PUBLICATIONS. Journal of Geophysical Research: Atmospheres

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1 PUBLICATIONS Journal of Geophysical Research: Atmospheres RESEARCH ARTICLE Key Points: Field waveform of LBEs occurred in winter thunderstorm in Japan is simulated FCCFs of LBEs are very different from that of lightning RS in summer thunderstorm Field of LBEs is related to channel length and gradient of injected current Supporting Information: Figures S1 S6, Table S1, and Data Sets S1 and S3 S6 Correspondence to: Q. Zhang, Citation: Chen, L., Q. Zhang, W. Hou, and Y. Tao (2015), On the field-to-current conversion factors for large bipolar lightning discharge events in winter thunderstorms in Japan, J. Geophys. Res. Atmos., 120, doi: / 2015JD Received 10 MAR 2015 Accepted 22 JUN 2015 Accepted article online 26 JUN American Geophysical Union. All Rights Reserved. On the field-to-current conversion factors for large bipolar lightning discharge events in winter thunderstorms in Japan Long Chen 1,2, Qilin Zhang 1,2, Wenhao Hou 1,2, and Yulang Tao 1,2 1 Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Key Laboratory for Aerosol-Cloud- Precipitation of China Meteorological Administration, Nanjing University of Information Science and Technology, Nanjing, China, 2 Jiangsu Engineering Research Center on Meteorological Energy Using and Control, Nanjing University of Information Science and Technology, Nanjing, China Abstract In this paper we have simulated the far-field waveform characteristic of large bipolar events (LBEs) occurred in winter thunderstorms in Japan and compared the field-to-current conversion factors (FCCFs) of LBEs with that of the lightning cloud-to-ground (CG) return stroke (RS) in summer thunderstorm. As for the physical process of LBEs, Wu et al. (2014) considered that LBEs may be very similar to the typical lightning RS (RS-like process) or caused by an initial continuous current pulse (ICC-like process) in upward lightning flashes. We assume that the lightning channel length of LBEs ranges from 500 m to 1000 m, and the height of tall object struck by LBEs is from 100 m to 300 m. By using the bouncing wave model, we found that only when the injected current waveform of LBEs is characterized with a symmetric Gaussian pulse, the simulated far-field waveform of LBEs both for RS-like process and ICC-like process is similar to that observed by Wu et al. (2014). For striking tall objects with heights from 100 m and 300 m, the FCCFs of LBEs are positively correlated with its channel length and derivatives of injected current waveform, and the FCCF for RS-like process is about similar to that for ICC-like process. However, the FCCFs of LBEs are very different from lightning RS in summer thunderstorm; that is to say, the FCCFs developed for the well-known lightning RS in summer thunderstorm are not suitable for LBEs. 1. Introduction Recently, Wu et al. [2014] have observed and analyzed a type of special discharge called LBEs (large bipolar lightning discharge events) in winter thunderstorm in Japan, and LBEs can be characterized with a single bipolar pulse with the average pulse width of 15 μs ranging from 10 μs to20μs and have similar pulse widths and peak value of positive and negative cycles. However, from their statistics data, about 70% of the field waveforms of LBEs are characterized with similar pulse widths and peak value of positive and negative cycles. In fact, there are many cases without any symmetrical bipolar pulses; that is to say, many bipolar field waveforms of LBE have no similar pulse widths and peak value of positive and negative cycles (see their Figure 5). LBEs bring negative charges from cloud to ground, and they are very different from any other lightning discharge types and probably associated with tall grounded objects. Wu et al. [2014] considered that the physical process of LBEs may be similar to return stroke (RS)-like process that occurred between the downward negative leader and upward positive connection leader for cloud-to-ground (CG) lightning or may be caused by an initial continuous current pulse (ICC-like) for upward lightning flashes [e.g., Flache et al., 2008]. However, although the physical mechanism and discharge process of RS-like process is very similar to the typical lightning RS in summer thunderstorm, its channel length is much shorter (maybe hundreds of meters) than that of the typical lightning RS, and also other discharge parameters of RS-like process may be much different from that of the lightning RS (e.g., the lightning current waveform and field waveform). Therefore, we call such a physical mechanism of LBEs as a RS-like process. It is also possible that LBE is similar to the initial current pulse (ICC) during the upward lightning flash. Ishii and Saito [2009] ever presented some field waveforms of upward lightning discharges associated with transmission line faults, which have some similar characteristics as that of LBEs. Also, from the observed results as shown in Wang and Takagi [2012], upward lightning discharges in winter thunderstorms usually occur from a tall object with a modest height of about 100 m in the western coast of Japan, and an upward lightning discharge includes many ICC pulses propagating downward from the channel top. CHEN ET AL. FIELD-TO-CURRENT CONVERSION FOR LBES 1

