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Dependence of lightning electric field waveform parameters on distance between the lightning channel and the field measuring point is examined. The analyses are performed based on representative wideband electric field waveforms that were obtained by averaging individual waveforms produced by negative return strokes at distances ranging from 10 to 500 km. The methodology employed for finding the representative waveforms using a large database is described in the companion paper. In this article, we present evolution with distance of the following waveform parameters: zero-to-peak rise time, zero-crossing time, ratio of the initial electric field peak to the opposite polarity overshoot, all for the ground wave, and the ratio of the ground wave initial electric field peak to the peak of the first skywave. We also present a catalog of representative waveforms for different distances, time of day, and stroke order. Additionally, we examine the peak-to-peak and zero-to-zero time intervals between the ground wave and the first skywave that are often used for estimating the apparent ionospheric reflection height.

A new approach to the characterization of CG lightning electric field waveforms using a large database is presented. The waveforms, recorded in a wide (160 Hz–500 kHz) frequency range, are categorized into groups, depending on stroke order (first or subsequent), time of day (to distinguish between the daytime and nighttime ionosphere heights), and distance range. For each group, a representative waveform (including the ground wave and one-hop skywave) was found by averaging a large number of individual amplitude-normalized waveforms on a -100 to 500 μs time scale ( t = 0 corresponds to the peak of the return-stroke ground wave). In this article, the methodology of waveform classification and averaging is presented and discussed. In the companion paper, the developed methodology is applied to analyzing variation of lightning electric field waveforms of different type with distance in the 10 to 500 km range.

In this article, vertical electric fields (including skywaves) produced by lightning return strokes at distances ranging from 100 to 958 km have been computed using the finite-difference time-domain (FDTD) method in the 2-D spherical coordinate system. The return stroke is represented by the original transmission-line (TL) model (with no current decay with height and abrupt current termination at the channel top), the modified TL model with linear current decay with height (MTLL model), the modified TL model with exponential current decay with height (MTLE model), or the Hertzian dipole (HD) model. All the TL-type models include propagation delay, while in the HD model the current changes with time, but does so simultaneously in all channel sections; that is, without any propagation delay. The HD model predicts considerably higher fields than the TL-type models, if the same channel length is employed. The HD model with an unrealistically small channel length of 0.7 km yields electric field peaks similar to those produced by TL-type models with a 7-km channel. Ground waves and skywaves computed using the HD model have faster rise and decay times (shorter pulsewidths) than those computed using a TL-type model. Electric fields produced by a longer risetime current are less attenuated due to propagation over lossy ground when a TL-type model is used, while they are more attenuated if the HD model is employed. The opposite trends are related to the fact that the radiation field peak is proportional to the product of the current and propagation speed for a TL-type model, while for the HD model, it is proportional to the product of the time derivative of current and channel length. In the TL model, abrupt termination of significant current at the channel top results in the so-called mirror image (abrupt radiation field polarity change). This artifact does not occur in the framework of the MTLL model and is negligible in the MTLE model with λ = 2 km and H = 7 km.

In this article, we present a sensitivity analysis to show under what conditions corona on vertical conductors may become significant. A lightning strike to a 600-m-tall grounded metallic object (tower) on a perfectly conducting ground is simulated using the 2-D finite-difference time-domain (FDTD) method in the cylindrical coordinate system and taking into account corona discharge from the lateral surface of the object. The tall object is represented by a cylinder having a radius of 0.1, 1, or 5 m (these values are representative of tower top, not the entire tower), where the extent of radial corona is most significant. The corona discharge is represented by a radially expanding higher conductivity region around the tall object. The corona radius is largest (up to about 5 m) at the object top with no corona at its bottom. It follows from the FDTD simulations that the wavefront of lightning current surge can be distorted significantly and the apparent propagation speed can be reduced. The reduction in propagation speed becomes more significant as the magnitude of lightning current increases.

