Return Stroke Speed Research Articles

A 3D Interferometer-Type Lightning Mapping Array for Observation of Winter Lightning in Japan

We have developed and deployed a 3D Interferometer-type Lightning Mapping Array (InLMA) for observing winter lightning in Japan. InLMA consists of three broadband interferometers installed at three stations with a distance from 3 to 5 km. At each interferometer station, three discone antennas were installed, forming a right triangle with a separation of 75 m along their two orthogonal baselines. The output of each InLMA antenna is passed through a 400 MHz low-pass filter and then recorded at 1 GS/s with 16-bit accuracy. A new method has been proposed for finding 3D solutions of a lightning mapping system that consists of multiple interferometers. Using the InLMA, we have succeeded in mapping a positive cloud-to-ground (CG) lightning flash in winter, particularly its preliminary breakdown (PB) process. A study on individual PB pulse processes allows us to infer that each PB pulse process contains many small-scale discharges scattering in a height range of about 150 m. These small-scale discharges in a series of PB pulses appear to be continuous in space, though discontinuous in time. We have also examined the positive return stroke in the CG flash and found a 3D average return stroke speed of 7.5 × 107 m/s.

Calculation Methods and Comparison for Lightning Optical Return-Stroke Speed

The optical return-stroke speed calculation is vital to analyze the lightning development process. The traditional calculation methods of lightning optical return-stroke speed, including the slope-intercept and percentage-of-peak methods, usually have considerable calculation errors in noise cases. In this article, we generate the simulated optical return-stroke signal within 100 m above the starting point along the lightning channel and use four cross-correlation methods and six traditional methods to calculate the return-stroke speed at different observation points along the channel. We optimize the cross-correlation method and reduce the calculation error to within ±10% by selecting a part of the waveform to participate in the cross-correlation operation and performing the exponential operation on the frequency-domain cross-correlation sequence. The calculation results of the quadratic-correlation method and two optimized cross-correlation methods do not change significantly at different observation points along the channel. Different channel-base waveforms affect the return-stroke speed variation trend. The smaller the dispersion factor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ_p</i> is, the more pronounced the variation of the calculation result is, and the greater the calculation error is. The optical waveform with generated Gaussian noise will significantly affect the traditional calculation method. In contrast, the cross-correlation calculation method with noise has only a tiny calculation error.

On the reconstruction of the attenuation function of a return-stroke current from the Fourier Transform of finite-duration measurements

A correct representation of the lightning current is crucial when the electromagnetic field radiated to a point of interest has to be computed. Based on the engineering models of Transmission Line type, such representation involves the knowledge of the return-stroke speed, the channel-base current, the channel height and the attenuation function. Whereas the first three quantities can be measured in different ways, no measurement technique can directly provide reliable information on the attenuation function. In the past decades, researchers have applied various strategies to address this problem. These strategies are all based on a common feature, i.e., the unknown function is postulated a priori and then validated through the comparison of the computed electromagnetic fields at one or more observation points with the corresponding measured waveforms. In this paper, we propose an alternative approach for the identification of the attenuation function: starting from appropriate measurements of the return-stroke speed, the channel-base current, the channel height and the radiated electromagnetic field, we first formulate an algebraic inverse and ill-posed problem, obtained from the discretization of integral equations relating the source to the radiated field in the frequency domain, and then we solve it by means of a Tikhonov regularization technique. The proposed framework is preceded by a detailed theoretical analysis, with special emphasis on the description and filtering of measurement noise and on the minimum duration of the measurement time-windows ensuring reliable results.

Polarity Asymmetry in Lightning Return Stroke Speed Caused by the Momentum Associated with Radiation

In positive lightning return strokes, the net momentum transported by the radiation field has the same direction as the momentum associated with electrons, whereas the momentum associated with electrons is in opposite direction to the momentum of radiation in negative return strokes. It is shown here that this polarity asymmetry could limit the maximum speed of positive return strokes with respect to the negative return strokes.

