On phenomenology of compact intracloud lightning discharges
Abstract
[1] We examined wideband electric fields, electric and magnetic field derivatives, and narrowband VHF (36 MHz) radiation bursts produced by 157 compact intracloud discharges (CIDs). These poorly understood lightning events appear to be the strongest natural 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 Detection Network (NLDN), and 149 of them were correctly identified as cloud discharges. NLDN-reported distances from the measurement station were 5–132 km. Three types of wideband electric field waveforms were observed. About 73% of CIDs occurred in isolation; 24% occurred prior to, during, or following cloud-to-ground or “normal” cloud lightning; and 4% occurred in pairs, separated by less than 200 ms (“multiple” CIDs). For a subset of 48 CIDs, the geometric mean of radiation source height was estimated to be 16 km. It appears that some CIDs actually occurred above cloud tops in clear air or in convective surges (plumes) overshooting the tropopause and penetrating deep into the stratosphere. For the same 48 CIDs, the geometric mean electric field peak normalized to 100 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 in negative cloud-to-ground lightning. The geometric means of total electric field pulse duration, width of initial half cycle, and ratio of initial peak to opposite polarity overshoot were 23 μs, 5.6 μs, and 5.7, respectively.
1. Introduction
[2] Cloud lightning discharges that produce both (1) single, usually solitary bipolar electric field pulses having typical full widths of 10–30 μs and (2) intense HF-VHF radiation bursts (much more intense than those from any other cloud-to-ground or “normal” cloud discharge process) are referred to as compact intracloud discharges (CIDs). These discharges were first reported by Le Vine [1980] and later characterized by Willett et al. [1989] and Smith et al. [1999, 2004], among others. Most of the reported electric field signatures of these discharges are produced by distant (tens to hundreds of kilometers) events and hence are essentially radiation. The radiation field pulses produced by CIDs are referred to as narrow bipolar pulses (NBPs). In the following, we will try to limit the use of term NBP for the following reasons. Since any radiation field signature produced by a spatially finite source that turns on and off in a finite time interval is bipolar [Yaghjian and Hansen, 1996], the adjective “bipolar” appears to be unnecessary. Also, there are many cloud discharge pulses that are as “narrow” as or more “narrow” than NPBs [e.g., Nag et al., 2009]. Close CID waveforms that are dominated by the induction and electrostatic field components are very rare, with only one being previously reported [Eack, 2004]. These, of course, are neither “narrow” nor “bipolar.” Both polarities of the initial half cycle of the CID radiation field signatures have been observed, with negative polarity (atmospheric electricity sign convention, according to which a downward-directed electric field vector is assumed to be positive) being more frequent. The term “CID” was coined by Smith et al. [1999] who inferred that the spatial extent of these discharges must be relatively small, 300–1000 m. CIDs tend to occur 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 emission observable by FORTE satellite. A recent summary of ground-based and space observations of CIDs is given by Hamlin et al. [2009].
[3] CIDs have recently attracted considerable attention because (1) they are likely to be the strongest natural producers of HF-VHF radiation [e.g., Thomas et al., 2001], (2) they are considered the prime candidate for proposed satellite-based VHF global lightning monitors [e.g., Wiens et al., 2008], and (3) it has been suggested that they may involve runaway electron breakdown [e.g., Gurevich and Zybin, 2004; Gurevich et al., 2004; Tierney et al., 2005]. Possible relation of CIDs to terrestrial gamma-ray flashes (TGFs) is debated. In this paper we present new experimental data that are needed for testing the validity of various models (including those involving runaway breakdown) of this phenomenon.
2. Experimental Data and Methodology
[4] We examine wideband electric fields, electric field derivatives (dE/dt), magnetic field derivatives (dB/dt), and narrowband VHF (36 MHz) radiation bursts produced by 157 CIDs. The initial polarity of distant (essentially radiation) wideband electric field pulses produced by 156 of these CIDs was negative (opposite to that of negative return strokes). One relatively close waveform did not exhibit the radiation field pulse, with only induction and static field components being evident (see Figure 7c). All the 157 events transported negative charge upward (or lowered positive charge). The data were acquired in August–September 2008 in Gainesville, FL. Typical measured waveforms for one CID are shown in Figure 1. We also recorded, over the same time period, 4 CIDs whose distant electric field waveforms had initial positive polarity. These four transported negative charge downward (or raised positive charge) and are not further considered here.
