Return Stroke Peak Current Research Articles

負極性下向きステップトリーダの継続時間と第一帰還雷撃の電流波高値との相関

負極性下向きステップトリーダの継続時間と第一帰還雷撃の電流波高値との相関

A review of advances in lightning observations during the past decade in Guangdong, China

This paper reviews recent advances in understanding the physical processes of artificially triggered lightning and natural lightning as well as the progress in testing lightning protection technologies, based on a series of lightning field campaigns jointly conducted by the Chinese Academy of Meteorological Sciences and Guangdong Meteorological Bureau since 2006. During the decade-long series of lightning field experiments, the technology of rocket-wire artificially triggered lightning has been improved, and has successfully triggered 94 lightning flashes. Through direct lightning current waveform measurements, an average return stroke peak current of 16 kA was obtained. The phenomenon that the downward leader connects to the lateral surface of the upward leader in the attachment process was discovered, and the speed of the upward leader during the connection process being significantly greater than that of the downward leader was revealed. The characteristics of several return strokes in cloud-to-ground lighting have also been unveiled, and the mechanism causing damage to lightning protection devices (i.e., ground potential rise within the rated current) was established. The performance of three lightning monitoring systems in Guangdong Province has also been quantitatively assessed.

Stroke multiplicity and horizontal scale of negative charge regions in thunderclouds

AbstractAn X‐band polarimetric radar and multiple lightning detection systems are used to document the initial cloud‐to‐ground lightning flash in a large number (46 cases) of incipient thunderstorms, as part of the CHUVA‐Vale field campaign during the 2011/2012 spring‐summer in southeast Brazil. The results show an exceptionally low stroke multiplicity (87% of flashes with single stroke) in the initial ground flashes, a finding consistent with the limited space available for the positive leader extension into new regions of negative space charge in compact cells. The results here are contrasted with the behavior of ground flashes in mesoscale thunderstorms in previous studies. Additionally, we found evidence for a minimum scale (radar echo >20 dBZ) for lightning initiation (>3 km in radius) and that the peak currents of initial cloud‐to‐ground flashes in these compact thunderstorms are only half as large as return stroke peak currents in general.

A unified engineering model of the first stroke in downward negative lightning

AbstractEach stroke in a negative cloud‐to‐ground lightning flash is composed of downward leader and upward return stroke processes, which are usually modeled individually. The first stroke leader is stepped and starts with preliminary breakdown (PB) which is often viewed as a separate process. We present the first unified engineering model for computing the electric field produced by a sequence of PB, stepped leader, and return stroke processes, serving to transport negative charge to ground. We assume that a negatively charged channel extends downward in a stepped fashion during both the PB and leader stages. Each step involves a current wave that propagates upward along the newly formed channel section. Once the leader attaches to ground, an upward propagating return stroke neutralizes the charge deposited along the channel. Model‐predicted electric fields are in reasonably good agreement with simultaneous measurements at both near (hundreds of meters, electrostatic field component is dominant) and far (tens of kilometers, radiation field component is dominant) distances from the lightning channel. Relations between the features of computed electric field waveforms and model input parameters are examined. It appears that peak currents associated with PB pulses are similar to return stroke peak currents, and the observed variation of electric radiation field peaks produced by leader steps at different heights above ground is influenced by the ground corona space charge.

A terrestrial gamma-ray flash recorded at the Lightning Observatory in Gainesville, Florida

A terrestrial gamma-ray flash (TGF) observed at ground level is presented. It was recorded at the Lightning Observatory in Gainesville, Florida, on June 13, 2014. Ground-based observations of TGFs are very rare. To date, only two positively identified ones are found in the literature. Our TGF was associated with a single-stroke negative cloud-to-ground discharge. It had a duration of 16μs and consisted of 6 pulses, two of which exceeded the upper measurement limit of 5.7MeV. The pulses apparently corresponded to individual photons, which is a characteristic feature of TGFs. The TGF began 191μs after the return-stroke electric field peak. The stepped leader duration was as short as 3.9ms. There was essentially no energetic radiation detected during the leader process. The NLDN-reported return-stroke peak current was as high as 224kA. The characteristics and occurrence context of the LOG-recorded TGF are compared to those of the two similar events found in the literature. In all three cases there was evidence of a channel carrying appreciable current to ground at the time of TGF, and the associated (preceding or concurrent) cloud-to-ground discharge processes were unusually intense.