Effects of Long Upward Connecting Leader Channel on Electromagnetic Fields for Lightning Striking to Tall Towers

The effects of long upward connecting leader (UCL) channel on electromagnetic fields for lightning striking to tall towers are studied via lightning transmission-line return-stroke model. The current distributions along the lightning channel and the tower are derived, and the resultant lightning electromagnetic fields with various UCL lengths above tower are calculated at close and far distances. It can be found that the contribution of the various components of the electric and magnetic fields depends strongly on the distance to the observation point. Electric field has a shading effect showing that the field amplitude generated by lightning striking to tall towers is smaller than that to ground, and that this shading effect depends on the UCL length and the tower height. However, we cannot find such an effect for the magnetic field. The shading effect of the electric field increases with the increase of the junction height above tower, but disappears when the observation distance exceeds a critical distance. Modeled results are also compared with their measured counterparts associated with lightning striking to the 600 m tall Canton Tower. The proposed model can explain why the ratios of peaks of luminosity to magnetic field of the downward first stroke are considerably larger than those of the subsequent strokes as being due to the fact that the junction height above tower for first stroke is higher than that for subsequent stroke, whereas the downward return stroke speed of first stroke is smaller than that of subsequent stroke.

Parameters Affecting the Polarity Inversion of the Vertical Electric Lightning Field to the CN-Tower

The aim of this paper is to perform a parametric study in order to analyze factors having an effect on the vertical lightning field polarization to the CN-Tower in Canada, and estimate with numerical simulation, the horizontal distance for which the reversed polarity will occur. The calculation is performed using the Finite-Difference-Time-Domain technique in two dimensions (2D-FDTD), the spatial-temporal current propagation through the lightning channel and through the high structure is represented by the lumped-series voltage-source model. The obtained results show that the vertical electric lightning field behavior has a dual polarity, the transition from a negative waveform to a positive one is observed at different observation points localized near the elevated object influencing by each modification made to the tower-parameters, the medium conductivity and the return stroke speed value. These results can contribute to the understanding of the lightning-phenomenon and allow to solve the problems of electromagnetic compatibility.

Modified Transmission Line Model with a Current Attenuation Function Derived from the Lightning Radiation Field—MTLD Model

In return strokes, the parameters that can be measured are the channel base current and the return stroke speed. For this reason, many return stroke models have been developed with these two parameters, among others, as inputs. Here, we concentrate on the current propagation type engineering return stroke models where the return stroke is represented by a current pulse propagating upwards along the leader channel. In the current propagation type return stroke models, in addition to the channel base current and the return stroke speed, the way in which the return stroke current attenuates along the return stroke channel is specified as an input parameter. The goal of this paper is to show that, within the confines of current propagation type models, once the channel base current and the return stroke speed are known, the measured radiation field can be used to evaluate how the return stroke current attenuates along the channel. After giving the mathematics necessary for this inverse transformation, the procedure is illustrated by extracting the current attenuation curve from the typical wave shape of the return stroke current and from the distant radiation field of subsequent return strokes. The derived attenuation curve is used to evaluate both the subsequent and first return stroke electromagnetic fields at different distances. It is shown that all the experimentally observed features can be reproduced by the derived attenuation curve, except for the subsidiary peak and long zero-crossing times. In order to obtain electromagnetic fields of subsequent return strokes that are in agreement with measurements, one has to incorporate the current dispersion into the model. In the case of first return strokes, both current dispersion and reduction in return stroke speed with height are needed to obtain the desired features.

The Energy, Momentum, and Peak Power Radiated by Negative Lightning Return Strokes

