Numerical Modeling Of Lightning Initiation And Stepped Leader Propagation

Initial breakdown pulses (IBPs) observed at the beginning of cloud-to-ground (CG) lightning flashes and stepped leaders that folloIBPs were modeled using multi-sensor electric field change (E-change) measurements. This study uses data collected with a network of ten E-change sensors located at Kennedy Space Center. Locations (x,y,z,t) of IBPs were found using a time-of-arrival technique called PBFA. Location errors were determined from Monte Carlo simulations and were usually less than 100 m for horizontal coordinates and several hundreds of meters for altitude. Comparison of PBFA source locations to locations from a VHF lightning mapping system shows that PBFA locates most of the `classic\u27 IBPs while the VHF system locates only a few percent of them. As the flash develops during the IB stage, PBFA and the VHF system obtain similar locations when they detect the same IBPs. PBFA also can reliably locate the IBPs of intra-cloud flashes and return stroke (RS) locations. PBFA locations were used as constraints to model six \u27classic\u27 IBPs using three modified transmission line (MTL) models (MTLL--linearly decaying current, MTLE—exponentially decaying current, MTLEI—exponentially increasing current) from the literature and a new model, MTLK, with the current following the Kumaraswami distribution. All four models did a good job of modeling all six IBPs; the MTLE model was most often the best fit. It is important to note that for a given pulse, there is good agreement between the different models on a number of parameters: current risetime, current falltime, two current shape factors, current propagation speed, and the IBP charge moment change. Ranges and mean values of physical quantities found are: current risetime [4.8–25, (13±6)] microseconds, current falltime [15–37, (25±6)] microseconds, current speed [0.78–1.8, (1.3±0.3)]×10 8 m/s (excluding one extreme case of MTLEI), channel length [0.20–1.6, (0.6±0.3)] km, charge moment [0.015–0.30, (0.12±0.10)] C km, peak current [16–404, (80±80)] kA , and absolute average line charge density [0.11–4.7, (0.90±0.90)] mC/m. Currents in the MTLL and MTLE models deposit negative charge along their paths and the mean total charges deposited (Qtot) were -0.35 and -0.71 C. MTLEI currents effectively deposited positive charge along their paths with Qtot = 1.3 C. MTLK is more special regarding how it handles the charges. Initially, along the lower current path, negative charge is deposited and positive charge is deposited onto its upper path making the overall charge transfer almost zero, (Qtot = 3.8×10 -5). Because of this the MTLK model apparently obeys conservation of charge (without making that a model constraint). Two stepped leaders were modeled to match multiple E-change measurements. Time evolution and 2-D locations of stepped leaders were obtained from data collected with a high-speed video camera operated at 50,000 frames/s. The Lu et al. 2011 TDMD (time dependent multidipole) model was used with some modifications. Negative charges were deposited at stepped leader tips based on measured light intensity, and positive charges were deposited at PBFA/LDAR2 locations of IBPs where the stepped leaders probably started. The method has unique advantage of obtaining locations of CG stepped leaders including its branches, unlike previous studies that used simpler paths. Some physical quantities calculated for both stepped leaders: average line charge density = -1.49 and -0.813 mC/m, average current = 0.39 and 0.38 kA, average 2-D stepped leader speed 2.67 and 4.8×105 m/s. These quantities are in excellent agreement with previous studies

Modeling Initial Breakdown Pulses of Lightning Flashes Using a Matrix Inversion Method

© 2019. American Geophysical Union. All Rights Reserved. This study describes a new method for modeling the radiated electric field (E) of initial breakdown pulses (IBPs) of lightning flashes. Similar to some previous models, it is assumed that E pulses are caused by a current propagating along a vertical path, and an equation based on Maxwell\u27s equations is used to determine E due to the current. A matrix inversion technique is used with the IBP radiation term of E to determine the IBP current waveform directly from far-field E measurements rather than assuming a parameterized current waveform and searching for appropriate parameters. This technique is developed and applied to observations of six previously modeled IBPs. Compared to the prior modeling, this matrix inversion method gives significantly better results, based on calculated IBP goodness of fit to the original E data. In addition, this model can match IBP subpulses along with representing the overall bipolar IBP waveform. This method should be useful for studying IBPs because once the IBP current is known, one can calculate other physical parameters of IBPs, such as charge moment change, total charge moved, and total power radiated. Thus, the more realistic IBP current waveform determined by this technique may offer new clues about the physical mechanism causing IBPs