Lightning current and luminosity at and above channel bottom for return strokes and M‐components

We measured current and luminosity at the channel bottom of 12 triggered lightning discharges including 44 return strokes, 23 M-components, and 1 initial continuous current pulse. Combined current and luminosity data for impulse currents span a 10–90% risetime range from 0.15 to 192 µs. Current risetime and luminosity risetime at the channel bottom are roughly linearly correlated (τr,I = 0.71τr,L1.08). We observed a time delay between current and the resultant luminosity at the channel bottom, both measured at 20% of peak amplitude, that is approximately linearly related to both the luminosity 10–90% risetime (Δt20,b = 0.24τr,L1.12) and the current 10–90% risetime (Δt20,b = 0.35τr,I1.03). At the channel bottom, the peak current is roughly proportional to the square root of the peak luminosity (IP = 21.89LP0.57) over the full range of current and luminosity risetimes. For two return strokes we provide measurements of stroke luminosity vs. time for 11 increasing heights to 115 m altitude. We assume that measurements above the channel bottom behave similarly to those at the bottom and find that (1) one return stroke current peak decayed at 115 m to about 47% of its peak value at channel bottom, while the luminosity peak at 115 m decayed to about 20%, and for the second stroke 38% and 12%, respectively; and (2) measured upward return stroke luminosity speeds of the two strokes of 1.10 × 108 and 9.7 × 107 ms−1 correspond to current speeds about 30% faster. These results represent the first determination of return stroke current speed and current peak value above ground derived from measured return stroke luminosity data.

A study of changes in apparent ionospheric reflection height within individual lightning flashes

Ionospheric reflection heights estimated using the zero-to-zero and peak-to-peak methods to measure skywave delay relative to the ground wave were compared for 108 first and 124 subsequent strokes at distances greater than 100km. For either metric there was a considerable decrease in average reflection height for subsequent strokes relative to first strokes. We showed that the observed difference cannot be explained by the difference in frequency content of first and subsequent return-stroke currents. Apparent changes in reflection height (estimated using the peak-to-peak method) within individual flashes for 54 daytime and 11 nighttime events at distances ranging from 50km to 330km were compared, and significant differences were found. For daytime conditions, the majority of the flashes showed either decrease (57%) or non-monotonic variation (39%) in reflection height with respect to the immediately preceding stroke. With respect to the first stroke, 91% of the flashes showed monotonic decrease in height. For nighttime flashes, patterns in reflection height changes with respect to the immediately preceding stroke were as follows: 46% no change, 27% monotonic decrease, and 27% non-monotonic variation. When changes were measured with respect to the first stroke, 54% of nighttime flashes showed monotonic decrease and 46% no change. Ionospheric reflection height tends to increase with return-stroke peak current. The observed daytime effects can be explained by (a) the dependence of EMP penetration depth on source intensity, which decreases with stroke order, (b) additional ionization associated with elves, or (c) combination of (a) and (b) above.

Characterization of negative cloud-to-ground lightning in Florida

We examined characteristics of negative cloud-to-ground lightning flashes using their electric field waveforms acquired at the Lightning Observatory in Gainesville (LOG), Florida in the summers of 2013 and 2014. Flash multiplicity, interstroke interval, flash duration, and first to subsequent stroke field peak ratio are determined for 478 flashes containing 2188 strokes and compared with previous results obtained in Florida and in other regions. We found that the average number of strokes per flash is 4.6 and the percentage of single-stroke flash is 12%. The geometric means of interstroke interval, flash duration, and first to subsequent stroke field peak ratio are 52ms, 223ms, and 2.4, respectively. About one-third (34%) of multiple-stroke flashes have at least one subsequent stroke whose field peak is greater than that of the first stroke. The geometric mean of normalized electric field peak shows a relatively weak tendency to decrease with increasing stroke order. We also found that the detectability of preliminary breakdown (PB) pulse train is affected by the signal/noise ratio, type of storm, peak current and distance. For 222 PB pulse trains, statistics on pulse duration, time interval between PB pulse train and return stroke (PB–RS interval), and PB–RS field peak ratio (PB/RS ratio) are presented. Very short PB–RS (≤6ms) intervals were observed to be associated with very high return-stroke peak currents and stepped-leader speeds.

