Locating initial breakdown pulses using electric field change network

Authors


Abstract

[1] Initial breakdown pulses (IBPs) observed in the fast electric field change (E-change) at the beginning of intracloud (IC) and cloud-to-ground (CG) lightning flashes are located using a time-of-arrival technique called Position By Fast Antenna (PBFA) with data from a network of 10 E-change sensors located at Kennedy Space Center. Location errors, estimated using a Monte Carlo method, are usually less than 100 m for horizontal coordinates and several hundreds of meters for altitude, depending on distance to the sensors and altitude of the source. Comparison of PBFA source locations to locations from a VHF lightning mapping system (Lightning Detection and Ranging II (LDAR2)) shows that PBFA locates most of the “classic” IBPs while LDAR2 locates only a few percent of them. As the flash develops during the IB stage, PBFA and LDAR2 obtain similar locations when they detect the same IBPs. The overall vertical motion indicated by the PBFA positions of IBPs was downward with time for CG flashes and upward with time for IC flashes. Location of the fast pulses due to return strokes of CG flashes is also determined using PBFA. Comparison to locations from the Cloud-to-Ground Lightning Surveillance System (CGLSS) shows that PBFA reliably locates ground strokes. These results are verified using ground truth data acquired with a high-speed video camera. After cross calibration with the CGLSS data set, peak currents of return strokes are also determined.

1 Introduction

[2] Electric field change measurements of lightning flashes usually begin with bipolar pulses called by several names: initial breakdown pulses (IBPs), preliminary breakdown pulses, characteristic pulses, or beginning pulses. These pulses typically last for 20–80 μs and occur during the first few milliseconds of the flash. Many studies have been carried out using electric field change (E-change) sensors to understand the properties and behavior of IBPs [e.g., Appleton and Chapman, 1937; Clarence and Malan, 1957; Kitagawa and Brook, 1960; Weidman and Krider, 1979; Beasley et al., 1982; Gomes et al., 1998; Nag and Rakov, 2008; Nag et al., 2009]. However, in the 75 years since IBP waveforms were first recorded by Appleton and Chapman [1937], no one has reported finding the (x,y,z) locations of IBPs, so it has been impossible to determine exactly what part of the physical development of a flash is causing IBPs. Recently, Stolzenburg et al. [2013] made high-speed (50,000 frames per second) videos of IBPs of cloud-to-ground (CG) flashes and compared them to E-change data. The data show that the initial leaders of the flashes produce a series of light bursts and that each burst is associated with a downward leader extension of a few hundred meters and a coincident IBP. These video data are extremely valuable for learning about IBPs, but they are difficult to obtain: in 180 flashes, a distinct initial leader was seen in only 10 flashes. Obtaining the location of these IB pulses should be useful toward understanding the physical processes that produce them. The main goal of the research reported herein was to develop a network of E-change sensors to locate IBPs and other similar pulses using a time of arrival (TOA) technique. We call the system developed Position By Fast Antenna, or PBFA. In this paper, we show that PBFA can locate a significant number of the IBPs occurring at the beginning of lightning flashes and is also excellent at locating return strokes of CG flashes.

2 Instruments and Data Sources

[3] The data used for this study were collected in the summer of 2011 around NASA/Kennedy Space Center (KSC), Florida; the data presented herein are from 14 August 2011. Ten E-change data collection stations were operated (Figure 1), covering a nearly 70 km × 100 km area; this network is an extension of a smaller system operated in 2010 [Stolzenburg et al., 2012]. Our array of E-change sensors is similar in many ways to LASA, the Los Alamos Sferic Array [Shao et al., 2006]. The four main differences between LASA and our array are as follows: (1) our sensors have a wider bandwidth, (2) our capture times for triggered data are typically 500 ms versus 500 μs for LASA, (3) our sensor array has more sensors (10 versus 6 for LASA) in a slightly smaller area, and (4) our data are sampled at 5 or 10 MHz versus 2 MHz for LASA. Each station was equipped with three flat plate antennas [e.g., Kitagawa and Brook, 1960], each measuring E-change and named ch1, ch2, and ch3. These three antennas differed from each other in decay time constant, gain, and bandwidth (Table 1). The ch1 was normally used for triggering the system and acted as a classic fast antenna. For this study, ch3 data were used except when this antenna was saturated due to its high gain, in which case ch2 data were used instead. Four (K02, K14, K17, and K24) of the 10 stations were located inside KSC, each within few a meters of a KSC electric field mill [e.g., Koshak and Krider, 1989].

Figure 1.

Google map© showing the data collection stations deployed on and around Kennedy Space Center in the summer of 2011. KXX sites were located within a few meters of a KSC field mill (K14 beside mill #14). All other sites were located outside KSC. The high-speed video camera was co-located with FFI sensor. The origin shown is for the LDAR2 coordinate system, which is used for all (x,y) plots herein.

