Initiation processes of return strokes in rocket-triggered lightning

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, , doi: /jgrd.50766, 2013 Initiation processes of return strokes in rocket-triggered lightning D. Wang, 1 N. Takagi, 1 W. R. Gamerota, 2 M. A. Uman, 2 J. D. Hill, 2 and D. M. Jordan 2 Received 29 April 2013; revised 6 August 2013; accepted 15 August 2013; published 6 September [1] Using a high speed optical imaging system operated at a time resolution of either 10 ns or 100 ns, we have documented the initiation process of 14 return strokes in four rockettriggered lightning flashes. Of the 14 strokes, nine occurred following dart leaders and five following dart-stepped leaders. The return strokes are found to initiate at heights ranging from 7.2 ± 1.4 to 21.0 ± 4.6 m above the lightning termination point. Return strokes with larger peak current tend to initiate higher. All the return strokes show initial bidirectional (upward and downward from their initiation height) propagation. We have been able to estimate the initial upward propagation speeds below 60 m for all of the return strokes. The resultant speeds range from to m/s. For the downward propagation speeds, only six strokes among the 14 strokes allow us to perform a reasonable estimation. Those downward speeds range from to m/s. Citation: Wang, D., N. Takagi, W. R. Gamerota, M. A. Uman, J. D. Hill, and D. M. Jordan (2013), Initiation processes of return strokes in rocket-triggered lightning, J. Geophys. Res. Atmos., 118, , doi: /jgrd Introduction [2] Wang et al. [1999a] presented the first observational evidence showing that a return stroke is initiated at a height where its preceding downward leader and an induced upward leader from the ground meet, from which point the return stroke propagates bidirectionally as shown in Figure 1. This scenario was hypothesized by Wagner and Hileman [1958] and used by a number of researchers to study numerically the relation between return stroke current and the corresponding electromagnetic field [e.g., Uman et al., 1973; Weidman and Krider, 1978; Willett et al., 1988, 1989; Leteinturier et al., 1990; Miyazaki and Ishii, 2006]. Since the initiation process occurs on a time scale usually less than 1 μs and on a spatial scale of some meters to tens of meters from the lightning termination point, its observation is extremely difficult [e.g., Idone, 1990]. To the authors knowledge, the data from which Figure 1 is inferred are the only experimental evidence in the literature showing such a return stroke initiation process. As shown by Miyazaki and Ishii [2006] through modeling, both the initiation height and the initial speed of the return stroke significantly influence the relationship between the return stroke current and electromagnetic radiation waveforms. Thus, better knowledge of how a return stroke is initiated is very important not only for developing more detailed lightning return stroke modeling but also for better understanding the mechanism of the so-called slow front and fast transition that appear in 1 Department of Electrical, Electric and Computer Engineering, Gifu University, Gifu, Japan. 2 Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida, USA. Corresponding author: D. Wang, Department of Electrical, Electric and Computer Engineering, Gifu University, Gifu, , Japan. (wang@gifu-u.ac.jp) American Geophysical Union. All Rights Reserved X/13/ /jgrd lightning return stroke waveforms [e.g., Weidman and Krider, 1978; Jerauld et al., 2007]. Additionally, better knowledge of the lightning initiation process may help shed light on the relation between the lightning return stroke peak current and the lightning striking distance. The striking distance is a parameter that has been used in designing lightning terminal height and spacing for lightning protection systems but has never been properly verified experimentally [e.g., Uman, 2008]. All of the factors noted above have motivated the authors to perform comprehensive high speed optical observations of the attachment process of return strokes. Using a high speed imaging system specifically designed for studying the lightning attachment process [Wang et al., 2011], the Lightning Attachment Process Observation System (LAPOS), we initiated such observations at the International Center for Lightning Research and Testing (ICLRT), located in north-central Florida in the summer of That summer, we succeeded in recording the initiation processes of 14 subsequent strokes in four lightning flashes triggered with the rocket-and-wire technique [e.g., Rakov and Uman, 2003]. In this paper, details of the initiation process of these 14 return strokes are reported. 2. Instrumentation and Observation [3] Figure 2 shows the schematic of the LAPOS. It consists of a camera body, a optical fiber array, multiple photodiodes and their amplifiers, and a digital storage oscilloscope. Its fibers are configured to form 15 horizontal lines with each line consisting of 108 fibers. The diameter of fibers is 0.33 mm. To align the fibers of two adjacent lines, a 0.13 mm-thick glass plate is inserted between them. All fibers at each horizontal line except the third line are bundled and optically guided into a photodiode through two lenses so that all the individual fiber signals are added together. The fibers at the third line are separated into left side and right side and are guided into two photodiodes, respectively, to monitor the 9880

