Effects of charge and electrostatic potential on lightning propagation

2.1. Balloon Data

[7] Balloon location, ambient pressure, temperature, and relative humidity were determined using data from a Global Positioning System (GPS) dropsonde (configured as an upsonde) flown on each balloon. The dropsondes were developed by the National Center for Atmospheric Research (NCAR) [Hock and Franklin, 1999]. For the SEET project, NCAR's Atmospheric Technology Division modified the dropsonde to compute the full GPS position in the sonde and then telemeter this position to the ground station. Only the horizontal GPS location is used directly; the vertical position of the balloon is calculated from the thermodynamic variables using the hypsometric equation. All altitudes given in this paper are measured relative to mean sea level (msl). In addition, we calculate relative humidity with respect to ice using an empirical expression [Buck, 1981] appropriate for the 0°C to −50°C temperature range.

[8] Each balloon also carried an electric field meter of the type described by Winn et al. [1978] and Marshall et al. [1995]. This instrument measures the magnitude of E up to 220 kV m⁻¹, the vertical component of the electric vector, E_z, and the polarity of E_z. (The convention used in this paper is that a positive E_z causes an upward force on positive charge.) The electric field meter senses the induced charge that moves back and forth between two spheres as they rotate about a horizontal axis. The horizontal axis rotates more slowly about a vertical axis. The balloon soundings of electric field in this paper show the magnitude of the component of E perpendicular to the horizontal axis, E_perp, multiplied by the sign of E_z. As the horizontal axis slowly rotates, E_perp will alternate between the total vector E and the vertical component E_z. When E has a substantial horizontal component, this alternation looks like noise in the graphs because the oscillations are too fast to be resolved in the graphs shown. The inner envelope of the oscillations is E_z (with sign) while the outer envelope of the oscillations is the magnitude of the total electric vector E times the sign of E_z. When these envelopes are nearly equivalent (as often happens), then E_z is the only significant component of the total E vector.

[9] On the basis of a one-dimensional (1-D) approximation to Gauss's law [e.g., Marshall and Rust, 1991; Stolzenburg and Marshall, 1994], we assume that changes in E_z with altitude are caused when the balloon rises through a region of charge in the cloud. (Changes in E with altitude could also be caused by temporal variations in E as the balloon rises or by approaching or receding from spatially localized charge regions.) The altitude and thickness of each charge region is given by the altitudes bounding a quasilinear portion of the E_z profile, while the polarity and charge density of the region are given by the 1-D approximation to Gauss's law:

where z is the sounding balloon's altitude, and ΔE_z is the change in E_z that occurs as the balloon's altitude changes by Δz. Stolzenburg and Marshall [1994] showed that the 1-D approximation is reasonably good if a charge region has a horizontal extent of about 4 km × 4 km or greater.

[10] Marshall and Stolzenburg [2001] presented electric potential profiles through 13 storms and found that voltages (relative to ground) within thunderclouds ranged approximately between ±100 MV. Many of these profiles showed a negative voltage peak at midlevel altitudes and a positive voltage peak at higher altitudes, with the potential difference between the peaks ranging between 20 and 130 MV. Since the electric potential is a useful quantity in energy determinations, we calculate the potential profile for each balloon sounding of E. As in the work of Marshall and Stolzenburg [2001], the electric potential, V, at any altitude in the sounding is given by

with the potential at the ground defined to be 0 V.

[11] This equation has two approximations. First, the integrand for the complete line integral would contain terms E_xdx and E_ydy associated with horizontal balloon motion. These two terms usually will be less than the term E_zdz because E and the vector tangent to the balloon path are often much more vertical than horizontal. The second approximation is that the true potential should be the integral at an instant in time, whereas the data only allow an integral with time increasing as the balloon ascends. Because it takes a relatively long time (typically 15–25 min) for a balloon to travel through the entire depth of a storm cloud, the balloon E or V sounding is a time-skewed, approximate measurement rather than an instantaneous one. During a balloon flight the E and V profiles in a cloud will change because of charging and discharging mechanisms and because of lightning flashes. Because lightning flashes alter the E profile used to calculate V, we do not consider the V magnitudes to be correct, but the shape of the V profile is probably similar to an instantaneous profile.

[12] Some aspects of the E and V profiles are essentially correct instantaneously. Two of these will be important in what follows. First, the local charge density is based on the slope of E_z versus z. If a lightning flash deposits charge in a region that a balloon is traversing (thereby changing the local charge density), the slope of E_z versus z will change immediately. Second, a maximum or minimum in the V(z) profile occurs at an altitude where E goes through zero, so the altitudes of the extrema in the V profile are correct at the moment that they occur (even if the magnitude of the extremum is incorrect).

2.2. Lightning Data

[13] The New Mexico Tech Lightning Mapping Array (LMA) was operated at Langmuir Laboratory in a configuration similar to that described by Rison et al. [1999]. This system locates sources of impulsive VHF radiation in the 60–66 MHz band by measuring the arrival times of the radiation at up to 10 receiving stations. The time and magnitude of the peak radiation event during each 100 μs time interval of the flash are recorded at each station. Events detected at 6 or more of the 10 stations are located in 3 spatial dimensions and in time. In this paper we refer to radiation peaks detected and located by the LMA as radiation sources or events. Each radiation source is characterized by its position, time, peak source power, and the goodness-of-fit (χ_v²) value of the location results.

