Return stroke peak current versus charge transfer in rocket triggered lightning

Transcription

1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009jd013066, 2010 Return stroke peak current versus charge transfer in rocket triggered lightning J. Schoene, 1 M. A. Uman, 2 and V. A. Rakov 2 Received 24 August 2009; revised 8 January 2010; accepted 19 February 2010; published 18 June [1] We examined data on 117 return strokes in 31 rocket and wire triggered lightning flashes acquired during experiments conducted from 1999 through 2004 at the International Center for Lightning Research and Testing at Camp Blanding, Florida, in order to compare the peak currents of the lightning return strokes with the corresponding charges transferred during various time intervals within 1 ms after return stroke initiation. We find that the determination coefficient (R 2 ) for lightning return stroke peak current versus the corresponding charge transfer decreases with increasing the duration of the charge transfer starting from return stroke onset. For example, R 2 = 0.91 for a charge transfer duration of 50 ms after return stroke onset, R 2 = 0.83 for a charge transfer duration of 400 ms, and R 2 = 0.77 for a charge transfer duration of 1 ms. Our results support the view that (1) the charge deposited on the lower portion of the leader channel determines the current peak and that (2) the charge transferred at later times is increasingly unrelated to both the current peak and the charge deposited on the lower channel section. Additionally, we find that the relation between triggered lightning peak current and charge transfer to 50 ms in Florida is essentially the same as that for subsequent strokes in natural lightning in Switzerland, further confirming the view that triggered lightning strokes are very similar to subsequent strokes in natural lightning. Citation: Schoene, J., M. A. Uman, and V. A. Rakov (2010), Return stroke peak current versus charge transfer in rockettriggered lightning, J. Geophys. Res., 115,, doi: /2009jd Introduction [2] The experimental data presented in this paper were acquired at the International Center for Lightning Research and Testing (ICLRT), an outdoor facility occupying about 1km 2 at the Camp Blanding Army National Guard Base in north central Florida. The ICLRT is located approximately midway between Gainesville, home of the University of Florida, and Jacksonville. At the ICLRT, lightning is triggered (artificially initiated) from natural overhead thunderclouds using the rocket and wire technique [e.g., Newman, 1958; Fieux et al., 1975; Uman et al., 1997; Rakov, 1999; Rakov and Uman, 2003]. Triggered lightning is typically composed of an initial stage involving an upward propagating positive leader initiating a relatively steady current of the order of 100 A with a duration of hundreds of milliseconds, followed by one or more dart leader return stroke sequences which are very similar to the strokes following the first stroke in natural downward lightning [e.g., Fisher et al., 1993]. [3] Knowledge of the charge deposited on channels of downward propagating stepped leaders that precede first return strokes in natural lightning is needed for understanding 1 EnerNex Corporation, Knoxville, Tennessee, USA. 2 Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida, USA. Copyright 2010 by the American Geophysical Union /10/2009JD the ground attachment process and hence is important in the design of lightning protection. If the charge distribution along the stepped leader channel is known, it can be used to calculate the electric field between the leader tip and objects on the ground, thus, determining the so called striking distance [e.g., Rakov and Uman, 2003; Cooray et al., 2007]. The striking distance is usually defined as the distance between the descending leader tip and the object to be struck at the time it is essentially certain that the object will indeed receive the strike. It is assumed that at this time the electric field enhancement at the object exceeds a critical breakdown value, so that an upward directed leader emerges from the object and eventually intercepts the downward moving stepped leader. The striking distance is important because of its use in so called electrogeometric models for the design of building and power line lightning protection [e.g., Rakov and Uman, 2003]. In the electrogeometric models, the striking distance S is generally related to the peak current I peak by the b power law expression S = AI peak, where A and b are constants, which are different in different studies because of the different assumptions made about the leader charge distribution, its relation to the return stroke peak current, and the breakdown electric field magnitude [Rakov and Uman, 2003]. [4] The statistical distribution of return stroke current peaks is reasonably well known [e.g., Rakov and Uman, 2003]. On the other hand, there exist limited statistical data on the channel charge deposited by leaders preceding first return strokes. The investigation of the correlation 1of7

