This paper reports the vertical electric field changes measured at 60 m and 550 m for two altitude-triggered lightning discharges and analyzes the data with two leader models. The results show that the field change waveform produced by bidirectional leader/return stroke at 60 m is asymmetrical V-shaped with the half-peak width of about 100 μs. The field waveform of the following dart leader/return stroke sequences at 60 m and 550 m also appear asymmetrical V-shaped, and the half-peak widths of the V-shaped for these two sites are 14 μs and 103 μs, respectively. The difference in the width of field waveforms can be explained by using the source charge leader model. The electric field changes of the dart leaders at 60 m and 550 m are 17.9 kV/m and 1.3 kV/m, respectively, yielding a horizontal distance dependence of d−1.18. At very close ranges (a few tens to hundreds of meters or less), the magnitude of the dart leader field change is not different from that of the following return stroke.
 Artificially triggered lightning discharges have been used to obtain insights into natural lightning processes. One technique for artificial lightning initiation involves launching a small rocket trailing a thin, grounded copper wire toward the charged cloud overhead. This technique is called ‘classical’ triggering. Another technique is called ‘altitude’ triggering. This triggering method refers to launching upward a small rocket trailing an electrically floating wire, with the bottom of the wire being typically some hundreds of meters above the ground [Laroche et al., 1991]. When the rocket reaches a height of several hundreds of meters in a favorable condition of thunderstorm electricity, a bidirectional leader initiates from the extremities of the floating wire. As the downward negative leader approaches the triggering facility, an upward positive connecting leader is initiated from the grounded object. Once the two leaders attach to each other, a so-called “abnormal” return stroke (the first return stroke) is initiated [Laroche et al., 1991; Rakov et al., 1998]. The following dart leader/return stroke sequences are similar to subsequent return strokes in natural cloud-to-ground lightning [Crawford et al., 2001]. Until now, there is not much observation of the directional leader/return stroke in altitude-triggered lightning [Saba et al., 2005]. Laroche et al.  and Lalande et al.  studied in detail the properties of inception and propagation of the bidirectional leader system, but they did not address significantly the first return stroke and the following dart leader/return stroke sequences. Rakov et al.  reported the electric and magnetic field measurements of the first return stroke at 80 m and 150 m from two altitude-triggered lightning flashes, but they were for two different lightning flashes. Chen et al.  and Zhang et al.  analyzed the electric field change of the bidirectional leader/return stroke at 60 m and 1300 m. However, the field change of the first return stroke at 60 m was saturated, and no electric field changes of the following dart leader/return stroke sequences were observed due to the limited record length. To summarize, complete field change measurement at different distances has not been reported for both the bidirectional leader/return stroke and the following dart leader/return stroke sequences for a single altitude-triggered lightning flash.
 This study investigates both the bidirectional leader/return stroke and the following dart leader/return stroke sequences involved in two altitude-triggered lightning discharges, by simultaneously making measurements of electric field changes and recording video with a high speed digital camera with 1 ms time resolution at close distances. Also in this paper, the measurement data will be analyzed with two leader models.
2. Experiment and Instrument
 Since the summer of 2005, triggered lightning activity has been conducted in the Shandong Artificially Triggered Lightning Experiment site in Shandong province (117°48′E, 37°42′N), China [Qie et al., 2007, 2009; Zhang et al., 2009]. Figure 1 shows a picture of this experiment site. At the center of Figure 1 is a Faraday Cage, in which there are three current sensors and three Electric/Optical converters, a copper lightning rod with a height of 5 m is fixed in the middle top of the Cage to attract lightning flashes. Up to six rockets can be launched during the same storm event.
 There were two observation sites for the triggering experiment. Site 1 (the rocket control room) was located 60 m away from the launching site, while Site 2 (the main observation site) was located 550 m away. Field mill, slow antenna and fast antenna were installed in both sites. Slow and fast antenna, with a bandwidth of 2 MHz and 5 MHz and a time constant of 6 s and 2 ms, respectively, were used to measure the fine electric field changes of lightning discharge in a high time resolution. The signals of electric field changes were digitized at a 2.5 MHz sampling rate and 16-bit amplitude resolution. The signals in two sites were synchronized by GPS with a time accuracy of 50 ns. A high speed digital video camera with 1 ms time resolution and spectrum measuring system were installed in Site 2.
 In this experiment, five lightning flashes were successfully triggered, and they were named 0501, 0502, 0503, 0504, and 0505, respectively. Among them, the 0501, 0502, and 0503 were classical triggering methods, and 0504 and 0505 were altitude triggering methods. Each flash was triggered in a surface electric field environment dominated by negative charge overhead, and thus transported negative charge to ground.
