Positive lightning: An overview, new observations, and inferences
Abstract
[1] We examine the various conceptual cloud charge configurations and scenarios leading to production of positive lightning with a view toward an explanation of its observed properties. Data for 52 positive cloud-to-ground flashes containing 63 strokes recorded in Gainesville, Florida, in 2007–2008 are presented and discussed. The U.S. National Lightning Detection Network (NLDN) located 51 (96%) of the positive strokes at distances of 7.8 to 157 km from the field-measuring station. In 42 (81%) of the 52 flashes, the first (or the only) leader-return stroke sequence was not preceded by in-cloud discharge activity. The average number of strokes per flash is 1.2. Single-stroke flashes constitute 81%. In three (38%) of eight two-stroke flashes, the second stroke likely followed the channel of the first stroke, and in five (62%) flashes it likely created a new termination on ground. Eight (15%) of the 52 positive flashes had detectable preliminary breakdown pulse trains in their electric field records. Electric field waveforms of 14 (27%) first strokes (also of one third stroke) are preceded by pronounced pulses, apparently indicative of leader stepping. NLDN-reported peak currents for 48 positive strokes in 40 flashes ranged from 20 to 234 kA with a geometric mean value of 75 kA. The median charge transfers in 1, 2, and 40 ms after the beginning of return stroke electric field change for an assumed height of 12 km were estimated to be 13, 18, and 34 C, respectively. Two bipolar lightning discharges are additionally examined.
Key Points
- In 38% of two-stroke flashes, both strokes were in the same channel
- Charge moment change is not correlated with peak current
- In 81% of the flashes, the first CG stroke was not preceded by an IC
1. Introduction
[2] Downward positive lightning, which is initiated by a downward leader and effectively lowers positive charge from the cloud to ground, accounts for about 10% of all cloud-to-ground discharges [e.g.,Rakov, 2003]. Due to their relative paucity, positive lightning discharges are considerably less studied and understood than their negative counterparts. The charge structure and evolution of thunderclouds that produce positive lightning, as well as in-cloud processes that can lead to its initiation, largely remain a mystery. Specifically, electric field measurements ofRust et al. [1981] and Fuquay [1982]appear to indicate that positive return strokes are preceded by significant in-cloud discharge activity lasting, on average, in excess of 100 or 200 ms, whereas our electric field measurements often do not show evidence of preceding in-cloud activity, other than the preliminary breakdown process.
[3] According to Rakov [2003], studies of positive lightning are of importance because of its severe threat to various objects and systems, close relationship to sprites, and its dominance during the cold season and during the dissipating stage of a thunderstorm. Also, the occurrence of positive flashes may be related to production of severe weather phenomena (strong winds, large hail, and tornadoes). Several properties of positive lightning (e.g., number of strokes per flash, occurrence of continuing current, leader propagation mode, and branching) appear to be distinctly different from those of negative lightning.
[4] Positive charge can be also transferred to ground by so-called bipolar lightning that sequentially lowers both positive and negative charge to ground. Bipolar lightning is generally not considered to be a significant component of the overall lightning activity, although this type of lightning discharge may be not less common than positive lightning [Rakov, 2005].
[5] In this paper, we first examine the various conceptual cloud charge configurations and scenarios leading to production of positive lightning discharges. Then, using new positive lightning data acquired in Florida and those found in the literature, we discuss the role of in-cloud discharge activity in initiation of positive lightning, the occurrence of subsequent strokes in positive lightning flashes, both in new and in previously created channels, as well as the occurrence of preliminary breakdown and leader stepping in positive lightning. We also estimate, using measured electric fields and the point charge model, the charge transfer (up to 40 ms) by positive strokes. Additionally, we present and discuss two bipolar lightning flashes.
[6] The “atmospheric electricity” sign convention according to which a downward directed electric field (or field change) vector is considered to be positive is used throughout the paper.
2. Conceptual Cloud Charge Configurations and Scenarios Leading to Production of Positive Lightning
[7] The gross charge structure of a “normal” thundercloud is often viewed as a vertical tripole consisting of three charge regions, main positive at the top, main negative in the middle, and an additional (typically smaller) positive below the main negative [Williams, 1989, and references therein]. Such a charge structure appears to be not conducive to production of positive cloud-to-ground lightning. In this section, we describe six conceptual cloud charge configurations and scenarios that were observed or hypothesized to give rise to positive lightning. Cloud electrification mechanisms leading to the various charge configurations are outside the scope of this paper.
2.1. Tilted Dipole
[8] This cloud charge structure was proposed by Brook et al. [1982] who suggested that positive flashes can originate from the upper positive charge of a vertical dipole that is displaced horizontally by vertical wind shear from the lower negative charge and thereby exposed to the ground as shown in Figure 1a. The titled dipole configuration was inferred from multiple station electric field change measurements and radar observations during winter thunderstorms in Japan.
2.2. Positive Monopole
[9] Kitagawa and Michimoto [1994], using a network of electric field mills and radar observations, inferred the existence of positive monopolar charge structure during the dissipating stage of Japanese winter thunderclouds. During the developing stage, electric charge distribution is a positive dipole, net positive charge being found in the top portion of the cloud and net negative charge at lower regions. In the mature stage, the thunderclouds exhibit a “normal” tripolar charge structure; that is, a positive dipole with an additional lower positive charge region below the negative charge region. According to Kitagawa and Michimoto [1994], the negative charge and the lower positive charge are carried mainly by graupel particles which fall out of the cloud relatively early in the cloud life cycle. As a result, the lifetimes of the dipolar and tripolar charge structures are very short (usually less than 10 min). During the dissipating stage, positive charge is dominant in the whole cloud, this charge being carried by ice crystals and snowflakes. It is this stage that is characterized by a positive monopolar charge structure. The dissipating stage has a much longer duration than the developing and mature stages and thus accounts for most of the lifetime of Japanese winter thunderclouds. According to Kitagawa and Michimoto [1994], the monopolar cloud charge structure (see Figure 1b) explains why positive lightning is the dominant lightning type in winter thunderstorms in Japan.
[10] The depletion of negative charge via negative lightning discharges to ground during the active stage of a thunderstorm may also be leading, in effect, to the positive monopole configuration in its dissipating stage [Pierce, 1955].