2 from the time of return stroke onset to different ending times up to 1 ms and (2) charge transfer for different starting times after return stroke initiation to a fixed ending time of 1 ms. Figure 1. ICLRT overview, Lightning currents were triggered from the stationary launcher (1999 through 2004) and from the mobile launcher (2002 and 2003) positioned at five different locations: (1) 11 m southeast of pole 15 as shown in the figure, (2) 30 m north of pole 7, (3) 100 m north of pole 7, (4) 7 m south of pole 4, and (5) 15 m south of pole 4. between the return stroke peak current and the leader charge allows inferences to be drawn on the less well defined leader charge statistics and hence, with assumptions, the striking distance to be calculated as a function of return stroke peak current. [5] All published experimental data regarding the relation between return stroke peak current and charge transfer in natural lightning are derived from the research of Berger and coworkers [e.g., Berger and Vogelsanger, 1965; Berger, 1967, 1972; Berger et al., 1975; Berger and Garabagnati, 1984], for lightning striking two towers in Switzerland and two towers in Italy, and have been analyzed by them and by Cooray et al. [2007]. According to Cooray et al. [2007], for natural first strokes, there is a linear regression Q 100ms = I peak (R 2 = 0.88) for charge transfer to 100 ms, and for natural subsequent strokes, Q 50ms =0.028I peak (R 2 not stated) for charge transfer to 50ms. In the above equations, charge transfer Q is in Coulombs and peak current I peak is in kilo Ampere. Additionally, Schoene et al. [2009] have shown that for triggered lightning strokes (which as noted above are similar to natural lightning subsequent strokes) the scatterplot of return stroke peak current versus charge transfer to 1 ms is surprisingly similar to the 1 ms natural lightning first stroke data of Berger [1972]. The regression equation for 143 triggered lightning strokes as given by Schoene et al. [2009] is I peak =12.3Q ms (R 2 = 0.76) and the regression equation for Berger s89natural lightning first strokes is I peak = Q 1 ms (R 2 =0.59).Qie et al. [2007] reported I peak = 18.5 Q ms for ten triggered lightning strokes in China. [6] In this paper, we compare the peak currents of the lightning return strokes with the corresponding charges transferred during various time intervals within 1 ms after return stroke initiation. We investigate charge transfers for two different types of time intervals: (1) charge transfer 2. Experiment Description [7] An overview of the ICLRT is given in Figure 1 including a depiction of the two test power distribution lines on which experiments were performed. Both direct lightning strike effects (lightning current injected directly into a power line conductor [Mata, 2000, 2003; Mata et al., 2003; Schoene et al., 2007a, 2007b; Schoene, 2007; Schoene et al., 2009]) and nearby lightning effects (lightning current injected into the ground near the power line to investigate the voltages and currents induced in the power line conductors [Paolone et al., 2004; Schoene, 2007] were studied. Also shown in Figure 1 are (1) the stationary tower rocket launching facility from which the triggered lightning current was directed to the power lines and (2) the mobile launcher from which lightning was triggered for the nearby lightning experiments. Note that peak currents for the case of current injection to overhead conductors were essentially the same as those for injection to ground nearby. [8] A low inductance resistor (1 mw) was mounted at the bottom of each launcher to measure directly the channelbase current of the triggered lightning. The measured voltage across the resistor was transmitted to the launch control trailer (Figure 1) via a Nicolet Isobe 3000 link (frequency response: DC to 15 MHz), composed of a receiver transmitter pair and a connecting fiber optic cable, where it was sampled with LeCroy digital oscilloscopes (sampling rate between 10 MHz and 50 MHz) and Yokogawa digital oscilloscopes (sampling rate 1 MHz or 2 MHz). The LeCroy oscilloscopes stored the data in a few millisecond long segments and the Yokogawa oscilloscopes sampled continuously for 1 or 2 s. The data were appropriately low pass filtered to avoid aliasing. The measurement settings for the experiments are described in detail by Mata [2000], Schoene et al. [2007a, 2007b], and Schoene [2007]. [9] Thirty one lightning flashes containing 117 return strokes were triggered during the power line experiments. The quality of the data for the experiments in which lightning current was directly injected into the test power line was ensured by a consistency check of the measured channelbase current with the individual currents measured on the various phase to neutral connections and groundings of the power line [Schoene et al., 2007a, 2007b]. Statistical parameters of the triggered lightning return stroke currents recorded in these experiments are presented by Schoene et al. [2009], including data for peak current and for charge transfer to 1 ms after return stroke onset (see also Discussion section), but no analysis for charge transfer times less than 1 ms is given. 3. Relation Between Return Stroke Current Peaks and Charge Transfers [10] We now examine the relation between triggeredlightning return stroke peak currents and the corresponding charge transfers for various time intervals from return stroke initiation. A typical triggered lightning return stroke current 2of7