Table 1. Flat Plate Antenna Characteristics
SensorDecay Time ConstantRelative GainBandwidthBit Depth
ch1100 μs10–201.6 kHz to12
   630 kHz 
ch210 s10.016 Hz to12
   2.6 MHz 
ch31s100.16 Hz to12
   2.6 MHz 

[4] Waveforms from each sensor were digitized at 12 bits, recorded, and time tagged using a GPS (1 sigma average of less than 2 ns). Each sensor's waveform was recorded continuously at 10 kHz and in triggered mode at 1, 5, or 10 MHz. For PBFA calculations, we use either 5 or 10 MHz data, and on 14 August 2011, 8 of the 10 stations were recording data at 5 MHz while the other two (BCC and FFI) were recording at 1 MHz. Throughout this paper, calibrated E-change data are presented, although the calibration is not relevant for the Time of arrival (TOA) method. For the calibration process, the calibrated KSC electric field mill data were used. The physics sign convention, where an upward positive electric field exerts an upward force on a positive charge, is used.

[5] In addition to E-change data, time-correlated high-speed video (HSV) data were acquired with a Vision Research Phantom V12.1 camera co-located with the FFI station. Camera data were recorded at 50,000 images per second (20 μs image interval). The HSV data are used in this paper as ground truth for PBFA locations of lightning return strokes.

[6] We will compare the PBFA locations to locations from two KSC operational systems, LDAR2 (Lightning Detection And Ranging II, also called 4DLSS) and CGLSS (Cloud-to-Ground Lightning Surveillance System) [e.g., Wilson et al., 2009]. The LDAR2 network determines the location of lightning pulses. Thomas et al. [2004] describe LDAR2 as a commercial version of the more well known Lightning Mapping Array, or LMA [Rison et al., 1999]. LDAR2 primarily locates pulses associated with negative stepped leaders [Rison et al., 1999; Thomas et al., 2001, 2004]. This system detects VHF lightning sources with a center frequency of 63 MHz and a bandwidth of 6 MHz [Lennon and Maier, 1991; Maier et al., 1995; Murphy et al., 2008] and calculates position of these sources in real time. However, LDAR2 detects relatively few IBPs. For example, Figure 2 shows that only five LDAR2 source locations were detected during the initial breakdown of a negative (CG) flash which contained 179 easily detected IBPs of which 23 were “classic” and 156 were “narrow.” As defined by Nag et al. [2009], classic IBPs have total durations of tens of microseconds while narrow IPBs have durations less than 4 μs. (Note that we expanded the definition of narrow IBP from <4 s to <10 s to include pulses within 4–10 s range.) Classic IBPs have larger amplitudes and have been studied extensively by Weidman and Krider [1979] and Nag et al. [2009]. Examples of classic and narrow IBPs are shown in Figure 2.

Figure 2.

E-change, LDAR2, and CGLSS data versus time for a negative CG flash that occurred about 10 km north-west of the LDAR2 origin beginning at 21:33:56.333 UT on 14 August 2011. (top) Calibrated ch3 E-change data (left vertical axis) from K02 site. This flash had eight return strokes, but only data from initial breakdown (IB) to the first return stroke (20 ms) are shown. LDAR2 source altitudes are plotted (right vertical axis) as black dots. Times of LDAR2 and CGLSS points were adjusted to include the propagation time to K02 sensor. IB occurred in the first 5 ms of the flash and had at least 179 IBPs and five LDAR2 source locations. (middle) E-change of IBPs (magenta dots) detected by K02 ch1. In this plot, “A” and “B” mark the examples of “narrow” and “classic” IBPs, respectively. (bottom left) Expanded view of the narrow IBP marked “A” in the middle panel. (bottom right) Expanded view of the classic IBP marked “B” in the middle panel.

3 Method and Calculations

[7] Time of arrival (TOA) techniques have been used to locate lightning pulses for many decades [e.g., Proctor, 1971; Proctor et al., 1988; Maier et al., 1995; Cummins et al., 1998, 2006; Krehbiel et al., 1996; Thomas et al., 2001, 2004]. Additional references and an excellent review of previous work for the TOA technique can be found in Koshak and Solakiewicz [1996].

[8] When a lightning pulse occurs, it excites antennas in different locations at different times. Arrival time difference for two distinct locations, multiplied by wave travel speed, can produce a hyperbola with the foci located at the antenna locations. Having at least four distinct antennas will produce three such hyperbolas. When absent of measurement errors, these three hyperbolas yield a unique point in space equal to the source location. Having more than four sensors improves the location retrieval when measurement errors are present. Most of the early TOA work has been conducted following this method and solving non-linear equations numerically to get the retrieval locations. However Koshak and Solakiewicz [1996] introduced a method to linearize these non-linear equations and introduced analytical solutions to get the location as well as the errors for each coordinate. In the perfect situation, five stations produce four linear equations, and getting analytical solutions to four unknowns (x,y,z,t) would be trivial. These authors also indicated that this linear system “can be taken as an under- or over-determined system of equations that can be solved using the general theory of constrained linear inversion.” Koshak and Solakiewicz [1996] applied this method for theoretical sensor configurations: a square network having a sensor at each corner, a triangular network having a sensor at each corner plus a fourth sensor at the center, and a symmetric seven-antenna network having sensors at each corner of a hexagon and one at the center. They determined that the mean location errors were smallest for the symmetric seven-antenna network.

