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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 ...

[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.

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 ...