[14] The LMA data are interpreted using the conceptual framework of bidirectional breakdown [Kasemir, 1960; Mazur, 1989]. As the bidirectional leaders of a lightning flash extend away from the initiation region, their ends are oppositely charged. The leader end with negative charge induced at its tip and along its length is called negative polarity breakdown; the other (positively charged) end is positive polarity breakdown [Kasemir, 1960; Mazur, 1989]. With care one can usually determine the type of breakdown associated with the radiation events. From interferometric observations of lightning [e.g., Shao and Krehbiel, 1996] it is known that negative polarity breakdown is a copious producer of VHF radiation. In contrast, positive polarity breakdown is much quieter in the VHF band. Thus the LMA tends to detect and locate many more events during negative than during positive polarity breakdown. For negative polarity breakdown, the VHF sources extend in a quasilinear, continuous fashion away from the initiation region [e.g., Shao and Krehbiel, 1996; Rison et al., 1999]. The positive polarity breakdown is also detected by the LMA to progress away from the initiation region, but its channels are often not well delineated by the widespread network of stations deployed during SEET. The interferometer measurements, which locate continuous rather than impulsive radiation events, detect the positive polarity breakdown as a series of retrograde negative polarity breakdown from successively greater distances along the path of undetected positive streamers [Shao and Krehbiel, 1996]. This behavior has also been observed and discussed by Mazur [1989]. Another indication of the polarity of the breakdown is given by the power of the radiation sources. Thomas et al. [2001] showed that negative polarity breakdown sources tend to have larger peak radiated power than positive breakdown sources.

[15] A flat-plate antenna was also operated during SEET and measured “slow” (10 s decay time constant) and “fast” (100 μs decay time constant) electric field changes of the discharges. The field change measurements provide information on flash type (IC or CG) and the time and number of CG return strokes [Kitagawa and Brook, 1960; Ogawa and Brook, 1964].

3.1. Flash A

[17] Flash A occurred at 2004:13 UT on 25 July 1999, in a small cell east of the Langmuir Laboratory area. The cell produced a total of five lightning flashes over a 14 min time interval. The first four discharges were CG flashes and the final discharge was the IC flash discussed here, Flash A. Both Flash A and the CG flash preceding Flash A developed horizontal channels to the west that passed close to and beyond the path of the sounding balloon. The CG flash is discussed later as Flash F. The balloon ascended through weak (≤36 dBZ) precipitation extending westward from the Flash A cell and southward from an earlier, more active cell that was dying. Cloud top in the vicinity of the balloon ascent was at about 8 km altitude but extended to 10–11 km in the convective cell.

[18] The radiation sources located for the flash are shown in Figure 1, along with the trajectory of the sounding balloon. The balloon was launched 19 min earlier, at 1945:10 UT, and was at 6.4 km altitude msl at the time of Flash A. The balloon location is indicated by the small diamond in Figure 1, and the initial radiation source is indicated by the “cross” symbol.

[19] Flash A initiated 3 km to the east of the balloon and had a complex bilevel structure, developing in several directions away from the initiation region. An initial upper level branch developed northward and upward to 10.5 km altitude, 3 km north of the flash initiation region. Radar observations (not presented) show that the upward channel extended into the upper part of a weakly precipitating cell that did not produce lightning. A subsequent upper level branch developed horizontally to the west, toward and past the balloon location, with the closest radiation sources located less than 100 m in plan position from the balloon. A side channel of this branch passed directly over or beside the balloon location, while the main channel of the branch passed 1 km to the north of the balloon. The radiation sources of the branch were between about 6.0 and 7.5 km altitude, indicating that the branch was mostly above the balloon altitude of 6.4 km. Other upper level branches developed in various horizontal directions away from the initiation region.

[20] Two lower level branches were detected from the flash. The first branch developed westward from the initiation region to immediately below and slightly beyond the balloon location, between 5.0 and 5.5 km altitude. The second lower level branch developed northwestward into the decaying cell north of the sounding balloon, increasing in altitude to between 6 and 7 km as it went. Except along the final parts of the second branch, the lower level branches had substantially fewer located radiation sources than the upper level branches. The decreased number of radiation sources in the lower level, coupled with the upward initial development of the flash, is characteristic of normal-polarity bilevel IC lightning flashes.

[21] The balloon data are shown in Figure 2. The electric field changes of several lightning discharges are seen as discontinuities in the E profile. The occurrence of Flash A is marked with an arrow in the E profile of the left panel. The flash changed E from −31 to +21 kV m⁻¹, i.e., from downward to upward pointing. The electric field was predominantly vertical both before and after the flash but developed a significant horizontal component (up to 20 kV m⁻¹) during parts of the sounding. The negative value of E prior to the flash indicated positive charge above the balloon and/or negative charge below the balloon and is consistent with the overall charge structure inferred from the sounding, as discussed in the next paragraph. The positive change in E indicates that the flash added net negative charge above and/or net positive charge below the balloon, consistent with the flash's charge deposition inferred from the radiation sources. The fact that E also reversed polarity indicates that charge deposited by the lightning strongly influenced the local field following the flash and is consistent with the closeness of the channels to the balloon.