The paper is devoted to the review of the data on the lightning parameters necessary for development and perfection of lightning protection systems. It is shown, that down to present time national and international lightning protection standards are based on the Berger’s data on distribution of lightning amplitudes currents. Experimental data on amplitude of the return-stroke current the received recently in Brazil, Japan, USA (Florida) and Austria are resulted. It is emphasized, that the given data on currents of a lightning are characterized by a wide scatter that specifies necessity of realization of the further researches. The detailed description of parameters of the return-stroke peak current, including duration of front time, duration of a pulse, a steepness of a current at the front is given. It is emphasized, that median value of amplitude of a current of the first making the return-stroke in 3-4 times is higher than a current of the subsequent components. The analysis measured median (50%) and severe (1%) values of lighting parameters which are necessary for construction of a curve of distribution in the assumption of its submission lognormal law is carried out. Results of theoretical researches are given according to extreme values of currents of a lightning. It is shown, that, depending on length of the lightning channel (from 4 up to 6 kms), the maximal current can vary from 300 kA up to 500 кА. The minimal value of lightning current is appreciated in 2 кА. The analysis of results of new direct measurements has shown, that for a lightning of positive polarity the maximal current can reach 340 кА, that appreciably is higher than a settlement maximum for a lightning of negative polarity (200 кА). Recent theoretical researches have allowed to prove experimentally received lognormal distribution of currents for lightning of negative polarity.

Lightning can be defined as a transient, high-current (typically tens of kA) electric discharge in air whose length is measured in km. As for any discharge in air, lightning channel is composed of ionized gas, that is, of plasma, whose peak temperature is typically 30,000 K, about five times higher than the temperature of the surface of the Sun. Lightning was present on Earth long before human life evolved and it may even have played a crucial role in the evolution of life on our planet. The global lightning flash rate is some tens to a hundred km per second. Each year, some 25 million cloud-to-ground lightning discharges occur in the United States, and this number is expected to increase by about 50% due to global warming over the 21st century. Lightning initiates many forest fires, and over 30% of all electric power line failures are lightning related. Each commercial aircraft is struck by lightning on average once a year. A lightning strike to an unprotected object or system can be catastrophic. In the first part of the article, an overview of thunderclouds and their charge structure is given, basic lightning terminology is introduced, and different types of lightning (including the so-called rocket-triggered lightning) are described. For the most common negative cloud-to-ground lightning, main lightning processes are identified and the existing hypotheses of lightning initiation in thunderclouds are reviewed.

We present a new engineering model for the M component mode of charge transfer to ground that can predict the observed electric field signatures associated with this process at various distances, including (a) the microsecond-scale pulse thought to be due to the junction of in-cloud leaders and the grounded, current-carrying channel and (b) the ensuing slow, millisecond-scale pulse due to the M component proper occurring below the junction point. We examine the features of 13 microsecond-scale, fast electric field pulses associated with M component processes in upward negative lightning initiated from the Santis Tower and recorded 14.7 km from it. Eleven out of the 13 pulses were found to be unipolar with pulse widths in the range of 9.8 to 35 mu s, and the other two were bipolar. To model the process that gives rise to microsecond-scale pulses, we hypothesize that the current pulses propagating away from the junction point along the main lightning channel (below the junction point) and along the feeding in-cloud leader channel (branch) carry the same amount of charge. We further assume that the pulse traversing the branch is similar to a subsequent return-stroke (RS) pulse. In the model, the RS-like process is represented by the MTLE model. The millisecond-scale field signature that follows the initial fast pulse in M components at close distances is simulated in our model using the guided-wave M component model. The proposed model successfully reproduces the vertical electric field waveforms associated with M-component processes in upward lightning flashes initiated from the Santis Tower at 14.7-km distance from the lightning channel, in which both the fast, microsecond-scale and the following slower, millisecond-scale pulses were observed. The model also reasonably reproduces the known features of electric field signatures at close distances (up to 5 km), where the amplitude of the millisecond-scale hook-like pulse is much larger than that of the microsecond-scale pulse, and at far distances (of the order of 100 km), where the microsecond-scale pulses are dominant. Key Points The new engineering M component model can reproduce the microsecond-scale electric field pulses thought to be due to the junction process The proposed model can be used to simulate both the microsecond- and millisecond-scale features of M component field signatures at close and far ranges The geometry of the in-cloud leader channel and the junction point height largely determine the presence of the microsecond-scale electric field pulses