Electromagnetic radiation fields generated by return strokes transport both energy and momentum from the return stroke to outer space. The momentum transported by the radiation field has only a vertical or z component due to azimuthal symmetry (cylindrical symmetry) associated with a vertical return stroke. In this paper, the energy, momentum, and peak power radiated by return strokes as a function of the return stroke current, return stroke speed, and the zero-crossing time of the radiation fields are studied. The results obtained by numerical simulations for the energy, vertical momentum, and the peak power radiated by lightning return strokes (all parameters normalized by dividing them by the square of the radiation field peak at 100 km) are the following: A typical first return stroke generating a radiation field having a 50 μs zero-crossing time will dissipate field normalized energy of about (1.7–2.5) × 103 J/(V/m)2 and field-normalized vertical momentum of approximately (2.3–3.1) × 10−6 Kg m/s/(V/m)2. A radiation field with a zero-crossing time of 70 μs will dissipate about (2.6–3.4) × 103 J/(V/m)2 in field-normalized energy and (3.2–4.3) × 10−6 Kg m/s/(V/m)2 in field-normalized vertical momentum. The results show that, for a given peak radiation field, the radiated energy and momentum increase with increasing zero-crossing time of the radiation field. The normalized peak power generated by a first return stroke radiation field is about 1.2 × 108 W/(V/m)2 and the peak power is generated within about 5–6 μs from the beginning of the return stroke. Conversely, a typical subsequent return stroke generating a radiation field having a 40 μs zero-crossing time will dissipate field-normalized energy of about (6–9) × 102 J/(V/m)2 and field-normalized vertical momentum of approximately (7.5–11) × 10−7 Kg m/s/(V/m)2. The field-normalized peak power generated by a subsequent return stroke radiation field is about 1.26 × 108 W/(V/m)2 and the peak power is generated within about 0.7–0.8 μs from the beginning of the return stroke. In addition to these parameters, the possible upper bounds for the energy and momentum radiated by return strokes are also presented.

On the return-stroke current estimation of Foshan Total Lightning Location System (FTLLS)

Return-stroke current and electric field play important roles in atmospheric electricity research. Aim of this paper is to examine the empirical formulas for calculating return-stroke peak-current in lightning location system according to sensored peak-electric-field, and to evaluate the detection efficiencies and the peak-current estimation of the Foshan Total Lightning Location System (FTLLS). Lightning was initiated artificially by rocket triggering procedure and the current waveform was recorded at the lightning channel-base. A total of 43 return-strokes in 8 flashes were triggered succesfully in 2014. Nine different regression formulas providing the best fit to the measured current-and-field data were derived. The empirical formulas were based on the directly measured return-stroke current and electric fields of 38 return-strokes within 4 flashes. The empirical formulas analyzed in the present study demonstrate the regional difference of the empirical formulas for various geographical-distributed stations of the FTLLS in Foshan, China. On the other hand, the return-stroke speeds were theoretically derived though the transmission line model considering the already known parameters of the corresponding measured-peak-current at triggering lightning site. The nine empirical formulas from the nine stations of the FTLLS were analyzed by the fact that the values of the inferred return-stroke speeds for each return-stroke and for each station are reasonable compared to those in the previous literatures. In addition, the detection efficiencies and peak-current estimation of the FTLLS and the LLS of Guangdong power grid in Guangdong Province were examined and were compared based on the directly measured current data at the triggering lightning site. It is shown that the detection efficiencies of the FTLLS for flashes and for return-strokes were 87.5% (7/8) and 93.0% (40/43), respectively. The peak-current estimation error reported by the FTLLS was 8% on average. The absolute value of the maximum error for the individual return-strokes were around 28%. Performance comparison to other global/regional lightning location systems are also presented.

The Propagation Effects of Lightning Electromagnetic Fields Over Mountainous Terrain in the Earth-Ionosphere Waveguide.

In this paper, a full‐wave two‐dimensional Finite‐Difference‐Time‐Domain model is developed to evaluate the propagation effects of lightning electromagnetic fields over mountainous terrain in the Earth‐ionosphere waveguide. In the model, we investigate the effect of the Earth‐ionosphere waveguide structure and medium parameters, including the effect of the ionospheric cold plasma characteristics, the effect of the Earth curvature, and the propagation effects over mountainous terrain. For the first time, the obtained results are validated against simultaneous experimental data consisting of lightning currents measured at the Säntis Tower and electric fields measured in Neudorf, Austria, located at 380‐km distance from the tower. It is shown that both the time delays and amplitudes of the lightning electromagnetic fields at 380‐km distance can be strongly affected by the ionospheric electron density profile, the mountainous terrain, and the Earth curvature. After taking into account the effect of the irregular terrain between the Säntis Tower and the field measurement station, the vertical electric fields calculated by using our model are found to be in good agreement with the corresponding measured cases occurred in both daytime and nighttime. The ideal approximation used in either the classical solutions or the simplified models might lead to inaccuracies in the estimated reflection height. Furthermore, we discuss the sensitivity of our results by considering different return stroke models, as well as different typical values of the return stroke speed and of the ground conductivity.