[5] The electric field measuring system included an elevated circular flat-plate antenna followed by an integrator and a unity-gain, high-input-impedance amplifier. The system had a useful frequency bandwidth of 16 Hz to 10 MHz, the lower and upper limits being determined by the time constant (about 10 ms) of the integrator and by the amplifier, respectively. The electric field derivative (dE/dt) measuring system included an elevated circular flat-plate antenna followed by an amplifier. The magnetic field derivative (dB/dt) measuring system employed two orthogonal loop antennas (measuring two orthogonal components of dB/dt), each followed by an amplifier. The antennas were installed on the roof of a five-storey building on the University of Florida campus in Gainesville, FL. The upper frequency responses of the dE/dt and dB/dt measuring systems were 17 and 15 MHz, respectively. The VHF measuring system used a whip antenna, and its center frequency was 36 MHz with a −3 dB bandwidth of 34–38 MHz. Fiber-optic links were used to transmit the wideband field and field derivative signals from the antennas and associated electronics to an 8 bit digitizing oscilloscope. In the VHF system, a double-shielded and sleeved coaxial cable was used for this purpose. The oscilloscope digitized the signals at 100 MHz. The record length was 500 ms including pretrigger time of 100 ms. Magnetic field waveforms were obtained by integration of measured dB/dt waveforms.
[6] CIDs were identified by their intense VHF radiation signature and characteristic wideband field (NBP or, in one case, its close-range counterpart) and field derivative waveforms. Different triggering schemes were employed in acquiring the data analyzed in this paper. For 80 events, the system was triggered on VHF only. The trigger threshold was empirically set at a relatively high level so as to minimize triggers on cloud-to-ground lightning (those were less than 6% of all triggers). For 77 events, the system could also trigger on wideband electric field, but the VHF threshold was always exceeded. Thus, we assume that for all the 157 events analyzed here, our measuring system was triggered on VHF. The sample of 157 was formed by manually searching all our strong VHF records for characteristic wideband field and field derivative CID signatures (see Figure 1) and accepting only those with electric field peaks greater than 1.5 times the background noise level. There were many strong VHF producers that did not satisfy the latter criterion, which probably introduced some amplitude bias, as discussed in section 5.
[7] GPS timestamps were used to obtain locations estimated by the National Lightning Detection Network (NLDN) for selected events. Out of 157 CIDs, 149 (95%) were correctly identified as cloud discharges and located by the NLDN. The distances of these events from the measurement station ranged from 5 to 132 km. One CID was misidentified by the NLDN as a positive cloud-to-ground (CG) discharge at 38 km with an estimated peak current of 24 kA. Seven CIDs were not detected by the NLDN. Table 1 gives the number of located events in different 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 used in sections 5 and 6 | 0 | 14 | 8 | 10 | 6 | 3 | 6 | 1 | 48 |
- a One hundred forty-nine events were identified by the NLDN as cloud discharges and one event as positive CG. The largest distance in the sample of 48 was 89 km.
. For R = 15–30 km, R/c = 50–100 μs, while Δt (NBP risetime) is typically a few microseconds. In order to check if our height estimation method is influenced by calibration of our field measuring systems, we computed Ez/Bϕ ratios for 43 first return strokes in negative lightning at distances ranging from 8 to 67 km. The return-stroke initial field peaks (essentially radiation) are produced by sources near ground (typically within 100 m), so that α ≈ 0 and expected ratio Ez/Bϕ ≈ c. We found that the 43 ratios were within ±16% of the speed of light with the arithmetic mean being 0.99c (essentially equal to the expected value), which gives us confidence in our electric and magnetic field measurements.
[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 the background noise level (in order to reduce the peak-measurement error). Each of these 48 CIDs was reported by 4–22 (11 on average) NLDN sensors with a length of the semimajor axis of 50% location error ellipse ranging from 400 m to 4.9 km (mostly 400 m, so that the median value was as small as 400 m).