We propose a scenario in which elevated ionic conductivity regions (EICRs) with dimensions of the order of 0.1–1 m are formed in the turbulent thundercloud environment. The starting point in this scenario is the occurrence of electron avalanches in the vicinity of colliding hydrometeors, leading to the formation of ion production centers. Their dimensions are of the order of $$1{0}^{-3}-1{0}^{-2}$$10−3−10−2 m, and their lifetime is of the order of $$1{0}^{-4}-1{0}^{-3}$$10−4−10−3 s. When a new ion production center is created inside the decimeter-scale residual ion concentration spot left behind by a previously established center, the local ion concentration steadily increases, which leads to the formation of decimeter-scale EICRs whose lifetime is measured in seconds. The relatively high conductivity of EICRs (up to $$1{0}^{-9}$$10−9 S/m or so) relative to the background conductivity ($$1{0}^{-14}$$10−14 S/m or less) ensures their polarization in external electric field within a few milliseconds or so. The EICR formation mechanism requires only one condition: the rate of occurrence of ion production centers per unit time in a unit volume should exceed the percolation-theory-based critical level of $$1{0}^{-1}$$10−1 m$${}^{-3}$$−3 s$${}^{-1}$$−1. Hydrometeor collision rates three and even four orders of magnitude higher than this value have been reported from observations. Presence of EICRs in the cloud provides local electric field enhancements and pre-ionization levels that will lead to the formation of additional ion production centers and may be sufficient for the initiation and development of streamers and, eventually, lightning.

The occurrence context of compact intracloud discharges (CIDs) is examined using their electric field waveforms and corresponding NLDN data. A total of 1096 CIDs transporting negative charge upward and 8 CIDs transporting positive charge upward were analyzed. The CIDs were categorized based on whether they were isolated or were followed, preceded, or both followed and preceded by other NLDN-reported lightning events. The percentages of isolated CIDs transporting negative charge upward decreased from 92% for 5 km search radius and ±10 ms time window to 31% for 10 km and ±1000 ms, this decrease being accompanied by an increase of the percentage of CIDs preceding (initiating) normal lightning events from 6.8% to 43%. GM NLDN-reported peak currents for isolated CIDs (33 kA) were similar to those initiating normal lightning events (34 kA). Some of our isolated CIDs could be viewed as precursors, because they apparently initiated normal lightning events at essentially the same location after time intervals measured in seconds. CIDs transporting positive charge upward (a) occurred at heights ranging from 16 to 19 km vs. 6 to 16 km for CIDs transporting negative charge upward and (b) had considerably higher NLDN-reported peak currents: 113 kA vs. 33 kA (GM values).

We analyzed wideband electric field waveforms of 1022 compact intracloud discharges (CIDs) that transported negative charge upward and were recorded in 2016 by the Lightning Detection and Waveform Storage System (LDWSS) operating at the Lightning Observatory in Gainesville (LOG), Florida. According to the NLDN, all the examined events occurred within 500 km of the LOG. CIDs, which are the strongest natural producers of HF-VHF radiation on Earth may represent a serious threat to airborne vehicles. They were distinguished from other lightning processes using their characteristic features in both the time-domain waveform and the frequency spectrum. Eleven types of CID electric field waveshapes were identified, seven of which have not been reported as separate types before. More than half of the observed CIDs showed pronounced ringing on the opposite-polarity overshoot of their bipolar electric field waveforms, which is indicative of a bouncing wave process. Two major lightning locating systems (NLDN and ENTLN) each reported most of our CIDs as CGs (essentially all as +CGs). The percentage of misclassified CIDs was higher for higher-intensity events: for peak current ranges of 0–20 kA, 20–50 kA, and ≥ 50 kA NLDN misclassified 10%, 97%, and 100% of CIDs, respectively. The corresponding percentages for ENTLN were 2%, 63%, and 100%.