2 50 m Lightning Terminus Downward Negative Leader Upward Positive Leader Return Stroke Junction Point Time (ns) Figure 1. A schematic illustration of the lightning initiation process. Adapted from Wang et al. [1999a]. effect of any scattered light. The fiber array is mounted at the camera s image plane. When a lightning strike occurs in the view of camera, its image formed by the camera lens is guided by the optical fibers to the photodiodes. To increase the dynamic range of the system, two types of photodiodes, relatively sensitive C5460 avalanche photodiode modules and relatively insensitive S3399 PIN photodiodes coupled with amplifiers, both made by Hamamatsu Photonics and resulting in a sensitivity difference of about 2500, were used and connected alternately to the LAPOS fiber bundles that form different horizontal lines as shown in Figure 2. The light signals are recorded with a Yokogawa DL850 digital storage oscilloscope. [4] For the present study, the LAPOS was installed 205 m away from one of two rocket launchers used for triggering lightning at the ICLRT and was aimed so that 13 of its 15 channels covered a range from the termination point of the rocket-triggered lightning, about 5 m above ground, to a vertical height about 60 m above the termination point, as shown from S1 to S13 in Figure 3. In the figure, the LAPOS channels are annotated on a still camera image of a lightning discharge triggered at 20:58:11 UT on 18 August 2011 at the ICLRT and analyzed in this paper. The vertical distance between the centers of two neighboring lightning channel sections, as viewed by LAPOS, is about 5 m. However, since two types of photodiodes with significantly different sensitivity were connected alternately to the LAPOS fiber array bundles, the resultant spatial resolution was reduced to only about 10 m in the cases when only one set of bundles could be used, when either leader light was too weak or return stroke light was too strong. Of the 13 channels, six were recorded at a sampling rate of 100 MHz and seven were recorded at a sampling rate of 10 MHz. The upper frequency responses for C5460 and S3399 are 10 and 100 MHz, respectively. Taking all factors into account, we estimated that two LAPOS channels (S2 and S4) have an upper frequency of 20 MHz limited by the digitizer input, three LAPOS channels (S1, S3, and S5) have an upper frequency of 10 MHz limited by the C5460 modules, and the remaining eight channels have an upper frequency of 3 MHz limited by the digitizer input. For each of the channels, the recording length is 1 s. [5] We have documented 14 return strokes in four rockettriggered lightning flashes, as detailed in Table 1. All these return strokes transferred negative charge to the ground with peak currents ranging from 7.5 ka to 27.4 ka. As an example, the entire light intensity waveform of the lightning flash UF 11-35, which consisted of seven return strokes, is shown in Figure 4, where the light intensity of all the return strokes is saturated in the channels with high sensitivity. As seen in Figure 4, prior to the return strokes, there is an initial continuous current (ICC) stage containing at least 11 ICC pulses [e.g., Rakov and Uman, 2003; Qie et al., 2011]. One of the ICC pulses is expanded and shown in the inset. As seen in the inset, the light signals from different heights show different amplitude. An ICC pulse is similar to an M-component [e.g., Wang et al., 1999b], and its light intensity should be the same across a vertical range of many tens of meters. The varying amplitude of waveforms in the inset may be caused either by the equipment itself or some ambient conditions like rain or both. In the following analysis for return strokes, either this ICC pulse or M-component light intensities contained in a given lightning flash are used to calibrate the LAPOS high sensitivity channels for the return strokes contained in the specific flash, that is, to normalize the channels to a common source output assuming the ICC/Mcomponent light is constant with height. For the low Lens Photodiode and its amplifier Camera body Fiber bundle C5460 S3399 C5460 Fiber array plane Figure 2. The high speed optical imaging system used in the present study. 9881