Evaluation of Horizontal Electric Field from the Lightning Channel by Electromagnetic Field Equations of Moving Charges

The horizontal electric field from the lightning return-stroke channel is evaluated by the electromagnetic field equations of moving charges in this paper. When a lightning flash strikes the ground, the charges move upward the lightning channel at the return-stroke speed, thereby producing the electromagnetic fields. According to the electromagnetic field equations of moving charges, the detained charges, uniformly moving charges, and decelerating (or accelerating) charges in each segment of the channel generate electrostatic fields, velocity fields, and radiation fields, respectively. The horizontal component of the sum is the horizontal electric field over the perfectly conducting ground. For the real soil with finite conductivity, the Wait formula is used here for the evaluation of the horizontal electric field over the realistic soil. The proposed method can avoid the oscillation of the fields in the long distance by the FDTD method and the singularity problem of the integral equation by the Sommerfeld integral method. The influences of the return-stroke speed, distance, and soil conductivity on the horizontal electric field are also analyzed by the proposed method. The conclusions can be drawn that the horizontal electric field decreases with the increasing of the return-stroke speed; the negative offset increases with the increasing of horizontal distance and with the decreasing of the soil conductivity, thereby forming the bipolar waveform. These conclusions will be practically valuable for the protection of lightning-induced overvoltage on the transmission lines.

On the Variation of Optical Return Stroke Speed Along the Bottom of Lightning Channel

In cloud-to-ground lightning flash, a varying return stroke speed during the propagation process along the lightning channel has been extensively reported. It is also reported that as the return stroke propagates upward, the waveform will be distorted, resulting in an increase in the rise time of waveform and a decrease in the magnitude. In this paper, we artificially generate the optical signal simulating the distortion along the lightning channel bottom 60 m. Using six slope-intercept methods and five percentage-of-peak methods, we analyze the influence of height-dependent distortion of the return stroke on the estimated optical return stroke speed. We show that the percentage-of-peak methods tend to underestimate the speeds, and that the slope-intercept methods, in general, but not always, first underestimate the actual speeds, and then overestimate them as the return stroke propagates upward. The deviations are more pronounced for higher actual return stroke speeds. Moreover, for an assumed constant actual return stroke speed, the estimated return stroke speeds by various methods increase with increasing heights in the channel bottom, although the increasing trends become weaker as the height increases. This artificial increase is observed from the estimated two-dimensional propagation speeds of return strokes along the lightning channel bottom 60 m in rocket-triggered lightning.

Analysis of a bipolar upward lightning flash based on simultaneous records of currents and 380-km distant electric fields

In this paper, we present and discuss simultaneous records of current and wideband electric field waveforms at 380 km distance from the strike point associated with an upward bipolar flash initiated from the Säntis Tower. The flash contains 23 negative strokes and one positive stroke. The intervals between the groundwave and skywave arrival times are used to estimate ionospheric reflection heights for the negative return strokes using the so-called zero-to-zero and peak-to-peak methods. A full-wave, finite-difference time-domain (FDTD) analysis of the electric field propagation including the effect of the ionospheric reflections is also presented. FDTD simulation results are compared with the measured radiated electric field associated with the studied flash to evaluate the reference reflection height of the conductivity profile. It is also found that the ratio of the peak field to the current peak is about two times smaller for the positive pulse compared to negative pulses. This difference in the amplitudes can be attributed to a lower return stroke speed for the positive stroke compared to that for negative strokes, and also to the fact that the enhancement of the electric field due to the presence of the tower and the mountain might be more significant for negative pulses, which are characterized by faster risetimes compared to the positive one.

Apparent Lightning Return Stroke Speed and the Correction

A varying return-stroke speed during the propagation process along the lightning channel is extensively reported. In this paper, we found, due to the propagation time difference of the emitted light by lightning in the propagation path from the lightning channel to the optical observation point, even in the case of an assumed constant return-stroke speed, the observed speed, termed as the apparent return-stroke speed, is not constant. For conventional return-stroke engineering models that the return stroke is assumed to propagate from the ground, we investigated the influence of the observation distance, the observation altitude, and the assumed value of the return-stroke speed on the variation trend of the apparent speed. In addition, the deviation of the apparent speed from its actual value is compared for the concerned influencing factors. The need of propagation time correction in obtaining the characteristics of return stroke propagation from the time-resolved optical records is emphasized here.