3. Relation of Compact Intracloud Discharges to 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., Smith et al., 2004]. Krehbiel et al. [2008] reported a CID that occurred 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 lightning process occurring prior to or following the CIDs within the length of the record (500 ms with a 100 ms pretrigger). About 24% of CIDs were found to occur prior to, during, or following cloud-to-ground (CG) or “normal” intracloud (IC) lightning discharges. Specifically, 18% (28 out of 157) of CIDs accompanied ordinary cloud discharges. NLDN locations were available for 8 IC flashes in all of which CIDs preceded IC impulsive processes. Five CIDs preceded IC impulsive processes by 5.3–67 ms with horizontal separation distances being 1 km or less. Seven CIDs were within 10 km of ICs and one beyond 25 km. An example of wideband electric field and VHF radiation from a CID followed by a cloud (IC) flash is shown in Figure 3. Further, 6% (9 out of 157) of the CIDs appeared to occur in association with CG flashes. NLDN locations were available for 7 CG flashes. In three cases, CIDs were found to precede CGs by 72–233 ms, while in four cases, they occurred during or after CGs. In three cases, CIDs were found to occur within 5 km of CG strokes, and in seven cases, they were within 20 km. Figure 4a shows the wideband electric field and VHF radiation from an eight-stroke CG (only the second through seventh strokes were recorded by our system), with a CID occurring between the third and fourth strokes at horizontal distances of 7–8 km from all strokes of this flash. Plan view of NLDN locations of this CID and the CG strokes is shown in Figure 4b. Interestingly, locations of seven out of eight strokes are within less than 1 km of each other, while one stroke (of order 4), which was immediately preceded 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 the pairs being 43, 66, and 181 ms. These intervals are comparable to interstroke intervals in CG flashes. The horizontal separation distances were 16, 24, and 11 km, respectively. The CIDs in the first pair were found to occur successively at heights of 18 and 15 km. Electric field record of one of the “multiple” CID events (the second pair) is shown in Figure 5.
[13] The occurrence context of CIDs is summarized in Figure 6. It is presently not clear how CIDs influence (if at all) the ordinary lightning processes.
4. Different Types of Electric Field Waveforms
[14] The electric field associated with lightning discharges is often viewed as being composed of the electrostatic, induction, and radiation field components. At larger distances (beyond several tens of kilometers) and at early times, the radiation component is generally the dominant one. As distance decreases, relative contributions of the other two components increase. Most of the CID waveforms found in the literature are essentially radiation (NBP pulses), with closer waveforms that exhibit both radiation and electrostatic field components being exceedingly rare. Only seven 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 the literature.
[15] In Figures 7a–7c, we present three types of CID electric field waveforms recorded in Gainesville, FL. CID that produced the essentially radiation field signature, shown in 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 about 6 V/m after the radiation pulse (induction field component might be significant, too, but is difficult to identify). NLDN did not detect the CID whose electric field signature is shown in Figure 7c, but its parent thunderstorm was observed to be overhead. For this event, the static and induction components are dominant and the radiation component is indiscernible (negligible). Results presented in Figures 7a–7c are consistent with observed [Eack, 2004] and model-predicted [Watson and Marshall, 2007] waveforms found in the literature, with the type of waveform shown in Figure 7c being previously recorded, as noted above, only once.
[16] Note that for a short vertical dipole at relatively large elevation angle α above ground (see Figure 2), the radiation field peak on the one hand and induction and static field changes on the other hand are expected to have opposite polarities. Specifically, it follows from equation (A.38) in the book by Uman [1987, p. 329] for the electric field at perfectly conducting ground due to a differential vertical dipole that the opposite polarities are expected for α > 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. Unfortunately, no source heights could be estimated for waveforms of types (b) and (c).