3 Dimensions: 1) 5.4 m; 2) 4.6 m; 3) 0.8 m; 4) 3.2 m; 5) 1.9 m Detail of the lightning terminus Figure 3. The LAPOS view with lightning termination structure s photo included. sensitivity channels, the ICC pulses and M-components are too weak to be used for calibration, and hence the low sensitivity channels were not calibrated. The intensity calibration has no effect on any of the measured parameters listed in Table 1. Where intensity calibration was possible, the calibrated data are shown in the figures of this paper (Sensitive channel sections in Figures 5, 7, 8, and 9). 3. Results 3.1. Representative Data Sets and the Corresponding Results [6] Included in Table 1 are the leader types, leader speeds, and return stroke speeds discussed in the following sections. Apparently, different return strokes show significant different characteristics. In this section, we examine four representative return strokes in detail The First Stroke of UF [7] Figure 5 shows the light signals from 13 different channel sections of the first stroke of UF The 13 channel sections are denoted as S1 to S13 in Figure 5 and their central heights sequentially increase from 2.3 m to 60.4 m above the lightning channel termination point. Each of the channel sections has a vertical extent of about 3.4 m. The signals from the lightning channel sections S1, S3, S5, S7, S9, S11, and S13 (odd number) are the outputs from the C5460 modules (relatively sensitive); while the signals from S2, S4, S6, S8, S10, and S12 (even number) are the outputs from the S3399 photodiodes coupled with amplifiers (relatively insensitive). Since S3399 is much less sensitive than C5460, the signals of S2, S4, S6, S8, S10, and S12 in Figure 5 appear much smaller than those from S1, S3, S5, S7, S9, S11, and S13. Between each two adjacent sampled data points at the waveforms recorded at a 10 MHz sampling rate (or during each time period of 0.1 μs), to match the data points recorded at the 10 MHz sampling rate to those at the 100 MHz sampling rate, nine dummy data with the same values as its preceding sampled data are automatically inserted by the DL850 data analysis software, and thus forming many artificial horizontal steps in the waveforms. These artificial steps do not affect our data analysis. An expanded version of the signals from S2, S4, S6, S8, S10, Table 1. Data List and the Observed Results Flash No. UF UF UF UF Time b (UT) Stroke No. Stroke Peak Current (ka) Leader Type Leader Speed ( 10 7 m/s) Upward Return Stroke Speed Measured With InsensitiveSignals ( 10 8 m/s) Upward Return Stroke Speed Measured With Sensitive Signals ( 10 8 m/s) Downward Return Stroke Speed Measured With Insensitive Signals ( 10 8 m/s) Downward Return Stroke Speed Measured With Sensitive Signals ( 10 8 m/s) Return Stroke Initiation Height (m) 23:39: Dart (S4-S10) ± /08/ Dart (S5-S13) (S3-S1) 14.0 ± Dart (S5-S13) ± :37: Dart (S4-S12) 2.5 (S5-S11) ± /08/ Dart-S a (S4-S12) (S3-S1) 16.9 ± :51: Dart (S4-S10) (S3-S1) 15.1 ± /08/ Dart-S a (S4-S10) 0.9 (S5-S11) (S3-S1) 15.8 ± :58: Dart (S4-S10) 2.1 (S3-S13) ± /08/ Dart (S4-S10) ± Dart (S5-S13) ± Dart-S a (S6-S10) (S4-S2) 0.7 (S3-S1) 21.0 ± Dart (S6-S10) (S3-S1) 15.9 ± Dart-S a (S5-S13) ± Dart-S a (S4-S10) 1.3 (S5-S13) ± 5.0 a Dart-stepped. b Dates are formatted as day/month/year. 9882

4 R 1 2 R3 R 4 R 5 R 6 R 7 Figure 4. One second recording of the optical signal of an example rocket triggered lightning flash which consists of an initial continuous current stage and seven return strokes. The inset shows an expanded ICC pulse signal. and S12 are shown in the inset at the top left of Figure 5. Time 0 on Figure 5 is subjectively chosen by comparing the features of all the waveforms to denote the approximate initiation time of the return stroke. As seen in Figure 5, the leader signal first appeared at S13 (60.4 m), and then sequentially at lower channel sections of S11, S9, S7, and S5 (21.2 m). In response to this downward leader, there should be an upward connecting leader, as reported by Wang et al. [1999a] and Biagi et al. [2009]. However, as evident on Figure 5, although there is some increase in the light signals at S1 and S3, we were not able to determine if these signals are caused by an upward leader or some scattered light from the downward leader. The return stroke signal first appeared around S3; and then one wave propagated upward to S4, S6, S8, S10, and S12 and another wave propagated downward to S2. The signal at S1 appeared to rise faster than the signal at S3, and the reason for this behavior remains unclear. [8] To measure