[22] Figure 2 also shows the inferred charge structure along the path of the balloon, estimated using equation (1). Starting from the ground, we can tentatively identify the various charge regions. The positive charge between 3.2 and 3.5 km was likely a layer of corona ions near the ground [e.g., Standler and Winn, 1979; Chauzy and Raizonville, 1982]. Lower positive charge was evident in the cloud between 4.3 and 5.1 km [e.g., Marshall and Winn, 1982]. Negative charge was located between 5.2 and 5.8 km [e.g., Stolzenburg et al., 1998c]. Above 5.8 km, it is more difficult to identify the charge regions, except for the uppermost positive charge between 7.3 and 7.7 km, which seems to be a screening charge at the upper cloud boundary [e.g., Marshall et al., 1989; Marshall and Rust, 1991]. Positive charge tended to dominate between 5.8 and 7.3 km, but was interspersed with negative and apparent neutral charge regions. The charge was predominantly positive in the macroscopic sense that E_z changed from −90 kV m⁻¹ at 5.8 km to +22 kV m⁻¹ at 7.1 km.

[23] From the initiation altitude of Flash A, we gain some information about the horizontal electrical structure of the storm. We note that the electric field reached its strongest values immediately above and below the midlevel negative charge region. The E extrema were −95 kV m⁻¹ at 5.85 km and +55 kV m⁻¹ at 5.2 km, respectively. An IC flash would be expected to initiate at the altitude of the maximum E above the negative charge region and a CG flash at the altitude of the maximum E below the negative charge region [Coleman et al., 2000]. Even though Flash A was initiated 3 km east of the balloon, its initial radiation sources were at 5.9 km altitude, the same height as the maximum negative E measured in the sounding. Also, we show in section 4.3 that the CG flash preceding Flash A was initiated at 5.2 km, the same height as the maximum positive E measured in the sounding. Although E was presumably stronger in the initiation region, these results indicate that the charge structure was relatively extensive and horizontally layered through this part of the storm. Such a charge structure is also consistent with the horizontal development of the lightning channels. However, the presumed stronger E in the initiation region and the measurable horizontal E during parts of this balloon sounding (Figure 2) are indicative of horizontal variations in the charge and potential structures.

[24] The sounding-inferred potential, V, reached its largest magnitude of −45 MV in the negative charge region. This occurred where E_z changed polarity, at a height of 5.5 km. The potential exhibited a relatively deep minimum within the negative charge region and as such constituted a potential “well” for positive charge. A similar but weaker potential maximum was observed between 6.4 and 6.7 km that constituted a potential well for negative charge. To the extent that the potential profile represents the instantaneous potential prior to a lightning flash, it provides a valuable way of predicting how the flash will behave from an energetic standpoint. In particular, for horizontally extensive charge structures, it will be energetically favorable for positive polarity breakdown to propagate into and spread out horizontally in a potential minimum, and for negative polarity breakdown to develop into and follow a potential maximum. Thus the lightning branches would tend to travel in potential energy minima corresponding to the sign of their leader charge.

[25] Figure 3 compares a histogram of the radiation source heights for Flash A with the inferred potential profile and charge values. The histogram includes only radiation sources that were within about 2 km of the balloon, as defined by the box in Figure 1. Although there is a relative paucity of lower level sources associated with the positive breakdown, the histogram illustrates the bilevel nature of the lightning channels. Each of the two levels agrees well with its corresponding potential energy minimum. Also, we can compare the altitudes of the horizontal branches to the altitudes of the charge regions in Figure 3. For the lower level branches, the peak of the radiation sources was in the lower part of the negative charge region. At upper levels, the radiation sources were in part of the predominantly positive charge region between 5.8 and 7.1 km. Due to the complex charge structure inferred in the upper part of the sounding, the agreement between the source histogram and the inferred charge densities is not as obvious as with the potential energy minima.

[26] Identification of the upper positive charge region becomes clearer when it is noted that the inferred negative charge between 6.4 and 6.6 km probably resulted from Flash A. In particular, the slope of E versus z suddenly changed from being zero immediately prior to the flash to being negative immediately following Flash A. If the E change between 6.4 and 6.6 km was due to a spatial variation in E, the fact that the change began immediately after the flash indicates that the negative charge was deposited by Flash A. This interpretation is supported by the close proximity of the lightning radiation sources above the balloon and by the lightning field change at the balloon. Alternatively, the change in E following Flash A could have been temporal, due to E recovery and regeneration following the flash. In this case the inferred negative charge was not real but an artifact of the charge analysis technique. This interpretation is not supported by data from a second balloon, located 110 m directly below the first balloon at the time of Flash A: for about 8–10 s after the flash both balloons showed identical changes in the magnitudes of E_z, but after this, the lower (second) balloon measured positive E_z values that were about 7 kV m⁻¹ larger. (We note that the charge density of about 0.6 nC m⁻³ inferred from these simultaneous E_z measurements is different from the value shown in Figure 2. The difference is likely due to the fact that the 1-D approximation is not appropriate for the localized charge deposited by a lightning channel.) These two simultaneous measurements indicate that negative charge was present between the balloons. From these measurements, we conclude that the negative charge inferred between 6.4 and 6.6 km was deposited there by the upper channel of Flash A.