3 the determination coefficient for peak current and charge transferred from 900 ms to 1 ms is [13] While the power law fit is used in Figure 3 and Figure 4, a linear regression equation of the form, Q t ¼ k t I peak ; ð1þ Figure 2. Typical triggered lightning return stroke waveform measured at the channel base (stroke FPL0315 2). The following return stroke parameters are illustrated: (a) current peak value and (b) charge transfer. waveform and definitions of its peak value and the corresponding charge transfer are shown in Figure 2. [11] The charge transfers were obtained by numerically integrating the measured return stroke current waveform (1) from the return stroke starting time to different ending times that range from 10 ms to 1 ms and (2) from different starting times ranging from 10 ms to 900 ms after return stroke initiation to a fixed ending time of 1 ms. The charge transfers obtained from both (1) and (2) were related to the corresponding peak currents. [12] Figure 3 gives peak current charge transfer scatterplots for charge transfer durations of 10 ms, 50 ms, 100 ms, 400 ms, 700 ms, and 1 ms after return stroke initiation. Each of the graphs in Figure 3 also shows a power law equation and the associated coefficient of determination (R 2 ). The graphs clearly illustrate the increase in scatter and decrease in R 2 (e.g., R 2 = 0.96 for 10 ms and R 2 = 0.77 for 1 ms) with increasing charge transfer duration. Note that the correlation with R 2 = 0.77 for the 1 ms charge transfer is still relatively good. This is partly due to the very strong correlation between the peak current and the charge transfer during the first tens of microseconds. We removed this strongly correlated portion of the charge transfer in order to focus on the correlation between peak current and charge transferred at later times by varying the starting time of the charge transfer and integrating the current to a fixed time of 1 ms. The results are presented in Figure 4, which shows peak current charge transfer scatterplots for charge transfer for different starting times, 10 ms, 50 ms, 100 ms, 400 ms, 700 ms, and 900 ms, after return stroke initiation to a fixed ending time of 1 ms. The graphs in Figure 4 illustrate that the correlation between peak current and the transferred charge gets weaker with increasing starting time of the partial charge transfer. For instance, excluding the first 100 ms of the transferred charge results in a relatively low determination coefficient of When the first 100 ms are included, the determination coefficient increases to 0.77 (see scatterplot for charge transfer from 0 to 1 ms in Figure 3). The charge transferred at later times (approaching 1 ms) only is very poorly correlated with the peak current. For instance, is employed in the literature [e.g., Cooray et al., 2007] to fit the charge Q t transferred from the initiation of the return stroke to time t, and the peak current I peak (k t is the regression line slope for time t). We found that linear regression fits our data well for charge transfer durations up to 400 ms, or so, after return stroke initiation. However, we found that for longer charge transfer durations, a power law equation provides a much better fit to the data than a linear one. In the following paragraphs, we derive a generalized linear equation based on our data that relates triggered lightning return stroke current peak and charge transferred from return stroke initiation to an arbitrary time up to 1 ms and compare the linear fit with the fit of the power law equations in Figure 3. [14] The variations of slope k t with charge transfer time t is illustrated in Figure 5. The data in Figure 5 can be fitted well with the equation shown (R 2 = 0.99). Inserting this equation into equation (1) results in the linear (with respect to I peak ) equation Q t ¼ 0:0068 t 0:39 I peak ; where Q t is in C, I peak in ka, and t in ms. [15] Equation (2) is a generalized linear equation that can be used to estimate the charge transfer of subsequent return strokes for an arbitrary charge transfer time between 10 ms and 1 ms (as opposed to each power law equation in Figure 3, which can only be used for a single charge transfer time). Note that the R 2 values for both the linear equation (2) and the power law equation in Figure 3 decrease with increasing charge transfer time. As stated above, for long charge transfer durations (above 400 ms, or so), the power law fit of the Figure 3 equations is more adequate than the linear fit in equation (2). For instance, the R 2 for a power law fit in Figure 3 for a charge transfer time of 1 ms is The linear equation (2) for the same charge transfer time fits the data less well (R 2 = 0.49, see Figure 5). On the other hand, for short charge transfer durations, both the power law equations in Figure 3 and the linear equation (2) produce a similarly good fit. For instance, the R 2 values for a charge transfer time of 100 ms are 0.88 for the power law fit and 0.80 for equation (2). 