3.1 Obtaining Locations

[9] As mentioned above, we call our TOA method PBFA. Although developed independently, our method is essentially the same as the method used by Shao et al. [2006]. The exact algorithm of Koshak and Solakiewicz [1996] has been coded in the MATLAB™ programming language, and the steps to utilize it can be summarized as follows. First, we load all available 5 MHz triggered E-change data for a given flash into memory and apply a simple 100 Hz Butterworth high-pass digital filter to remove slow E-changes like those due to continuing current. Then, the data are cross-correlated to line up corresponding peaks in the data from the different sensor sites. Next, we identify the arrival times of a peak at the different sensor locations. For classic bipolar IBPs, we locate the negative peak for negative CG flashes and the positive peak for normal intracloud (IC) flashes, since these are the leading peaks in the bipolar waveform and also since they are sharper than the opposite-polarity overshoot [Weidman and Krider, 1979]. Arrival times (good to the nearest 0.2 μs, restricted by the 5 MHz sampling rate) and sensor site locations (given by the GPS to within 5 m) are then used with the Koshak and Solakiewicz [1996] TOA method to retrieve (x,y,z,t) coordinates. Our coordinate system is centered at the LDAR2 origin and has x oriented east-west, y north-south, and z upward (altitude relative to mean sea level).

[10] Next, the (x,y,z,t) location is re-calculated using only the sensors located more than 6 km horizontally from the event. The reason for this step is as follows: if the sensors are too close to the event, the electrostatic and induction fields [e.g., Uman et al., 1975; Watson and Marshall, 2007] will distort the shape of the pulse and its peak location, thereby causing errors in the TOA calculation. We used the model of Watson and Marshall [2007] to determine how close a sensor could be to the event without having near field effects distort the pulse peak time; the result was roughly 6 km horizontally from the event (though this value is only an estimate since it depends on the event details such as propagation speed and current rise time).

[11] As a final step, we optimized the results using the “Levenburg-Marquardt” algorithm [e.g., Thomas et al., 2004]. We call the above sequence of calculations “Method 1.”

[12] “Method 2” begins with the result of Method 1 before the optimization and then re-calculates the z coordinate. We use a different method to estimate the z coordinate because the arrival times at closer sensors are more sensitive to the altitude of the source, as discussed by Betz et al. [2004]. As the distance between a sensor and a source increases, the arrival time does not change much if the altitude is changed from one value to another. For example, a pulse that occurs at 5 km altitude would arrive at a sensor 100 km away after about 333.7 μs; if the pulse occurred at 0 km altitude it would arrive at the same sensor after about 333.3 μs, making only a 0.4 μs arrival time difference (or 2 of the 0.2 μs sample intervals) between the two cases. On the other hand, if a similar calculation were done for a sensor only 30 km away, the arrival time difference would be 1.4 μs (or 7 of the 0.2 μs sample intervals), which is more prominent. Thus, for re-calculation of the z coordinate we use all the sensors available within 6–30 km. In cases where there are no sensors within this range, no re-calculation of the altitude can be done (so the altitude from Method 1 is used).

[13] We perform error calculations for both methods using a Monte Carlo algorithm as described in the following section. For both methods, we calculate reduced chi-square (math formula) for the arrival times of the calculated event (x,y,z,t) at the stations to determine the goodness of fit. Finally, we compare results of the locations, errors, and math formula from Methods 1 and 2 to insure that both methods are in reasonable agreement. If the agreement is good, then we record the solution with the lower math formula value.

3.2 Error Estimations

[14] PBFA location errors come from two main sources, arrival time errors, and sensor location errors; these can be identified as random errors and systematic errors, respectively. Since the GPS gives the location of stations to within 5 m accuracy, our largest source of error is in the arrival time; an error of one sampling interval (0.2 μs) is equivalent to 60 m. Therefore, we neglect the systematic station location errors and focus on the random timing errors. The timing errors depend critically on the ability of our sensors (with the bandwidths shown in Table 1) to reproduce the E-change pulse faithfully so that the pulse peak is correct. Another important factor is the data sampling rate: is it fast enough to locate the pulse peak correctly? Nag et al. [2009] show examples of classic IBPs recorded with a bandwidth of 16 Hz to 10 MHz, sampling intervals of 4 or 10 ns, and 8 bit digitizer. Our classic IBPs (recorded with a bandwidth of 0.16 Hz to 2.6 MHz, sampling intervals of 200 ns, and 12 bit digitizer) look identical to their classic IBPs. We conclude that our E-change sensors are capable of reproducing all of the significant details of IBPs and therefore of providing good PBFA locations.

[15] We use a Monte Carlo method to estimate location errors resulting from random errors in arrival times; this method was derived independently but seems identical to the location error simulation used by Shao et al. [2006]. Given a source at a known location, one can calculate arrival times at each sensor location. Then a random Gaussian error with σ=±(0.5×time resolution) was introduced to each arrival time. Next, these arrival times are used to calculate the location using the same algorithms as described above. After 1000 iterations, the standard deviations of the difference between each calculated position and the actual position were considered as estimates of the error for each (x,y,z,t) coordinate.