the leader speed and the return stroke speed, we need to determine their beginning points at two different heights (or channels). For this, the so-called slopeintercept method of Olsen et al. [2004] was used. As an example, the signals of S5 and S13 are redrawn in Figure 6 Figure 5. Light signals of the first stroke of the UF rocket-triggered lightning flash at 13 sequentially increased heights above the lightning channel termination point. Channel sections denoted with odd numbers are sensitive channels and channel sections with even numbers are insensitive channels. Time 0 corresponds to the initiation time of the return stroke. Expanded return stroke signals of the insensitive channel sections are shown in the inset. 9883

5 Time difference between S13 and S5 Average slope line Average slope line Leader beginning at S13 Reference level Leader beginning at S5 Reference level Figure 6. Illustration of the slope-intercept method of Olsen et al. [2004]. The two waveforms are replots of S5 and S13 signals in Figure 5. to illustrate how the beginning of the leader at S5 and S13 were determined. On each waveform, we draw two dashed lines, one along the noise level prior to the leader and another along the wavefront of the leader as shown in Figure 6. The intersection of these two dashed lines was regarded as the beginning of the leader at the height. For this event, the resultant leader speed measured over the distance from S13 to S5 is m/s. For the return stroke, upward speed can be measured in a similar way but generally with the low sensitivity signals. The resultant speed from S4 to S10 is m/s The Second Stroke of UF [9] Figure 7 shows the light signals from 13 different channel sections of the second stroke of UF As seen in Figure 7, this stroke s leader light signal appeared first at S13 and then at S11, S9, S7, and S5. The leader radiated light pulses at all these channel sections. Two of those pulses that started at S11 and S7 apparently traversed several channels. These pulses are evidence of leader steps [e.g., Wang et al., 1999c], and hence we identify this downward leader as a dart-stepped leader. The leader s speed averaged over the distance from S13 to S5 is m/s. Also, as seen in Figure 7, the last step of the leader occurred at S5 and did not immediately initiate the following return stroke. Instead, the return stroke was initiated around S3, 1.1 μs later, and then propagated bidirectionally, one wave upward to S4, S6, S8, S10, and S12 and another downward to S2. For this event, its initial upward return stroke speeds can be Figure 7. Light signals of the second stroke of UF rocket-triggered lightning flash at 13 sequentially increased heights above the lightning channel termination point. 9884

6 Figure 8. Light signals of the fourth stroke of UF rocket-triggered flash at 13 sequentially increased heights above the lightning channel termination point. measured with both the low and the high sensitivity signal sets. The resultant 1-D speeds from S4 to S10 and from S5 to S11 are and m/s, respectively The Fourth Stroke of UF [10] Figure 8 shows the light signals from 13 different channel sections of the fourth stroke of UF 11-35, which has the largest-peak current, 27.4 ka, among the 14 return strokes reported in this study. Its downward leader is a dartstepped leader with a speed of m/s. The return stroke started at a height between S4 (16.4 m) and S6 (26.0 m). The downward return stroke wave traveled over two insensitive channel sections (S4 and S2) and two sensitive channel sections (S3 and S1). This allows the measurement of its initial downward propagation speed with both the insensitive and sensitive signals. The resultant downward speed measured from S4 to S2 and from S3 to S1 are and m/s, respectively. Its upward speed from S6 to S10 is m/s The Fifth Stroke of UF [11] Figure 9 shows the light signals of the fifthreturnstroke of UF For this event, from its electric field derivative (de/dt) waveforms (not presented here), the downward leader is inferred to be a chaotic dart leader [e.g., Hill et al., 2012], although from comparison of its light signals shown in Figure 9 to typical dart leader light, we are not able to identify any difference. The leader speed is m/s. The return stroke started at a height around S4 and the downward return stroke wave traveled over two sensitive channel sections (S3 and S1). This allows the measurement of its initial downward propagation speed with the sensitive channels, and the resultant speed is m/s. The upward return stroke speed from S6 to S10 is m/s. Figure 9. Light signals of the fifth stroke of UF at 13 sequentially increased heights above the lightning channel termination point. 9885