2 Therefore, we call such a discharge physical mechanism of LBEs as ICC-like process, which may be different from ICC pulses with longer channel of typical 4 5 km in summer thunderstorm (e.g., current waveform and discharge channel length). In order to estimate the current peak of LBEs, Wu et al. [2014] have extended the FCCFs that is widely used in LLS (Lightning Location System) to that of LBEs [Zhang et al., 2014; Baba and Rakov, 2007; Bermudez et al., 2005; Pavanello et al., 2009], and it is found that the very rough estimation of mean peak current of LBEs is 68.8 ka. However, the single and symmetric bipolar pulse of LBEs means that its discharge characteristic has much difference from lightning RS. For the lightning RS, it occurs in summer thunderstorm with a grounded discharge channel whose overall lengths typically exceed 4 5 km and has a current pulse waveform with a typical risetime of several microseconds, the field peak is formed when the current wave propagates within the channel bottom section of about 1 km, and the current peak value is proportional to far-field peak. That is to say, the far-field peak for lightning RS in summer thunderstorm has nothing to do with its length of discharge channel and current risetime within several microseconds. In contrast, LBE has a much shorter channel length within 1 km and the characteristic of its electromagnetic radiation may be similar to that of compact intracloud lightning discharges (CIDs) [Nag and Rakov, 2009; Nag et al., 2010, 2011], and the predicting method of current peak of LBEs may be much different from that of typical lightning RS in summer thunderstorm. Therefore, in this paper we will simulate the field waveform characteristic of LBEs, analyze its possible discharge characteristics, and further compare the field-to-current conversion factors (FCCFs) of LBEs with that of the well-known lightning RS in summer thunderstorm. 2. The Model Introduction Here in order to simulate the discharge process of LBEs strike to tall objects, we will use the so-called engineering models, extended to include the presence of a tall strike object on the basis of a distributed source representation of the lightning channel presented by Rachidi et al. [2002]. The lightning current distribution along the lightning channel is expressed in terms of the undisturbed current, object height, and current reflection coefficients at the top and bottom of the tall object. The undisturbed current is defined as the current that would flow in the channel when the current reflection coefficients at both ends of the strike object are equal to zero, which means that the characteristic impedances of the lightning channel and the strike object are equal to each other and equal to the grounding impedance of the strike object. In the most practical cases of lightning strike to tall objects, Rakov and Uman [1998] found that the lumped grounding impedance is typically much smaller than the characteristic impedance of lightning channel (hundreds of ohms to some kilo-ohms), and further, most of natural lightning currents measured at the top of tall objects or at the bottom of tall objects of relatively small height within 60 m are not much affected by the transient process excited in the object [Rakov, 2001; Visacro et al., 2004] and therefore as well can be viewed as short-circuit currents, which is also equal to the current that is assumed to be measured at the lightning channel bottom for strike to flat ground. Considering the possible electric charge structure in winter thunderstorm in Japan presented by Wu et al. [2014], we assumed that the channel length of LBEs ranging from H = 500 m to 1000 m, and the height of tall objects struck by LBEs is h = 100 m or 300 m. Also, for the possible physical mechanism of LBEs (RS-like process or ICC-like process), due to its small gap and lower discharge voltage, we assume that the undisturbed injected current for two possible physical mechanism is the symmetric Gaussian pulses with total duration t2 and zero-to-peak risetime of t1, as