2.3. Inverted Dipole
[11] The highest incidence of storms producing predominantly positive ground flashes in the United States is in the High Plains region (northwestern Kansas and eastern Colorado) [Orville and Huffines, 2001; Lang et al., 2004; Fleenor et al., 2009]. Rust et al. [2005]used balloon-borne electric field soundings and lightning VHF mapping in the Severe Thunderstorm Electrification and Precipitation Study (STEPS) program to examine the electrical structure of these storms. They found the positive and negative charge regions to be at altitudes where negative and positive charges, respectively, would be found in “normal,” positive dipole thunderclouds. Specifically, the positive charge region in their storms was at altitudes between 5 to 8 km above mean sea level and the negative charge region between 11 and 13 km. They also detected a positive charge region between 13 and 14 km which was possibly the screening layer charge near the top of the thundercloud. Accordingly, this charge structure was termed an inverted dipole (negative charge region above positive charge region). Cloud flashes bridging the upper negative and the lower positive charge regions (inverted polarity cloud flashes) and predominantly positive ground flashes (originating from the positive charge region, as shown inFigure 1c) are common in such storms. Rust et al. [2005] described two inverted polarity storms that produced predominantly positive ground flashes and one inverted polarity storm which produced inverted polarity cloud flashes, but no flashes to ground.
[12] In addition to main positive and negative charge regions, Figure 1c shows an additional negative charge region near the bottom of the cloud, which was found by Wiens et al. [2005], Kuhlman et al. [2006], and Tessendorf et al. [2007]to facilitate positive cloud-to-ground lightning initiation; that is, to play same role in the inverted dipole clouds as the lower positive charge region in “normal” dipole ones. Interestingly,Wiens et al. [2005]noted that VHF sources associated with the initial breakdown of positive cloud-to-ground flashes progressed upward from the lower negative charge region into the positive charge region of the inverted dipole.
[13] Williams and Yair [2006] suggested that the inverted dipole is often the dominant charge structure during the dissipating stage of ordinary thunderstorms and in the stratiform precipitation region of mesoscale convective systems, with the positive charge being near the 0°C isotherm (about 5 km above sea level in Florida summer storms).
2.4. Unusually Large Lower Positive Charge Region
[14] Cui et al. [2009]inferred from seven-station electric field measurements that thunderstorms in the Tibetan Plateau region have a “normal” tripolar charge structure: positive at the top, negative in the middle, and an additional positive below the negative [see alsoQie et al., 2005]. However, these storms are characterized by a larger-than-usual lower positive charge region (Figure 1d). They produce mostly intracloud discharges (between the upper positive and negative charge regions as well as between the negative and lower positive charge regions) and a relatively small numbers of negative and positive cloud-to-ground flashes [Qie et al., 2009]. For one storm, Cui et al. [2009] reported a total of 112 flashes, of which 98 were cloud flashes, 12 negative ground flashes, and 2 positive ground flashes. It is not clear why the unusually large lower positively charged region was apparently unlikely to launch a positive leader toward ground, although Qie et al. [2009]reported that the storm on 13 August 2003, the strongest one during their 5 year period of observations, produced a high percentage of positive cloud-to-ground flashes. The upper positive charge region was inferred byCui et al. [2009] to be located at a height of about 7.5 km, negative charge region at about 6.0 km and lower positive charge region at about 4.0 km above mean sea level (the altitude of the local terrain was about 2 km above mean sea level). It appears that if the upper positive charge were not detected, the Tibetan Plateau cloud charge structure could be interpreted as an inverted dipole. It is also possible that the detected upper positive charge was associated with the screening layer at the cloud top.
[15] Liu et al. [1994] described the results of triggered lightning experiments in Gansu province in northwestern China with the ground level electric field being apparently dominated by a large lower positive charge region. They reported 10 triggered lightning flashes initiated during three summers from 1989 to 1991 with all of them being composed of the initial stage only (upward moving negative leader followed by initial continuous current), effectively transferring positive charge to ground.
2.5. Negative In-Cloud Leader Channel Cutoff
[16] Positive flashes in mesoscale convective systems are often thought to be preceded by intracloud discharges with negatively charged channels (leaders) originating in the convective region and propagating horizontally over several tens of kilometers, apparently into the upper positive charge layer (5 to 8 km above ground) in the stratiform region. When a negatively charged horizontal leader becomes cutoff from the older (near the origin) channel and the newly formed rear end of this leader gets positively charged, a positive leader is launched from the rear end of the advancing negative leader channel resulting in a positive cloud-to-ground flash, as shown inFigure 1e. This positive flash typically occurs tens of kilometers away from the origin of the parent cloud discharge, under the stratiform, but may occur under the convective. Such a scenario was apparently first suggested by Krehbiel [1981]. Perhaps the best examples of positive cloud-to-ground flashes belonging to this category are presented byLu et al. [2009]who used lightning mapping array (LMA) observations of very high frequency (VHF) sources in conjunction with NLDN data and ultralow-frequency (ULF) magnetic field observations. They examined eight positive cloud-to-ground strokes in a mesoscale convective system in Alabama along with their parent intracloud discharges and observed that VHF sources associated with the positive CG return stroke propagated only toward the advancing end of the negative in-cloud leader (not to its origin in the convective region) and viewed this fact as an evidence of the negative leader channel cutoff. It is possible that the so-called spider lightning (heavily branched channel system crawling along the lower cloud boundary), known to be associated with positive discharges to ground, follows the same scenario [Boccippio et al., 1995; Mazur et al., 1998].
2.6. Branching of In-Cloud Channel
[17] Positive cloud-to-ground discharges can be produced by branching of in-cloud discharge channels, probably most often when these channels occur near or below the cloud base, as shown inFigure 1f. High-speed video images of such flashes are found in the works ofKong et al. [2008] and Saba et al. [2009].
[18] It is important to note that in the scenarios in Figures 1e and 1fthe primary source of charge for positive cloud-to-ground discharge (at least its impulsive component) is a polarized or current-carrying in-cloud lightning channel (including its corona sheath) that was formed prior to the positive discharge, as opposed to a charged cloud region (initially an insulator) in the scenarios inFigures 1a–1d. The in-cloud channel source, which is likely to result in very large continuing currents and charge transfers, was also hypothesized byRakov [2003]to explain millisecond-scale positive lightning current pulses measured by K. Berger at instrumented towers in Switzerland [e.g.,Berger et al., 1975]. Long-duration electric field changes (lasting, on average, in excess of 100 ms and indicative of full-fledged cloud discharges) prior to positive strokes to ground were reported byRust et al. [1981], Fuquay [1982], Qie et al. [2002], and da Silva et al. [2011].