7 60 m Downward leader speed: v L tlr Upward return stroke speed: v R Sn [14] From (1), h ri ¼ h snðv l þ v r Þ t lr v l v r (2) v l þ v r Lightning terminus level hsn Time (µs) Figure 10. A schematic showing how the return stroke initiation height is estimated. S n is a given channel section above the return stroke initiation height. In this study, we chose the channel section which is closest to the return stroke initiation height as S n Return Stroke Initial Speeds and Initiation Heights [12] For all the return strokes, we have estimated the preceding leader speeds and the upward and, when possible, the downward propagation speed of return stroke. The results are listed in Table 1. The return stroke speeds range from to m/s while the leader speeds range from to m/s. All of the leader speeds and the return stroke speeds are similar to those reported in the literature [e.g., Orville and Idone, 1982; Idone and Orville, 1982, 1984; Jordan et al., 1992, 1997; Wang et al., 1999b]. [13] Assuming that over the range covered by LAPOS, both the downward leader and the upward return stroke propagate at constant speeds, denoted v l and v r, respectively, as shown in Figure 10; the time difference t lr between the leader and the return stroke at a given channel section which is higher than the return stroke initiation height h ri and is denoted S n with its central height h sn can be expressed as hri t lr ¼ h sn h ri þ h sn h ri (1) v l v r [15] In (2), since h sn, v l, and v r are already known, measuring t lr allows us to estimate h ri. Through this method, we have estimated the return stroke initiation height for all of the 14 return strokes. In the estimation, the return stroke speeds obtained with the low sensitivity signals were preferentially used. In the cases where the return stroke speeds could be measured with only high sensitivity signals, the latter were necessarily used. In addition, to avoid any unnecessary errors, we have chosen the channel section that is closest to the return stroke initiation height as S n. Since return stroke speed is usually much larger than dart or dart-stepped leader speed, as seen in (2), error in h ri mainly comes from uncertainty in the leader speed v l and the time difference t lr. In this study, according to our estimation, the errors for both v l and t lr are less than 10% resulting in errors in the distance (h sn h ri ) of about 20%. As shown in Figures 5, 6, 8, and 9, there are some variations in the time intervals of leader light signals between two adjacent sensitive channel sections. Since the vertical distance between two adjacent channel sections are roughly same, the variation in the time interval may reflect some variation in the propagation speed. We estimated that the error in the distance (h sn h ri ) caused by such speed variation could reach as large as 10%. In addition, we should point out that in the cases of the dart-stepped leaders, the onset time of the leader at a given channel section was usually dominated by a leader stepped pulse which did not necessarily occur at the central position of the given channel section. That is, in the cases of dart-stepped leaders, additional uncertainty of ± m (3.4 m is the vertical height of each channel section) in h sn should be taken into consideration. Listed in the last column of Table 1 are the estimated return stroke initiation heights with all the Figure 11. A scatterplot of return stroke initiation height versus return stroke peak current. 9886

8 Figure 12. Striking distance versus return stroke peak current. The red curve was obtained in this study and is overlaid in Figure 3.6, for various proposed natural first stroke striking distances, given by Uman [2008]. Three first stroke curves common to the literature are given in black. The shaded area encompasses all of the first stroke curves found in the literature. uncertainty sources considered. The initiation heights of the 14 return strokes ranged from 7.2 ± 1.4 to 21.0 ± 4.6 m above the lightning termination point. [16] Figure 11 presents the scatterplot between the return stroke initiation heights and the corresponding peak return stroke currents. As seen in Figure 11, a return stroke with a larger peak electric current tends to initiate higher above its termination point. [17] The only observed propagation speed of an upward connecting leader in a rocket triggered lightning discharge is similar to that of its corresponding downward dart leader [Wang et al., 1999a]. We assume that this is the case for the 14 return strokes studied here, so that doubling the return stroke initiation height will yield the striking distance, the distance between the tip of a downward leader at the instant when its upward leader is initiated, the striking distance usually being defined only