follows: 8 >< aexp ðgt ð t1þþ 2 t t1 i 0 ðþ¼ t (1) >: aexp ðgt ð t1þ=kþ 2 t > t1 where k=(t2 t1)/t1, t2=2 t1, a is a constant, and the parameter g controls the current waveform shape. However, for simulating the far-field waveform radiated by CID, Nag and Rakov [2010] ever employed the asymmetric Gaussian current pulses. Here we employ the symmetric Gaussian current pulses, because we want to simulate the single bipolar pulse with similar pulse widths and peak value of positive and negative cycles that is about 70% of field waveform radiated by LBEs, which is very different from that of CID. Therefore, we assume that the current waveform of LBEs is different from that of CID. CHEN ET AL. FIELD-TO-CURRENT CONVERSION FOR LBES 2

3 Figure 1. The undisturbed injected current waveform of LBEs with a symmetric Gaussian pulse (a) for RS-like process and (b) for ICC-like process. As shown in Figure 1, we assume that the undisturbed injected current for two possible physical mechanism is characterized by symmetric Gaussian pulse with different waveform parameters, because the lightning-radiated characteristics of RS-like process is different from that of ICC-like process, the former propagates upward from the channel bottom or tall object top while the latter propagates downward from the channel top. It is found that only such different current waveforms (e.g., different parameters t1) both for two cases (RS-like process and ICC-like process) can result in the same bipolar field pulse similar to that observed by Wu et al. [2014]. Here it is worthy noting that the symmetric Gaussian pulses for two physical cases are assumed to have the same peak, which is convenient for us to analyze the FCCFs of LBEs. Note that the different current peak of LBE has no effect on its FCCF, because the current peak of LBEs is proportional to its far-field peak both for strike to flat ground and tall objects, and the FCCF is the coefficient ratio of current peak to far electric field peak. Obviously different from the typical lightning RS with the longer channel length of 4 5 km in summer thunderstorm, LBEs have much shorter channel length within hundreds of meters, its current pulse may reflect at both ends of the lighting channel and both ends of the tall object, which will make the current distribution of LBEs along the channel or tall strike object more complicated than that of lightning RS in summer thunderstorm. As shown in Figure 2, on the basis of the evidence of multiple reflections, we also postulate that from the electromagnetic point of view, the LBEs discharge may be also essentially a bouncing wave phenomenon (the bouncing wave model), similar to the discharge process of CID. It can be viewed as beginning with injection of current pulse at one end of a relatively short conducting channel, which is reflected multiple times successively at either end of the channel or the object. According to Rachidi et al. [2001] and Baba and Rakov [2005a, 2005b], when the LBE strikes the tall object, one current wave propagates upward from the top of tall object and the other downward at light speed c, both of which have thesamemagnitude(1 ρ t )I 0 (t) (ρ t is the reflection coefficient at the object top for the upward waves). However, the tall object is modeled as a single, uniform, and lossless transmission line, because the characteristic wavelength of the input lightning current of LBEs is comparable to or larger than the height of tall object. Therefore, the total current waveform of LBEs along the short channel or tall object is the sum of multiple reflections, and then we can compute the vertical electric field by using the general time domain equation presented by Uman [1987] and Thottappillil et al. [1997]. Also, from Nag and Rakov [2010], it is found that the far electric field of CID can be well simulated by Hertzian Dipole Approximation, because its channel length is very short compared with the shortest significant excitation wavelength λ, assuming that the current waveform is uniform without considering the spatially change along the finite channel. In this paper, we also employ the Hertzian Dipole Approximation for CHEN ET AL. FIELD-TO-CURRENT CONVERSION FOR LBES 3

