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We studied simultaneous electric field changes, microsecond-scale (VLF/LF) magnetic field pulses, and VHF emissions associated with K processes in 37 cloud and 54 cloud-to-ground lightning flashes ...

Assuming that the lightning return stroke transmission-line model is applicable, we derive an expression for the return-stroke magnetic field for an arbitrary return stroke speed and from that expression show that for a return stroke speed equal to the speed of light c the electric and magnetic field waveforms at all points in space and the current waveform are identical. Recent measurements indicate that the electric field and current waveforms are similar for about 100 ns for triggered lightning return strokes, potentially implying that the initial return stroke speed is actually near c for that time, that is, for the bottom 30 m or so of the triggered lightning channel. While for the transmission-line model the current waveform and the total electric field waveform are identical for a return stroke speed of c, we show that each of the three individual components (electrostatic, induction, and radiation) that comprise the total field varies significantly with distance.

Three different approaches to the computation of lightning electric fields are compared. These approaches are the traditional dipole (Lorentz condition) technique and two versions of the monopole (continuity equation) technique. The latter two techniques are based on two different formulations of the continuity equation, one used by Thottappillil et al. [1997] and the other by Thomson [1999], the difference between the formulations being related to different treatments of retardation effects. The three approaches involve the same expression for the vector potential but different expressions for the scalar potential. It is analytically shown that the three different expressions for the scalar potential are equivalent and satisfy the Lorentz condition. Further, the three approaches yield the same total fields and the same Poynting vectors. However, expressions in the three approaches for the individual electric field components in the time domain, traditionally identified by their distance dependence as electrostatic, induction, and radiation terms, are different, suggesting that explicit distance dependence is not an adequate identifier. It is shown that the so identified individual field components in the electric field equation in terms of charge density derived by Thottappillil et al. [1997] are equivalent to the corresponding field components in the traditional equation for electric field in terms of current based on the dipole technique. However, the individual field components in the electric field equation based on Thomson's [1999] approach are not equivalent to their counterparts in the traditional dipole technique equation. Further, in Thottappillil et al.'s [1997] technique and in the traditional dipole technique, the gradient of scalar potential contributes to all three electric field components, while in Thomson's [1999] technique it contributes only to the electrostatic and induction components. Calculations of electric fields at different distances from the lightning channel show that the differences between the corresponding field components identified by their distance dependence in different techniques are considerable at close ranges but become negligible at far ranges.

Reconstruction of lightning currents and return stroke model parameters using remote electromagnetic fields

Analyses of electric and magnetic fields measured at distances from tens to hundreds of meters from the ground strike point of triggered lightning at Camp Blanding, Florida, and at 10 and 20 m at Fort McClellan, Alabama, in conjunction with currents measured at the lightning channel base and with optical observations, allow us to make new inferences on several aspects of the lightning discharge and additionally to verify the recently published “two-wave” mechanism of the lightning M component. At very close ranges (a few tens of meters or less) the time rate of change of the final portion of the dart leader electric field can be comparable to that of the return stroke. The variation of the close dart leader electric field change with distance is somewhat slower than the inverse proportionality predicted by the uniformly charged leader model, perhaps because of a decrease of leader charge density with decreasing height associated with an incomplete development of the corona sheath at the bottom of the channel. There is a positive linear correlation between the leader electric field change at close range and the succeeding return stroke current peak at the channel base. The formation of each step of a dart-stepped leader is associated with a charge of a few millicoulombs and a current of a few kiloamperes. In an altitude-triggered lightning the downward negative leader of the bidirectional leader system and the resulting return stroke serve to provide a relatively low-impedance connection between the upward moving positive leader tip and the ground, the processes that follow likely being similar to those in classical triggered lightning. Lightning appears to be able to reduce, via breakdown processes in the soil and on the ground surface, the grounding impedance which it initially encounters at the strike point, so at the time of channel-base current peak the reduced grounding impedance is always much lower than the equivalent impedance of the channel. At close ranges the measured M-component magnetic fields have waveshapes that are similar to those of the channel-base currents, whereas the measured M-component electric fields have waveforms that appear to be the time derivatives of the channel-base current waveforms, in further confirmation of the “two-wave” M-component mechanism.

