Characteristics of the optical pulses associated with a downward branched stepped leader

Authors


Abstract

[1] A stepped leader that preceded a natural first return stroke was recorded using a high-speed optical imaging system with a time resolution of 0.1 μs and a spatial resolution of about 40 m. Within the view of the imaging system, 440 m × 480 m just above ground level, the leader produced one ground termination (main channel for the return stroke) and six ungrounded branches. A total of 153 optical pulses associated with the leader were identified for analysis, with 61 originating from the main channel and 92 from the six branches. The pulses originating from the main channel and from the branches are almost identical in terms of geometric mean (GM) values of 10–90% risetime and half-peak width, near 0.4 μs and 1.1 μs, respectively. The pulses from the main channel show smaller interpulse intervals than those from the branches. When the interpulse intervals for pulses from both the main channel and all branches are combined, of a total of 152 intervals, five are essentially 0 and 58 are between 0 and 1 μs. Thus a significant percentage of optical pulses occurred almost simultaneously in different channel sections separated by distances up to several hundred meters. The light intensity just prior to each pulse exhibited a tendency to increase as the leader approached ground, while the other parameters, such as pulse peak, risetime, half-peak width, and interpulse intervals, showed no systematic changes with time.

1. Introduction

[2] A stepped leader is so named because this lightning process, which usually leads to a main discharge or return stroke, propagates in a stepwise fashion, as seen in high-speed photographs [e.g., Schonland, 1953]. Formation of each of its so-called steps is associated with a pulse of electric current, which necessarily emits an electromagnetic pulse as well as a light signal. Many characteristics of the stepped leader have been identified by studying its electromagnetic and light signatures. From electromagnetic measurements, it has been reported that the electric field pulses associated with leader steps are characterized by interpulse intervals of 5 to 20 μs, 10–90% risetimes of 0.2–0.3 μs, and half-peak widths of 0.4–0.5 μs [e.g., Krider and Radda, 1975; Krider et al., 1977; Beasley et al., 1982]. As is known, not only does a stepped leader typically exhibit many branches, but the leader step pulse current also propagates vertically over some distances [e.g., Wang et al., 1999b; Chen et al., 1999]. In order to study the detailed characteristics of leader step pulses, some measurement with fine spatial resolution are also required. A high-speed digital imaging system, like ALPS (Automatic Lightning Progressing Feature Observation System, [Yokoyama et al., 1990; Wang et al., 1999a]), is very useful for studying stepped leader pulses. To date, several stepped leaders have been documented using ALPS [Wang et al., 1999b; Chen et al., 1999]. Here we report on a branched stepped leader which was recorded by ALPS with better time and spatial resolution than in previous studies. The observed characteristics of this leader provide new details on its light pulses associated with stepping and allow a direct comparison between pulses originating from leader branches and from the leader main channel. Since leader pulse VHF radiation has been widely used to map the 3D progression of lightning discharges, our results may also be helpful for improving 3D VHF lightning location systems.

2. Instrumentation and Data

[3] The optical data presented here were recorded by an ALPS during the summer of 2000 at International Center for Lightning Research and Testing at Camp Blanding, Florida [e.g., Uman et al., 1997; Rakov et al., 2005]. The ALPS consists of a conventional camera lens, a 16 × 16 pin photodiode array (each 1.3 × 1.3 mm2 in size, with a space of 0.2 mm between neighboring photodiodes), 256 identical amplifiers, a 256-channel 8-bit digitizer, and a personal computer system. Each photodiode operates at wavelengths from 400 to 1000 nm with a response time of less than 3 ns. The outputs of photodiodes are amplified, digitalized, and then recorded by the computer. The dynamic range of the system is 60 dB. The ALPS can operate at a time resolution from 0.1 μs to 50 ms with either internal or external trigger and can record up to about 16,000 frames for each event. A lens with a focal length of 50 mm was used in this experiment.

[4] The lightning discharge examined here occurred at 06:04:44 LT (local time) on 29 August 2000. Its stepped leader was imaged by the ALPS at a time resolution of 0.1 μs. The cumulative still image, reconstructed from the ALPS recordings, is schematically shown in Figure 1. Each square (pixel) corresponds to one diode of the 16 × 16 pin photodiode array. The channel that was most strongly illuminated by the return stroke (not shown here) in ALPS images was identified as the main channel (branch). The vertical dimension 480 m shown in Figure 1 is estimated from the corresponding propagation time taken by the return stroke along the main channel by assuming a return stroke speed of 1.5 × 108 m/s [e.g., Rakov and Uman, 2003]. From this dimension, the ALPS spatial resolution of this lightning flash is estimated to be 40 m. Then, from this spatial resolution, the known diode size and the focal length of the camera lens, the distance of the lightning flash from ALPS is estimated to be about 1.3 km. The leader has six ungrounded branches (five major and one sub) in the view range of ALPS. In Figure 1, the main channel (which supports the return stroke) is labeled M and the associated pixels are sequentially numbered according to leader propagation. The center of M13 is estimated to be at ground level. The five major branches are labeled from B1 to B5 and the sub-branch of B1 from B12 is labeled B1B. The pixels associated with all those branches are also sequentially numbered according to leader propagation. ALPS allows us to analyze the optical pulses produced by the stepped-leader on a sub-microsecond timescale (time resolution of 0.1 μs) and to distinguish the optical pulses produced almost simultaneously by spatially separate multiple sources.