3. Experimental Setup and Data
[19] The data presented here were acquired at the Lightning Observatory in Gainesville (LOG) located on the University of Florida campus in Gainesville, Florida. The LOG includes instrumentation to measure electric field and electric field derivative (dE/dt) waveforms. The electric field sensor consisted of a 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 RC time constant (about 10 ms) of the integrator and by the amplifier, respectively. The electric field derivative (dE/dt) measuring system included a circular flat-plate antenna followed by an amplifier. The upper limit of frequency bandwidth of the dE/dt measurement was 17 MHz. Fiber optic links were used to transmit the signals from the antennas and associated electronics to an 8 bit digitizing oscilloscope. The oscilloscope digitized the signals at 100 MHz and recorded them in its memory unit. The record length was either 240 ms with a pretrigger of 80 ms or 500 ms with a pretrigger of 100 ms. The calibration of the electric field and electric field derivative measuring systems is discussed byNag [2010] and Nag et al. [2010]. In particular, the presence of the building on which the antennas were placed was accounted for using FDTD calculations of Baba and Rakov [2007]. The electric field measurement errors are discussed in detail by Nag et al. [2010, Appendix A1].
[20] Presented here are 52 positive cloud-to-ground flashes containing 63 return strokes recorded at the LOG in 2007–2008. Of these 52 discharges, 39 occurred during the warmer (April–October) season and 13 during the colder (November–February) season.
[21] We obtained GPS timing information for 45 positive flashes containing 53 strokes. Out of these 53 strokes, the U.S. National Lightning Detection Network (NLDN) located 51 (96%), of which 48 (91%) were correctly identified and 3 return strokes (all in single-stroke flashes) were misidentified as cloud discharges. NLDN-reported distances from the field-measuring station (LOG) to the 48 correctly identified strokes ranged from 7.8 to 157 km and from 1.8 to 5 km for 3 misidentified strokes. The majority (31 out of the 48) of strokes were within 60 km of LOG, with 6, 14, 11, and 17 occurring in the 5–20, 20–40, 40–60, and 60–160 km ranges, respectively. NLDN-reported peak currents for the 48 correctly identified strokes ranged from 20 to 234 kA (with the geometric mean value of 75 kA and arithmetic mean of 88 kA) and from 10 to 34 kA for the 3 misidentified strokes. The minimum NLDN-reported peak current tends to increase with distance, but the dependence of the peak current on distance is characterized by a large scatter. This reflects our observation bias toward recording larger events from larger distances. The bias is actually beneficial in our studies of the occurrence of in-cloud discharge activity prior to the return stroke, leader stepping, and preliminary breakdown pulse trains, because the bias toward larger events at larger distances tends to compensate the decrease of our system's detection efficiency with distance.
[22] We examine the occurrence of in-cloud discharge activity before and after the positive return stroke, the number of strokes per flash, as well as the occurrence of preliminary breakdown and stepped leader signatures in our electric field records. In order to estimate charge transfers up to 40 ms using our electric field records and the point charge model, we processed the electric field waveforms to compensate for the 10 ms instrumental decay time constant. Charge transfers in 1 ms and 2 ms after the beginning of return stroke electric field change were estimated for 19 positive return strokes that occurred at distances ranging from 17 to 46 km. For 17 of the 19 strokes, we also computed charge transfer in 40 ms. Additionally, two bipolar cloud-to-ground flashes, also recorded at the LOG in 2007–2008, are presented and discussed in this paper.
4. Occurrence Context
[23] Our field-measuring system could trigger either on cloud discharges or on return strokes (quasi-static electric field changes at relatively close distances or radiation field pulses at relatively far distances). When the system triggered on the return stroke pulse, we interpreted the lack of quasi-static electric field changes and/or radiation field pulses indicative of cloud flashes [e.g.,Villanueva et al., 1994] during our 80 or 100 ms pretrigger time as evidence of no intracloud discharge activity leading to initiation of that stroke. The preliminary breakdown and following leader signatures were not considered intracloud discharge activity. Examples of application of this approach are found in Figures 2a and 2b. We considered the probability of intracloud discharge activity completely ending 80 to 100 ms prior to the return stroke, but still leading to initiation of that stroke to be remote.
[24] Out of the 52 positive cloud-to-ground discharges examined here, 39 (75%) were not accompanied by in-cloud discharge activity (other than the preliminary breakdown process), as detected in the electric field records. An example of such a flash is shown inFigure 2a. Out of the 13 which were accompanied by in-cloud discharge activity, 3 flashes were not preceded (only followed) by in-cloud activity (an example is shownFigure 2b), while for 8 flashes in-cloud activity was detected both before and after the return stroke pulse (an example is shown inFigure 2c). For 2 other flashes, presence of in-cloud activity before and after the return stroke could not be unambiguously determined due to insufficient record length. Thus, in 39 + 3 = 42 (81%) of the 52 flashes, the first leader-return stroke sequence was not preceded by in-cloud activity and, hence, apparently did not follow the scenarios inFigures 1e and 1f. In other words, the overwhelming majority (81%) of our positive flashes were not byproducts of cloud flashes and apparently followed one or more of the scenarios implied by cloud charge configurations in Figures 1a–1d, for which the source of charge was a charged cloud region. These, with appropriate polarity reversals, could have yielded negative flashes. In this sense, most of our positive flashes were apparently initiated in the way similar to that negative lightning flashes are initiated.
[25] This is in contrast with positive lightning reports of Mazur et al. [1998], Mazur [2000], and Lu et al. [2009] that are concerned only with the scenario depicted in Figure 1e, for which the charge source is a previously created in-cloud channel. The disparity between our results and those favoring the scenario inFigure 1e can be related to storm type or/and differences in observation techniques. Specifically, VHF mapping systems utilized by Mazur et al. [1998] and Lu et al. [2009] are generally incapable of recording positive leaders and are apparently most suitable for imaging extensive negative leaders, as in the scenario in Figure 1e. In contrast, our inferences from wideband electric field waveforms are based on identification of characteristic signatures of various lightning processes, regardless of the polarity of charge transferred.
5. Multiplicity and Number of Ground Terminations
[26] The term multiplicity is often used to denote the number of strokes per flash, not necessarily along the same channel to ground. The multiplicity is defined here as the number of return strokes identified in our electric field records of 240 or 500 ms duration. Positive flashes are usually composed of a single stroke, whereas about 80% of negative flashes contain two or more strokes [e.g., Rakov et al., 1994; Rakov, 2007; Saba et al., 2010]. Multiple-stroke positive flashes do occur but they are relatively rare. Out of the 52 positive flashes presented here 42 (81%) were single-stroke, 9 (17%) two-stroke, and 1 (2%) three-stroke flashes, as shown inFigure 3. The overall electric field of the three-stroke flash and time expansions for individual strokes are shown inFigure 4(GPS timing information for this flash was not available and hence no NLDN data could be obtained). There was no preliminary breakdown pulse train or other accompanying in-cloud discharge activity observed in the electric field record of this flash. As described in the caption ofFigure 4, the first and second strokes have similar overall waveshapes which suggests that the second stroke followed the first-stroke channel. The third stroke apparently formed a separate channel to ground. There were a total of 63 return strokes in 52 flashes with an average number of strokes per flash (multiplicity) of 1.2. For comparison,Rakov and Uman [1990b]reported an average multiplicity of 4.6 for 76 negative cloud-to-ground flashes in Florida.