The analytical treatment of retardation effects in calculating lightning electromagnetic fields far from the source has often involved the use of a so-called F factor. The literature concerning the ...

We derive exact expressions for remote electric and magnetic fields as a function of the time- and height-varying charge density on the lightning channel for both leader and return-stroke processes. Further, we determine the charge density distributions for six return-stroke models. The charge density during the return-stroke process is expressed as the sum of two components, one component being associated with the return-stroke charge transferred through a given channel section and the other component with the charge deposited by the return stroke on this channel section. After the return-stroke process has been completed, the total charge density on the channel is equal to the deposited charge density component. The charge density distribution along the channel corresponding to the original transmission line (TL) model has only a transferred charge density component so that the charge density is everywhere zero after the wave has traversed the channel. For the Bruce-Golde (BG) model there is no transferred, only a deposited, charge density component. The total charge density distribution for the version of the modified transmission line model that is characterized by an exponential current decay with height (MTLE) is unrealistically skewed toward the bottom of the channel, as evidenced by field calculations using this distribution that yield (1) a large electric field ramp at ranges of the order of some tens of meters not observed in the measured electric fields from triggered-lightning return strokes and (2) a ratio of leader-to-return-stroke electric field at far distances that is about 3 times larger than typically observed. The BG model, the traveling current source (TCS) model, the version of the modified transmission line model that is characterized by a linear current decay with height (MTLL), and the Diendorfer-Uman (DU) model appear to be consistent with the available experimental data on very close electric fields from triggered-lightning return strokes and predict a distant leader-to-return-stroke electric field ratio not far from unity, in keeping with the observations. In the TCS and DU models the distribution of total charge density along the channel during the return-stroke process is influenced by the inherent assumption that the current reflection coefficient at ground is equal to zero, the latter condition being invalid for the case of a lightning strike to a well-grounded object where an appreciable reflection is expected from ground.

[1] We examine in detail the simultaneous lightning current waveforms, close electric field changes, and lightning location system data for upward lightning discharges initiated from the Gaisberg Tower (GBT) from 2005 to 2009. Out of 205 upward flashes, most of them (87% or 179/205) were initiated from the tower top without any nearby preceding lightning activity (called “self-initiated”), whereas 26 upward flashes (13%) were initiated from the tower top with immediately preceding nearby lightning activity (called “nearby-lightning-triggered”), including 15 positive ground flashes, one negative ground flashes, and 10 cloud discharges. The possible reasons for self-initiated upward flashes dominating at the GBT could be the field enhancement due to the Gaisberg Mountain above the surrounding terrain and low altitude of charge region during non-convective season (September to March), since we note that self-initiated lightning at the GBT occurred predominantly (79% or 142/179) during non-convective season. On the other hand the majority (85% or 22/26) of nearby-lightning-triggered upward flashes at the GBT occurring during convective season (April to August) and 80 nearby-lightning-triggered upward flashes out of 81 upward flashes observed at the ten tall towers in Rapid City in South Dakota of USA occurring during summer seasons, could be due to the result of high altitude of charge region. The triggering flashes were detected to be within 1 and 18 km distance and the time intervals between them and upward lightning initiation are in the range of 0.3 to 90.7 ms.

We report the measured current characteristics of positive lightning discharges to the Gaisberg Tower (GBT) in Austria from 2000 to 2009. On the basis of the recorded current waveforms, a total of ...

We analyze current records for 21 upward initiated bipolar lightning flashes observed at the Gaisberg Tower (GBT) in Austria from 2000 to 2009. A bipolar lightning flash occurrence of 3% (21/652) i ...