3.2. Flash B

[27] Figure 4 shows a simpler bilevel IC flash that occurred at 2254:27 UT on 31 July 1999. It was one of a steady sequence of IC and CG flashes from a 6 min time interval of the storm that we analyze later in this study. The lightning was occurring immediately to the south and to the northeast of Langmuir Laboratory and often produced horizontal channels above the laboratory area where the sounding balloon ascended. The lightning was much more frequent than in the 25 July storm; approximately 40 discharges occurred over the 6-min time interval, 36 of which were within or had significant components within a 6 km × 6 km plan area around Langmuir Laboratory. Radar echo tops were typically 9–12 km in the vicinity of the balloon ascent, and the radar reflectivity reached 55 dBZ in the precipitation core to the south (and in another lightning producing cell to the southeast).

[28] From Figure 4, Flash B initiated at 8.2 km altitude in the southern lightning-producing region. The balloon was at 6.9 km altitude at the time of the flash, immediately above Langmuir Laboratory and 3 km northeast of the flash initiation region. As is typical of bilevel IC lightning, the flash began with negative-polarity breakdown that developed upward in the cloud and soon turned horizontal. Radar comparisons (not shown) indicate that the initiation region was 3–4 km west of the closest precipitation core; the initial upper level breakdown propagated horizontally eastward into the core region and then turned upward into the upper part of the core. The flash subsequently developed northward horizontal branches at both the upper and lower levels. The lower level breakdown was between 6.9 and 7.6 km altitude and progressed past the balloon location, passing about 1 km to the west of the balloon and slightly higher in altitude. This breakdown was of positive polarity. The upper level, negative polarity breakdown was between 9.0 and 9.5 km altitude and further to the west. The radiation sources indicate the occurrence of several extensive K changes between the extremities of the lower and upper level channels at the end of the flash [Shao and Krehbiel, 1996]. The effect of the K changes and of the flash as a whole would have been to transfer negative charge into the upper level channels and to leave positive charge behind on the lower level channels.

[29] Flash B occurred during the sounding shown in Figure 5. The flash caused a small change in E at the balloon, from −26 to −30 kV m⁻¹. This is consistent with the addition of net positive charge above and off to the side of the balloon. Prior to the flash, the E sounding indicated that the balloon passed through negative charge between 6.0 and 6.9 km altitude; shortly after the flash, the balloon passed through alternating regions of positive and negative charge between 6.9 and 7.8 km. The complicated charge structure between 6 and 8 km altitude is typical of that found outside the updraft in the convective regions of storms [Stolzenburg et al., 1998a, 1998b, 1998c]. These charge structures are characterized as having: (1) four or more closely spaced charge layers between the altitudes of 5 and 9 km, and (2) several E peaks of both polarities with relatively large magnitudes (at least 25 kV m⁻¹ and often greater than 100 kV m⁻¹) in the same altitude range. Regions of alternating positive and negative charge were also inferred above 9 km altitude.

[30] Figure 6 shows the charge regions and the potential profile compared with the LMA source-altitude histogram for Flash B. The balloon trajectory was such that the instrument passed 1–2 km to the east of both the lower and upper level northward branches of the flash (Figure 4). The radiation sources associated with the negative polarity breakdown in the upper level branches of the flash exhibited a peak in the histogram at about 9.3 km, close to the bottom of the potential well for negative charge at 9.7 km. Also, these sources overlapped positive charge inferred along the balloon path between 9.3 and 9.9 km altitude. (The smaller peak in the histogram at 10.1 km altitude was associated with the final, upward part of the initial branch in the core of the storm. These sources were 3–4 km to the south of the balloon's position when it reached 10 km altitude.)

[31] The smaller number of radiation sources associated with positive polarity breakdown were located mostly between 7.0 and 7.4 km altitude, with a histogram peak at 7.2 km. These sources were within the deep potential well for positive charge centered at about 7 km. The potential well had two minima in this region due to the presence of embedded positive charge between 6.8 and 7.3 km. The lower level radiation sources overlapped this positive charge and adjacent negative charge regions, in apparent disagreement with the expectation that they would be found in a region of negative charge only. However, as we later discuss, the embedded positive charge seen by the balloon was probably deposited there by positive polarity breakdown of one or more flashes 1–2 min prior to Flash B. In addition, the lower level channel traversed around the region where the positive charge was encountered by the balloon, consistent with the expectation that the deposited positive charge would have been localized along the previous lightning channels. As in Flash A, the charge deposition was in the bottom of the potential well (in this case a well for positive charge).