[27] As noted in section 3, for the data set presented here, the record length was either 240 ms with a pretrigger of 80 ms or 500 ms with a pretrigger of 100 ms. There is a small chance that a subsequent stroke of a multiple-stroke flash triggered our field-measuring system and, due to insufficient pretrigger, the first stroke of the flash was missed. In order for this to happen, the field peak of the “missed” first stroke would have to be smaller than that of the subsequent stroke and it would have to occur at least 80 ms (the minimum pretrigger time of our electric field records) prior to the subsequent stroke. Thus, some first return strokes in our data set may actually (but are unlikely to) be subsequent strokes, and some single-stroke flashes may actually be multiple-stroke flashes. If that were the case, the calculated multiplicity of 1.2 would be an underestimate.
[28] For 8 out of the 9 positive two-stroke flashes, NLDN estimated locations for both strokes were available. We now examine these 8 flashes in detail. The flashes occurred at distances ranging from 10 to 157 km from the field-measuring station. Four of these flashes had preliminary breakdown pulse trains prior to the first stokes detectable in their electric field records, but none of the eight flashes was accompanied by any other in-cloud discharge activity. Of the 8 two-stroke flashes, the distance between the first and second strokes was less than 1 km in 1 flash, within 1 to 4 km in 3 flashes, and within 10 to 15 km also in 3 flashes. In one flash, the two strokes were separated by 29 km. The interstroke interval and distance between the first and second strokes for each flash, as well as the NLDN median location error, defined as the semimajor axis (SMA) length of NLDN 50% location error ellipse for each stroke, are given inTable 1. Additionally given in Table 1 are 10%–90% risetimes for both first and second strokes in each flash.
| Flash | Interstroke Interval (ms) | NLDN-Reported Distance Between First and Second Strokes (km) | Median Location Error (km) | Distance Between Strokes Is Smaller Than Largest Location Error | Similarity of First and Second Stroke Electric Field Waveshapes | 10% to 90% Risetime (μs) | Remarks Regarding Second Stroke Following or Not Following the First Stroke Channel | ||
|---|---|---|---|---|---|---|---|---|---|
| First Stroke | Second Stroke | First Stroke | Second Stroke | ||||||
| 06/20/07_00 | 19 | 1.7 | 4.0 | 0.5 | Yes | Yes | 7.5 | 1.6 | Same channel |
| 01/22/08_05 | 79 | 12 | 0.7 | 0.4 | No | No | 7.5 | 3.5 | Different channel |
| 01/22/08_06 | 8.5 | 2.0 | 2.4 | 0.5 | Yes | Yes | 6.9 | 2.2 | Same channel |
| 05/16/08_49 | 116 | 14 | 0.4 | 0.4 | No | Yes | 4.1 | 4.1 | Different channel |
| 06/02/08_431 | 83 | 0.22 | 0.8 | 0.5 | Yes | Yes | 4.5 | 2.5 | Same channel |
| 08/14/08_85 | 70 | 10 | 0.6 | 0.8 | No | No | 2.9 | 3.9 | Different channel |
| 08/23/08_350 | 201 | 29 | 0.5 | 0.4 | No | No | 3.4 | 5.4 | Different channel |
| 11/30/08_01 | 41 | 3.7 | 0.4 | 0.4 | No | No | 5.8 | 10 | Different channel |
| Arithmetic Mean | 77 | 9.1 | 1.2 | 0.5 | - | - | 5.3 | 4.2 | - |
| Geometric Mean | 54 | 4.4 | 0.8 | 0.5 | - | - | 5.0 | 3.6 | - |
| Minimum | 8.5 | 0.22 | 0.4 | 0.4 | - | - | 2.9 | 1.6 | - |
| Maximum | 201 | 29 | 4 | 0.8 | - | - | 7.5 | 10 | - |
| N | 8 | 8 | 8 | 8 | - | - | 8 | 8 | - |
- a One more two-stroke flash (not located by the NLDN and hence not included in Table 1) is characterized by an interstroke interval of 106 ms and the first and second stroke 10%–90% risetimes of 1.4 μs and 2.1 μs, respectively. The overall electric field waveshapes for the two strokes are not similar, suggesting that the second stroke created a new termination on ground.
[29] There is evidence that remote lightning electric field waveforms are significantly influenced by channel geometry, with fields produced by strokes developing in the same channel exhibiting similar waveshape features [e.g., Willett et al., 2008]. Therefore, a second stroke that exhibits a waveshape features similar to that of the corresponding first stroke probably followed the same channel to ground as the first one. Further, the NLDN-reported distance between strokes being smaller than the larger NLDN median location error is also an indication of the two strokes sharing the same channel. We applied the two above criteria to the 8 two-stroke positive flashes with the results being summarized inTable 1.
[30] Out of 8 two-stroke flashes, 3 contained strokes characterized by both similar electric field waveshapes (determined by comparing waveforms on different time scales to identify common features, such as the number and relative magnitudes of major peaks) and NLDN-estimated spatial channel separations (location differences) that are smaller than stroke location uncertainties. We inferred that in these three cases the second stroke followed the first-stroke channel. Note that in each of these three cases the 10%–90% risetime for the second stroke was considerably shorter than that for the first one, which gives additional support to the single-channel inference. Two cases of positive subsequent strokes likely occurring in preexisting channels are illustrated inFigures 5a and 5b.
[31] For four two-stroke flashes, appreciably different field waveshapes were accompanied by distances between channel locations larger than location errors. Additionally, for one flash (05/16/08_49), field waveshapes for two strokes were similar, but separation (14 km) was much larger than the median location errors (0.4 km for both strokes). We inferred that in all these five cases the second stroke created a new termination on ground. Interestingly, only in one case out of eight the two criteria were inconsistent with each other.