From electric field records of 27 ground flashes near Tampa, Florida, and 19 ground flashes at the NASA Kennedy Space Center (KSC) the occurrence and waveshape of microsecond-scale electric field pulses associated with both millisecond-scale steplike K changes and millisecond-scale hook-shaped M changes are examined to test and disprove the following two hypotheses: (1) that K changes contain a microsecond-scale pulse component which can be described by the characteristic pulse waveform proposed by Arnold and Pierce (1964) and (2) that there is essentially no difference between K and M processes, as argued by Kitagawa et al. (1962). Microsecond-scale electric field variations exceeding by at least 50% the system noise level were observed in 23% of 135 K changes from Tampa and in 25% of 128 K changes from KSC, while such field variations were found in 44% of 88 M changes from Tampa and in 77% of 30 M changes from KSC. In the majority of the K changes having microsecond-scale pulse activity, that activity did not occur at the beginning of the K step, while in most cases the pulses associated with M changes occurred at the initial portion of the M hook. These results can be interpreted to imply that K changes and M changes are associated with dissimilar physical processes, in refutation of hypothesis (2) above. The microsecond-scale pulse activity during K changes and M changes was highly variable and sometimes irregular in waveshape. Not all the pulses had the same polarity as the K step or the initial portion of the M hook on which they were superimposed. The relation of the microsecond-scale variations to the overall K changes in ground flashes as regards the frequency of occurrence, the position of pulses within the slower field change, and the shape of the pulses is similar to that reported by Bils et al. (1988) for K changes in cloud flashes. The observed microsecond-scale field variations associated with K changes are not consistent with the characteristic electric field pulse waveform attributed by Arnold and Pierce (1964) and some other investigators to K changes, in refutation of hypothesis (1) above. No relation was observed between the magnitude of a K change and the presence or absence of corresponding microsecond-scale field variations. M changes during continuing-current field changes of relatively short duration (less than 20 ms or so) are more likely to have pulses than M changes during continuing-current field changes of longer duration.

[1] Weanalyzedhigh-speedvideoimagesandcorresponding current records for eight upward lightning flashes initiated by the Peissenberg tower (160 m) in Germany. These flashes contained a total of 33 measurable initial stage (IS) current pulses, which are superimposed on steady IS currents. Seven IS pulses had relatively short ( 8 ms) risetimes. Six (86%) of seven IS current pulses with shorter risetimes each developed in a newly-illuminated branch, and 25 (96%) of 26 IS pulses with longer risetimes occurred in already luminous (current-carrying) channels. These results support the hypothesis that longer risetimes are indicative of the M-component mode of charge transfer to ground, while shorter risetimes are associated with the leader/return stroke mode. Similar results were obtained for M-component pulses thataresuperimposedoncontinuingcurrentsfollowingreturnstroke pulses. Citation: Flache, D., V. A. Rakov, F. Heidler, W. Zischank, and R. Thottappillil (2008), Initial-stage pulses in upward lightning: Leader/return stroke versus M-component mode of charge transfer to ground, Geophys. Res. Lett., 35, L13812, doi:10.1029/2008GL034148.

[1] Electromagnetic fields produced at high altitudes by return strokes in cloud-to-ground lightning are needed in studies of transient luminous events in the mesosphere. Such calculations require the use of a lightning return stroke model. Two of the widely used return stroke models are (1) the modified transmission line model with exponential decay (MTLE) of current with height and (2) the modified transmission line model with linear decay (MTLL) of current with height. In this paper, simplified expressions based on the MTLE and MTLL models are derived for calculating far (radiation) electric fields produced at an arbitrary elevation angle by lightning return strokes. It is shown that different (for example, containing either spatial or time integral), but equivalent equations can be derived for each of the models. Predictions of simplified expressions are compared with electric fields computed using exact expressions, including all the field components, and the validity of simplified expressions for distances that are much greater than the radiating channel length is confirmed.

In summary, SJF present a new approach to deriving a radiation electric field equation for the TL model when there is no current discontinuity at the return stroke front. This approach (see their e ...