Modeling initial breakdown pulses of intracloud lightning flashes

In this study 29 initial breakdown pulses (IBPs) from four intracloud (IC) lightning flashes are modeled using data from five or more electric field change (E-change) sites. For each flash the first 5–9 located IBPs are investigated. For each IBP the modeling first extracts the IBP current waveform from the E-change data by matrix inversion and then determines the best channel length and current velocity to match the IBP data. Derived IBP quantities of total charge, charge moment, peak current, peak radiated power, and total energy are calculated. Resulting IBP vertical lengths varied from 27 m to 1300 m; most values were 100–500 m. Current velocities ranged over 4.0–20.0 × 107 m/s, with most values 10–16.5 × 107 m/s. Two of these IC flashes had two “extraordinary” IBPs each with very large E-change amplitude and multiple subpulses; these four extraordinary IBPs had longer current rise times than fall times and charge moments of −3.45 to −20.06C km. Subpulses of classic IBPs were coincident with, and likely caused by, smaller current pulses superimposed on the main IBP current. Overall, most of the 29 IC IBPs had peak current amplitudes \u3c120 kA and total (negative) charge \u3c2C, while the four extraordinary IB pulses had peak currents of 217–359 kA and total charges of −8.4C to −71.7C. The four extraordinary IBPs all have the characteristics of Energetic In-cloud Pulses (EIPs), which are thought to be the radio signals of events producing terrestrial gamma-ray flashes (TGFs). The extraordinary IBPs may have caused double-pulse TGFs and overlapping TGFs

Inception of subsequent stepped leaders in negative cloud-to-ground lightning

© 2019, The Author(s). Time-correlated high-speed video and electric field change data for 139 natural, negative cloud-to-ground (CG)-lightning flashes reveal 615 return strokes (RSs) and 29 upward-illumination (UI)-type strokes. Among 121 multi-stroke flashes, 56% visibly connected to more than one ground location for either a RS or UI-type stroke. The number of separate ground-stroke connection locations per CG flash averaged 1.74, with maximum 6. This study examines the 88 subsequent strokes that involved a subsequent stepped leader (SSL), either reaching ground or intercepting a former leader to ground, in 61 flashes. Two basic modes by which these SSLs begin are described and are termed dart-then-stepped leaders herein. One inception mode occurs when a dart leader deflects from the prior main channel and begins propagating as a stepped leader to ground. In these ‘divert’ mode cases, the relevant interstroke time from the prior RS in the channel to the SSL inception from that path is long, ranging from 105 to 204 ms in four visible cases. The alternative mode of SSL inception occurs when a dart leader reaches the end of a prior unsuccessful branch—of an earlier competing dart leader, stepped leader, or initial leader—then begins advancing as a stepped leader toward ground. In this more common ‘branch’ mode (85% of visible cases), there may be no portion of the subsequent RS channel that is shared with a prior RS channel. These two inception modes, and variations among them, can occur in different subsequent strokes of the same flash

Groups of narrow bipolar events within thunderstorms

This investigation is focused on groups of Narrow Bipolar Events (NBEs), defined as NBEs that occurred within 10 km horizontally and ±660 ms of a located, large-amplitude NBE from a dataset of positive NBEs that occurred in Mississippi thunderstorms. In two months only 15 groups were found, with a total of 31 positive and 4 negative NBEs. Each group had 2 to 5 NBEs; four groups had both positive and negative polarity NBEs. About half of the NBEs had typical values for range-normalized fast antenna (FA) electric field change magnitudes (4–15 V/m) and typical VHF powers (1000–45,000 W), but 17 NBEs had FA magnitudes 0.2–2.5 V/m, and 17 NBEs had VHF powers 30–900 W. Seven weak NBEs had FA magnitudes of 0.2–1.0 V/m and VHF powers of 30–100 W. These findings indicate that weak NBEs are more common than previously thought. None of the NBEs in groups initiated a lightning flash, and (with one possible exception) none of the later NBEs in a group were initiated by earlier NBEs in the group. The data of the NBE groups are consistent with the turbulence-extensive air shower (EAS)/relativistic runaway electron avalanche (RREA) mechanism, which states that each NBE occurs in a separate 1-km3 volume containing many small regions with electric field ≥3 MV/(m∙atm); an EAS/RREA passing through the 1-km3 volume initiates the positive streamers that comprise the NBE. Relative to thunderstorm radar reflectivity, 23 NBEs occurred in or above the reflectivity core, 10 NBEs occurred high in the storm anvil, and 2 NBEs occurred beside the storm core. We speculate that the occurrence of many of the NBE groups was associated with dynamically intense convection