[32] Occurrence of positive flashes with different number of strokes from different studies is summarized in Table 2. As noted earlier, strokes may belong to the same flash, but develop in different channels to ground. In Florida, about 50% of negative flashes produce multiple terminations on ground [Rakov et al., 1994].
| Reference | Location | Sample Size | Occurrence (Percentage) of Flashes With Different Number of Strokes | Average Multiplicity | |||
|---|---|---|---|---|---|---|---|
| Single Stroke | Two Strokes | Three Strokes | Four Strokes | ||||
| Heidler and Hopf [1998] | Germany (1988–1993) | 44 | 33 (75%) | 8 (18%) | 2 (5%) | 1 (2%) | 1.3 |
| Heidler et al. [1998] | Germany (1995–1997) | 32 | 28 (88%) | 4 (13%) | 0 | 0 | 1.1 |
| Fleenor et al. [2009] | U.S. Central Great Plains (Kansas and Nebraska) | 204 | 195 (96%) | 9 (4%) | 0 | 0 | 1.0 |
| Saba et al. [2010] | Brazil, Arizona, Austria | 103 | 83 (81%) | 19 (18%) | 1 (1%) | 0 | 1.2 |
| Brazil | 70a | 54 (77%) | 15 (21%) | 1 (1%) | 0 | 1.2 | |
| Present study | Florida | 52 | 42 (81%) | 9 (17%) | 1 (2%) | 0 | 1.2 |
- a Subset for Brazil only of the 103 events recorded in Brazil, Arizona, and Austria.
[33] Ishii et al. [1998], using five-station wideband electric field records and the time-of-arrival method, examined ground strike point locations of 11 two-stroke and 3 three-stroke positive flashes in winter storms in Japan. Observations were performed in summer as well, but no positive flashes were recorded. All the subsequent strokes created new terminations on ground. In 71% of cases, a new termination was more than 10 km away from the first-stroke termination. The average distance between ground terminations for positive flashes (all in winter) was 13.4 km versus 2.1 km (2.1 km in summer and 2.2 km in winter) for negative flashes.
[34] Fleenor et al. [2009]examined the video records of nine two-stroke positive flashes in the U.S. Central Great Plains (Kansas and Nebraska) and found that in four flashes, second strokes created new terminations on ground, while in five flashes second strokes remained in the previously formed (first-stroke) channel.
[35] Saba et al. [2010], using high-speed video records and lightning locating system data, found that, out of 21 subsequent strokes in 20 multiple-stroke positive flashes, 1 stroke followed previously formed channel and 20 strokes created new terminations on ground.
[36] In our data, we inferred that three (38%) subsequent strokes in positive lightning likely followed the previously created (first-stroke) channel and five (62%) likely created new ground terminations. Our inferences are based on NLDN locations and detailed examination (see above) of electric field waveform features.
[37] Occurrence of positive subsequent strokes in a previously created channel is summarized in Table 3. It follows from Table 3 that most of the experimental data are not in support of Mazur's [2002] conjecture that “positive CG flashes cannot have multiple return strokes” repeatedly traversing the same channel to ground.
| Reference | Location | Occurrence (Percentage) of Subsequent Strokes in a Previously Created Channel | Sample Size (Total Number of Subsequent Strokes) | Remarks |
|---|---|---|---|---|
| Ishii et al. [1998] | Japan | 0 (0%) | 17 | Winter storms; five-station electric field records |
| Fleenor et al. [2009] | U.S. Central Great Plains (Kansas and Nebraska) | 5 (56%) | 9 | Summer storms; video records, electric field records (LASAa), NLDN |
| Saba et al. [2010] | Brazil, Arizona, Austria | 1 (4.8%) | 21 | Probably summer storms; high-speed video records, lightning locating systems |
| Present study | Florida | 3 (38%) | 8 | Summer (2 flashes) and winter (1 flash) storms; electric field records, NLDN |
- a LASA, Los Alamos Sferic Array.
6. Preliminary Breakdown Pulse Trains
[38] The first return stroke in a negative cloud-to-ground lightning flash is thought to be preceded by the initial or preliminary breakdown, which is defined as an in-cloud process that initiates or leads to the initiation of the downward moving stepped leader [Rakov and Uman, 2003, chapter 4]. The preliminary breakdown process in negative ground flashes sometimes (in 18% of cases in Florida [Nag and Rakov, 2008]) produces a train of relatively large microsecond-scale electric field pulses whose initial polarity is the same as that of the following return stroke pulse. The preliminary breakdown pulse train in negative cloud-to-ground discharges may be viewed as a manifestation of interaction of a downward extending negative leader channel with the lower positive charge region [Nag and Rakov, 2009]. The typical total pulse duration of individual pulses in the train is 20 to 40 μs with typical interpulse interval in the range of 70 to 130 μs [Rakov et al., 1996].
[39] In the data set presented here, 8 (15%) out of 52 positive flashes had detectable preliminary breakdown pulse trains within 80 or 100 ms of our pretrigger time, when the system triggered on return stroke pulse, an example of which is shown in Figure 6. Time intervals between the largest preliminary breakdown pulse and the return stroke pulse, which can be viewed as a measure of leader duration, ranged from 17 to 130 ms. Five flashes occurring in summer and three in winter. There was no preceding in-cloud discharge activity in any of these eight events (see examples inFigures 2a and 2b), and in two events the return strokes were followed by in-cloud activity, as detected in their electric field records. The percentage (15%) of positive flashes with detectable preliminary breakdown pulse trains is comparable to that (18%) for negative flashes in Florida and becomes even closer (19%) to it if we consider only 42 positive flashes not preceded by in-cloud discharge activity.
[40] The geometric mean current for the eight return strokes preceded by preliminary breakdown pulse trains was 95 kA, somewhat higher than the 75 kA for all the 48 strokes located and correctly identified by the NLDN. Three events occurred in the 5–20 km range, two in each 40–60 km and 80–100 km ranges, and one in the 60–80 km range.
[41] The mean total pulse duration of individual pulses in the trains is 25 μs with mean interpulse interval of 157 μs. For preliminary breakdown pulse trains in positive cloud-to-ground discharges in Japanese winter storms,Ushio et al. [1998] reported a mean total pulse duration of 18 μs and a mean interpulse interval of 54 μs. The geometric mean leader duration (defined here as the time interval between the largest pulse of the preliminary breakdown pulse train and the first return stroke pulse in electric field record) was 40 ms, which is longer than 23 ms reported by Nag and Rakov [2008] and similar to 35 ms reported by Rakov and Uman [1990a] (who measured leader duration using their overall electric field waveforms) for negative lightning in Florida.