3.3. Flash C

[32] Figure 7 shows another bilevel IC flash that occurred about 1.5 min after Flash B, at 2255:48 UT on 31 July. The sounding balloon had risen to 7.6 km altitude by the time of this flash; the flash's occurrence is denoted by the arrow in Figure 5. Flashes B and C were both initiated at 8.2 km altitude, 2–3 km south of Langmuir Lab; this was also the altitude of the largest negative sustained E (−60 kV m⁻¹) along the balloon trajectory. Three upper level branches of negative polarity breakdown emanated outward from above the flash initiation region. The final branch propagated northward through the eventual path of the balloon, crossing the path at an altitude between 9 and 10 km. The branch continued to the northeast, descending to between 7 and 8 km altitude. The lower level radiation sources associated with positive polarity breakdown also developed northward and northwestward from the initiation region. Many of the sources were in a relatively well-defined channel that passed almost directly below the balloon. The channel began at 7.5–8 km altitude in the initiation region and steadily descended to between 6 and 7 km as it passed below the balloon. Flash C caused a field change at the balloon of +19 kV m⁻¹ (from −32 to −13 kV m⁻¹), consistent with the addition of net positive charge below the balloon and/or net negative charge above the balloon.

[33] Figure 8 shows the comparison of the inferred charge regions and potential profile with the LMA source-altitude histogram. The comparison is restricted to the portion of the flash within the 5 km square box of Figure 7. As found for Flash B, the heights of the radiation sources during Flash C agree well with the potential energy minima for each polarity of breakdown. The upper level sources, associated with negative polarity breakdown, overlapped with net positive charge between about 9 and 10 km altitude; the balloon passed through the location of these radiation sources 2–3.5 min after the flash. (The separate group of sources between 10 and 11 km altitude were located several kilometers to the northeast of the balloon's path.) The lower level breakdown exhibited a range of altitudes in the vicinity of the balloon, but the main channel corresponded to the lower grouping of sources in Figure 8 and was at the same altitude as the negative charge region between 6 and 6.8 km encountered by the balloon 2 min earlier and a kilometer to the south. Like Flash B, the lower level channel appeared to avoid the embedded positive charge region at 7 km altitude thought to have been deposited there by earlier flashes. The breakdown path was close to that of the lower level channel of Flash B, except generally lower in altitude.

4.1. Flash D

[36] Our first example of a CG flash, shown in Figure 9, occurred at 2252:26 UT during the 31 July sounding shown in Figure 5. It is denoted as Flash D in Figure 5 and occurred 2 min before IC Flash B. At the time of Flash D, the balloon was at 5.7 km altitude and ascending through the inferred lower positive charge region. Prior to the flash, E at the balloon was positive, consistent with the balloon being partway through the lower positive charge and below the midlevel negative charge. Flash D reduced the field from its preflash value of +67 kV m⁻¹ to +38 kV m⁻¹, consistent with the addition of negative charge below the balloon and/or positive charge above the balloon, as indicated by the LMA observations that the flash had negative polarity breakdown below and positive polarity breakdown above the balloon.

[37] Flash D was detected by the NLDN as a single stroke negative CG flash; this is confirmed by the fast antenna data and is consistent with the LMA observations. The initial radiation source was detected at an altitude of 6.1 km, which was also the altitude of the maximum positive E measured during the balloon sounding 2.5 km to the east-northeast of the initial source. Negative polarity breakdown initially progressed downward and then horizontally to the northeast, over a 4 km distance between 4 and 5 km altitude. The breakdown passed about 1 km to the northwest and 0.7–1.7 km below the balloon location. This initial breakdown lasted for about 50 ms; comparisons with radar observations show that it propagated into the core of a heavily precipitating cell at its furthest extent. Subsequent to this, new breakdown began close to the initial radiation source. The new breakdown indicated the start of the stepped leader, which traveled directly downward to the ground and initiated the return stroke 35 ms later.

[38] Radiation sources associated with positive polarity breakdown were detected only after the return stroke, and for the remainder of the flash all of the sources were associated with positive polarity breakdown in the upper level of the flash. Two sets of branches simultaneously developed away from the initiation region in the upper level, one eastward and northeastward from the initiation region and the other northward from the initiation region. The eastward and northeastward branches passed 0.5–1 km above the balloon between 6.4 and 7.2 km altitude, then gradually descended to between 5.2 and 6.4 km altitude. The northward branch was between 6.0 and 6.5 km altitude.

[39] Figure 10 shows the comparison of the LMA sources with the inferred charge regions and potential profile from Figure 5. The LMA source-altitude histogram is for the portion of Flash D within the box shown in Figure 9. The box excludes mainly the vertical portions of Flash D in the initiation region 2–3 km west of the balloon and focuses on the upper and lower level horizontal branches that passed near the balloon. The resulting histogram shows two well-defined levels of activity. The upper level sources associated with positive polarity breakdown are between about 6.5 and 7.2 km altitude and were situated in the lower part of the potential well for positive charge centered at 7 km.