Recent progress in studying the breakthrough phase (BTP) of the attachment process in lightning and long sparks is reviewed. The main focus is on the new insights gained from recent observations for 3 types of electric discharges: natural lightning (Nag et al., 2012; Tran and Rakov, 2017a,c), rocket-and-wire triggered lightning (Howard et al., 2010; Hill et al., 2016), and long sparks (Kostinskiy et al., 2016). The BTP (also known as the final jump) starts when the poorly-conducting streamer zones, developing ahead of the hot channels of negative downward leader (DL) and positive upward connecting leader (UCL), come in contact and a common streamer zone (CSZ) is formed. The beginning of BTP (establishment of CSZ) is usually marked by an abrupt current rise, a burst of dE/dt pulses (referred to as leader burst or LB), and hard X-ray emission. During the BTP, hot channels of both DL and UCL extend toward each other inside the CSZ, resulting in its shrinking, until the high-impedance CSZ is eliminated and low-impedance connection of DL to the grounded object is established. The process of bridging of CSZ by hot leader channels is accompanied by the formation of slow front (SF) in the channel current and in electric and magnetic field waveforms at both close and far distances from the channel. Attempted or relatively weak hot-channel connections producing current surges and associated field pulses superimposed on the SF (SF pulses) can occur. The SF lasts some microseconds and ends at the onset of the submicrosecond-scale fast transition (FT), which signifies the end of BTP. During the BTP, the current rises from the UCL level of the order of tens to hundreds of amperes to about 50% of the overall (SF + FT) current peak, which is of the order of tens of kiloamperes (for negative first strokes). This two orders of magnitude current rise during the BTP occurs before the collision of hot leader channels inside the CSZ; that is, before the onset of return stroke proper.

We examined the occurrence characteristics of the lightning observed at the Gaisberg Tower (GBT) in the years 2000 to 2018 and analyzed current waveforms (measured using a 0.25-mΩ shunt) of upward flashes initiated from the tower. During this period, 865 flashes were recorded at the GBT, of which 823 (95%) were upward and 4 (0.5%) were downward. For 18 flashes, the current waveforms were ambiguous and for 20 flashes they were unsuitable for analysis. Of the 823 upward flashes, 651 (79%) were negative, 35 (4.3%) were positive, and 137 (17%) were bipolar. The median initial stage (IS)-current durations in upward negative, positive, and bipolar flashes were 275, 96, and 282 ms, respectively. The median IS-current peaks in these flashes were 1.4, 3.2, and 1.8 kA, respectively. We expanded the traditional classification of bipolar flashes to include five categories. Of the 137 bipolar flashes, 45% were of Type 1S (single reversal of current polarity during IS), 47% of Type 1M (multiple reversals of current polarity during IS), 5.1% of Type 2 [different polarities of current during IS and return stroke (RS)], 1.5% of Type 3 (RSs of different polarities), and 0.73% (one flash) of Type 4 (different polarities of RS and the following continuing current).

Recent upgrades of the low-cost lightning detection and waveform storage system (LDWSS) are presented. The system has been developed for research and operational use in the Amazon region of Brazil and it has been in operation in this region since November 1, 2017. The original version of the LDWSS operated for 10 months at the Lightning Observatory in Gainesville, Florida, where it was calibrated and tested. Two main modifications implemented include the improvement of the effective dynamic range and the capability to detect lightning in different frequency bands. The improvements were achieved by using two pre-amplifiers working in parallel, a new processing (smart saving) algorithm, and programmable analog filters. As a result, a single, low-cost lightning electric field measuring system allows one to record both close and far lightning events with good amplitude resolution and without saturation, and study both wideband and narrow-band (for example, very low frequency) field signatures of lightning, without modifying the hardware.