4. Discussion [16] Cooray et al. [2007] analyzed the first and subsequent stroke data of Berger and coworkers [Berger and Vogelsanger, 1965; Berger, 1967, 1972; Berger et al., 1975] and found the following relation between subsequent return stroke current peaks I peak and the corresponding charge transfer within the first 50 ms after return stroke initiation: Q 50 s; Berger ¼ 0:028 I peak; Berger : [17] Cooray et al. [2007] do not give the coefficient of determination for equation (3). The linear regression equa- ð2þ ð3þ 3of7

4 Figure 3. Relation between return stroke peak current and charge transfer for different charge transfer durations, starting at return stroke initiation. tion (see equation (4)) for our 50 ms rocket triggeredlightning data is very similar to equation (3) for Berger s natural lightning subsequent stroke data. Q 50 s; Camp Blanding ¼ 0:027 I peak; Camp Blanding : ð4þ The coefficient of determination for equation (4) is R 2 = [18] The similarity of Berger s regression equation (derived by Cooray et al. [2007]) for natural lightning subsequent return strokes and our regression equation for triggered lightning return strokes suggests that the current waveshapes from natural lightning subsequent strokes are similar to the current waveshapes from triggered lightning return strokes, at least for the initial 50 ms; providing further support to the view that the characteristics of naturallightning subsequent strokes and triggered lightning strokes are very similar. [19] The overall return stroke current measured at the bottom of the lightning channel is in general associated with (1) negative charge deposited on the downward propagating leader channel core which carries the leader current and in the radial corona sheath surrounding the core (note that there is no clear demarcation between core charge and corona charge and that part of the core charge may be indistinguishable from the inner corona charge) and (2) negative charge effectively drained from the cloud charge reservoir, although this latter contribution is often specifically attributed to continuing current rather than to return stroke current [e.g., Pierce, 1955; Rakov and Uman, 2003]. For both first and subsequent return strokes, the charge contribution from the cloud charge reservoir can probably be neglected during the first tens of 4of7

5 Figure 4. Relation between return stroke peak current and charge transfer for different charge transfer durations starting with delays after return stroke initiation. microseconds after return stroke initiation due to the finite travel time of the return stroke wavefront from the return stroke initiation point near ground to the cloud charge region. In Figure 3, the strong correlation between peak current and charge transfer for the first tens of microseconds of the triggered lightning strokes (e.g., R 2 =0.91forthe 50 ms charge transfer) suggests that (1) the charge responsible for the return stroke peak formation, which occurs within the first microsecond or so and (2) the charge that is transferred for the first tens of microsecond are associated with the lower portion of the leader channel core. After the first tens of microseconds, the charge transferred to ground is the remaining charge in the leader channel (i.e., charge stored in the upper portion of the leader channel core and in the corona sheath surrounding the leader channel core) and possibly charge from the cloud charge reservoir. The poorer determination coefficient (R 2 = 0.77) for the 1 ms charge transfer is indicative of the charge tapped at a later time being less related or perhaps even unrelated to the current peak and to the charge deposited on the core of the lower portion of the leader channel. Figure 4 reinforces this point by depicting the current charge relation for different charge transfer duration starting times after the return stroke onset to 1 ms (e.g., 50 ms to 1 ms, 100 ms to 1 ms). Figure 3 and Figure 4 show that there is some correlation (R 2 = 0.77) for the full 0 to 1 ms charge transfer and that the correlation becomes progressively weaker with increasing charge transfer duration starting time (e.g., R 2 = 0.36 for 700 ms to 1 ms). It is logical to think that the charge stored in higher leader channel sections has little if anything to do with the return stroke current peak. In this view, the correlation between peak current and charge transfer should be stronger for 5of7

