heavner (2005), Comparison of narrow bipolarevents with ordinary lightning as proxies for severe convection, Mon.Weather Rev., 133, 1144–1154.

Krehbiel, P. R., J. A. Riousset, V. P. Pasko, R. J. Thomas, W. Rison, M. A.Stanley, and H. E. Edens (2008), Upward electrical discharges from thun-derstorms, Nature Geosci., 1, 233–237, doi:10.1038/ngeo162.

Le Vine, D. M. (1980), Sources of the strongest RF radiation from light-ning, J. Geophys. Res., 85, 4091–4095.

Light, T. E. L., and A. R. Jacobson (2002), Characteristics of impulsiveVHF lightning signals observed by the FORTE satellite, J. Geophys.Res., 107(D24), 4756, doi:10.1029/2001JD001585.

Nag, A., B. A. DeCarlo, and V. A. Rakov (2009), Analysis of microsecond‐and submicrosecond‐scale electric field pulses produced by cloud andground lightning discharges, Atmos. Res., 91, 316–325, doi:10.1016/j.atmosres.2008.01.014.

Rakov, V. A., and M. A. Uman (2003), Lightning: Physics and Effects,Cambridge Univ. Press, New York.

Romps, D. M., and Z. Kuang (2009), Overshooting convection in tropicalcyclones, Geophys. Res. Lett., 36, L09804, doi:10.1029/2009GL037396.

Santina, M. S., and A. R. Stubberud (2005), Basics of sampling and quan-tization, in Handbook of Networked and Embedded Control Systems,

edited by D. Hristu‐Varsakelis, and W. S. Levine, pp. 45–69, Birkhäuser,Boston.

Smith, D. A., X. M. Shao, D. N. Holden, C. T. Rhodes, M. Brook, P. R.Krehbiel, M. Stanley, W. Rison, and R. J. Thomas (1999), A distinctclass of isolated intracloud discharges and their associated radio emis-sions, J. Geophys. Res., 104, 4189–4212.

Smith, D. A., M. J. Heavner, A. R. Jacobson, X. M. Shao, R. S. Massey,R. J. Sheldon, and K. C. Wiens (2004), A method for determining intra-cloud lightning and ionospheric heights from VLF/LF electric fieldrecords, Radio Sci., 39, RS1010, doi:10.1029/2002RS002790.

Suszcynsky, D. M., and E. H. Lay (2009), Case Study of a Strong Narrow‐Bipolar‐Event‐Producing Storm on 2–3 July 2005, Abstract AE43B‐0278,AGU Fall Meeting, San Francisco, Calif.

Taylor, J. R. (1997), An introduction to error analysis: The study of uncer-tainties in physical measurements, 2nd ed., Univ. Sci. Books, Sausalito,Calif.

Thomas, R., P. Krehbiel, W. Rison, T. Hamlin, J. Harlin, and D. Shown(2001), Observations of VHF source powers radiated by lightning,Geophys. Res. Lett., 28(1), 143–146.

Tierney, H. E., R. A. Roussel‐Dupré, E. M. D. Symbalisty, W. H. Beasley(2005), Radio frequency emissions from a runaway electron avalanchemodel compared with intense, transient signals from thunderstorms,J. Geophys. Res., 110, D12109, doi:10.1029/2004JD005381.

Uman, M. A. (1987), The lightning discharge, Academic, New York.Watson, S. S., and T. C. Marshall (2007), Current propagation model for anarrow bipolar pulse, Geophys. Res. Lett., 34, L04816, doi:10.1029/2006GL027426.

Wiens, K. C., T. Hamlin, J. Harlin, D. M. Suszcynsky (2008), Relation-ships among narrow bipolar events, “total” lightning, and radar‐inferredconvective strength in Great Plains thunderstorms, J. Geophys. Res., 113,D05201, doi:10.1029/2007JD009400.

Willett, J. C., J. C. Bailey, and E. P. Krider (1989), A class of unusual light-ning electric field waveforms with very strong high‐frequency radiation,J. Geophys. Res., 94, 16,255–16,267.

Yaghjian, A. D., and T. B. Hansen (1996), Time domain far fields, J. Appl.Phys., 79, 2822–2830.

J. A. Cramer, Vaisala Inc., 2705 East Medina Rd., Tucson, AZ 85756,USA.A. Nag, V. A. Rakov, and D. Tsalikis, Department of Electrical and

Computer Engineering, University of Florida, 553 Engineering Building33, PO Box 116130, Gainesville, FL 32611, USA. ([email protected];[email protected])


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on phenomenology of compact intracloud lightning discharges

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