[42] In contrast with negative discharges, the initial polarity of preliminary breakdown pulses in positive discharges can be either the same as or opposite to that of the following return stroke pulse [see, e.g., Ushio et al., 1998; Gomes and Cooray, 1998]. Zhang et al. [2011] examined electric field waveforms of preliminary breakdown in 79 positive lightning flashes in Guangdong province of China and found that 84% had the same polarity as the return stroke pulse, 10% had opposite polarity, and 6% exhibited both polarities. Out of the eight preliminary breakdown pulse trains in the data set presented here, pulses in seven trains had the same initial polarity as that of the following return stroke pulse, while pulses in one train had opposite polarity (see Figure 7). There were no significant differences in the characteristics of the two types of pulse trains apart from their polarity.
[43] In the case of “normal” cloud charge structure and in the absence of lower positive charge region, the preliminary breakdown pulse train with the same initial polarity as that of the following positive return stroke may be viewed as a manifestation of the interaction of a positive leader (moving downward from the upper positive charge region) with the main negative charge region. For an inverted polarity cloud shown in Figure 1c, such preliminary breakdown pulse train could be due to interaction of a positive leader from the main positive charge region with the lower negative charge region).
[44] According to Cooray and Scuka [1996], the opposite polarity preliminary breakdown in positive lightning takes place between the main negative and the lower positive cloud charge regions, similar to the preliminary breakdown in negative lightning, but the negative charge is largely expended in neutralizing the lower positive charge. As a result, the vertical channel created by the preliminary breakdown process is “repolarized” in the field of the main positive charge region and serves to launch a positive leader toward ground. As of today, there is no explanation of preliminary breakdown pulse trains observed by Zhang et al. [2011] to exhibit both polarities.
7. Leader Stepping
[45] It appears that positive leaders can move through virgin air either continuously or intermittently (in a stepped fashion), as determined from time-resolved optical images [e.g.,Rakov and Uman, 2003, chapter 5 and references therein]. This is in contrast with negative leaders, which are always optically stepped when they propagate in virgin air. Further, distant (radiation) electric and magnetic field waveforms due to positive discharges are less likely to exhibit step pulses immediately prior to the return stroke waveform than are first strokes in negative lightning. Out of 63 positive return strokes (52 first strokes, 10 second strokes, and 1 third stroke) in the data set presented here, 14 (27%) first strokes (see Figures 4b, 5a (top), 5b (top), and 7), none of the second strokes, and the only third stroke (see Figure 4d) were preceded by pronounced step pulses. We did not observe any dependence of the occurrence of stepping on distance. The occurrence was essentially uniform from 20 to 160 km, with no events in the 5–20 km range. This is not surprising, since (1) step pulse amplitudes are correlated with the corresponding return stroke ones, and (2) the minimum return stroke peak current in our data tends to increase with distance.
[46] The largest amplitude of the step pulses ranged from 8 to 19% (AM = 14%) of the peak of the following return stroke pulse. Hojo et al. [1985] found that 26–30% of return stroke waveforms in Japanese thunderstorms in both summer and winter exhibited pulses indicative of leader stepping process. Our percentage of strokes exhibiting stepping (24% for all positive strokes combined) is similar to that reported by Hojo et al. [1985]. Brook [1957] also noted that 2 (22%) of 9 positive lightning electric field changes in New Mexico exhibited stepping. On the other hand, Schumann et al. [2011] found that 14 (74%; that is, the majority) of 19 positive strokes in Brazil appeared (from electric field records) to be initiated by stepped leaders.
[47] The step pulses in the data set presented here were observed to start 74 to 626 μs before the positive return stroke pulse with the AM interval between pulse peaks being 20 μs (ranging from 5.8 to 37 μs). This is comparable to the average time interval of 17 μs (ranging from 3 to 31 μs) between leader pulses that occurred during the last 500 μs prior to the positive return stroke examined by Kong et al. [2008]. Figure 8 shows an example of electric field (integrated dE/dt) signature of one of the positive first strokes in the data set presented here that apparently involved a stepped leader. For stepped leader electric field pulses prior to the negative return stroke pulse, Krider et al. [1977] reported the AM interpulse intervals of 16 μs and 25 μs for Florida and Arizona, respectively. Cooray and Lundquist [1982] reported that the mean time interval between the electric field pulses just preceding first (or the only) return strokes in Sweden was 26 μs for positive lightning versus 14 μs for negative lightning.
[48] The reason for the occurrence of field pulses indicative of stepping prior to the return stroke pulse in some positive cloud-to-ground discharges is not known. It could be associated with a descending positive leader, an upward connecting negative leader, which may be launched in response to the nonstepped positive downward leader, or both.Wang and Takagi [2011]recently observed, using a high-speed optical imaging system, a downward positive leader that radiated optical pulses like a negative stepped leader.
8. Charge Transferred by Positive Strokes
[51] Our electric field measurements, with an instrumental decay time constant of 10 ms, are suitable for measuring ΔE values at 1 ms, but not at 2 ms and particularly at 40 ms. We have processed our positive stroke waveforms (in the time domain) by performing the convolution of our measured fields with the impulse response of transfer function that, in effect, eliminates our system's integration with 10 ms time constant and introduces the integration with 10 s time constant [Rubinstein, 2001]. In other words, we change, in effect, the decay time constant from 10 ms to 10 s. Measurements of electric field changes (assumed to be essentially electrostatic) at 1, 2, and 40 ms are illustrated in Figure 9.
[52] Table 4 summarizes the values of charge transfer in different times for H = 12 km. Histograms of charge transfers for H = 12 km are shown in Figures 10a–10c. The median charge transfers in 1, 2, and 40 ms ranged from 3.1 to 37 C, 6.2 to 42 C, and 7.1 to 116 C, respectively, and the median charge transfers were 13, 18, and 34 C, respectively. For the case of H = 7 km, the corresponding median values are 19, 24, and 55 C. The median values for 1 and 2 ms are comparable to the median impulse charge (excluding continuing current) of 16 C for 26 positive return strokes reported by Berger et al. [1975], but all three values are considerably smaller than the median total (including continuing current) charge transfer of 80 C. Total charge transfers of hundreds of coulombs or more have been reported for positive discharges in Japanese winter thunderstorms [Goto and Narita, 1995]. As noted earlier, our electric field records were not suitable for estimating total charge transfers due to relatively short decay time constant of the measuring system. The average currents (ratio of charge transfer and corresponding time interval) for H = 12 km and Δt = 1 ms, 2 ms, and 40 ms vary from 3.1 to 37 kA, 3.1 to 21 kA, and 0.2 to 2.9 kA, respectively.