Electric field derivative waveforms from dart-stepped-leader steps in triggered lightning

Electric field derivative (dE/dt) pulse waveforms from dart-stepped-leaders in rocket-and-wire triggered lightning, recorded a distance of 226 m from the channel base, are characterized. A single dE/dt pulse associated with a leader step consists of a fast initial rise of the same polarity as the following return stroke followed by an opposite polarity overshoot of smaller amplitude and subsequent decay to background level, without superimposed secondary pulses. A “slow front” often precedes the fast initial rise. For 47 single dE/dt leader pulses occurring during the final 15 µs of 24 dart-stepped-leaders, the pulse mean half-peak width was 76 ns, mean 10-to-90% risetime 73 ns, and mean range-normalized peak amplitude 2.5 V/m/µs. For integrated dE/dt, the mean half-peak width was 214 ns and the mean range-normalized peak amplitude 0.21 V/m. Most dart-stepped-leader dE/dt pulses are more complex than a single pulse. Interpulse interval and average peak amplitude range normalized to 100 km were measured for both single and complex dE/dt pulses during the final 15 µs of 10 dart-stepped-leaders preceding triggered return strokes with peak currents ranging from 8.1 to 31.4 kA. The average range-normalized dE/dt and numerically integrated dE/dt (electric field) peak amplitude increased from 0.9 to 4.9 V/m/µs and 0.13 to 0.47 V/m, respectively, with increasing return stroke peak current while the interpulse interval remained relatively constant at about 2 µs. Strong positive linear correlations were found between both average range-normalized peak pulse amplitude and interstroke interval versus the following return stroke peak current.

Rocket‐and‐wire triggered lightning in 2012 tropical storm Debby in the absence of natural lightning

AbstractLightning Mapping Array source locations, channel base currents, and electric field waveforms are presented for a lightning flash triggered in the rainbands of 2012 tropical storm Debby. The National Lightning Detection Network reported no natural cloud‐to‐ground discharges within 60 km of the North Florida triggering site for at least 20 h before and 8 h after the triggered flash. Additionally, local electric field mill and wideband antenna networks show no close cloud or cloud‐to‐ground flashes. The triggering rocket was launched with negative charge overhead producing an electric field at the ground of 5 kV m−1 and in coordination with X‐band, dual‐polarimetric radar observations of streamers of enhanced precipitation descending from the melting level as they approached the site. The Debby flash consisted of an initial stage (IS) followed by eleven leader/return stroke sequences. The flash exhibited all the processes of normal triggered and natural cloud‐to‐ground lightning: leader/return stroke sequences, continuing currents, K events, and M components. Additionally, the flash exhibited several exceptional characteristics: three return stroke peak currents greater than 25 kA, one very long, 352 ms, continuing current that transferred about 35 C of charge to ground, and a relatively short, 202 ms, IS containing no initial continuous current pulses. Following a near‐vertical upward positive leader attaining 2.8 km height, the IS branched and propagated horizontally at 3.5 km altitude. The flash, exhibiting strokes and continuing current, then ascended to and propagated horizontally at 5.5 km, extending about 25 km south and 15 km east. The 0°C level was near 4.5 km above sea level. It follows from the above that clouds that are not producing natural lightning can represent a triggered lightning hazard to launch vehicles and aircraft.

Power and energy dissipation in negative lightning return strokes

In this paper the temporal variation of the electric field along the negative return stroke channel is calculated and this information in turn is used to evaluate the power and energy dissipation in negative return strokes. Moreover, by plugging in the results obtained here with the spark equation of Braginski, the temporal and spatial variations of the return stroke speed, the radius and the resistance of the return stroke channel were investigated. The results of the study showed that for a typical subsequent return stroke current pulse having a peak current of 12kA in the return stroke channel: (a) The peak power dissipation is about 4×109W/m; (ii) the energy dissipation over the first 70μs or so is about (2–3)×103J/m; (iii) the maximum channel radius is about 1cm; and (iv) the resistance of the channel is about 0.5Ω/m. The study also revealed that the speed of the return stroke is governed not only by the peak current, but also by the risetime of the current. The study shows that the speed of the return stroke increases with increasing peak current but it decreases with increasing current risetime. The results obtained using available experimental data on first return strokes indicate that the risetime of the return stroke current increases with increasing peak current. It is shown that this tendency for the first return stroke current risetime to increase with return stroke peak current could completely mask the relationship between the first return stroke speed and return stroke peak current. It is suggested that the apparent absence of such a relationship in experimental data is caused by these variations.