We examine the characteristics of the initial stage (IS) in object-initiated lightning derived from current measurements on the Gaisberg tower (100 m, Austria), the Peissenberg tower (160 m, Germany), and the Fukui chimney (200 m, Japan) and their counterparts in rocket-triggered lightning in Florida. All lightning events analyzed here effectively transported negative charge to ground. For rocket-triggered lightning the geometric mean (GM) values of the three overall characteristics of the initial stage, duration, charge transfer, and average current, are similar to their counterparts for the Gaisberg tower flashes and the Peissenberg tower flashes, while the Fukui chimney flashes are characterized by a shorter GM IS duration and a larger average current. The GM IS charge transfer for the Fukui chimney flashes is similar to that in the other three data sets. The GM values of the action integral differ considerably among the four data sets, with the Fukui action integral being the largest. The observed differences in the IS duration between the Fukui data set and all other data considered here are probably related to the differences in the lower current limits, while the differences in the action integral cannot be explained by the instrumental effects only. There appear to be two types of initial stage in upward lightning. The first type exhibits pulsations (ringing) during the initial portion of the IS, and the second type does not. The occurrence of these types of IS appears to depend on geographical location. The characteristics of pulses superimposed on the initial continuous current (ICC pulses) in object-initiated (Gaisberg, Peissenberg, and Fukui) lightning are similar within a factor of 2 but differ more significantly from their counterparts in rocket-triggered lightning. Specifically, the ICC pulses in object-initiated lightning exhibit larger peaks, shorter risetimes, and shorter half-peak widths than do the ICC pulses in rocket-triggered lightning.

[1] The ideal and exact solution for a vertical wire antenna of infinite length above a ground plane excited at the bottom, all conductors being perfect, is spherical TEM. Currents along such an antenna do not suffer from attenuation and dispersion. The energy lost due to radiation from such an antenna appears to originate from the source at the bottom. Practical systems are different from this ideal case because there are no ideal sources and no ideal conductors. However, ideal analytical solutions should be used, when possible, as a validation of numerical solutions in the appropriate limit.

Channel base currents from triggered lightning were measured at the NASA Kennedy Space Center, Florida, during summer 1990 and at Fort McClellan, Alabama, during summer 1991. An analysis of the return stroke data and overall continuing current data has been published by Fisher et al. [1993]. Here an analysis is given of the impulsive processes, called M components, that occur during the continuing current following return strokes. The 14 flashes analyzed contain 37 leader-return stroke sequences and 158 M components, both processes lowering negative charge from cloud to ground. Statistics are presented for the following M current pulse parameters: magnitude, rise time, duration, half-peak width, preceding continuing current level, M interval, elapsed time since the return stroke, and charge transferred by the M current pulse. A typical M component in triggered lightning is characterized by a more or less symmetrical current pulse having an amplitude of 100–200 A (2 orders of magnitude lower than that for a typical return stroke [Fisher et al., 1993]), a 10–90% rise time of 300–500 μs (3 orders of magnitude larger than that for a typical return stroke [Fisher et al., 1993]), and a charge transfer to ground of the order of 0.1 to 0.2 C (1 order of magnitude smaller than that for a typical subsequent return stroke pulse [Berger et al., 1975]). About one third of M components transferred charge greater than the minimum charge reported by Berger et al. [1975] for subsequent leader-return stroke sequences. No correlation was found between either the M charge or the magnitude of the M component current (the two are moderately correlated) and any other parameter considered. M current pulses occurring soon after the return stroke tend to have shorter rise times, shorter durations, and shorter M intervals than those which occur later. M current pulses were observed to be superimposed on continuing currents greater than 30 A or so, with one exception out of 140 cases, wherein the continuing current level was measured to be about 20 A. The first M component virtually always (one exception out of 34 cases) occurred within 4 ms of the return stroke. This relatively short separation time between return stroke and the first M component, coupled with the observation of Fisher et al. [1993] that continuing currents lasting longer than 10 ms never occur without M current pulses, implies that the M component is a necessary feature of the continuing current mode of charge transfer to ground.