Observed Variation of Three‐Dimensional Return Stroke Speeds Along the Channel in Rocket‐Triggered Lightning

AbstractAn improved very high frequency location system, multiple antenna radiation continuous observation system (MARCOS), is combined with high‐speed video observation to explore radiation source evolution during return stroke (RS) stages in triggered lightning. A three‐dimensional (3‐D) channel reconstruction is performed for speed measurement of the RS processes. The 3‐D average speeds for the two selected strokes (RS1 and RS3) over the bottom channel within 1 km are 9.24 × 107 m/s and 1.07 × 108 m/s, respectively. The high temporal‐spatial resolution of MARCOS permits thorough examination of the speed variation. Our observation shows that the 3‐D RS speeds of both RS1 and RS3 are increased initially with height for the first several hundred meters, maximized, and then decreased with height. To the best of our knowledge, this is the first evidence regarding nonmonotonic 3‐D RS speed variation in triggered lightning.

Modeling of artificially triggered lightning currents by multi-peaked analytically extended functions

PurposeThis paper aims to present the approximation of lightning currents waveshapes by the multi-peaked analytically extended function (MP-AEF) for the experimentally measured channel-base currents in the artificially triggered lightning discharges. Modified transmission line model of lightning return strokes having the channel current both linearly decaying and sinusoidally changing with height (MTLSIN) is used to calculate the lightning electromagnetic field.Design/methodology/approachMP-AEF’s parameters for the artificially triggered lightning channel-base currents are calculated by using Marquardt least squares method (MLSM). Lightning electromagnetic fields are calculated based on electromagnetic theory relations, thin-wire antenna model of the vertical lightning channel and the assumption of the perfectly conducting ground. MTLSIN model as an engineering model of lightning strokes is used to obtain the electric field results as these are simultaneously measured in rocket-triggered lightning experiments together with the channel-base currents.FindingsMP-AEF approximates multi-peaked pulse waveshapes. Some important function parameters are chosen prior to the approximation procedure, such as current peaks and the corresponding time moments of those peaks, which presents an advantage in comparison to other functions. The desired accuracy of approximation is obtained by choosing an adequate number of function terms. MLSM is used for the estimation of unknown parameters. Using MTLSIN model, the influence of the channel height and return stroke speed on the lightning electromagnetic field waveshape is analyzed in this paper.Research limitations/implicationsMP-AEF may be used for approximation of various multi-peaked waveshapes. It has no errors in the points of maxima which is important for the lightning protection systems design. MTLSIN model may be validated by using simultaneously measured lightning electromagnetic fields at various distances from the channel and for channel heights estimated in the experiments. It is also possible to approximate measured current derivatives by MP-AEF and use them for further computation.Originality/valueMTLSIN model is proposed in this paper for the evaluation of lightning electromagnetic fields induced by artificially triggered lightning discharges. The procedure is based on the approximation of lightning channel-base currents by the multi-peaked analytically extended function previously proposed by the authors. This function may be used not only for representing lightning currents but also for other waveshapes as current derivatives, electric and magnetic fields and their derivatives, which are all important for the lightning protection design. MTLSIN gives lightning electromagnetic fields results which are in better agreement with measured fields than those obtained by other models from literature.

Modeling of Return Strokes With Their Initiation Processes Under Consideration

We developed an engineering return-stroke model specifically for studying the effects of return-stroke initiation processes. In the model, two current waves with identical wave shapes propagate upward and downward at two independent speeds from a height-variable return-stroke initiation point. Using that model and several results recently observed on the lightning return-stroke initiation processes, we have studied the electromagnetic fields produced by a return stroke at a horizontal distance from the strike termination point. It is shown that, depending on the front steepness of the current waveform, the presence of the downward return-stroke current wave may result in a visible initial peak in the rising portion of the return-stroke-produced field waveforms. A larger initiation height appears to result in an initial field peak with a larger amplitude, and also longer duration time. Moreover, a larger downward return-stroke speed tends to produce a sharper initial field peak.