Figure 1.

Cumulative still picture of the leader recorded by ALPS. Encircled labels 1, 1B, 2, 3, 4, and 5 are used to identify ungrounded branches. Each square (pixel) corresponds to one diode in the photodiode array of ALPS. The letters inside the squares are used for identification of different channel sections. The pixel of B22 is filled with crossed lines to indicate its high noise level, as can be seen in Figure 2c. The dimensions of the lightning channel are estimated by assuming that the return stroke speed is 1.5 × 108 m/s.

3. Results

3.1. Overall Propagation Characteristics of the Leader

[5] Figure 2 presents the light waveforms as a function of time in various sections of the main channel and branches. Channel sections are labeled sequentially according to the propagation of the leader schematically shown in Figure 1, and the labels are given on the left of Figure 2. In Figure 2a, the heights of the center of main-channel sections are shown in the parentheses. Time 0 is set at the onset of return stroke. This leader is identified as a stepped leader because a series of pronounced pulses can be seen in most of the light signals. Each pulse presumably corresponds to one step. As seen in Figure 2, because of light scattering and high-speed propagation of pulses, each step pulse may be detected by two or more adjacent pixels simultaneously. Additionally, more than one step can occur within 40 m, the spatial resolution of the present data. All of them make identification of pulse source location a difficult task. In this paper, we assume that the largest light pulse is the “source” pulse of each step. In Figure 2, all these “source” pulses are marked with small symbols. As seen in Figure 2, although most of the “source” light signals occur later in time at lower heights, which indicates that the leader is propagating downward, there are some optical pulses occurring in channel sections over which the tip of the leader has already passed. They are probably produced by small branches of the channel which could not be identified with the limited spatial resolution of the present data. In this study, these pulses are called disordered pulses and marked with stars in Figure 2. All other “source” pulses are called sequential pulses and marked with triangles. In the same channel section, for example, M5 in Figure 2a, usually several (five in section M5) sequential pulses occurred. This indicates that several steps occurred within this channel section. Solid triangles mark the first sequential pulse in each channel section, and hollow triangles mark subsequent sequential pulses. Pulses that are not marked by either triangle or star are assumed to be due to light scattering or propagation effects of source pulses originated in another channel section. In this study, since the pulse propagation effects can't be distinguished clearly from the light scattering, the pulse propagation characteristics are not studied.

Figure 2.

The light signal waveforms as a function of time in different channel sections as shown in Figure 1. (a) Main channel. (b) Branches B1 and B1B. (c) Branch B2. (d) Branch B3. (e) Branch B4. (f) Branch B5. Time 0 is set at the time of return stroke. The small symbols below the waveform mark the source pulses, where solid triangles mark the first sequential pulse in each channel section, hollow triangles mark subsequent sequential pulses, and stars mark disorder pulses.

[6] Using only the first sequential pulse in each corresponding pixel, we have estimated the propagation distance and the average speed for the main channel and the six branches. The results are given in Table 1. Here 2D propagation distances are measured from M1 for the main channel and from the branching point for branches, e.g., from M5 for B3 and from B12 for B1B. The leader extends along the main channel at a 2D average propagation speed of 1.5 × 106 m/s between the heights of 80 m and 440 m above ground. The average 2D propagation speeds along the branches are between 1.2 × 106 and 1.9 × 106 m/s. These speeds are larger than those reported by Schonland [1956], Orville and Idone [1982], and Chen et al. [1999], but in the upper range reported by Thomson et al. [1985].