for the cases of natural first strokes [e.g., Cooray et al., 2007; Uman, 2008]. For the striking distance, Armstrong and Whitehead [1968] suggested an analytical expression of the form r s ¼ ki p (3) where r s is the striking distance, k and p are constants, and i is the return stroke peak current. We have used this expression to fit the inferred initiation heights and the measured peak currents shown in Figure 11 with least squares method and obtained the following approximate relation: h ri ¼ 3:7i 0:49 (4) where h ri is in meters and i is in kiloamperes. Additionally, with the assumption on upward and downward leader speeds stated above, we can write r s ¼ 2h ri ¼ 7:4i 0:49 (5) where r s is the striking distance of our subsequent strokes in meters. Based on (5), a r s versus i curve can be drawn, as shown in red in Figure 12. In Figure 12, the range of striking distance versus peak current for natural lightning first strokes found in the literature is shown shaded and three explicit formulations are shown as black curves, all taken from Uman [2008]. It is interesting to note that the striking distances obtained in the present study are very close to the lower limit of the shaded area in Figure 12 for first-stroke striking-distance estimates and are significantly smaller than the three specifically calculated curves from different individual studies. According to Uman [2008], the lower limit to the shaded area is near the curve recommended by Golde [1945, 1973] for negative lightning to flat Earth, for which there appears to be some experimental support. Perhaps, there is not much difference between natural first stroke and natural subsequent or triggered-stroke striking distance, if they all have the same peak current. 4. Discussion and Concluding Remarks [18] Our observation showed that all the 14 return strokes were initiated at a height with a range from 7.2 ± 1.4 to 21.0 ± 4.6 m above the lightning termination point and then propagated initially in opposite directions. These results support the Wagner and Hileman [1958] hypothesis which assumes that a return stroke initiates at a height and then propagates bidirectionally from that height. Our results for the first time show experimentally that a return stroke with a larger peak electric current tends to initiate higher above its termination point, a result that is physically reasonable. For a larger return stroke current, the charge density along its preceding leader channel should be larger, and therefore a corresponding upward leader should be induced earlier and hence propagated longer before the return stroke is initiated [e.g., Rakov and Uman, 2003; Uman, 2008]. [19] The largest-peak-current return strokes observed in this study exhibited relatively slow initial speeds, as illustrated in Figure 13. A slower propagating return stroke wave will radiate smaller electromagnetic waves [e.g., Miyazaki and Ishii, 2006]. According to our data, the slow propagation usually occurred on a time scale of μs. This time scale is quite similar to that on which a slow front usually occurred in the initial rising stage of the electromagnetic waveform of a subsequent return stroke [e.g., Weidman and Krider, 1978; Jerauld et al., 2007]. The initial slow propagation of a return stroke as observed in this study may be one factor in forming the slow front. [20] Finally, we should point out that three of the four return strokes for which we were able to estimate speeds separately from both low and high sensitivity signals show some discrepancy in their two sets of the speeds, as evident from Table 1. For the three cases where the high sensitivity signals are used to measure speeds, the return stroke beginning time can be measured only at their very initial 60 m The 4 stroke of UF Lightning terminus level Downward speed: m/s Time (µs) Upward speed: m/s Downward speed: m/s Figure 13. Schematic of the initiation processes of the strongest return strokes, the fourth stroke of UF 11-35, observed in this study. It was preceded by a dart-stepped leader. 9887