[16] Since the sensors are widely spread over a nearly 70 km × 100 km area, PBFA errors for the horizontal coordinates are usually less than 100 m close to KSC. On the other hand, in Florida, the altitude variation of ground-based sensors is small, so the errors for the altitude estimation are larger. It is also worth noting that for events at the same horizontal position, the estimated altitude errors are larger for lower event altitudes. Figure 3 shows the PBFA altitude error estimations for sources occurring 5 and 10 km above the ground. The smallest z errors occur within 10 km horizontally of the LDAR2 origin, where they are less than 300 m (150 m) for event altitudes of 5 km (10 km). Beyond about 30 km horizontally the z errors are greater than 1000 m (500 m) for event altitudes of 5 km (10 km). To generate the plots in Figure 3, we assumed that all eight E-change sensors were available for the TOA calculations described above. However, in reality, some sensors might have saturated or not have triggered on a particular flash. In such cases, the errors might be larger. The actual errors of an event location will depend on several factors, including which sensors are used in the PBFA calculation, the signal to noise of the sensors for that event, the time resolution of the data, and the relative pulse location in space.

Figure 3.

Estimated altitude errors for pulses located using E-change data. The altitude errors are color coded according to magnitude. The top row shows a smaller area while the bottom row shows a wider area near KSC. These plots are for pulses occurring at 5 km altitude assuming all eight sensors contribute to the calculation. Left and right columns show the error calculations done using the Methods 1 and 2, respectively. The origin of these plots coincides with LDAR2 origin shown in Figure 1. Plots for pulses occurring at 10 km altitude look essentially identical except the z errors are uniformly smaller by approximately a factor of 2. As per our algorithm, we do not use any sensor within 6 km horizontal radius to calculate altitudes. The artifacts produced due to this can be seen as a 6 km shaded area around some sensors.

3.3 Peak Current Estimations

[17] The E-change data can also be useful in estimating peak currents associated with return strokes (RSs) and other fast pulses. At this time LDAR2 does not report peak current (or VHF power) for detected sources. CGLSS does report the peak currents of every return stroke it detects [e.g., Wilson et al., 2009]. We use the method described by Shao et al. [2006] to estimate peak currents of RSs. As discussed in Shao et al. [2006], extending the peak current estimations to IBPs “is not necessarily valid” and “should be treated only as rough estimates.” Such estimates might be useful in identifying large-amplitude IBPs.

4 Results

[18] In this section we show PBFA location estimates of IBPs for a typical negative CG flash and a typical IC flash. These locations will be compared with the LDAR2 data in the same IB time period. However, a caveat on this comparison (discussed below) is that we cannot be completely certain that our PBFA event is the same event detected by LDAR2. Hence, we also compare PBFA return stroke locations to those from CGLSS, since we can be certain that both systems are detecting the same events in this case. Lastly, we compare the PBFA and CGLSS return stroke locations to ground-truth data obtained with the HSV camera.

4.1 IB Pulses of a CG Flash

[19] CG flashes initiate with a short and very intense train of IBPs. For our example, we have chosen the negative CG flash shown in Figure 2. This flash occurred about 9.5 km west and 6 km north of the LDAR2 origin and triggered all eight sensors for which we have 5 MHz data. Figure 4 (top) shows the E-change versus time for the eight sensors used for PBFA locations. In the E-change data the flash has 23 classic and more than 156 narrow IBPs during the first 5 ms (Figure 2). The TOA method applied to the E-change data allowed us to calculate PBFA locations of 66 of the 179 pulses, including almost all of the classic IBPs, which are typically the largest amplitude IBPs in CG flashes. The math formula values were calculated for the arrival times; all math formula values were less than 2 for all the 66 PBFA locations. During the IB stage of this flash, LDAR2 located only five VHF sources. Since no fast pulse was seen in our E-change data at the time of the fifth of these LDAR2 sources, only four of them were roughly collocated with IBPs, for an IBP relative detection efficiency of about 2%. A similar analysis of another 15 CG flashes showed that LDAR2 VHF sources were roughly coincident (to within ±5 μs) with 97 of more than 1700 IBPs for a relative detection efficiency of <6%. Since the IBPs that we counted were easily seen in our E-change data (meaning they had significant amplitudes in the bandwidth of our E-change sensors), it is hard to imagine that the lack of LDAR2 sources was due to lack of LDAR2 sensitivity unless the IBPs did not radiate significantly in the LDAR2 VHF bandwidth. Based on the number of IBPs located (especially the large-amplitude classic IBPs), we see that PBFA provides much more information about IBPs and therefore about CG flash development in the IB stage than LDAR2.

Figure 4.

(top) E-change data (versus time) from eight sensor sites used to calculate PBFA locations of IBPs of the CG flash shown in Figure 2. Data are offset for easier viewing. (middle) First 1.6 ms of K14 data including first four LDAR2 (black dots) sources and all 66 PBFA sources (red dots) showing more detail of the individual pulses. The first LDAR2 source is circled since it is hidden by a PBFA source. (bottom) The expanded wave forms around first three LDAR2 sources for K14 sensor. (Axes are similar to above panels). The times of the LDAR2 and PBFA sources were adjusted to include propagation time to K14 sensor.