[40] Like Flashes B and C, the positive polarity breakdown of Flash D overlapped both positive and negative charge seen by the balloon between 6.0 and 7.3 km altitude. Unlike Flashes B and C, whose breakdown traversed around the positive charge region, the Flash D breakdown propagated either through or close to the path of the balloon. The balloon did not reach the altitude of the positive charge until 2 min after Flash D, however, during which time two additional flashes occurred whose positive breakdown channels passed either through or close to the positive charge region. The positive charge was encountered by the balloon between about 6.8 and 7.2 km altitude shortly after Flash B, at 2254:27 UT. At this time, the balloon was directly above the Langmuir Annex LMA station (Figure 4). In addition to Flash D, the positive polarity breakdown of a bilevel IC flash at 2252:41 UT developed directly over the Annex station from the south, while that of a branch of a CG discharge at 2253:19 UT developed over the Annex station from the northeast. In all three instances, the altitude of the breakdown was the same as that of the positive charge (7 km). The flashes would have been expected to deposit positive charge along the positive polarity breakdown channels in question, so that any or all of the three flashes are likely to have been responsible for the positive charge subsequently seen by the balloon.

[41] The lower level sources of Flash D, associated with negative polarity breakdown, were between about 4 and 5.5 km altitude in the histogram of Figure 10. These sources partially overlapped the altitude range of positive charge seen along the balloon path but did not correspond to a well in the potential profile. Rather, the potential steadily increased from the ground up, due to E being positive all along the lower part of the balloon trajectory.

[42] To further understand the observations in the lower positive charge region, we have examined electric field measurements made at the ground beneath the storm. Figure 11 shows a 10-min interval of electric field data at two ground stations. The bottom record is from the “Annex” ground station, which was colocated with the Annex LMA station. This station was the southeastern-most of the two LMA stations shown in Figure 9, which served as the coordinate origin for the analyses. The balloon was located 0.7 km southeast of the Annex station and 2.5 km above it at the time of Flash D. The top record is from the “Kiva” station situated 1.8 km northwest of the Annex station, immediately north of the northwestern LMA station in Figure 9. The balloon was launched partway between the two sets of stations and drifted southeastward over the Annex site as it ascended into the base of the storm.

[43] At the time of Flash D, an electric “field excursion associated with precipitation” (or FEAWP) [Holden et al., 1983; Marshall and Winn, 1982] was occurring at the ground. As seen in Figure 11, the FEAWP caused the electric field at the ground to reverse from positive to negative polarity during the course of the balloon flight prior to Flash D. The field reversal occurred over an approximate 2 min interval between about 2249:00 and 2251:00 UT. A FEAWP is believed to result from an increase in the lower positive charge of a storm, causing E at the ground to be dominated by positive charge overhead rather than negative charge [Holden et al., 1983; Marshall and Winn, 1982]. FEAWPs are often interrupted by lightning-produced “lockovers” that cause the field to revert temporarily back to positive polarity, i.e., to return to being dominated by negative charge overhead.

[44] Flash D produced a lockover at the Annex station that lasted about 20 s. This is consistent with the LMA and sounding observations, which indicate that the flash deposited negative charge in the lower positive charge region near the Annex station. Wiens et al. [1999] and Wiens [2000] obtained similar results from a detailed study of LMA, ground electric field, and balloon observations in the early stages of the 25 July storm. Also, the sounding observations support the interpretation that FEAWPs are due to the presence of lower positive charge [Holden et al., 1983; Marshall and Winn, 1982]. Radar comparisons (not presented) show that the lower level breakdown of Flash D terminated in strong (50–55 dBZ) precipitation in a major convective cell northeast of the laboratory area, supporting the idea that the lower positive charge is associated with precipitation.

[45] The FEAWP caused the polarity of E to be negative over a wide area at the ground just prior to Flash D. At the same time, the polarity of E at the balloon location remained positive. The latter was a result of the balloon being in the upper part of the lower positive charge region, and below the main negative charge. Thus an instantaneous profile from the ground up to the balloon would have exhibited a change in the polarity of E at some height and therefore a potential maximum at that height. This is illustrated in Figure 12, which shows the balloon sounding data (E and V) from the ground to the altitude where Flash D occurred. The figure also shows a hypothetical sounding in which the E values have been shifted by −11 kV m⁻¹ to give the measured E at the ground at the time of Flash D.

[46] The fact that E was negative at low altitudes results in the formation of a potential well for negative charge. As indicated in Figure 12, the potential well would have been relatively broad and not very deep, on the order of 10 MV. However, the depth is similar to that of the potential well in the upper positive charge region of the soundings of Figures 2 and 6, which was associated with the horizontal spreading of negative polarity breakdown in the upper levels of the IC flashes. A relatively broad and not very deep well is consistent with the development of the low level branch during Flash D and also with the fact that the channel eventually reached ground. The presence of the well would energetically favor horizontal lightning development and charge deposition through the lower positive charge region, just as the upper level channel of Flash D was energetically favored to travel through the midlevel potential well.