9 wavefront limited by saturation. The average slope line as shown in Figure 6 may just reflect very initial characteristics and thus cause the discrepancy. For this reason, we preferentially choose the return stroke speeds obtained with the low sensitivity signals to estimate the return stroke initiation heights in section 3.2. [21] Acknowledgments. This work was supported by the Ministry of Education, Culture, Sports, Science, and Technology of Japan (Grant ) and the U.S. program DARPA NIMBUS. Authors would like to thank T. Watanabe and H. Ishikawa for their help in setting up the high speed optical observation equipment. References Armstrong, H. R., and E. R. Whitehead (1968), Field and analytical studies of transmission line shielding, IEEE Trans. Power App. Syst., 87, Biagi, C. J., D. M. Jordan, M. A. Uman, J. D. Hill, W. H. Beasley, and J. Howard (2009), High-speed video observations of rocket-and-wire initiated lightning, Geophys. Res. Lett., 36, L15801, doi: / 2009GL Cooray, V., V. Rakov, and N. Theethayi (2007), The lightning striking distance Revisited, J. Electrost., 65, Golde, R. H. (1945), The frequency of occurrence and the distribution of lightning flashes to transmission lines, Trans. Am. Inst. Electr. Eng., 64(12), Golde, R. H. (1973), Lightning protection, Edward Arnold, Ltd., London. Hill, J. D., M. A. Uman, D. M. Jordan, J. R. Dwyer, and H. Rassoul (2012), Chaotic dart leaders in triggered lightning: Electric fields, X-rays, and source locations, J. Geophys. Res., 117, D03118, doi: / 2011JD Idone, V. P., and R. E. Orville (1982), Lightning return stroke velocities in the Thunderstorm Research International Program (TRIP), J. Geophys. Res., 87, Idone, V. P., and R. E. Orville (1984), Three unusual strokes in a triggered lightning flash, J. Geophys. Res., 89, Idone, V. P. (1990), Length bounds for connecting discharges in triggered lightning subsequent strokes, J. Geophys. Res., 95, 20,409 20,416. Jerauld, J., M. A. Uman, V. A. Rakov, K. J. Rambo, and G. H. Schnetzer (2007), Insights into the ground attachment process of natural lightning gained from an unusual triggered-lightning stroke, J. Geophys. Res., 112, D13113, doi: /2006jd Jordan, D. M., V. P. Idone, V. A. Rakov, M. A. Uman, W. H. Beasley, and H. Jurenka (1992), Observed dart leader speed in natural and triggered lightning, J. Geophys. Res., 97, Jordan, D. M., V. A. Rakov, W. H. Beasley, and M. A. Uman (1997), Luminosity characteristics of dart leaders and return strokes in natural lightning, J. Geophys. Res., 102, 22,025 22,032. Leteinturier, C., C. Weidman, and J. Hamelin (1990), Current and electric field derivatives in triggered lightning return strokes, J. Geophys. Res., 95, Miyazaki, S., and M. Ishii (2006), Reproduction of time derivative of electromagnetic field associated with rocket-triggered lightning in submicrosecond range, J. Geophys. Res., 111, D22203, doi: / 2005JD Olsen, R. C., III, D. M. Jordan, V. A. Rakov, M. A. Uman, and N. Grimes (2004), Observed one-dimensional return stroke propagation speeds in the bottom 170 m of rocket-triggered lightning channel, Geophys. Res. Lett., 31, L16107, doi: /2004gl Orville, R. E., and V. P. Idone (1982), Lightning leader characteristics in the Thunderstorm Research International Program (TRIP), J. Geophys. Res., 87, 11,177 11,192. Qie, X., R. Jiang, C. Wang, J. Yang, J. Wang, and D. Liu (2011) Simultaneously measured current, luminosity, and electric field pulses in a rocket-triggered lightning flash, J. Geophys. Res., 116, D10102, doi: /2010jd Rakov, V. A., and M. A. Uman (2003), Physics and Effects, Cambridge Univ. Press, Cambridge, U. K. Uman, M. A., D. K. McLain, R. J. Fisher, and E. P. Krider (1973), Currents in Florida lightning return strokes, J. Geophys. Res., 78, Uman, M. A. (2008), The Art and Science of Lightning Protection, pp , , Cambridge Univ. Press, Cambridge, U. K. Wagner, C. F., and A. R. Hileman (1958), The lightning stroke, Am, Inst., Electr. Eng. Trans., 77, Wang, D., V. A. Rakov, M. A. Uman, N. Takagi, T. Watanabe, D. E. Crawford, K. J. Rambo, G. H. Schnetzer, R. J. Fisher, and Z.-I. Kawasaki (1999a), Attachment process in rocket-triggered lightning strokes, J. Geophys. Res., 104, Wang, D., V. A. Rakov, M. A. Uman, M. I. Fernandez, K. J. Rambo, G. H. Schnetzer, and R. J. Fisher (1999b), Characterization of the initial stage of negative rocket-triggered lightning, J. Geophys. Res., 104, Wang, D., N. Takagi, T. Watanabe, V. A. Rakov, and M. A. Uman (1999c), Observed leader and return-stroke propagation characteristics in the bottom 400 m of a rocket-triggered lightning channel, J. Geophys. Res., 104, 14,369 14,376. Wang, D., T. Watanabe, and N. Takagi (2011), A high speed optical imaging system for studying lightning attachment process, Proc. of 7th Asia-Pacific Lightning Conference, Chengdu, China. Weidman, C. D., and E. P. Krider (1978), The fine structure of lightning return stroke wave forms, J. Geophys. Res., 83, Willett, J. C., V. P. Idone, R. E. Orville, C. Leteinturier, A. Eybert-Berard, L. Barret, and E. P. Krider (1988), An experimental test of the transmission-line model of electromagnetic radiation from triggered lightning return strokes, J. Geophys. Res., 93, Willett, J. C., J. C. Bailey, V. P. Idone, A. Eybert-Berard, and L. Barret (1989), Submicrosecond intercomparison of radiation fields and currents in triggered lightning return strokes based on the transmission-line model, J. Geophys. Res., 94, 13,275 13,