6 Figure 5. k t factor in equation (1) versus charge transfer time (circular markers). The coefficient of determination (R 2 ) of equation 1 is given for each value of k t (solid square markers). subsequent strokes than for first ones, since first strokes store charge in a relatively large and random numbers of branches. The charge stored in the one branch that connects to ground should be well correlated with the current peak while the uncorrelated charge (if the view above is true) in the unconnected branches should result a weaker correlation between current peak and total charge transfer. On the other hand, the amount of charge stored in the branches could be correlated with the line charge density near the bottom of the channel trunk, and hence, the charge in the unconnected branches may be correlated with the current peak. Note that, according to Berger and Garabagnati [1984], the determination coefficient for the relation between peak current and charge transfer to 1 ms for branched first strokes is 0.64, higher than that for typically branchless subsequent strokes, [20] According to Schoene et al. [2009], the coefficient of determination for a power law fit of triggered lightning return stroke peak current versus 1 ms charge transfer was 0.76, and in this paper it is 0.77 for a power law fit and 0.49 for a linear fit. The small discrepancy in the determination coefficients for the power law fits is due to the fact that slightly different data sets were analyzed in this paper (the data collected during the 2001 experiment were mainly excluded from the analysis presented in this paper, since return stroke current waveforms to determine charge transfers at times other than 1 ms were not available). The significantly smaller determination coefficient for the linear fit (R 2 = 0.49) compared to the determination coefficient for the power law fit determined in this paper (R 2 = 0.77) implies that for longer charge transfer durations (longer than 400 ms, or so) one should use a power law equation (see Figure 3). On the other hand, for shorter (up to 400 ms) charge transfer durations, linear regression equations (see our generalized equation (2)) give sufficiently accurate results. 5. Summary [21] We examined the peak currents of rocket triggeredlightning return strokes and the corresponding charges transferred during various time intervals within 1 ms after return stroke initiation. The results of our study can be summarized as follows: [22] 1. Comparing the return stroke peak currents with charges transferred from the return stroke onset to different ending times that range from 10 ms to 1 ms, we find that the magnitude of the determination coefficient between lightning return stroke peak current and the corresponding charge transfer decreases with increasing duration of the charge transfer after return stroke onset and that the correlation is the strongest for charge transfers up to a few tens of microseconds. We infer that the channel base current peak and charge transferred within a few tens of microseconds are primarily determined by line charge density in the lower portion of the dart leader channel core. [23] 2. Comparing the return stroke peak currents with charges transferred from starting times that range from 10 ms to 900 ms after return stroke onset to a fixed ending time of 1 ms after the return stroke initiation, we find that the determination coefficient between lightning return stroke peak current and the corresponding charge transfer decreases with increasing charge transfer starting time and the correlation essentially disappears for starting times of a few hundreds of microseconds. We infer that the charge transferred at later times is increasingly unrelated to both the current peak and the charge deposited on the channel core near ground. [24] 3. The significantly smaller determination coefficient for charge transfer versus peak current for the linear fit compared to the power law fit for times longer than a few hundred microseconds suggests that in this case one should use a power law equation. On the other hand, for charge transfer durations up to a few hundreds of microseconds, linear regression equations give sufficiently accurate results. [25] 4. A generalized linear regression equation that relates triggered lightning return stroke current peak and charge transferred from return stroke initiation to an arbitrary time up to 1 ms is derived. This equation produces an adequate fit for charge transfer times up to 400 ms or so. A power law equation should be used for longer charge transfer times. [26] 5. We show that the current charge relation for a charge transfer time of 50 ms is essentially the same for triggered lightning strokes and natural lightning subsequent strokes. [27] Acknowledgments. This research was supported primarily by the Florida Power and Light Corporation with additional support from the NSF, the FAA, and the Lawrence Livermore National Laboratory. References Berger, K. 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