4 Figure 2. Schematic representation of the bouncing wave mechanism of LBE for (a, b) strike to flat ground and (c, d) tall object, which are reflected multiple times successively at either end of the channel or the object. analyzing the electric field radiated by LBEs for strike to flat ground and found that the simulated results by using Hertzian Dipole Approximation is very similar to that of bouncing wave model. However, it is worthy noting that the Hertzian Dipole Approximation cannot be used to analyze the case of LBEs for strike to tall object. Therefore, in the following section of this paper we will only use the bouncing wave model to study FCCFs of LBEs both for strike to flat ground and tall objects. 3. Analysis of the Simulated Results Figure 3 shows the simulated far-field waveform of LBEs for RS-like process (a) and ICC-like process (b) for strike to tall objects and flat ground, respectively. The channel length of LBEs is H = 500 m or 1000 m, and the object height is h = 100 m or 300 m. The reflection coefficient at the channel top for the upward waves is ρ T = 0, the reflection coefficient at the object top for the upward waves is ρ t = 0.5, and the reflection coefficient at the ground level for the downward current waves is ρ g = 1 (for example, Z ch = 900 Ω, Z ob = 300 Ω, and Z gr =0Ω,, as shown in Baba and Rakov [2005a, 2005b, 2007]). It is noted that only when the injected current waveform of LBEs is characterized with a symmetric Gaussian pulse as shown in Figure 1, the computed field waveform is characterized with a symmetric bipolar pulse which is similar to that field pulse shape observed by Wu et al. [2014]. For the RS-like process propagating upward, the field bipolar pulse with an average width of 15 μs ranging from 10 μs to 20μs observed by Wu et al. [2014] corresponds to the symmetric Gaussian current pulse with an average value of t1=39μs from 26 μs to52μs (see Figure 1a). However, for ICC-like process propagating downward, it corresponds to an average value of t1=33μs ranging from 17 μs to48μs (see Figure 1b). Therefore, because our simulated field waveforms for both cases are similar to that observed by Wu et al. [2014] which means that our chosen current parameters and the computed model in this paper are valid and reasonable for about 70% of field waveform radiated by LBEs. Also, it is seen that strike to tall objects causes a field increment due to a result of transient process in the object [e.g., Bermudez et al., 2001; Rachidi et al., 2001, 2002; Cooray et al., 2006; Mosaddeghi et al., 2010; Baba and Rakov, 2005a, 2005b, 2007], and a taller object results in a larger field; for example, strike to 300 m tall object causes an extra field increment of about 55% for the channel length of H = 500 m, and about 29% for the channel length of 1000 m, compared with the case of strike to flat ground. A higher lightning channel also results in an obviously larger field peak; for example, the channel length of 1000 m causes a field increment of about 78% for RS-like process, and about 42% for ICC-like process, compared CHEN ET AL. FIELD-TO-CURRENT CONVERSION FOR LBES 4

5 Figure 3. The effect of the height of tall object and channel length on the far-field waveform of LBEs for (a) RS-like process and (b) ICC-like process for strike to tall objects and flat ground, respectively. The observation distance from the lightning strike point is r, h is the height of tall object, and H is the channel length. with the case of channel length of 500 m. However, the case of strike to tall object nearly has the same waveform as that of strike to flat ground. Figure 4 further shows the effect of reflection coefficients ρ T at the channel top and ρ g at the ground level on the far-field waveform of LBEs. From Figures 4a and 4b, we can see that a different reflection coefficient ρ T results in a different field waveform, and when ρ T is 0, the corresponding field waveform of LBEs is a better symmetric bipolar pulse similar to that average waveform characteristics by Wu et al. [2014]. Therefore, it is reasonable that we assume that ρ T is 0 both for RS-like process and ICC-like process. Also, for the ICC-like process of LBEs (see Figure 4c), the reflection coefficient ρ g has nearly no effect on the far-field waveform, and the reflection coefficient ρ g = 1 results in a better symmetric bipolar pulse of the far-field waveform. Therefore, from Figure 4, it is reasonable that we assume ρ g =1andρ T =0. Further, a less risetime of current t1 results in a larger field (see Figure 5). Therefore, together with Figure 3, it is noted that the far field of LBEs obviously depends on its channel length and derivatives of the injected current waveform. Typically, when the LBEs strike the flat ground, we found that the field waveform radiated by LBE is proportional to the channel length and its derivatives of current waveform, similar to the CID [Nag and Rakov, 2010]. However, when the LBEs strike the tall object, its far-field waveform is positively correlated with the channel length and derivatives of the injected current waveform due to the result of transient process in the object [e.g., Zhang et al., 2014]. Contrast to LBEs, the well-known lightning RS in summer thunderstorm has a longer lightning channel typically exceeds 4 5 km and with a less risetime of current pulse within several microseconds [e.g., Heidler, 1985; Zhang et al., 2009; Qie et al., 2009, 2011], and the far-field peak value is only proportional to its lightning current peak. CHEN ET AL. FIELD-TO-CURRENT CONVERSION FOR LBES 5