5. Source Heights
[18] Smith et al. [2004] used two methods to estimate CID heights above ground. One was based on measuring delays of ionosphere and ground-ionosphere reflections with respect to direct-path wave in VLF/LF ground-based (Los Alamos Sferic Array) field records. The other one employed FORTE satellite VHF records showing direct-path and ground-reflection signals. The ground-based estimates were on average 1 km higher than the satellite estimates, the latter being 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 shown in Figure 8. The minimum and maximum source heights were 8.8 and 29 km, respectively. The geometric mean was 16 km and median was 15 km, the latter being similar to the median source height of 13 km reported for the same 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 height estimates before attempting their interpretation and discussing their significance. There are two primary sources of error in our estimated source height: elevation angle error and horizontal distance error. The angle error is due to inaccuracies in the measurements of the electric and magnetic field peaks. The distance error can be estimated using NLDN-reported 50% location error ellipses. Detailed analysis of errors in source heights is presented in Appendix A. As seen in Figures A1 and A2, 42 of 48 events had height errors less than 30% and 39 had errors less than 25%. The overall error range is 4.7%–95% with a mean of 17%. If events with height errors greater than 25% were excluded, the geometric mean height would be equal to that for the original sample of 48. Thus, the apparently unrealistic source heights cannot be explained by their estimation errors (assuming that there are no additional, presently unknown error sources). There are nine CIDs in our data set for which heights were estimated to be greater than 20 km, with errors ranging from 6% to 23%. We found them unremarkable in all respects, except for their height. All nine were isolated, occurred at horizontal distances ranging from 32 to 63 km, and had cosα 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 in Florida occurred above 15 km and a few occurred above 20 km (see their Figure 8), with the height distribution peak being at 13–14 km. Their altitude measurement uncertainties were less than 2 km, and they specifically stated that it is likely that at least some of their events were truly occurring above the nominal tropopause (that is, above cloud tops), whose altitude they estimated to be about 15 km. In our data set, 17 (about 35%) out of 48 CIDs appeared to occur at heights ranging from 15 to 20 km, which is a larger percentage than that (about 20%) in the study of Jacobson and Heavner [2005]. The discrepancy could be due to our relatively small sample size. Further, Smith et al. [2004], who examined 115,537 CIDs (mostly in the vicinity of Florida), reported hundreds of them occurring above 20 km, up to as high as 30 km (see their Figure 5). In fact, the median height for their CIDs with negative (physics sign convention) initial polarity radiation field signature was as high as 18 km; that is, 50% of those CIDs were located above 18 km, which is higher than 33% in our study. Observations of Smith et al. [2004] are supported by more recent data reported by Suszcynsky 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 at heights greater than 20 km (see their p. 130, Figure 5.12a). In summary, very large (>20 km) source heights have been observed using three different methods: ionospheric and ground reflections [Smith et al., 2004; Suszcynsky and Lay, 2009], 3-D VLF/LF TOA [Betz et al., 2009], and Ez/Bϕ ratio (present study).
[22] It is possible that some of the CIDs observed at heights greater than 15 km or so were associated with convective surges overshooting the tropopause and penetrating deep into the stratosphere [e.g., Romps and Kuang, 2009]. Darrah [1978] observed tropopause overshoots up to 5 km in severe storms. As of today, there is no explanation for the occurrence of CIDs above 20 km (in clear air). One of the reviewers stated that, if the source heights greater than 20 km are correct, “some of our fundamental assumptions about atmospheric electricity are incorrect.” We wonder if at least some of the CIDs inferred to occur well above the cloud top (in the stratosphere) could be associated with gigantic jets. Krehbiel et al. [2008] described gigantic jets as resembling negative upward leaders exhibiting impulsive rebrightening and extending from cloud tops to the ionosphere.
6. Electric Field Waveform Characteristics
[24] Willett et al. [1989] reported an arithmetic mean distance-normalized NBP initial peak of 8.0 ± 5.3 V/m at 100 km for 18 Florida CIDs that occurred in a storm at a distance of 45 km (no distances for individual events were available). Further, Smith et al. [1999] found a mean of 9.5 ± 3.6 V/m at 100 km for 24 CIDs at horizontal distances ranging from 82 to 454 km (there might have been significant propagation effects) in New Mexico and West Texas. Our arithmetic mean (±standard division) is 21 ± 8.9 V/m at 100 km for all the 48 events and 15 ± 3.4 V/m for 22 events within 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, for the 48 CIDs. The total durations range from 9.6 to 38 μs with arithmetic and geometric means of 24 and 23 μs, respectively. The total width of the initial half cycle ranges from 2.8 to 13 μs with arithmetic and geometric means being 6.1 and 5.7 μs, respectively. Smith et al. [1999] found the arithmetic mean total pulse duration to be 26 ± 4.9 μs, which is similar to our estimate.
[26] Figure 10c shows the distribution of the ratio of initial electric field peak to opposite polarity overshoot for the 48 CIDs. The ratio ranges from 3.5 to 17 with arithmetic and geometric means being 6.1 and 5.7, respectively. Willett et 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 different storms in Florida, while Smith et al. [1999] found the arithmetic mean ratio to be 2.7 for 24 CIDs in New Mexico and West Texas. Our estimate is between the previously reported values.