4.2. Flash E

[47] Our next CG example, shown in Figure 13, was a multiple stroke negative CG flash that occurred at 2226:26 UT on 31 July 1999, during the first balloon sounding made on that day. The balloon ascended along a nearly vertical path into a major lightning-producing storm directly above the laboratory area and extending to the north and northeast of the laboratory. Classic bilevel IC flashes were occurring about every 40 s directly over the laboratory area during the time of the balloon ascent. CG discharges were occurring about every 80 s immediately northeast and north of the laboratory.

[48] Flash E occurred as the IC activity started to wane overhead. The flash differed from the storm's preceding CG flashes in two ways: (1) it went to ground west of the laboratory area, and (2) its radiation sources did not indicate extensive horizontal breakdown at low levels (below 5.5 km altitude) in the process of going to ground. As seen in Figure 13, nine ground strokes were located by the NLDN during Flash E. The NLDN ground strike locations indicate multiple strike points close to the horizontal position of the initial radiation event, but each stroke was probably down the same channel to ground, as evidenced by the presence of only a single stepped leader in the LMA observations.

[49] The fast electric field observations (not presented) show that the stepped leader reached ground within 14 ms of the initial radiation source and that the first and second stroke of the flash were not located by the NLDN. The stepped leader therefore went directly to ground, along an essentially vertical channel. In the course of their development, the upper level channels progressed almost 15 km northward in the storm. The flash therefore was similar to the multiple-stroke discharges studied by Krehbiel et al. [1979], in which the horizontally progressing breakdown was the source of negative charge for the successive strokes to ground.

[50] The sounding data from the balloon are shown in Figure 14. The balloon stopped ascending at 7.2 km altitude, 43 s before Flash E, and had descended to 7.1 km altitude by the time of the flash. (It is not known why the balloon stopped rising; it was presumably ruptured by lightning or hail.) The occurrence of Flash E is not depicted in Figure 14, which shows only the ascent sounding. During its ascent, the balloon passed through apparent lower positive charge and at least part of a negative charge region.

[51] Figure 15 compares the radiation events from the inner box in Figure 13 to the inferred charge regions and potential profile (from Figure 14). In the upper level, positive polarity breakdown peaked at 7.0 km, consistent with the inferred altitude of negative charge and the potential well for negative charge. However, few or none of the radiation sources were associated with horizontal branching in the inferred lower positive charge. The basic question posed by Flash E is why such branching at low levels did not occur.

[52] An analysis of the complete sequence of lightning around the time of Flash E shows that the region of lower level LMA activity during the preceding CG flashes was relatively localized immediately northeast and north of the laboratory area, and that the sounding balloon ascended through the edge of this activity. Based on the restricted horizontal extent of the lightning activity, it is likely that the lower positive charge encountered during the sounding did not extend westward to the vicinity of Flash E's channel to ground. Additional evidence of horizontal (or temporal) variability comes from the fact that the initial radiation source of Flash E was located at 6.6 km altitude, while the strongest electric field measured during the sounding was at 5.5 km.

[53] The lack of lower level horizontal branching during Flash E would also be consistent with the ground electric field data, which indicated that a FEAWP was not being produced below the lower positive charge of the sounding and therefore no potential well existed that would have influenced such development. Finally, some of the E increase measured by the balloon as it ascended into the storm may not have been caused by lower positive charge, but by the balloon approaching localized charge higher in the storm or by the ongoing field increases associated with the charging process in the storm.

4.3. Flash F

[54] Our final example, shown in Figure 16, is of a negative CG flash that occurred at 2001:13 UT on 25 July 1999, in the storm that produced Flash A. Flash F occurred 3 min before Flash A while the balloon was ascending through negative charge at 5.6 km altitude in the sounding of Figure 2. Both flashes produced substantial field changes at the balloon that are marked on the sounding. Like Flash A, Flash F originated in a cell 2–3 km east of Langmuir Laboratory and produced a horizontal branch that propagated westward close to the sounding balloon. Radar comparisons show that the radiation sources during the first 100 ms of the flash were concentrated in and around the precipitation core of the eastern cell.

[55] The initially located radiation source of Flash F was at the same altitude, 5.2 km, as the peak in the positive E values seen during the balloon sounding (Figure 2). The height-time panel in Figure 16 shows that three ground strokes occurred during the first 100 ms of the flash. Each stroke was preceded by downward developing radiation sources indicative of a new channel to ground. Fast electric field change data confirmed the development of a fourth channel to ground later in the flash, at 2001:14.00 UT, associated with the descending radiation sources immediately prior to that time. The first return stroke occurred within 5 ms of the start of the flash, indicating that its leader appeared to go directly to ground. The descending negative leaders for the subsequent channels exhibited a larger number of radiation sources and took longer to reach ground, sometimes traveling horizontally for a kilometer or more before coming to ground.

[56] Subsequent to the third return stroke, two horizontal branches of positive polarity breakdown developed away from the initiation region of the channels to ground. The branches are best seen in the plan view of Figure 16. Like Flash A, the first branch propagated westward close to and past the balloon location; the second branch propagated northwestward, into the remnants of an earlier cell. Although they were at similar altitudes, the positive polarity branches of Flash A constituted the lower level breakdown of that IC flash, while those of Flash F constituted the upper level breakdown of the CG flash.