6 Figure 4. The effect of reflection coefficients (a and b) at the top of lightning channel ρt and (c) ρg at the channel bottom on the far-field waveform of LBEs. In the following, we will compare the FCCFs of lightning RS in summer thunderstorm (for example, LLS data) with that of LBEs in winter thunderstorm. Here considering that LLS outputs an estimated current peak of lightning RS by using the arithmetic mean of range-normalized (to 100 km) field signal strengths from all sensors allowed by the central analyzer to participate in the peak current estimate, therefore, we show the relationship of field peak and current peak for LBEs at the observation site of 100 km from the lightning strike point. That is to say, the lightning current peak of LBEs is estimated by using the field-to-current conversion factors (FCCFs) as given by A ¼ i p =E p (2) where i p is the short-circuit current peak measured at the channel base without considering the existence of tall object, which is 2 times of undisturbed injected current (i p =2i 0 ), and E p is the corresponding vertical electric peak normalized to the distance of 100 km from the lightning strike point. However, for the well-known RS in summer thunderstorm, according to the lightning RS transmission line model, the ideal field-to-current conversion factors (FCCFs) for perfectly conducting ground without considering the field propagation attenuation are shown as follows A ¼ 2πε 0 c 2 d=v (3) where d = 100 km is the normalized observed distance, v is the RS speed ranging from c/2 to 2c/3 (c is the light speed), and ε 0 is the permittivity of free space. In most practical cases, the conversion procedure should include the compensation for the field attenuation due to its propagation over lossy ground [Cummins and Murphy, 2009]. Based on the data for 28 triggeredlightning strokes observed by Willett et al. [1989] at the Kennedy Space Center (KSC), Florida, Rakov et al. [1992] proposed the following empirical formula to estimate the CG RS peak current: i p ¼ 1:5 þ 0:037d E p (4) CHEN ET AL. FIELD-TO-CURRENT CONVERSION FOR LBES 6

7 Figure 5. The effect of undisturbed injected current on the far-field waveform of LBEs (a) for RS-like process and (b) for ICC-like process. where i p is the short-circuit current peak in unit ka that is assumed to be directly measured at the channel bottom and E p is the positive value in V/m at an observation distance of d in kilometers. The fields data in equation (4) are measured within distances of about 5 km from the lightning strike point and the field propagation path is over brackish water, and the corresponding propagation effects is very little [e.g., Zhang et al., 2012a, 2012b, 2012c]. Also, by using the electric fields of 89 strokes in triggered lightning at a distance of 45 km from the lightning channel at Camp Blanding (CB), Florida, Mallick et al. [2014] presented a new empirical formula (linear regression equation) as follows: i p ¼ 0:66 þ 0:028d E p (5) where the sign conventions and notation in equation (5) are the same as that in equation (4). The difference between equations (4) and (5) is based on the different region KSC data and CB data, including of different return stroke speeds v in these two samples and different observation distance d related with the propagation effect, and also due to the discrepancy of data paucity (28 events from KFC and 89 events from CB). However, for the estimated method of lightning current peak based on the observed far field, equation (5) may be more reasonable and validation, because it considers the propagation attenuation of the field along the finitely conducting Earth within distances of 45 km. Figure 6 shows the detailed comparison of FCCFs of LBEs with that of lightning RS in summer thunderstorm. H is the channel length of LBEs ranging from 500 m to 1000 m, and the inputted undisturbed current parameters are from Figure 1. It is found that FCCFs of LBEs are much different from that of lightning RS in summer thunderstorm, and FCCFs of LBEs are closely related to its current waveforms, channel length, and height of tall objects. Table 1 shows the detailed FCCFs for predicting lightning peak of LBEs. First, when the LBE is assumed to strike the flat ground (see Figures 6a and 6b), for RS-like process, the coefficient factor A (or