Analysis of simultaneous measurements of the channel-base current and the vertical electric field 30 m from triggered lightning reveals that the fields associated with M components, although essentially electrostatic, appear to be proportional to the time derivatives of the associated M currents. Based on this finding, coupled with other observations and modeling, a mechanism for the lightning M component is proposed. According to this mechanism an M component involves a downward progressing incident wave (the analog of a leader) followed by an upward progressing reflected wave (the analog of a return stroke). However, as opposed to a leader-return stroke sequence in which the latter removes the charge deposited by the former, both the upward and the downward processes contribute about equally to the total charge flowing from the bottom of the channel at any instant of time. Such a mode of charge transfer to ground, distinctly different from a leader-return stroke sequence, is possible because of the presence of a path capable of supporting the propagation of a traveling wave (facilitated by a continuing current flowing to ground) and the fact that the ground is essentially a short circuit for the downward incident wave, so that the magnitude of the current reflection coefficient at ground is virtually equal to unity. We show that some observed properties of M components can be explained if the lightning channel traversed by an M-current wave is represented as a linear R-C transmission line. In this view, the preferential attenuation of the higher-frequency components on an R-C line is responsible for the lack of frequencies above several kilohertz in both the M-current pulses measured at the channel base and the M-light pulses observed in the bottom 1 km or so of the channel. Further, the relatively high characteristic impedance of the channel, of the order of tens to hundreds of kilohms for frequencies below some kilohertz, inferred from the linear R-C line approximation, is consistent with the observation that even a relatively poor ground is sensed by an incident M wave as essentially a short circuit. However, on a linear R-C transmission line the higher-frequency components travel faster than lower-frequency components (this velocity dispersion implying that the original pulse would spread while propagating along the line), whereas the shape of the M-light pulses does not change much within the bottom 1 km or so, as if the channel were a distortionless transmission line. We speculate, on physical grounds, that the front of the traveling M-current pulse heats the channel so that the pulse tail encounters a lowered resistance and, as a result, accelerates. By virtue of these two opposing effects, velocity dispersion and channel nonlinearity, an M pulse is formed whose more-or-less symmetrical shape is preserved over a relatively large distance, as in the case of a soliton.

Vertical electric field waveforms of leader-return stroke sequences measured 500 m and 30 m from rocket-triggered lightning are presented. The 500-m data were recorded during the boreal summer of 1986, the 30-m data during the summer of 1991, both at the NASA Kennedy Space Center, Florida. The 40 leader-return stroke field waveforms at 500 m and the 8 waveforms at 30 m all appear as asymmetrical V-shaped pulses, the bottom of the V being associated with the transition from the leader to the return stroke. Applying a widely used and simple leader model to the measured leader electric fields at 500 m, the authors infer, for the bottom km or so of the leader channel, leader speeds between 2×106 and 2×107 m/s and leader charges per unit length of 0.02×10-3 to 0.08×10-3 C/m. From two measured leader electric field changes at 30 m the authors infer, using the same leader model, for the bottom 100 m or so of the leader channel, speeds of 3×107 and 1×107 m/s and charges per unit length of 0.14×10-3 and 0.02×10-3 C/m, respectively. The corresponding measured return stroke peak currents for the above two cases are 40 kA and 7 kA, respectively. A positive correlation is observed between the magnitude of the leader field change at 500 m and the ensuing return stroke current peak

From analysis of simultaneous electric field and TV records of 76 negative cloud-to-ground lightning flashes in Florida, various lightning properties have been determined and several new facets of ...

A new lightning return stroke model is proposed in which the lightning channel, previously charged by the leader, is exponentially discharged with the discharge time constant being a general functi ...

Five return-stroke models, each allowing the use of measured channel-base current and return-stroke speed as inputs for the computation of channel current distribution and remote electric field, ar ...