3. Result and Analysis
Figure 2 shows two pictures of the altitude triggered lightning 0504 taken at Site 2. The left panel is recorded with a common camera, and mainly focuses on the bottom part of the channel. The right panel is a picture selected from the high-speed digital camera with 1 ms time resolution, the straight bright section is associated with the melting of the triggered wire, and the luminous part exhibiting a jagged shape from the extremities of the channel is associated with the lightning channel in the air. The triggering height is about 336 m, the bottom of the wire is about 80 m above the ground, and this shows a bidirectional leader initiating from the extremities of the floating wire. The surface electric field environment was dominated by negative charge overhead, so the upward leader at the top of the wire is a positive leader and the downward leader at the bottom of the wire is a negative leader.
Figures 3a and 3b show the overall time waveforms of electric field for flash 0504, that were recorded simultaneously by the flat-plate slow antenna at Sites 1 and 2. This flash duration time is about 750 ms, and the portion “A” in both records is produced by the bidirectional leader/return stroke process. The five electric field pulses (marked as R1–R5) are due to the dart leader/return stroke sequences with interstrokes interval times ranging from 20 to 125 ms. The bidirectional leader/return stroke process produces a bigger field change than the following dart leader/return stroke sequences.
3.1. Bidirectional Leader/Return Stroke Sequences
Figures 4a and 4b show the expansions of portion “A” in Figures 3a and 3b, respectively. The field change waveforms measured simultaneously at Sites 1 and 2 are very different, with the former showing an asymmetrical V-shaped feature and the latter monotonic positive. The half-peak width of the V-shaped at 60 m is about 100 μs. At t1 = 26.05 ms the bidirectional leader starts its stable propagation as indicated by the field changes measured at both sites. At the time t2 = 26.24 ms it is associated with the transition from the bidirectional leader to the first return stroke.
 From Figure 4a, it is found that the electric field at Site 1 begins to decrease stepwise and then continuously decrease. The total negative electric field change is −14.6 kV/m, and the decreasing slope of the field change is −73 V/m/μs. There are a total of 12 field steps around t1, and the field steps have a mean amplitude of −509 V/m with the step interval being about 17 μs. (As will be discussed in regard to Figure 6a, each step may be predominantly attributed to some stepwise discharge processes of the downward negative leader from the bottom of the wire (leader B).) The electric field change of the first return stroke is 22.3 kV/m, and the increasing slope of the field change is about 1115 V/m/μs, much faster than that of the bidirectional leader process.
 At Site 2 during time t1 to t2 the electric field begins to increase continuously (refer to Figure 4b), the total electric field change is 0.16 kV/m, and the increasing slope of the electric field change is 0.8 V/m/μs, which is much less than that in Site 1. (As will be discussed in regard to Figure 6b, this continuously increasing field could be predominantly produced by the upward positive leader at the top of the wire (leader A).) At t2, the first return stroke is initiated with a narrow unipolar radiation pulse (Er in Figure 4b). The peak of the pulse Er is 0.74 kV/m with a half-peak width of about 0.28 μs. Based on the transmission line model [Uman and Mclain, 1970] and the observed radiation field pulse Er, assuming the return stroke speed of (1.3–1.5) × 108 m/s [Wang et al., 1999], the current peak of the first return stroke is estimated to be about 13.6–15.7 kA, larger than that observed by Lalande et al. . (They observed that the first stroke in an altitude-triggered flash is composed of two unipolar current pulses with the peak of 5 kA and 12 kA, respectively.)
 At distances within hundreds of meters of the lightning channel, the electric field due to the descending leader is primarily electrostatic. The difference in the field change waveforms at both sides could be explained by the bidirectional leader model [Kasemir, 1960]. This model assumes that a vertical bidirectional leader starts at a nucleus placed in uniform E field above the ground at height of HT and propagates toward and away from the ground (Figure 5). The induced charges flowing in the conducting and expanding channel are the source of the leader's continuous current. The vertical electric field change dE measured at a horizontal distance d from the channel due to a charge element dQ = q(z)dz at height z is given by the following equation:
where z is vertical coordinates with the zero on the ground, the charge per unit length ρL(z) in a conducting channel, located in a uniform E field, changes linearly with the zero being at the point of leader initiation (at height of HT). The slope k is determined by the ambient field and channel diameter.