Three‐Dimensional Reconstruction of Cloud‐to‐Ground Lightning Using High‐Speed Video and VHF Broadband Interferometer

AbstractThe time resolved three‐dimensional (3‐D) spatial reconstruction of lightning channels using high‐speed video (HSV) images and VHF broadband interferometer (BITF) data is first presented in this paper. Because VHF and optical radiations in step formation process occur with time separation no more than 1 μs, the observation data of BITF and HSV at two different sites provide the possibility of reconstructing the time resolved 3‐D channel of lightning. With the proposed procedures for 3‐D reconstruction of leader channels, dart leaders as well as stepped leaders with complex multiple branches can be well reconstructed. The differences between 2‐D speeds and 3‐D speeds of leader channels are analyzed by comparing the development of leader channels in 2‐D and 3‐D space. Since return stroke (RS) usually follows the path of previous leader channels, the 3‐D speeds of the return strokes are first estimated by combination with the 3‐D structure of the preceding leaders and HSV image sequences. For the fourth RS, the ratios of the 3‐D to 2‐D RS speeds increase with height, and the largest ratio of the 3‐D to 2‐D return stroke speeds can reach 2.03, which is larger than the result of triggered lightning reported by Idone. Since BITF can detect lightning radiation in a 360° view, correlated BITF and HSV observations increase the 3‐D detection probability than dual‐station HSV observations, which is helpful to obtain more events and deeper understanding of the lightning process.

A leader‐return‐stroke consistent macroscopic model for calculations of return stroke current and its optical and electromagnetic emissions

AbstractA downward lightning flash usually starts with a downward leader and an upward connecting leader followed by an upward return stroke. It is the preceding leader that governs the following return stroke property. Besides, the return stroke property evolves with height and time. These two aspects, however, are not well addressed in most existing return stroke models. In this paper, we present a leader‐return stroke consistent model based on the time domain electric field integral equation, which is a growth and modification of Kumar's macroscopic model. The model is further extended to simulate the optical and electromagnetic emissions of a return stroke by introducing a set of equations relating the return stroke current and conductance to the optical and electromagnetic emissions. With a presumed leader initiation potential, the model can then simulate the temporal and spatial evolution of the current, charge transfer, channel size, and conductance of the return stroke, furthermore the optical and electromagnetic emissions. The model is tested with different leader initiation potentials ranging from −10 to −140 MV, resulting in different return stroke current peaks ranging from 2.6 to 209 kA with different return stroke speed peaks ranging from 0.2 to 0.8 speed of light and different optical power peaks ranging from 4.76 to 248 MW/m. The larger of the leader initiation potential, the larger of the return stroke current and speed. Both the return stroke current and speed attenuate exponentially as it propagates upward. All these results are qualitatively consistent with those reported in the literature.

Effect of Shield Wires on the Lightning-Induced Currents on Buried Cables

The effect of a shield wire, which is a bare conductor buried above an insulated metallic cable, on lightning-induced currents on the cable has been studied using the three-dimensional (3-D) finite-difference time-domain (FDTD) method. In the 3-D FDTD model, a 1-km-long insulated cable is buried at depth 0.6 m in 1850-Ω·m ground, and a 1-km-long shield wire is installed 0.3 m above the cable (at the depth 0.3 m from the ground surface). A 1-km-long vertical lightning return-stroke channel, attached to a 30-m-high tower or flat ground, is located 25 m away from the cable and the shield wire. The validity of this model has been shown by comparing the FDTD-computed lightning-associated currents on the cable and the shield wire with the corresponding measured currents associated with rocket-triggered lightning. The FDTD-computed results show that the presence of the shield wire reduces the induced current on the cable and the voltage across the outer insulation layer of the cable, as expected, but the series resistance of the shield wire has a negligible effect on this reduction. The presence of 30-m-high strike object slightly reduces the cable current. The ground permittivity and the return-stroke speed have negligible effects on the cable current, but the higher the ground resistivity, the higher is the cable current. The increase of bonding points between the cable sheath and the shield wire increases the cable current, but decreases the voltage across the outer insulation layer of the cable.