For 46 multiple-stroke flashes in which each stroke ground termination was located using a TV camera network and thunder ranging, 15 flashes (33%) had one or more subsequent return strokes whose initial electric field peak normalized to 100 km was greater than the first-stroke field peak of the flash. In 9 of these 15 flashes the subsequent strokes with field peaks greater than the first stroke followed the same channel as the first stroke; in five flashes the subsequent strokes with the greater peaks followed a different channel to ground; and in one flash the subsequent strokes with the greater peaks occurred both in the first-stroke channel and in a different channel. The interstroke intervals immediately preceding the 13 larger subsequent strokes that followed the first-stroke channel had a geometric mean (GM) duration of 98 ms, 1.7 times greater than the GM of 57 ms for all 199 interstroke intervals (46 flashes) without any selection. Eight of the 13 larger subsequent strokes for which leader durations were measurable had a GM leader duration of 0.55 ms, 3.3 times smaller than the GM of 1.8 ms for 117 subsequent leaders with measurable duration in a previously formed channel of the 46 multiple-stroke flashes. For the six larger subsequent strokes that created a new channel to ground, the preceding interstroke interval had a GM of 130 ms, and the leader duration had a GM of 15 ms. No subsequent stroke with peak field exceeding the first in any category had a preceding interstroke interval less than 35 ms. Analysis of direct current measurements from Switzerland shows that subsequent-stroke currents exhibit many features similar to those of Florida subsequent-stroke electric fields. In 22 Florida single-stroke and multiple-stroke ground flashes the distances between multiple channel terminations in a given flash (33 measurements) ranged from 0.3 km to 7.3 km, with a GM of 1.7 km.

The empirical formula proposed by Willett et al. (1989) for the estimation of lightning return-stroke peak current, I, from measured peak electric field, E, at a range D, is analyzed and discussed. The formula of Willett et al. (1989), obtained from the regression of E on I, is not the least squares fit and hence is not the best expression for predicting the peak current from the measured peak electric field. Based on the same data, the least squares fit and, hence, the best expression is obtained from the regression of I on E, given by I = 1.5 − 0.037DE, where I is in kA and taken as negative, E is positive and in V/m, and D is in km. The Willett et al. (1989) formula results in an error with respect to the best peak current estimating expression that varies from −15% to +2.6% over the range of peak field values of 1.9 to 11 V/m (normalized to 100 km) used to derive the two relations. When the data of Willett et al. (1989) are separated into a high returnstroke speed group (1.5 × 108 to 1.9 × 108 m/s) and a low return-stroke speed group (1.2 × 108 to 1.4 × 108 m/s), the I-E regression lines differ for the two groups, with the difference in the regression line slopes being statistically significant at the 0.01 significance level. If the difference between intercepts of these two regression lines, found to be statistically insignificant, is neglected, the observed difference in slopes suggests that the group with the higher measured return-stroke speed is associated with a lower peak electric field for the same peak current. Finally, the practical applications of the Willett et al. (1989) formula presently found in the literature are reviewed, and the several cases of improper use, mostly related to misinterpretation of Willett et al. 's (1989) sign convention, are corrected.

A new lightning return stroke model has recently been proposed by Diendorfer and Uman (1990). In this model, if one specifies a current at the channel base (ground), a constant return stroke speed, and a channel discharge time constant, one can derive analytically the current and charge as a function of time and height associated with the channel above ground. Here we present a more general and more straightforward derivation of the Diendorfer-Uman model. In the new formulation we allow a variable return stroke speed that can be any arbitrary function of height. The influence of a decrease in speed with height, as occurs in nature, on the channel current and charge distributions and on the radiated electric and magnetic fields is determined and compared with the constant speed case. For a given channel base current, a decreasing speed with height does not change the initial peak electric and magnetic fields appreciably from the values found for a constant speed having the same value as the variable speed at the channel base, but a decreasing speed can cause considerable changes in field waveshapes for both the distant radiation fields and the near electrostatic fields. In addition to allowing an arbitrary return stroke speed, the new formulation of the Diendorfer-Uman model allows the downward propagating current waves released by the return stroke front also to have an arbitrary variable speed, whereas the original model assumed that speed to be constant at the speed of light.

Electric field changes produced by K and M processes in Florida lightning ground flashes at distances within 12 km are analyzed and compared. The geometric-mean time durations were similar: 0.7 ms ...