 Let HA be the height of the upward positive leader tip (leader A), HB the height of the downward negative leader tip (leader B). Assuming the same propagation speed for both leaders, the vertical leader field change at any time t is given by:
When the leader B reaches the ground, HB = 0, HA = 2HT, the vertical field change EL0 is:
 Here, as shown in Figure 1, the estimated height HT is about 208 m. Based on equation (4), the coefficient k of the charge distribution along lightning channel is estimated to be (1.2–3.8) × 10−7 C/m2. The ratio HT/d that corresponds to EL0 = 0 can be found by the graphical solution of equation (4) and is 0.98, so the reversal distance of the directional leader field change is about 212 m, much less than that of the first stroke in natural cloud-to-ground lightning (about 3.4∼5.1 km) [Zhang et al., 2005].
 The vertical field changes produced by the bidirectional leader at both sites have been calculated, and the results are shown Figure 6. It is shown that the field at a distance of 60 m (Site 1) is predominantly determined by the downward negative leader (leader B) of the bidirectional leader, with a maximum contribution at a height of about 40 m. While the field at Site 2 is predominantly determined by upward positive leader (leader A) above the height of HT = 208 m, with a maximum contribution from the channel at a height of about 1 km. Therefore, the field changes at 60 m are negative, and the field changes at 550 m are positive. The simulated result above is consistent with that observed as in Figure 4.
3.2. Dart Leader/Return Stroke Sequences
Figures 7a and 7b show the expansion of the electric field waveforms produced by the fourth dart leader/return stroke sequence (marked as R4 in the Figure 3) at Site 1 and Site 2. The waveforms of the field changes are characterized by an asymmetrical V-shaped structure, similar to that of other strokes. The electric field begins with a relatively slow negative field changes consistent with the lowering of negative charge of the dart leader. This slow change is followed by a fast positive field change due to the removal of dart leader charge by the return stroke. The bottom of asymmetrical V-shaped corresponds to the end of dart leader and the start of return stroke. Table 1 shows the parameters for six dart leader/return stroke sequences in the two altitude-triggered lightning flashes. The field change EL is produced by the downward dart leader, and is mainly composed of electrostatic field. The geometric mean value of EL is 17.9 kV m−1 and 1.3 kV m−1 at Site 1 and Site 2, respectively, and the decreasing slope of EL at both sites is 60 V/m/μs and 1 V/m/μs, respectively. ER is produced by the return stroke, and its mean value is 18.7 kV m−1 and 1.48 kV m−1 at both sites, respectively. The increasing slope of ER at both sites is 267 V/m/μs and 29 V/m/μs, respectively. Although the magnitude of the dart leader field change is not different from that of the following return stroke, the rate of change is much faster for the return stroke.
Table 1. Parameters of Electric Field Change Waveforms of Dart Leader/Return Stroke Sequencesa
Interstrokes Interval Time (μs)/σlog
σlog is the standard deviation of the logarithm (base 10) of the parameter.
17.9 ± 7.0
18.7 ± 6.0
14.4 ± 6.4
68 ± 59
1.3 ± 0.41
1.48 ± 0.54
103 ± 18
68 ± 59
 On the basis of the electric fields change at both sides, the relationship between the electric field change EL (kV m−1) and the horizontal distance of d(m) from the channel can be nearly drawn as
 The variation of the dart leader electric field with distance is somewhat faster than the inverse proportionality predicted by the source charged leader model, perhaps due to the influences of the lightning channel geometry, variation of charge density with height, the metallic lightning rod with a height of 5 m and limited sample sizes. In addition, the real ground has a limited conductivity, the real ground surface is not even, and attenuation effect during the transmission of electromagnetic field should not be neglected.
 Compared with Figures 7a and 7b, it can be seen that although the electric fields measured at both sites exhibit asymmetrical V-shaped signatures, the width of V-shaped is appreciably smaller at Site 1 than that at Site 2. The difference of the V-shaped width can be explained using a source charge leader model [Uman, 1987] (Figure 8), which views the leader as a charge column moving downward from a source charge center. The vertical electric field change at a horizontal distance d from the lightning channel, due to an elemental section of channel dz at height z with a charge density ρL, and including the effect of charge depletion in the cloud, can be written as the following:
where, f(z) = − , H is the height of the source charge center, HB is the height of the downward negative leader tip. For a uniformly charged leader, the vertical leader field change at any time t is given by
where HB = H − vt is the height of the bottom of the leader at time t, v is the leader speed. For very close field measurements, where H ≫ d2, and for HB = 0 (leader touching the ground), equation (7) becomes approximately
 That is, for very close to the channel the vertical electrostatic field at ground falls off as 1/d, as opposed to 1/d3 far from the channel (H ≪ d2). Interestingly, equation (8) is exactly the same expression as the horizontal field from an in finitely long, uniform line charge. Based on equation (8) and the measurement of the leader electric field changes at 60 m (Table 1), the dart leader charge density is estimated to be about 6 × 10−5 C/m, which is consistent with that of the subsequent return stroke in natural cloud-to-ground lightning [Zhang et al., 2005].