FCCF) has an average value of 7.80 ka m V 1 ranging from 3.59 to ka m V 1, and for ICC-like process, the coefficient factor A (or FCCF) has an average value of 7.25 ka m V 1 ranging from 4.95 to ka m V 1. However, for the well-known lightning RS, the theoretical (ideal) estimation factor A (see equation (3)) is a constant 2.5 ka m V 1 that is less about 3 times than that of LBE, which means that the current peak of LBEs predicated by using the ideal FCCFs of the lightning RS in summer thunderstorm is about underestimated by 3 times. Second, for strike to the tall objects of 100 m or 300 m (see Figures 6c 6f), the FCCFs of LBEs decrease with the increase of tall object height, because strike to taller object results in a larger field peak. For example, when the LBE strikes a 100 m tall object, the average factor A for RS like is 5.87 ka m V 1 and is 5.94 ka m V 1 for ICC like, while for LBE striking a 300 m tall object, the average factor A for RS like is 4.69 ka m V 1 and 4.3 ka m V 1 CHEN ET AL. FIELD-TO-CURRENT CONVERSION FOR LBES 7

8 Figure 6. Comparison of the FCCFs of the (a) RS like and (b) ICC like with that of the well-known RS in summer thunderstorm. H is the channel length of LBEs ranging from 0.5 km to 1 km, and input current risetime parameters t1 are the same as that in Figure 1. for ICC like. It is worthy noting that the factor A forrs-likeprocessisaboutsimilartothatforicc-likeprocessboth forstriking100mand300mtallobjects,aswellasforstriketoflat ground. Therefore, the FCCFs developed for lightning RS are not suitable for LBEs, and the peak currents of LBEs does not follow the same rule as lightning RS. Also, further analysis shows that the simulated results in Figure 6 can be applied to the distance range beyond about 20 km because the corresponding field of LBEs is mainly radiation field component. 4. Conclusion In this paper we have simulated the waveform characteristic of large bipolar lightning discharge events (LBEs) occurred in winter thunderstorms in Japan, by using the bouncing wave model, and we found that only when CHEN ET AL. FIELD-TO-CURRENT CONVERSION FOR LBES 8

9 Table 1. FCCFs of LBEs Both for RS-Like Process and ICC-Like Process a RS-Like Process ICC-Like Process Minimum Maximum Average Minimum Maximum Average h = (3.59) (6.77) (5.15) 5.52 (4.95) (6.68) 8.81 (5.68) h = (3.16) 9.73 (5.48) 7.43 (4.31) 4.44 (4.57) 9.3 (5.76) 6.84 (5.03) h = (2.75) 7.4 (4.72) 5.65 (3.73) 3.23 (2.45) 7.05 (3.99) 5.13 (3.46) a In brackets the height of LBEs H = 1 km and outside brackets H = 0.5 km, and the values in italics represent the average value both for H = 1 km and 0.5 km. the injected current waveform is characterized with a symmetric Gaussian pulse, the simulated far-field waveforms of LBEs are similar to that observed field of LBEs characterized with similar pulse widths and peak value of positive and negative cycles. When the LBEs are assumed to strike the flat ground, the simulated results by using Hertzian Dipole Approximation are very similar to that of bouncing wave model, and the field waveform radiated by LBE is proportional to the channel length and its derivatives of current waveform, similar to the CID. However, the Hertzian Dipole Approximation only can be used to analyze the case of LBEs for strike to flat ground, but not for the case of strike to tall object, while the bouncing wave model can be used for two cases. When the LBEs strike the tall object, its field waveform is only positively related to (not proportional to) the channel length and derivatives of the injected current waveform due to the result of transient process in the object, and a different strike tall object causes a different field of LBE. The comparison shows that the FCCFs developed for the well-known RS in summer thunderstorm is not suitable for LBEs. It is worthy noting that the FCCF for RS like is about similar to that for ICC like both for striking flat ground and tall objects from 100 m and 300 m, and with the increase of the object height, its FCCF (coefficient factor A) decreases. The FCCFs of LBEs are very different from that of lightning RS in summer thunderstorm, and the current peak of LBEs predicted by using the FCCFs of RS in summer thunderstorm is obviously underestimated. Acknowledgments Simulation data are available in the supporting information. This work was supported in part by the National Key Basic Research Program of China (2014CB441405), in part by the National Natural Science Foundation of China under grant , and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and by Commonwealth Industry Research Project of China (GYHY ). References Baba, Y., and V. A. 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