[20] Although LDAR2 located only five VHF sources during the IB stage of the CG flash in Figure 2, we compare them with the PBFA events as a test of the PBFA location algorithm. Figure 4 (middle) displays E-change at the K14 sensor and the altitudes of the 66 PBFA and four LDAR2 events in the first 1.6 ms of the IB stage of the CG flash. Average values of the PBFA location errors for IPBs were 70 m, 50 m, and 250 m for x, y, and z directions, respectively. LDAR2 location errors for this flash were similar, approximately 100 m in the horizontal and 250 m in the z direction [Murphy et al., 2008; Thomas et al., 2004]. We focus on the four LDAR2/PBFA pairs that were roughly coincident with four IBPs in the E-change data. Figure 4 shows that the pairs were also roughly coincident in altitude (within the altitude error bars). Figure 5 shows the (x,y) locations of the PBFA and PBFA events. The four LDAR2/PBFA pairs are connected by lines; the pairs are quite close (within the location error bars) to each other and to the other IBPs located by PBFA. Detailed comparisons of the LDAR2 (x,y,z,t) locations relative to the PBFAs are shown in Table 2.

Figure 5.

Horizontal positions (relative to LDAR2 origin) of PBFA sources (diamonds) and LDAR2 sources (colored dots with black circles) for the first 1.6 ms of the negative CG flash shown in Figure reffig:CG-example. The occurrence time of the sources is color coded. The small square region in the inset figure has been expanded to generate the main plot. Black stars in the inset figure show some of the sensors. A black line connects the PBFA source that is closest in time to each LDAR2 source; the horizontal distance between these LDAR2/PBFA pairs were 130, 170, 50, and 200 m, respectively, in time. Overall, the PBFA locations indicate that the flash propagated from northwest to southeast.

Table 2. Comparison Between PBFA and Closely Occurring LDAR2 Sources for the CG Flasha
LDAR2 No.IBP TypeΔt (μs)Δx (m)Δy (m)Δz (m)
  1. aAll the Δ values are relative to the corresponding PBFA source.
1narrow0.0110500
2classic−1.9−10−20480
3narrow−2.0120280−290
4classic−0.7−15050−240
5not seenNANANANA

[21] Figure 4 (bottom) shows expanded views of the first three LDAR2/PBFA pairs. The first LDAR2 source was at exactly the same altitude and time as the PBFA location of the corresponding IB pulse (a narrow, nonclassic IBP); the slight difference in arrival time at the K14 sensor was due to the slight difference in (x, y) positions. The fourth pair (not shown) is similar to the first. For each of the other two pairs shown in Figure 4 (bottom), the LDAR2 event precedes the peak of the IBP by about 2 μs, which is larger than timing uncertainties (0.075 μs for LDAR2 and 0.2 μs for PBFA). There are at least two possible reasons for the time difference found for these two pairs: (a) it is real, meaning LDAR2 and PBFA are locating different events that are closely located in space and time (and may, therefore, be causally related to each other) or (b) it is an artifact caused by the physical length of each IBP. The second possibility is based on the fact that LDAR2 is known to have larger uncertainties when locating events longer than its RF wavelength of 5 m [Thomas et al., 2004], combined with the finding of Stolzenburg et al. [2013] that classic IBPs of CG flashes are associated with currents a few hundred meters long. In either case, we conclude that the four LDAR2/PBFA locations of IBPs were in good agreement.

[22] As seen in Figure 4 (middle), the PBFA locations of fast pulses within each classic IBP show a general downward trend with time for the IB stage of this CG flash. We have determined the PBFA locations of classic IBPs in four additional CG flashes from 14 August 2011; in these flashes, the PBFA locations also show a general downward trend with time. Based on the negative polarity of the fast pulses at sensors beyond the reversal distance [Rakov and Uman, 2003] and the pulses' downward development, these pulses are likely associated with the downward motion of negative charge. Although the PBFA and LDAR2 sources during the IB period of CG flashes move along close to each other, descending with time and propagating horizontally together, the PBFA data show this motion in more detail. Based on high-speed video and E-change data, Stolzenburg et al. [2013] found that the activity during the IB period of CG flashes is mainly repeated “initial leader” extensions with each individual extension (of 100–300 m) associated with a classic IBP. The E-change, PBFA, and LDAR2 comparisons above seem to indicate that narrow IB pulses occur throughout the IB period and may initiate initial leader extensions and associated classic IBPs, but are mainly occurring at times other than when classic IBPs occur.

[23] Because a classic IBP has a linear channel a few hundred meters long [Stolzenburg et al., 2013], the meaning of the PBFA location is uncertain. In order to understand the meaning of the real position calculated with PBFA, we used the Watson and Marshall [2007] model to generate waveforms at each of our sensor locations due to exponentially decreasing current [Thottappillil et al., 1997] moving vertically upward along a 300 m channel at a known location; this choice fits the observation of IB initial leader extensions of CG flashes [Stolzenburg et al., 2013]. Then we applied the same TOA technique to obtain the PBFA location. The resulting PBFA location was at the bottom of the channel where the current was the maximum. We did similar modeling for linearly decreasing [Rakov and Dulzon, 1987], linearly increasing, and exponentially increasing currents [Watson and Marshall, 2007] moving both vertically upward and downward; for each of these current surges, the PBFA location corresponded to the location of the peak current. However, for a constant current, the PBFA location was not uniquely defined, changing when we changed parameters in the model like initial and final heights, current direction, (x,y) location, etc. Based on these modeling results, we assume that PBFA is locating the peak current location of a long channel if the PBFA location has an acceptable math formula (less than 2).