Electric field change and VHF waveforms of Positive Narrow Bipolar Events in Mississippi thunderstorms

© 2020 The Authors Positive Narrow Bipolar Events (+NBEs) in Mississippi thunderstorms were studied using fast antennas (FA, bandwidth 16 Hz - 2.6 MHz) and VHF antennas (Log-RF, bandwidth 186–192 MHz). The waveform characteristics of 201 positive NBEs were determined using both sensors. The +NBEs were classified in two ways: by FA waveform into Types A-D and by +NBE occurrence relative to other lightning events into three groups called Isolated, Not-Isolated, and INBE. (An INBE initiates an intracloud flash.) The FA waveform properties of 188 positive NBEs were mainly in reasonable agreement with previous studies. The VHF waveform properties of +NBEs have not been studied previously. The VHF powers of 201 positive NBE ranged from 0.1–88.4 kW with an average value of 7.8 kW. Types C and D positive NBEs tended to be more energetic (average VHF powers of 9.2 and 13.2 kW) than Types A and B (average powers of 1.9 and 4.0 kW). The INBE group of +NBEs had a larger range of VHF powers (0.2–88.4 kW) than the combined power range of the Not-Isolated and Isolated groups (0.1–26.7 kW). The INBE group also had a larger average peak power (9.9 kW) than the Not-Isolated and Isolated Groups (4.0 and 8.7 kW, respectively). However, 53% of INBEs had peak VHF power \u3c 5 kW, so an INBE does not require a large power to initiate an intracloud flash. For 90% of the 201 positive NBEs the magnitude of the time difference between the FA peak amplitude and the Log-RF peak power was ≤2 μs, but the FA peak amplitude showed almost no correlation with the Log-RF peak power

Characterizing three types of negative narrow bipolar events in thunderstorms

© 2019 The Authors Data from fast antennas (FAs)with bandwidth of 16 Hz–2.5 MHz and VHF power sensors (Log-RF)with bandwidth of 186–192 MHz are used to examine negative narrow bipolar events, or NNBEs. The main focus is on low-altitude (8.0 km)NNBEs are also examined. The low-altitude NNBEs are found to have two types called NNBE(L)and NNBE(H). NNBE(L)s have a bipolar FA waveform typical of NBEs while NNBE(H)s have a unipolar FA waveform. It is hypothesized that NNBE(H)s may be weak versions of NNBE(L)s in which the second, overshoot part of the bipolar waveform is too weak to detect amid the FA sensor noise. Together the 33 NNBE(L)s and NNBE(H)s occurred at an average altitude of 6.2 km (range 4.6–7.8 km), had average range-normalized (to 100 km)amplitude of 0.4 V/m (range 0.06–1.5 V/m), and had average VHF power of 130 W (range 1–1300 W). These low-altitude NNBE properties are substantially smaller and weaker than the same properties of the high-altitude NNBEs and of positive NBEs that initiate intracloud (IC)flashes; these analyses indicate that -CG flashes are easier to initiate than IC flashes. Visual inspection of the FA and Log-RF data of 868 -CG flashes showed that only 33 flashes (4%)were preceded by either an NNBE(L)or NNBE(H), so 96% of the -CG flashes investigated probably did not begin with an NNBE

A study of lightning flash initiation prior to the first initial breakdown pulse

© 2018 The Authors This study examines the initiation of two intracloud (IC) and two cloud-to-ground (CG) lightning flashes using electric field change (FA) sensors and VHF (LogRF) sensors located at seven sites near Oxford, Mississippi, USA. For each flash the initiating event caused a pulse in the LogRF data and started an Initial E-Change (IEC) in the FA data. The initiating LogRF pulses had powers ~1 μs. Numerous LogRF pulses occurred during each IEC; these pulses had durations ≤3 μs. Fewer FA pulses occurred during each IEC; these pulses had durations of ≤7 μs. During each IEC, a few of the LogRF pulses were coincident with a FA pulse, and most such pairs of pulses enhanced the IEC; no IEC enhancing events occurred without such a coincident pair. Each flash had 1 or 2 IEC enhancing events soon after the initiating event and 1 or 2 enhancing events shortly before the first classic initial breakdown (IB) pulse occurred. The point dipole moments and durations of IECs of the two IC flashes were (–520C m, 620 μs) and (–770C m, 1790 μs) and for the two CG flashes were (9C m, 124 μs) and (36C m, 130 μs). We speculate that the LogRF events were positive corona streamers, that enhancing events occurred when a new streamer extended a previous streamer path, and that this process during the flash initiation developed a nascent channel needed for the negative breakdown of the IB pulses