A 3-D Self-Organized Leader Propagation Model and Its Engineering Approximation for Lightning Protection Analysis

This paper presents a 3-D self-organized model of a downward stepped leader in negative cloud-to-ground lightning. In the model, the characteristic features of stepped leaders are generalized, so that parameters, such as the charge density along with the leader channel, leader corona sheath radius, leader step length, step time interval, and step advance speed, are calculated. Stepwise growth of the 3-D leader channel is developed stochastically. Parameters predicted by the model are qualitatively compatible with observation results, while the engineering approximation of the model for convenient lightning protection analysis is derived thereafter. The model is operated under various conditions at different leader initiation heights and electric potentials. Based on statistics of the simulation results, analytical relationships between the height and potential of leader initiation in the cloud and the charge distribution along the leader channel are approximated. Moreover, the lightning striking distance to flat ground is defined and calculated. Depending on the present model, the striking distance is found to be well associated with the charge density (or electrical potential) of the leader tip near to ground rather than the total charge in the leader channel. Based on appropriate physical understanding, the striking distance is connected to the return stroke peak current.

Locating initial breakdown pulses using electric field change network

Initial breakdown pulses (IBPs) observed in the fast electric field change (E‐change) at the beginning of intracloud (IC) and cloud‐to‐ground (CG) lightning flashes are located using a time‐of‐arrival technique called Position By Fast Antenna (PBFA) with data from a network of 10 E‐change sensors located at Kennedy Space Center. Location errors, estimated using a Monte Carlo method, are usually less than 100 m for horizontal coordinates and several hundreds of meters for altitude, depending on distance to the sensors and altitude of the source. Comparison of PBFA source locations to locations from a VHF lightning mapping system (Lightning Detection and Ranging II (LDAR2)) shows that PBFA locates most of the “classic” IBPs while LDAR2 locates only a few percent of them. As the flash develops during the IB stage, PBFA and LDAR2 obtain similar locations when they detect the same IBPs. The overall vertical motion indicated by the PBFA positions of IBPs was downward with time for CG flashes and upward with time for IC flashes. Location of the fast pulses due to return strokes of CG flashes is also determined using PBFA. Comparison to locations from the Cloud‐to‐Ground Lightning Surveillance System (CGLSS) shows that PBFA reliably locates ground strokes. These results are verified using ground truth data acquired with a high‐speed video camera. After cross calibration with the CGLSS data set, peak currents of return strokes are also determined.

High-speed video observations of natural cloud-to-ground lightning leaders – A statistical analysis

The aim of this investigation is to analyze the phenomenology of positive and negative (stepped and dart) leaders observed in natural lightning from digital high-speed video recordings. For that intent we have used four different high-speed cameras operating at frame rates ranging from 1000 or 11,800 frames per second in addition to data from lightning locating systems (BrasilDat and NLDN). All the recordings were GPS time-stamped in order to avoid ambiguities in the analysis, allowing us to estimate the peak current of and the distance to each flash that was detected by one of the lightning locating systems. The data collection was done at different sites in south and southeastern of Brazil, southern Arizona and South Dakota, USA. A total of 62 negative stepped leaders, 76 negative dart leaders and 29 positive leaders were recorded and analyzed. From these data it was possible to calculate the two-dimensional speed of each observed leader, allowing us to obtain its statistical distribution and evaluate whether or not it is related to other characteristics of the associated flash. In the analyzed dataset, the speeds of positive leaders and negative dart leaders follow a lognormal distribution at the 0.05 level (according to the Shapiro–Wilk test). We have also analyzed how the two-dimensional leader speeds change as they approach ground through two different methodologies. The speed of positive leaders showed a clear tendency to increase while negative dart leaders tend to become slower as they approach ground. Negative stepped leaders, on the other hand, can either accelerate as they get closer to ground or present an irregular development (with no clear tendency) throughout their entire development. For all the three leader types no correlation has been found between the return stroke peak current and the average speed of the leader responsible for its initiation. We did find, however, that dart leaders preceded by longer interstroke intervals cannot present speeds of the order of 107ms−1. Finally, we have analyzed the impact of recoil activity during positive leaders over their average speed and the return stroke peak current. Even though the analysis considering the leader speed was not conclusive it was possible to show that there is no apparent minimum or maximum peak current value for return strokes preceded by leaders with or without recoil activity (considering the most common range of values in literature, 20–80kA).