| Flash | r (km) | Δt = 1 ms | Δt = 2 ms | Δt = 40 ms | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ΔE (V/m) | ΔQ (C) | ΔQ/Δt (kA) | ΔQH (C km) | ΔE (V/m) | ΔQ (C) | ΔQ/Δt (kA) | ΔQH (C km) | ΔE (V/m) | ΔQ (C) | ΔQ/Δt (kA) | ΔQH (C km) | ||
| First Strokes | |||||||||||||
| 12/16/07_49 | 38 | 28 | 7.9 | 7.9 | 95 | 32 | 9.2 | 4.6 | 110 | 25 | 7.1 | 0.2 | 86 |
| 08/13/08_31 | 20 | 282 | 17 | 17 | 209 | 303 | 19 | 9.4 | 225 | 338 | 21 | 0.5 | 251 |
| 08/13/08_57 | 23 | 166 | 13 | 13 | 158 | 228 | 18 | 9.1 | 218 | 602 | 48 | 1.2 | 576 |
| 08/13/08_58 | 28 | 180 | 23 | 23 | 273 | 201 | 25 | 13 | 305 | 220 | 28 | 0.7 | 333 |
| 08/14/08_84 | 42 | 47 | 19 | 19 | 223 | 46 | 18 | 9.1 | 218 | 113 | 44 | 1.1 | 533 |
| 08/14/08_87 | 18 | 104 | 4.7 | 4.7 | 57 | 180 | 8.2 | 4.1 | 98 | - | - | - | - |
| 08/14/08_90 | 25 | 178 | 18 | 18 | 220 | 196 | 20 | 10 | 243 | - | - | - | - |
| 08/23/08_173 | 24 | 121 | 11 | 11 | 137 | 148 | 14 | 7.0 | 167 | 248 | 23 | 0.6 | 280 |
| 08/23/08_338 | 40 | 38 | 13 | 13 | 156 | 75 | 26 | 13 | 313 | 300 | 104 | 2.6 | 1244 |
| 08/23/08_339 | 21 | 55 | 3.5 | 3.5 | 42 | 96 | 6.2 | 3.1 | 74 | 265 | 17 | 0.4 | 204 |
| 08/23/08_343 | 26 | 126 | 14 | 14 | 168 | 135 | 15 | 7.5 | 181 | 115 | 13 | 0.3 | 154 |
| 08/23/08_344 | 46 | 6 | 3.1 | 3.1 | 37 | 21 | 10 | 5.0 | 120 | 129 | 63 | 1.6 | 754 |
| 08/23/08_345 | 46 | 53 | 26 | 26 | 318 | 70 | 35 | 17 | 418 | 234 | 116 | 2.9 | 1396 |
| 08/23/08_346 | 26 | 83 | 8.9 | 8.9 | 107 | 116 | 12 | 6.2 | 148 | 319 | 34 | 0.9 | 409 |
| 08/23/08_348 | 42 | 43 | 17 | 17 | 203 | 71 | 28 | 14 | 332 | 251 | 98 | 2.4 | 1173 |
| 08/23/08_350 | 42 | 93 | 37 | 37 | 441 | 105 | 41 | 21 | 496 | 200 | 79 | 2.0 | 950 |
| 08/24/08_783 | 35 | 150 | 36 | 36 | 430 | 176 | 42 | 21 | 504 | 339 | 81 | 2.0 | 974 |
| Second Strokes | |||||||||||||
| 08/14/08_85a | 17 | 213 | 9.4 | 9.4 | 113 | 286 | 13 | 6.3 | 151 | 384 | 17 | 0.4 | 203 |
| 08/23/08_350 | 32 | 32 | 5.8 | 5.8 | 69 | 57 | 10 | 5.2 | 124 | 152 | 28 | 0.7 | 330 |
| Arithmetic Mean | 30 | 105 | 15 | 15 | 182 | 134 | 19 | 10 | 234 | 249 | 48 | 1.2 | 579 |
| Standard Deviation | 10 | 72 | 10 | 10 | 115 | 81 | 11 | 5.3 | 126 | 128 | 34 | 0.9 | 409 |
| Geometric Mean | 28 | 77 | 12 | 12 | 146 | 107 | 17 | 8.5 | 203 | 209 | 36 | 0.9 | 436 |
| Median | 27 | 93 | 13 | 13 | 158 | 116 | 18 | 9.1 | 218 | 248 | 34 | 0.9 | 409 |
| Minimum | 11 | 6.4 | 3.1 | 3.1 | 37 | 21 | 6.2 | 3.1 | 74 | 25 | 7.1 | 0.2 | 86 |
| Maximum | 46 | 282 | 37 | 37 | 441 | 303 | 42 | 21 | 504 | 602 | 116 | 2.9 | 1396 |
- a The electric field record of the first stroke in flash 08/14/08_85 is saturated; hence, electric field change could not be measured.
[53] Schoene et al. [2009]reported the charge transfer in 1 ms after the beginning of the return stroke for 151 negative rocket-triggered lightning strokes at Camp Blanding, Florida. These strokes are similar to subsequent strokes in natural downward lightning. The minimum and maximum charge transfers in 1 ms after the return stroke onset were 0.3 C and 8.3 C, respectively, with the AM and GM values being 1.4 C and 1.0 C, respectively. The mean values are about an order of magnitude smaller than the AM and GM values of 15 C and 12 C, respectively, for charge transfer in 1 ms for 19 positive return strokes (17 first and 2 subsequent) in this study.
[54] Cummer and Lyons [2005]examined charge moment changes (ΔQH) in the first 2 ms after the beginning of the return stroke in cloud-to-ground lightning for three night thunderstorms in Colorado, Nebraska, and Kansas High Plains. They found that strokes having charge moments above 600 C km in two storms and 350 C km in the other produced sprites after short delays (<5 ms). We multiplied our charge transfers by the assumed channel length of 12 km to obtain corresponding charge moment changes given inTable 4. Scatterplot of ΔQH in 2 ms (for H = 12 km) versus NLDN-reported peak current for 19 positive return strokes at distances ranging from 17 to 46 km is shown inFigure 11a and a histogram of NLDN peak currents for these 19 strokes is shown in Figure 11b. No dependence of charge moment changes on peak current is found (determination coefficient = 0.08). The median NLDN-reported peak current for the 19 strokes was 56 kA.
[55] Our charge moment changes in 2 ms for H = 12 km vary from 74 to 504 C km, with 16% (3 out of 19) strokes having charge moment changes greater than 350 C km. Only one out of three strokes with ΔQH > 350 C km was accompanied by in-cloud activity (after the return stroke). For the case H = 7 km, the range is 58 to 451 C km, with only two events with charge moment changes exceeding 350 C km. It is likely that the majority of our positive return strokes did not produce detectable sprites.