7. Summary
[27] We examined wideband electric fields, electric and magnetic field derivatives, and narrowband VHF (36 MHz) radiation bursts produced by 157 CIDs. These lightning events appear to be the strongest natural producers of HF-VHF radiation. The initial polarity of distant wideband electric field pulses produced by these CIDs was negative (opposite to that of negative return strokes). NLDN located 150 of the 157 CIDs at distances ranging from 5 to 132 km from the measurement station and correctly identified 149 (95%) of them as cloud discharges. Different types of electric field waveforms are presented and discussed. The majority (about 73%) of CIDs appeared to occur in isolation from any other lightning process, while about 24% were found to occur prior to, during, or following CG or “normal” IC lightning. About 18% were associated with cloud flashes and 6% with ground ones. In three cases, two CIDs occurred within 43, 66, and 181 ms of each other (the first documented “multiple” CIDs), with a total of 4% of CIDs occurring in pairs. For 48 CIDs, the geometric means of source height (estimated from measured electric to magnetic field ratio and horizontal distance reported by the NLDN) and the electric field peak normalized to 100 km, and zero elevation angle were estimated to be 16 km and 20 V/m, respectively. It appears that some CIDs actually occurred above cloud tops in clear air or in convective surges (plumes) overshooting the tropopause and penetrating deep into the stratosphere. For nine CIDs, estimated heights were greater than 20 km, with errors ranging from 6% to 23%. As of today, there is no explanation for the occurrence of CIDs above 20 km (in clear air). The geometric means of total electric field pulse duration, width of initial half cycle, and ratio of initial peak to opposite polarity overshoot were 23 μs, 5.6 μs, and 5.7, respectively.
Acknowledgments
[35] This research was supported in part by National Science Foundation grants ATM-0346164 and ATM-0852869 and by Defense Advanced Research Projects Agency. The authors thank Y. Baba and anonymous reviewers for their comments on the paper.
Appendix A: Analysis of Errors in CID Heights
[28] In section 5, we estimated CID heights assuming that the CID channel is vertical. In this Appendix, we first examine errors in height for this most likely geometry and then consider the case when the CID channel deviates from the vertical.
A1. Vertical CID Channel
[29] The errors in source height were estimated in the following manner [Taylor, 1997]. The total height error was found by combining in quadrature (the square root of the sum of squares) the error components due to the error in horizontal distance r and the error in field ratio Ez/CBϕ, which were assumed to be random and independent of each other. Each of the error components was found using the derivative method of evaluation of error in function, h = r tan (cos−1x), from errors in its variables (r and x).
[30] Errors in Ez and Bϕ were estimated as quantization errors of 8 bit digitizers used to measure the fields. The RMS value of quantization error for an 8 bit digitizer is 1/256/√12 = 0.113% [Santina and Stubberud, 2005]. This error and the field peaks were used to compute quantization errors for individual events. For magnetic field waveforms, the derivative method was additionally employed to account for the error due to combining the north-south (NS) and east-west (EW) field components to compute the total magnetic field, and it was found that the error in magnetic field may be increased relative to the quantization error given above by up to 20% (depending on the ratio of the NS and EW components). In order to simplify calculations, we applied an average increase of 10% to all the events. The resultant range of errors in Ez was 1.1%–3.0% (AM = 2.1%), and for Bϕ, it was 0.34%–1.6% (AM = 0.73%). These two errors were combined in quadrature to yield a range of errors in the field ratio of 1.2%–3.4% (AM = 2.3%).
[31] The error in h due to error in x is given by Δhx = 
Δx; for r, it is Δhr = 
Δr [Taylor, 1997]. Note that Δx and Δr are in absolute units with the corresponding errors in relative units being 
and 
. Errors in r were estimated using NLDN-reported 50% location error ellipses. The resulting range of errors in h due to errors in x is 3.3%–95% (AM = 17%), and for r, it is 0.63%–21% (AM = 2.1%). Note that, except for one event, errors in h due to errors in r are less than 5%.
[32] Finally, we combined in quadrature the two components of the error in h with the resultant error range being 4.7%–95% (AM = 17%), almost the same as that due to errors in x alone, which implies that the error component due to error in r is negligible.
[33] Errors in h versus cos α = x and height value are shown in Figures A1 and A2, respectively. Note that (a) the error in source height is a sensitive function of the ratio x = cos α only when this ratio exceeds 0.95 (α < 18°) or so (see Figure A1) and (b) the largest heights estimated in our study are associated with relatively small errors. In fact, two events with the largest height errors were estimated to occur at heights of 10 km or less as seen in Figure A2. As noted in 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 than 25% or 30% were excluded, the geometric mean height would be the same in both cases and equal to that for the original sample of 48.
.
A2. Nonvertical CID Channel