Correlation analysis between the channel current and luminosity of initial continuous and continuing current processes in an artificially triggered lightning flash

Using simultaneous high-speed camera records and channel-base current records in an artificially triggered negative lightning event, the correlation between the channel-base current and the integrated luminosity (IL) of the air-ionized part of the lightning channel is analyzed during the periods of the initial continuous current (ICC) process and eight continuing current (CC) processes. Depending on the current's changing trend (ascending or descending) and the luminosity property of the pixels used to calculate the IL from the high-speed camera records (including saturated pixels or not), the ICC and eight CC processes are divided into the saturated ascending stage (Stage-A), the saturated descending stage (Stage-B), the unsaturated ascending stage (Stage-C) and the unsaturated descending stage (Stage-D), including the descending tail stage (Stage-T, in which the channel-base current falls to zero). The analysis shows the following: (1) the IL is linearly correlated with the logarithmic value of the current in both Stage-A and Stage-B of two long CC processes, the ICC process and the CC process after the 7th return stroke, although the regression parameters (intercept and slope) in Stage-B are higher than those in Stage-A. This rule can also be found in most pulses of the long CC processes, where the IL in the descending stage is higher than that in the ascending stage at the same current value, regardless of which threshold index or height range used to calculate the IL are selected and regardless of whether the IL includes saturated pixels or not. (2) In the unsaturated stage of long CC processes, the channel current shows a significant linear correlation with the square root of the IL, and the fit of this relationship is much better than that in the saturated stage. Additionally, in each Stage-T of the eight CC processes following return strokes, the square root of the IL is significantly and linearly correlated with the current, and the regression slope is negatively correlated with the corresponding return stroke peak current. This result means that for the same channel current variation, the lower the return stroke peak current associated with the Stage-T of the CC process, the greater the luminosity variation. (3) For each of the above stages, the statistical model has a better fit when a higher threshold index, a more perpendicular channel or a greater height range is selected in the calculation of the IL.

On remote measurements of lightning return stroke peak currents

Return-stroke peak current is one of the most important measures of lightning intensity needed in different areas of atmospheric electricity research. It can be estimated from the corresponding electric or magnetic radiation field peak. Electric fields of 89 strokes in lightning flashes triggered using the rocket-and-wire technique at Camp Blanding (CB), Florida, were recorded at the Lightning Observatory in Gainesville, about 45km from the lightning channel. Lightning return-stroke peak currents were estimated from the measured electric field peaks using the empirical formula of Rakov et al. (1992) and the field-to-current conversion equation based on the transmission line model (Uman and McLain, 1969). These estimates, along with peak currents reported by the U.S. National Lightning Detection Network (NLDN), were compared with the ground-truth data, currents directly measured at the lightning channel base. The empirical formula, based on data for 28 triggered-lightning strokes acquired at the Kennedy Space Center (KSC), tends to overestimate peak currents, whereas the NLDN-reported peak currents are on average underestimates. The field-to-current conversion equation based on the transmission line model gives the best match with directly measured peak currents for return-stroke speeds between c/2 and 2c/3 (1.5 and 2×108m/s, respectively). Possible reasons for the discrepancy in the peak current estimates from the empirical formula and the ground-truth data include an error in the field calibration factor, difference in the typical return-stroke speeds at CB and at the KSC (considered here to be the most likely reason), and limited sample sizes, particularly for the KSC data. A new empirical formula, I=−0.66–0.028rE, based on data for 89 strokes in lightning flashes triggered at CB, is derived.