[57] Figure 17 compares the source-altitude histogram from the portion of Flash F closest to the balloon (the inner box in Figure 16) with the inferred charge regions and potential profile from Figure 2. A larger number of sources were located in the upper level of Flash F than in the lower level of Flash A; however, in both instances their heights agreed with the altitude of negative charge and with the altitude of the potential minimum as inferred from the balloon data. The lower level sources in Figure 17 were at and below the altitude of positive charge inferred from the balloon sounding, but were 2–4 km east of the balloon's trajectory.

[58] The upper level branch of positive polarity breakdown that passed near the balloon was incompletely located after it passed west of the balloon but was well located near the balloon. Detailed analysis of the radiation sources in the vicinity of the balloon shows that the branch traveled horizontally between 5.4 and 5.5 km altitude, i.e., slightly below the balloon altitude of 5.6 km, and about 0.2 km immediately northeast of the balloon. Flash F changed the vertical electric field at the balloon from −59 to −10 kV m⁻¹ and eliminated a substantial horizontal field component that had developed as the balloon rose above 5.4 km altitude. These results are qualitatively consistent with the branch adding positive charge below and off to the side of the balloon's location. E_z at the balloon went through zero at 5.5 km altitude, indicating that the potential well for positive charge was locally at the same altitude, and in excellent agreement with the altitude of the positive breakdown. The polarity transition in E_z occurred in the presence of a significant horizontal component of E (E_h about 20–25 kV m⁻¹), indicating that V also varied horizontally.

[59] Observations from a second sounding balloon at an altitude of 5.1 km almost directly below the first balloon showed that E was saturated, corresponding to an electric field of at least +220 kV m⁻¹, and consistent with the second balloon being slightly below strong negative charge. Flash F reduced E at the second balloon to +25 kV m⁻¹, consistent with positive charge having been added above the balloon.

[60] The simultaneous E measurements from the two balloons give information about the time independent V profile in the cloud. Using the 1-D approximation to Gauss's law, ΔE_z equaled or exceeded −280 kV m⁻¹ over a vertical distance of 500 m, corresponding to a negative charge density of at least −5 nC m⁻³ between the altitudes of the two balloons. (Since the earlier balloon recorded only 60 kV m⁻¹ at 5.1 km altitude (Figure 2), it appears that the charge responsible for the 220 kV m⁻¹ field was either localized or not present earlier. Either of these possibilities could explain the difference between the −5 nC m⁻³ just calculated and the −3 nC m⁻³ shown in Figure 2.) Also, the opposite polarity of E_z at the two balloons further confirms the existence of a well in the vertical potential profile between 5.1 and 5.6 km altitude. Thus the time-independent data indicate that the positive polarity branch of Flash E traveled through a region of dense negative charge near the altitude of a potential minimum.

[61] Ground measurements at four locations beneath the lower part of the balloon trajectory showed positive E values prior to Flash F ranging from +4 to +8 kV m⁻¹, that is, dominated by negative charge overhead. Due to the relatively low lightning rate, the ground E values were approximately steady leading up to both Flashes F and A, as a result of the field being limited by corona from the earth's surface. Both Flashes F and A produced substantial negative field changes (−10 to −20 kV m⁻¹) at each of the ground stations, consistent with the deposition of positive charge overhead by the positive polarity breakdown of the flashes. The fact that the field change of Flash F was negative (rather than positive as in the “lockover” change of Flash D) is consistent with its lower level breakdown being east and northeast of the ground stations and not having extended into the lower positive charge seen along the balloon path.

[62] Flash F differed from CG Flashes D and E in that it developed several channels to ground. As noted earlier, the fast antenna and LMA data for Flash F showed evidence of four return strokes, each along different channels, three of which were located by the NLDN. This is contrasted with Flash E, which produced 11 or more strokes apparently down a single channel to ground. Like Flash E, the initial stroke of Flash F went quickly to ground. However, the LMA observations and NLDN locations indicate that the subsequent strokes were along different paths to ground. The negative breakdown for each of the strokes was spatially widespread and “noisy” looking, characteristic of stepped leaders and also indicating the occurrence of lower level breakdown in the process of going to ground.

[63] As noted, for example, by Uman [1987], it is common for CG flashes to develop multiple channels to ground. The question is why this happens. A partial answer to the question has been suggested by multistation electric field change measurements of lightning [Krehbiel, 1981]. The results show that, as a stroke begins to die out, negative charge continues to flow into the upper part of the channel to ground but does not reach ground. The channel appears to cut off from the ground up and to become “filled up” with negative charge as it does so, tending to cause the subsequent leader to take a different path to ground.

[64] The above argument is readily cast in terms of electric potential. As the channel to ground cuts off, the presumed flow of negative charge into the channel would tend to charge the upper part of the channel to the potential of the negative charge region. The result would make it energetically favorable for a subsequent leader to break down a new path to ground rather than follow the previous path. In Flash F, the new leaders to ground showed evidence of substantial branching while the initial leader did not. This would be consistent with the initial stroke reversing the polarity of the field at the ground and developing a potential well associated with lower positive charge.