4.2 IB Pulses of an IC Flash

[24] Compared to CG flashes, IC flashes usually have fewer IBPs. In addition, the time between IBPs of IC flashes is typically much longer and the average duration of individual pulses is larger [Kitagawa and Brook, 1960; Weidman and Krider, 1979]. The long interval between pulses makes it easy to identify them at separate sensors, but their slow rise times makes the peaks not so well defined at all the sensors. The example IC flash we have chosen occurred about 13 km west and 12 km north from LDAR2 origin at 21:35:30.26 UT on 14 August 2011. The IB portion of the flash can be seen in Figure 6. Since this flash happened within 20 km of the LDAR2 origin, and the event altitudes were relatively high, the altitude errors of the flash were smaller than in the CG flash example shown above. Position errors were approximately 100 m, 60 m, and 160 m for x, y, and z, respectively. We were able to estimate PBFA locations for most of the IBPs in the E-change data. During the first 15 ms, LDAR2 located eight sources while PBFA located 14 sources with math formula less than 2. Of the eight LDAR2 events, only the third, sixth, and eighth were roughly coincident with IBPs in the E-change data; there were no E-change pulses at the times of the other five LDAR2 events.

Figure 6.

Similar to Figure 4, but showing a portion of calibrated E-change data for the IB stage of IC flash at 21:35:30.2665 UT on 14 August 2011. The altitude estimations from PBFA (red dots), and LDAR2 (black dots) have been adjusted to include the propagation time to K24 sensor. The top panel shows the first 15 ms of data of all the sensors used to calculate PBFA points while the bottom panel displays 1 ms of K24 data including the biggest IBP shown in the top panel followed by three shorter-duration classic IBPs.

[25] The third LDAR2 source occurred at the time of a small, fast E-change (not locatable with PBFA) which was a part of a classic IBP located by PBFA. As explained in section 4.1, we believe that the LDAR2 source either was slightly mislocated because IBP event was longer than 5 m, or it may have caused a shorter, smaller current surge that led on to a longer, larger classic IBP. The other two LDAR2 sources (sixth and eighth in the top panel of Figure 6) show very small fast E-changes (i.e., narrow IBPs) on some sensors which were not big enough for us to obtain PBFA locations. The horizontal plan-view of PBFA and LDAR2 locations together (Figure 7) shows that the IBPs were initially clustered near (−14 km, 12 km), then propagated northeast. Despite the fact that there were few coincident LDAR2/PBFA sources during the IB stage of this IC flash, the LDAR2 and PBFA sources moved upward together (Figure 6) and horizontally together (Figure 7) in the same small region of the cloud. The similar flash development indicated by LDAR2 and PBFA sources shows that the PBFA locations are in agreement with the LDAR2 locations.

Figure 7.

Similar to Figure 5 but showing the horizontal locations of PBFA (diamonds) and LDAR2 (dots) for the first 15 ms of the IC flash that occurred at 21:35:30.2665 UT on 14 August.

[26] We performed a coincidence analysis for LDAR2 event times and E-change data peaks for 15 IC flashes. There were 585 IBPs and only 199 LDAR2 sources: 13 (6%) of the LDAR2 points were close (within ±5 μs) to classic IBPs, 107 (54%) were close to narrow IBPs, and 79 (40%) of LDAR2 points occurred without any detected IBP in the E-change data. These results are similar to the findings of the similar analysis (above) for CG flashes.

[27] As seen in Figure 6, the PBFA locations of fast pulses within each classic IBP show a general upward trend with time for this IC flash. We have determined the PBFA locations of classic IBPs in seven additional IC flashes from 14 August 2011; in these flashes, the PBFA locations also show a general upward trend with time. Based on the positive polarity of the fast pulses at sensors beyond the reversal distance and the pulses' upward development, the pulses are likely associated with the upward motion of negative charge.

4.3 Return Stroke Locations

[28] In most cases, LDAR2 does not locate a source at the same time as an IBP seen in the E-change data. Therefore, in the above section we compared the locations of nearly coincident LDAR2/PBFA events (within ±5 μs), which showed that the PBFA locations are within 200 m horizontally and 200–500 m vertically from the LDAR2 sources. However, a direct comparison can be made when two systems are locating the same event. To accomplish this, we compared return stroke (RS) locations obtained from CGLSS to the corresponding PBFA RS locations. Figure 8 shows the comparison of x,y coordinates (relative to LDAR2 origin) for 2627 RSs that occurred within a 50 km radius from the LDAR2 origin on 14 August 2011. These RSs are not all the ones that happened on that day within 50 km radius, but just a subset of those which triggered all eight E-change sensors. For each RS included in the comparison, we required that the RS time agreed to within ±0.5 ms, then for each flash we plotted in Figure 8 the PBFA x value versus the CGLSS x value; a similar comparison plot was done for the RS y values. Ideally the best fit line for both plots in Figure 8 should have a slope of 1. For the x coordinate comparison, the slope was approximately 1.017, while for the y it was 0.990. The correlation coefficients for both coordinates were also quite close to 1.00. Histograms of temporal and spatial difference between the RS located by the two systems are also shown in Figure 8 along with their statistics. From these comparisons to CGLSS locations, we conclude that PBFA reliably finds return stroke locations. This result is not surprising, since Shao et al. [2006] showed that LASA, which is quite similar to PBFA, “can easily pinpoint the ground strike points of return strokes.”

Figure 8.