Far-Field Power of Lightning Strokes as Measured by the World Wide Lightning Location Network

Abstract The World Wide Lightning Location Network (WWLLN) is a long-range network capable of locating lightning strokes in space and time. While able to locate lightning to within a few kilometers and tens of microseconds, the network currently does not measure any characteristics of the strokes themselves. The capabilities of the network are expanded to allow for measurements of the far-field power from the root-mean-square electric field of the detected strokes in the 6–18-kHz band. This is accomplished by calibrating the network from a single well-calibrated station using a bootstrapping method. With this technique the global median stroke power seen by the network is 1.0 × 106 W, with an average uncertainty of 17%. The results are validated through comparison to the return-stroke peak current as measured by the New Zealand Lightning Detection Network and to the previous ground wave power measurements in the literature. The global median stroke power herein is found to be four orders of magnitude lower than that reported earlier for the measurements, including the nearby ground and sky wave. However, it is found that the far-field waveguide mode observations herein are consistent with the previous literature because of differences in observational techniques and the efficiency of coupling into a propagation wave in the Earth–ionosphere waveguide. This study demonstrates that the WWLLN-determined powers can be used to estimate the return-stroke peak currents of individual lightning strokes occurring throughout the globe.

New measurements of lightning electric fields in Florida: Waveform characteristics, interaction with the ionosphere, and peak current estimates

We analyzed wideband electric field waveforms of 265 first and 349 subsequent return strokes in negative natural lightning. The distances ranged from 10 to 330 km. Evolution of first‐ and subsequent‐stroke field waveforms as a function of distance is examined. Statistics on the following field waveform parameters are given: initial electric field peak, opposite‐polarity overshoot, ratio of the initial electric field peak to the opposite polarity overshoot, zero‐to‐peak risetime, initial half‐cycle duration, and opposite polarity overshoot duration. The overwhelming majority of both first and subsequent return‐stroke field waveforms at 50 to 330 km exhibit an opposite polarity overshoot. At distances greater than 100 km, electric field waveforms, recorded under primarily daytime conditions, tend to be oscillatory. Using finite difference time domain modeling, we interpreted the initial positive half‐cycle and the opposite‐polarity overshoot as the ground wave and the second positive half‐cycle as the one‐hop ionospheric reflection. The observed difference in arrival times of these two waves for subsequent strokes is considerably smaller than for first strokes, suggesting that the first‐stroke electromagnetic field caused a descent of the ionospheric D‐layer. We speculate that there may be cumulative effect of multiple strokes in lowering the ionospheric reflection height. Return‐stroke peak currents estimated from the empirical formula, I = 1.5–0.037DE (where I is considered negative and in kA, E is the electric field peak considered positive and in V/m, and D is distance in km), are compared to those reported by the NLDN.

Attractive radii of vertical and horizontal conductors evaluated using a self consistent leader inception and propagation model—SLIM

A self consistent lightning connecting leader inception and propagation model (SLIM) is utilized to study the attachment of lightning flashes to grounded structures and hence to evaluate the lightning attractive radii of vertical cylindrical structures and horizontal conductors as a function of height of the structure and peak current of the first return stroke. The attractive radius is defined as the maximum lateral distance from where the structure would be able to attract a down-coming stepped leader. The results are compared with the ones that one would obtain using Electro-Geometrical Method (EGM). The results show that for structure heights of the order of 30m or less the attractive radii obtain from SLIM do not deviate significantly (i.e. the error is less than about 20%) from the EGM values. However, for taller objects SLIM predicts significantly larger attractive radii than EGM and the error increases with increasing height.

Electric field within lightning protection volume in presence of a descending leader

Electric field distributions within lightning protection volume of a single lightning rod are studied for the case of a vertical downward leader. The boundaries of volumes with the electrical strength exceeding its critical value for ionization in air are determined, for the rod itself and for objects within its lightning protection (LP) volume. Distance from the leader channel related to the initial achievement of this critical electric strength is found. Simulations are performed using a software based on a FEM (Finite Element Method) for the leader parameters (charge, dimensions, etc.) related to return stroke peak currents of 5 and 30kA, a rod height of 18.2m and its tip radius of 1cm, distances from the channel to rod of 0.5, 30m and larger, an object height of 5.3m, widths of 2 and 10cm, and considering different values for the top edge radius (0.1, 1 and 5cm). Results show a significant extent of possible ionization zones within the LP volume. The proposed approach allows preliminary estimating the dimensions of such zones for protected objects of various types (including those in electric power systems, explosive materials storages, etc.), and its development can also be used for the improvements of LP norms and for the analysis of conditions related to upward discharge initiation, and of safety aspects.