 If a uniform charged channel is assumed, the relative contribution of each channel section of equal length to the total field is given by f(z) in equation (6). In Figure 9 we plot f(z) versus z from equation (6) for Site 1 (Figure 9a) and Site 2 (Figure 9b), assuming the charge source center height of H = 5 km. It can be shown from Figure 9a that the leader field change at 60 m is due to the channel section below a height of 110 m, with a maximum contribution at a height z = 40 m. The electric field at 550 m (refer to Figure 9b) is predominantly determined by the channel section below a height of 1.8 km, with a maximum contribution at a height z = 420 m. Therefore, with the increasing of the distance, the leader electric field change that can be measured on the ground is of longer duration time, corresponding to the larger of the half width shown as in Figure 7. Based on the measurement of the pulse widths at 60 m and 550 m (Table 1), the model-estimated leader speeds are 7.9 × 106 m/s and 7.1 × 106 m/s, respectively. The estimated leader speed is larger at 60 m than that at 550 m because leaders exhibit an increasing speed in propagating downward over the bottom some hundreds of meters.
 In order to investigate the influence of the leader speed on the half-peak width, Figures 10a and 10b show the field change calculated by using a source charge leader model for a downward negative leader with three different values of speed 2 × 106 m/s, 5 × 106 m/s, and 2 × 107 m/s, respectively, assuming the charge source center height of H = 5 km. The left is at 60 m, and the right is at 550 m. The half widths predicted by the source charge leader model at two sites are inversely proportional to the assumed leader speed. For example, the half widths of 50 μs and 16 μs at Site 1 correspond to speeds of 2 × 106 m/s and 5 × 106 m/s, respectively. It is also found that a same leader speed will produce a different half widths at two sites, the farther the distance, the larger the half width. For example, assuming the leader speed of v = 2 × 106 m/s, the half widths at 60 m and 550 m are 50 μs and 380 μs, respectively.
4. Conclusion and Discussion
 On the basis of the simultaneous observation of the electric field changes in submicrosecond time resolution at 60 m and 550 m from two altitude-triggered lightning flashes, the electric field changes produced by bidirectional leader/return stroke and following dart leader/return stroke sequences are analyzed in this paper. The results show that the field change waveform produced by bidirectional leader/return stroke at 60 m is asymmetrical V-shaped with the half-peak width of about 100 μs. The electric field change produced by the first return stroke is 22.3 kV/m at 60 m, and the increasing slope of the field change is 1115 V/m/μs, much faster than that of the bidirectional leader process.
 The field changes produced by dart leader/return stroke sequences at both sides also appear as asymmetrical V-shaped pulses, and the half-peak widths of the V-shaped for these two sites are 14 μs and 103 μs, respectively. The difference in the width of field waveforms can be explained using the source charge leader model. The field changes produced by dart leaders at both sites are 17.9 kV/m and 1.3 kV/m, respectively, yielding a horizontal distance dependence of d−1.18, and the decreasing slopes of the dart leader field at both sites are 60 V/m/μs and 1 V/m/μs, respectively. The magnitude of the dart leader field change is not different from that of the following return stroke. Of course, the rate of change is still much faster for the return stroke, and thus it will dominate induced electromagnetic fields which can be an important consideration for overvoltage on overhead lines [Diendorfer, 1990]. In addition, within a few tens or hundreds of meters from the lightning channel, the magnitude and rate of change of the electric field produced by the first return stroke are larger than that of the subsequent return stroke in altitude-triggered lightning.
 This research was supported by Jiangsu Key Laboratory of Meteorological Disaster (KLME050101) (Nanjing University of Information Science and Technology); the Main Direction Program of the Knowledge Innovation of Chinese Academy of Sciences (grant KZCX2-YW-206), and the scientific fund of Nanjing University of Information Science and Technology. Special thanks to editor Tarek Habashy and two anonymous reviewers for their valuable suggestions and comments, which much improved the quality of this paper.