Left column shows the x,y coordinate comparisons of RS locations obtained by PBFA and CGLSS for 2627 return strokes that occurred within 50 km of the LDAR2 origin on 14 August 2011. The best fit line for both x and y shows the slope close to 1.00 with good correlation. Right column shows the temporal and spatial difference between RSs located by the two systems along with their statistics. Inset figures of right column are the zoomed versions of the tails of the corresponding figures.

[29] During the data acquisition period, we recorded a number of CG flashes with the HSV camera (at 50,000 images per second). To directly compare the PBFA return stroke locations to the HSV data, we use photogrammetry. The calculated PBFA location for one RS in a flash is used as a reference point to define the camera's image plane: the image plane is then assumed to go through the reference point and is assumed perpendicular to the line connecting the camera location and the reference point. The other PBFA locations for the other return strokes are then projected onto this plane. The distance difference from the video return stroke to the projected PBFA location onto the plane will be called the projection error. Since the camera shows a 2-D picture, location errors perpendicular to the plane of the picture are not seen in this analysis. As an additional check, CGLSS return stroke locations are also included on the video images.

[30] Figures 9-11 show individual frames for the CG flash at 21:33:56.333 UT (discussed above and shown in Figures 2 and 4) along with the projected PBFA and CGLSS data. Figure 9 also includes comparison plots of the CGLSS and PBFA (x,y) locations of the eight RSs. Table 3 shows the PBFA and CGLSS (x,y) locations of each RS along with the number of sensors used in obtaining the PBFA and CGLSS locations, the peak current estimations, location difference between PBFA and CGLSS, and projection error. The fifth return stroke was chosen as the reference point, since the PBFA and CGLSS positions were close to the same. The flash had eight RSs and five separate ground connections. Figure 9 (top) shows seven of the eight RSs. The fourth return stroke is excluded from Figure 9 because it connected approximately 3.3 km to the right of the first return stroke and had more horizontal structure than the other RSs. The fourth RS is shown in Figure 10. Projection errors from PBFA were estimated at 0–183 m with an average of 49 m for this flash. Projection errors from CGLSS were estimated to 0–200 m with 110 m average. An overview of this flash along with LDAR2, PBFA, and CGLSS events is shown in Figure 11 and indicates good correlation between the calculated source positions and the visually observed paths of the flash. Overall, both the CGLSS and PBFA RS locations are in good agreement with the “ground truth” video RS locations. The intercomparison of CGLSS and PBFA locations for individual RSs also seems reasonable. According to the video data, the last four RSs of this flash had the same ground connection. Perhaps the best test of the ability of PBFA to locate RSs is seen in the (x,y) comparison plots in Figure 9, especially the locations of RSs 5–8, all four of which should have the same location. It is easy to see that the PBFA locations of these four RSs make a tighter cluster than the CGLSS locations. This finding should not be surprising, since Table 3shows that PBFA used seven or eight sensors in determining the locations while CGLSS used only four sensors. PBFA usually uses all of its sensors for RS locations because the RS pulse amplitude is usually quite large and therefore is easily seen by all sensors.

Figure 9.

(top) Individual video frames (20 μs exposure) showing (from left to right) return strokes 1–3 and 5–8 of the CG flash shown in Figures 2, 4, and 5. PBFA (red dots) and CGLSS (green dots) return stroke locations have been mapped to the images as described in the text. Each video frame is 80×190 pixels (width versus height); for this flash, the square video pixels are approximately 31 m on a side. The flash had eight RSs with five separate ground connections. Strokes 5–8 had the same ground connection and appear to re-illuminate the same path to the cloud. The fourth RS location was 3.3 km to the right of the first return stroke and is shown in Figure 10. (bottom left) (x,y) locations of PBFA and CLGSS for the eight RSs. Dashed lines show the direction of the camera from the reference RS. (bottom right) Zoomed version of the square region shown in the left. The PBFA locations of strokes 5–8 which had the same ground connection were circled. Detailed location comparisons along with projection errors for all RSs can be found in Table 3.

Figure 10.

Similar to Figure 9, but showing the fourth return stroke of the CG flash shown in Figure 11. The image is a single complete video frame (320×240 pixels) that occurred in four frames (80–100 μs) after the start of the fourth RS. The image shows several branches illuminated during the continuing current. The return stroke originally propagated upward from the ground and then moved to the left to the region where the IBPs occurred. The CGLSS (green square) and PBFA (red dot) locations both had the same projection error of about 180 m, though they were separated by 450 m horizontally (see Table 3).

Figure 11.

Integrated image combining the individual frames from Figures 910. The PBFA (red dots), LDAR2 (black and cyan dots), and CGLSS (green squares) locations for this flash are projected onto the image. The PBFAs include only 41 IBPs and 8 return strokes; the LDAR2s include five sources (black) that occurred during the IB period. The additional LDAR2 sources (cyan) associated with stepped leaders are included to show that their projection closely follows the lightning path.