Table 1. 2D Leader Propagation Speeds Along the Main Channel and Branches
 MB1B1BB2B3B4B5
Average speed (×106 m/s)1.52.01.81.41.22.21.9
2D Propagation distance (m)450330150300200300240

3.2. Characteristics of Optical Pulses

[7] For each of the “source” pulse (“source” is omitted for convenience in the following), we have measured (referring to Figure 3) its preceding light intensity (IP), pulse peak (PP), 10–90% risetime (TR), half-peak width (TH) and interpulse interval (TI). Here IP is the relative light intensity immediately prior to the pulse; pulse peak PP is measured with respect to IP; TR is the time interval on the wavefront between the 10% and 90% values of PP; TH is the time interval between the half value of PP on the rising and the falling portions of waveform, and TI is the time interval between peaks of successive source pulses. Only the pulses that occurred in the source sections (that is, the largest pulses if scattered light signals were seen on other pixels or if direct light fell on two or more pixels) were included in the statistics. The pulses with pulse peak less than 10 were ignored. A total of 153 optical pulses were identified with 61 originating from the main channel and 92 from the six branches, as noted in Table 2. For pulses that overlapped each other, some parameters such as preceding light intensity, pulse peak, risetime, and half-peak width could not be adequately measured. For this reason the sample sizes for different parameters analyzed here are not the same.

Figure 3.

Two optical pulses that occurred in section M3, showing the method of measurement of the preceding light intensity IP, pulse peak PP, 10–90% risetime TR, half-peak width TH, and interpulse interval TI of the optical pulses recorded by ALPS.

Table 2. Number of Optical Pulses That Occurred in the Main Channel and Branches
Type of PulsesChannel/Branch
MB1B1BB2B3B4B5
Sequential pulses461551791711
Disordered pulses153110112
Total number6118627101813

[8] The distributions of the optical pulse risetime and half-peak width for the main channel and for different branches are shown in Figure 4 and Figure 5, respectively. The GM values of optical pulse 10–90% risetime and half-peak width for the main channel are 0.4 μs and 1.1 μs, respectively. For the six branches, pulse 10–90% risetime and half-peak width vary between 0.3–0.4 μs and 1.0–1.2 μs, respectively. If all 153 optical pulses are combined, the GM values of optical pulse 10–90% risetime and half-peak width are essentially the same as those for the main channel. From the histogram and cumulative percentage distributions of these two parameters for the main channel and all branches, it can be seen that the main channel and all branches have almost the same type of individual optical pulses. This could be the case because there is no “main channel” until the return stroke occurs. For all optical pulses observed in this event, the GM value of 10–90% risetime is 0.4 μs, and that of the half-peak width is 1.1 μs. The values are greater than those for electric field pulses observed by Krider et al. [1977], and less than those observed by Chen et al. [1999]. In the bottom 400 m of a rocket-triggered lightning channel, Wang et al. [1999b] observed that the optical pulses associated with dart-stepped leader steps have a 10–90% risetime ranging from 0.3 to 0.8 μs with a mean value of 0.5 μs and a half-peak width ranging from 0.9 to 1.9 μs with a mean value of 1.3 μs, which are quite similar to the present results. As shown in Figure 4b and Figure 5b, about 80% of the values of 10–90% risetime are between 0.2 μs and 0.6 μs, and about 80% of the values of half-peak width are between 0.7 μs and 1.7 μs. To show the characteristics of optical pulse risetime and half-peak width in detail, Table 3 shows their distributions according different pulse peak range. It appears that the risetime and the half-peak width parameters of pulses are not sensitive to pulse amplitudes.

Figure 4.

Statistical distribution of optical pulse 10–90% risetime. (a) Histogram. (b) Cumulative percentage.

Figure 5.

Statistical distribution of optical pulse half-peak width. (a) Histogram. (b) Cumulative percentage.

Table 3. Distribution of Optical Pulse Risetime and Half-Peak Width for Different Pulse Peak Rangesa
Optical Pulse Peak Range10–90% RisetimeHalf-Peak Width
Min. (μs)Max. (μs)GM (μs)Sample SizeMin. (μs)Max. (μs)GM (μs)Sample Size
  • a

    Some pulses are saturated and the corresponding parameters are measured in the adjacent unsaturated channel sections. The pulse peak values of optical pulses that occurred in B22 (4 pulses) cannot be determined, so the sample sizes in this table are smaller than those in Figures 4 and 5.

10–320.10.60.3250.51.00.718
32–640.20.90.4290.51.81.125
64–1280.21.10.4240.71.91.117
128–2560.21.20.5300.72.11.423
256–5120.20.90.4170.81.81.314
≥5120.40.90.570.91.91.37
Saturated0.30.50.3110.71.71.111
Unsaturated0.11.20.41320.52.11.1104
All combined0.11.20.41430.52.11.1115

[9] Figure 6a shows how the pulse parameters vary with leader propagation time. It can be seen that the preceding light intensity of pulses (in relative units) exhibits an increasing trend with time as the leader propagates toward ground. Its arithmetic mean value is 198. From the first optical pulses recorded by ALPS to a time of about 50 μs preceding the return stroke (the leader tip is in M9 with a height about 160 m above the ground), about 80% of the values are lower than 200. In the last 50 μs of propagation of the stepped leader, above 90% of the values are higher than 200. Unlike the preceding light intensity, the pulse peak, 10–90% risetime, half-peak width and interpulse interval of the optical pulse show no obvious relationship with the propagation of the stepped leader. Optical pulses with different waveform parameters can occur at any stage of the leader propagation. Figure 6e shows that some of the interpulse interval values for branches are apparently higher than those for the main channel.