9. Bipolar Lightning Discharges
[56] Bipolar lightning discharge is a cloud-to-ground lightning flash that sequentially lowers both positive and negative charge to ground. The majority of bipolar flashes is initiated by upward leaders from tall objects; that is, are of upward type. Downward bipolar flashes are very rare. Only five events have been documented to date, one byJerauld et al. [2009] and four by Fleenor et al. [2009].
[57] There are two bipolar cloud-to-ground flashes, apparently both of downward type, in the data set presented in this paper.Figure 12 shows the electric field signature of a bipolar flash composed of three negative strokes followed by a positive stroke and then by a negative one. The interstroke interval between the third stroke (negative) and the fourth stroke (positive) was 69 ms and that between the fourth and the fifth strokes was 20 ms. Figure 13 shows electric field waveforms of individual return strokes of this flash. No GPS time stamps (and hence no NLDN information) are available for this flash. It is not clear if the fourth (positive) stroke shared a channel with any of the negative strokes of the flash.
[58] The other bipolar flash was composed of three strokes, the first and the third being negative and the second being positive. The interstroke interval between the first (negative, shown in Figure 14a) and second (positive, shown in Figure 14b) strokes was 130 ms and that between the second and third (negative, shown in Figure 14c) strokes was 249 ms. The two negative strokes (the first and the third ones) were, therefore, separated by 379 ms. The first stroke was preceded by a cloud discharge lasting for about 660 ms. Both the first and third strokes occurred at a distance of 46 km from the field-measuring station (median location errors are 400 m for both strokes), from which we infer that they occurred in the same channel. NLDN-estimated peak currents are 52 kA and 25 kA, respectively. The NLDN reported the second (positive) stroke as an intracloud discharge at a distance of 39 km (median location error of 1.2 km). It is likely that the second (positive) stroke formed a channel to ground different from that of the first and third (negative) strokes.
[59] Jerauld et al. [2009]examined a six-stroke natural bipolar lightning flash that occurred at Camp Blanding, Florida, produced two channel terminations on ground, and contained two positive strokes (strokes 1 and 2) followed by four negative strokes. The positive strokes were in separate channels, while strokes 3 to 6 (all negative) followed the same channel as stroke 2.
[60] Fleenor et al. [2009] examined the video and electric field records of four bipolar flashes that occurred in the U.S. Central Great Plains. Each of these four flashes began with a positive first stroke that was followed by one or two negative strokes. The time intervals between the positive first and negative second strokes ranged from 43 ms to 348 ms. Two of their four negative second strokes remained in the same channel as the preceding positive stroke and two negative second strokes and one negative third stroke created new terminations on ground.
10. Summary
[61] It appears to us that at least six different scenarios can give rise to downward positive lightning. For four of them, tilted positive dipole, positive monopole, inverted dipole, and unusually large lower positive charge region (Figures 1a–1d, respectively), the primary source of charge is a charged cloud region, while for the other two, negative in-cloud leader channel cutoff and branching of in-cloud channel (Figures 1e and 1f, respectively), the primary source of charge is a polarized or current-carrying in-cloud lightning channel formed prior to the positive discharge to ground. The overwhelming majority (81%) of 52 positive flashes examined in this paper were not preceded by intracloud discharge activity and, hence, were not of type (e) or (f). We infer that they were initiated in the way similar to that negative lightning flashes are initiated (in the sense that the source of charge was a charged cloud region; that is, they were not byproducts of cloud flashes).
[62] From observations in different locations to date, positive flashes are usually composed of a single stroke, although up to four strokes per flash were observed. Similar to negative lightning, subsequent strokes in positive flashes have been observed to occur both in a new and in the previously formed channel. Out of the 52 positive cloud-to-ground flashes presented in this paper 42 (81%) were single-stroke, 9 (17%) two-stroke, and 1 (2.0%) three-stroke flashes. We inferred that 3 subsequent strokes in our data likely followed the previously created (first-stroke) channel and 5 likely created new ground terminations.
[63] In our data, only 8 (15%) out of 52 positive cloud-to-ground discharges had detectable preliminary breakdown pulse trains. The mean total pulse duration of individual pulses in the trains was 25 μs with mean interpulse interval of 157 μs.
[64] Out of 63 positive return strokes (52 first strokes, 10 second strokes, and 1 third stroke) in our data set, 14 (27%) first strokes and 1 third stroke were preceded by pronounced step-like pulses. The AM interval between pulse peaks was found to be 20 μs, which is similar to the average time interval of 17 μs between leader pulses prior to the positive return stroke examined by Kong et al. [2008].
[65] Charge transfers in 1 and 2 ms were estimated for 19 positive return strokes that occurred at distances ranging from 17 to 46 km and for 17 strokes also in 40 ms. The median NLDN-reported peak current for the 19 strokes was 56 kA. For the assumed height of 12 km, the median charge transfers in 1, 2, and 40 ms after the beginning of return stroke electric field change were estimated to be 13, 18, and 34 C, respectively. The median values for 1 and 2 ms are comparable to the median impulse charge (excluding continuing current) of 16 C for a sample of 26 positive return strokes reported byBerger et al. [1975]. Only three strokes had charge moment changes in 2 ms in excess of 350 C km, a sprite initiation threshold value suggested by Cummer and Lyons [2005]. The charge moment change is not correlated with NLDN-reported peak current.
[66] Two bipolar lightning discharges, which sequentially lowered both positive and negative charge to ground, were examined. One of them was composed of three negative strokes followed by a positive stroke and then by a negative one. It is not clear if the fourth (positive) stroke shared a channel with any of the negative strokes of the flash. The other bipolar flash was composed of three strokes, the first and the third being negative and the second being positive. NLDN reported the positive stroke in this flash as an intracloud discharge. It appears that the second (positive) stroke formed a channel to ground different from that of the first and third (negative) strokes.
[67] In spite of recent progress, our knowledge of the physics of positive and bipolar lightning remains considerably poorer than that of negative lightning. Many questions regarding the genesis of positive and bipolar lightning and their properties cannot be answered without further research.
Acknowledgments
[68] This research was supported in part by NSF grants ATM-0346164 and ATM-0852869 and by DARPA grant HR0011-10-1-0061. The authors would like to thank D. Tsalikis for his help in developing instrumentation and acquiring experimental data, J. A. Cramer of Vaisala for providing NLDN data, and three anonymous reviewers for their helpful comments. Thanks are also due to M. Rubinstein, who provided his computer program for compensation of instrumental decay, and to V. B. Somu for his help with charge calculations.