Table 3. Location Comparison From Video Imagery of the Eight Return Strokes for the CG Flash at 21:33:53.333 UT on 14 August a
RSNx (km)y (km)Peak Curr. (kA)Loc. Diff. (m)Proj. Diff. (m)
  1. aSecond column N shows the number of stations used to calculate the locations. Loc. Diff. means location difference between the PBFA and CGLSS locations while Proj. Diff. means projection difference, which is the distance difference along the video frame between the visual RS location and the projected PBFA and CGLSS locations as shown in Figures 911.
1 - PBFA8−9.075.37−14.65900
1 - CGLSS4−9.665.43−29.9 200
2 - PBFA8−10.094.93−23.67600
2 - CGLSS4−10.664.96−32.7 −127
3 - PBFA8−9.546.19−23.1270117
3 - CGLSS4−9.806.26−27.3 0
4 - PBFA8−9.342.10−18.4450−183
4 - CGLSS4−9.792.12−28.0 −184
5 - PBFA8−9.685.92−17.3300Reference
5 - CGLSS4−9.985.92−23.2 56
6 - PBFA7−9.636.08−13.83600
6 - CGLSS4−9.985.98−18.9 32
7 - PBFA7−9.566.08−16.44800
7 - CGLSS4−9.116.26−21.9 83
8 - PBFA7−9.595.99−6.122090
8 - CGLSS4−9.795.89−18.4 167

5 Conclusions

[31] As described herein, we have developed a system called PBFA (Position By Fast Antenna) that uses an array of E-change meters together with a TOA technique to obtain the locations of initial breakdown pulses (IBPs) of lightning flashes. We tested the PBFA locations of IBPs by comparing them to the relatively few LDAR2 locations of IBPs and found good agreement between the two systems. PBFA can locate most or all classic IBPs of both CG and IC flashes.

[32] In addition to classic IBPs, PBFA can also locate some narrow IPBs, which we define as having durations less than 10 μs (although the original definition of Nag et al. [20092009] was less than 4 μs). We have also shown that PBFA can be used to determine return stroke (RS) locations. PBFA has the following characteristics:

  1. [33] It uses data from a network of 10 E-change sensor sites that cover a horizontal area approximately 70 km × 100 km. It is focused on giving the best location accuracy over the Kennedy Space Center (KSC) area. PBFA requires E-change data from at least five sensor sites to obtain the (x,y,z,t) position of an IBP or E-change data from 4 sensors to obtain the (x,y,t) position of a RS.

  2. [34] The primary E-change sensors have a bandwidth from 0.16 Hz to 2.6 MHz (essentially spanning the ELF-MF frequency bands) and a sampling interval of 0.1 or 0.2 μs.

  3. [35] Event location errors within 10 km of the center of KSC (chosen at the LDAR2 origin) are typically less than 100 m in horizontal (x,y) position and less than 300 m (150 m) in altitude (z) for events occurring at an altitude of 5 km (10 km).

  4. [36] Event timing errors are less than 0.25 μs within 20 km of the center of KSC.

  5. [37] It is cross-calibrated with CGLSS to estimate the peak current of each return stroke and to give a rough estimate of the peak current of elevated sources like IB pulses.

  6. [38] Modeling suggests that the PBFA (x,y,z,t) location is at the position along the linear current surge where the peak current occurred.

[39] Although our main aim with this paper has been to show that PBFA can correctly locate IB pulses, we can draw a few conclusions from the PBFA locations of IB pulses in the 13 flashes analyzed so far (including the CG flash and IC flash shown herein plus four CG and seven IC flashes not shown). First, PBFA locates most classic IB pulses and some narrow IBPs of flashes occurring within 20 km of the LDAR2 origin, and these locations are in the same small region of the cloud as the (relatively few) LDAR2 sources located during the same time period. Second, the general vertical progression with time of the PBFA positions of the IBPs was downward for CG flashes and upward for IC flashes. Third, based on these motions and the polarity of the observed E-changes, we conclude that the general vertical motions of IBPs are due to the motion of negative charge downward for CG flashes and upward for IC flashes. These charge motions are similar to the development of negative leaders detected with VHF lightning mapping systems such as the KSC LDAR2 [Wilson et al., 2009], the system used by Proctor and colleagues [e.g., Proctor et al., 1988], and the LMA [e.g., Rison et al., 1999; Thomas et al., 2004]. However, none of these VHF measurements have shown a one-to-one connection between a VHF source and an IB pulse seen in E-change data (and the data presented herein show that LDAR2 is locating only a few percent of the IB pulses). Thus, another new finding is that IBP locations show the detailed progression during the IB stage of a flash's initial negative leaders. In conclusion, locating IB pulses with PBFA (or systems like it) provides an important new tool for understanding the physical mechanisms occurring at the beginning of lightning flashes.

Acknowledgments

[40] This project was supported by the National Science Foundation (grants AGS-1016004 and AGS- 1110030) and the NASA/Mississippi Space Grant Consortium (grants NNG05GJ72H and NNX07AM36A). The camera was made available via NSF grant AGS-0813672. We thank all persons who helped with E-change sensor design, data collection, and processing, especially Clay Conn, Chris Maggio, Mark Stanley, Richard Sonnenfeld, and Frank Merceret of NASA/KSC. Thanks go to our E-change sensor hosts, Kennedy Space Center in Titusville, Florida Institute of Technology Department of Physics and Space Sciences in Melbourne, Hickory Tree Elementary School in St. Cloud, Brevard Community College Planetarium in Cocoa, St. Lukes Lutheran School in Oviedo, Massey Ranch Airpark in Edgewater, and Fairfield Inn in Titusville.

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