Figure 6.

Distributions. (a) Preceding light intensity. (b) Pulse peak. (c) 10–90% Risetime. (d) Half-peak width. (e) Interpulse interval of the optical pulses versus time.

[10] The statistical distributions of the interpulse interval for optical pulses are shown in Figure 7. For the main channel, 60 values of the interpulse interval were obtained, and they range from 0.2 to 15.7 μs with a GM value of 3.3 μs. For the branches, different branches exhibit very different GM values as shown in Figure 7a. It is interesting to note that all the branches have larger GM values than the main channels. Although the data sample sizes are small, a simple statistical test indicates that the differences in the interpulse intervals of the main channel and the branches are significant. If all the 153 optical pulses are combined regardless of their origin on the channel, as shown in Figure 7b, the 152 interpulse intervals vary from 0 to 13.6 μs, with an arithmetic mean value of 2.0 μs, and about 90% of them are between 0.1 to 6.5 μs. Five of the 152 interpulse intervals are essentially zero and fifty-eight of them are between 0 and 1 μs, which means that about 40% of the optical pulses occurred with interpulse intervals less than 1 μs, and some optical pulses even occurred essentially simultaneously in different channel sections. Figure 8 shows an example of three optical pulses that occurred in three different channel sections, M10, B26, and B46, with interpulse intervals less than 1 μs. B26 and B46 are separated from M10 by about 250 m and 80 m, respectively.

Figure 7.

Statistical distributions of optical pulse interpulse interval. (a) Histogram for the main channel and all branches. (b) Cumulative percentage for all optical pulses. The interpulse intervals in Figure 7a are for the main channel and each branch separately, while those in Figure 7b are for all 153 optical pulses combined.

Figure 8.

Three optical pulses that occurred in M10, B26 and B46 with interpulse intervals less than 1 μs. The 2D distances between M10 and B26, B26 and B46, M10 and B46 are about 250, 330, and 80 m, respectively.

[11] The distributions of the 63 2D distances between successive two source channel sections with the interpulse interval of less than 1 μs are shown in Figure 9. The distances range from 0 to 480 m with an arithmetic mean value of 180 m. Twenty-nine of them (about 46%) are larger than the distances that the light (at 3.0 × 108 m/s) can propagate during the corresponding interpulse intervals. Totally, thirty-one of 152 (about 20%) exhibit this behavior. All the above data are obtained by assuming a return stroke speed of 1.5 × 108 m/s. A lower return stroke speed value would result in shorter distances between different channel sections. However, for a lower return stroke speed of 0.8 × 108 m/s, eighteen of 152 (about 12%) events still show the same tendency.

Figure 9.

The distributions of the 2D distances between two successive source channel sections with an interpulse interval less than 1 μs. The value 0 means that the two successive optical pulses occurred in the same channel section.

4. Concluding Remarks

[12] The optical pulse characteristics of a downward branched stepped leader have been reported. For this leader, a total of 153 optical pulses were identified, with 61 of them originating from the main channel (which made contact with the ground) and 92 from the six ungrounded branches. A statistical study of the pulses shows that the pulses originated from the main channel and the branches are almost identical in terms of geometric mean (GM) values of 10–90% risetime and half-peak width, which are around 0.4 μs and 1.1 μs, respectively. In terms of interpulse intervals, the pulses from the main channel show apparently smaller values than those from the branches. The interpulse intervals for all pulses regardless of whether they originated from the main channel or from the branches are also studied. Of the resulting 152 intervals, five are essentially zero and 58 are between 0 and 1 μs. Thus a considerable percentage of optical pulses apparently occurred simultaneously or almost simultaneously in different channel sections separated by distances up to several hundred meters. All these observed facts combined suggest that lightning branches propagate independent of one another and their stepping occurs randomly. With the propagation of the leader toward ground, the light intensity just prior to each pulse exhibited an apparent tendency of increase, while for the remaining parameters pulse peak, risetime, half-peak width, and pulse intervals, no systematic changes are observed.

Acknowledgments

[13] This research was supported in part by the National Natural Science Foundation of China (grant 40605004), the Ministry of Science and Technology of China (grant GYHY2007622), and the U.S. National Science Foundation (grants ATM-0003994 and ATM-0346164).

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