Lightning can be defined as a transient, high-current (typically tens of kiloamperes) electric discharge in air whose length is measured in kilometers. As for any discharge in air, lightning channel is composed of ionized gas, that is, of plasma, whose peak temperature is typically 30,000 K, about five times higher than the temperature of the surface of the Sun. Lightning was present on Earth long before human life evolved and it may even have played a crucial role in the evolution of life on our planet. The global lightning flash rate is some tens to a hundred per second or so. Each year, some 25 million cloud-to-ground lightning discharges occur in the United States, and this number is expected to increase by about 50% due to global warming over the twenty-first century. Lightning initiates many forest fires, and over 30% of all electric power line failures are lightning related. Each commercial aircraft is struck by lightning on average once a year. A lightning strike to an unprotected object or system can be catastrophic. In this chapter, an overview of thunderclouds and their charge structure is given, basic lightning terminology is introduced, and different types of lightning (including the so-called rocket-triggered lightning) are described. For the most common negative cloud-to-ground lightning, main lightning processes are identified and the existing hypotheses of lightning initiation in thunderclouds are reviewed. Additionally, current and electromagnetic field signatures of lightning are characterized and the techniques to measure lightning electric and magnetic fields are discussed.

In this chapter, we give an overview of lightning discharges, which can cause electromagnetically induced effects in power and telecommunication systems. Then, we describe modeling of the lightning return stroke and explain “engineering” models, in which the spatial and temporal distribution of the current or the line charge density along the lightning channel is specified based on such observed lightning return-stroke characteristics as current at the channel base, the speed of the upward-propagating front, and the channel luminosity profile. Also, we discuss the equivalency between the lumped-source and distributed source representations, and the extension of engineering models to include a tall grounded strike object. Further, we describe two primary approaches to test lightning return-stroke models that are referred to as “typical-event” and “individual-event” approaches.

In [1] it was established that collective dynamics of charged hydrometeors that involved in turbulent motion play a fundamental role in thundercloud electrostatic energy redistribution and dissipation. The main reservoirs for accumulating electrostatic energy in thunderclouds are i) the large-scale field of the main charged layers that appear due to the large-scale separation of oppositely charged hydrometers, ii) the intermediate-scale field of charged hydrometeors distributed in the turbulent flow, and finally iii) the small-scale field of net and polarization charges on the surface of individual solid and liquid water particles. Since three different spatial scales are involved into the process of electrostatic energy dissipation, we represent the lightning initiation scenario as a sequence of two transitions of discharge activity to progressively larger spatial scales: the first one is from small-scale avalanches to intermediate-scale streamers; and the second one is from streamers to the lightning seed. At the first stage of the proposed scenario, the essentially non-conducting cloud becomes seeded by elevated ion conductivity regions with spatial extent of 0.1 - 1 m and a lifetime of 1 - 10 s. These regions can serve to promote the intermediate electric field enhancements and increase in pre-ionization level that is sufficient for the initiation and development of streamers. Due to the positive the proposed streamer generation mechanism has an important feature: streamers in our scenario are not exponentially rare events, but continuously fill the entire volume. The collective dynamics of such a nearly continuous, volume filling streamer network appears to be very sensitive to both the magnitude of external large-scale electric field and longitudinal extent of the region occupied by the field. Moving in the course of its development along the external field, a positive streamer can get into the negative trails left by other streamers (relay race effect). In this way, the size of the streamer discharge along the external field can grow, providing the emergence of a kind of streamer trees, thereby tapping electrostatic energy from a relatively large cloud volume. Over time, many streamer trees are feeding their current into narrow channels, where the heating occurs (the bottleneck effect). The hot segments of the network can get polarized and grow within its overall channel system even if the ambient field amplitude is much smaller than the critical field of streamer propagation. Successful initiation of lightning also requires that potential difference across the layer occupied by the large-scale electric field makes about three megavolts. The proposed scenario can possibly lead to a paradigm shift in our approaches to the still unsolved mystery of lightning initiation, because it does not require the presence of super-energetic cosmic ray particles, unrealistic potential difference inside the cloud, or unrealistically large hydrometeors. 1. Iudin, D.I., Rakov, V.A., Syssoev, A.A. et al. Formation of decimeter-scale, long-lived elevated ionic conductivity regions in thunderclouds. npj Clim Atmos Sci 2, 46 (2019) doi:10.1038/s41612-019-0102-8.