Four classes of models of the lightning return stroke are reviewed. These four classes are: (1) the gas dynamic models; (2) the electromagnetic models; (3) the distributed-circuit models; and (4) the "engineering" models. Validation of the reviewed models is discussed. For the gas dynamic models, validation is based on observations of the optical power and spectral output from natural lightning. The electromagnetic, distributed-circuit, and "engineering" models are most conveniently validated using measured electric and magnetic fields from natural and triggered lightning. Based on the entirety of the validation results and on mathematical simplicity, we rank the "engineering" models in the following descending order: MTLL, DU, MTLE, BG, and TL. When only the initial peak values of the channel-base current and remote electric or magnetic field are concerned, the TL model is preferred. Additionally discussed are several issues in lightning return-stroke modeling that either have been ignored to keep the modeling straightforward or have not been recognized, such as the treatment of the upper, in-cloud portion of the lightning channel, the boundary conditions at the ground, including the presence of a vertically extended strike object, the return-stroke speed at early times, the initial bi-directional extension of the return stroke channel, and the relation between leader and return stroke models. Various aspects of the calculation of lightning electric and magnetic fields in which return stroke models are used to specify the source are considered, including equations for fields and channel-base current, as well as a discussion of channel tortuosity and branches.

/pdf/review-and-evaluation-of-lightning-return-stroke-models-198e2ag3lz.pdf

Review and evaluation of lightning return stroke models including some aspects of their application

The physical and geographical characteristics of over 216 million cloud-to-ground lightning flashes recorded during the first decade (1989–98) of operation of the National Lightning Detection Network (NLDN) covering the entire continental United States are presented. These characteristics include the total cloud-to-ground flash density, the positive flash density, the percentage of positive flashes, the first stroke negative and positive peak currents, and the multiplicity for negative and positive flashes. All analyses were done with a spatial resolution of 0.2° corresponding to an approximate resolution of 20 km. Flash densities were not corrected for detection efficiency; the measured values are presented. The maximum measured flash density is found to exceed 9 flashes km−2 across Florida in the Tampa–Orlando–Cape Canaveral corridor, near Fort Myers, and between Lake Okeechobee and the Atlantic Ocean. The mean monthly flash count peaks in July at approximately 5.5 million flashes. Positive fla...

Cloud-to-ground lightning in the United States: NLDN results in the first decade, 1989-98

A detailed study of the complete sequence of VHF radiation events during intracloud (IC) flashes in Florida has shown that IC flashes often have a bilevel structure connected by a single upward channel. The lower and upper level channels appear to correspond to the main negative and upper positive charge regions of the storm, respectively. The IC flashes are characterized by active and final stages, each comprising about half of the overall flash duration. During the active stage, negative charge is transported upward in the cloud, first as a result of initial breakdown, which establishes the upward channel, and subsequently as a result of repeated breakdown events from the lower to the upper level. For the flashes of this study, the initial breakdown lasted 10 to 20 ms and propagated upward at a speed of 1.5 to 3×10 5 m s -1 . It also established the beginning of one or more horizontal branches in the upper positive charge region, which were extended by the subsequent breakdown. Little or no radiation was detected along the upward channel during the subsequent breakdown, indicating that the channel remained more or less continuously conducting following the initial breakdown. After a time delay, the subsequent breakdown extended the lower-level channels in a retrograde manner horizontally away from the flash origin. At the end of the active stage the upward channel ceases to be conducting and the remaining, final stage of a flash is characterized by fast (10 6 to 10 7 m s -1 ), well-defined K-type streamers that begin at successively greater distances along the lower-level channel and transport negative charge toward or into the base of the upward channel. The streamers are identical to those observed during the interstroke intervals and final stages of cloud-to-ground (CG) flashes. Typically, a few late-flash K streamers continue through the flash origin into and along an upper-level channel. The overall results are consistent with other observations of IC flashes and explain several features of the observations. Similar results are obtained for IC flashes in New Mexico storms. Comparison of the initial breakdown of IC and CG flashes shows that the IC breakdown is more intermittent than that of CG flashes, even though both have the same polarity and propagate at about the same average speed.

The spatial and temporal development of intracloud lightning

Lightning charges, locations, and currents have been determined for 12 flashes from four winter storms observed on the Hokuriku coast of Japan during December 1977 through January 1978. Additional data is available from a total of eight winter storms. The heights and magnitudes of the charges in strokes-to-ground were calculated from simultaneous measurements of electric field changes made at seven stations covering an area of about 150 km2. Discharges lowering positive charge to earth often exhibit large continuing currents (>104 A) for periods up to 10 ms. One positive discharge involved a peak current value of ≃105 A and a charge that exceeded 300°C after 4 ms. Negative continuing current strokes are generally an order of magnitude smaller, ≃4×103 A, involving charges of 100°C or less. The positive lightning charges are located higher than the negative charges of the same storm, constituting a ‘normal’ bipolar system similar to the charge configuration found in summer thunderstorms. For the eight storms observed during this study, 26 out of a total of 63 strokes-to-ground were positive. A strong correlation exists between the fraction of positive ground strokes and the vertical wind shear in the cloud layer. On the basis of this study we suggest that the occurrence of positive strokes-to-ground is a consequence of the wind shear. The shear provides a horizontal displacement between the charges that helps to ensure that an initiating positive streamer will continue down to ground rather than into the negatively charged region that would normally be located directly below it. The data suggest that positive strokes-to-ground should appear at a threshold shear value in the cloud layer of about 1.5 m/s/km.

The electrical structure of the Hokuriku winter thunderstorms

Five ground-based VHF receivers were used to trace paths followed by flashes of lightning. Every lightning flash radiates a succession of radio noise pulses, and three Cartesian coordinates of the positions of pulse sources were determined by measuring the times at which the noise pulses arrived at each of the spaced receivers. Lightning channels were mapped in space and time by locating a large number of radio noise sources for each flash, whose shape and position then became apparent despite the presence of intervening hydrometeors. A center frequency of 253 MHz was chosen for the receivers and their bandwidths were wide enough for time differences to be measured with rms errors of 140 ns. Hence two of the three spatial coordinates of a particular source could be determined to an accuracy of 25 m rms and the vertical coordinate could be found to an accuracy which was typically 140 m rms, but the actual height accuracy depended on source position. Some factors that affect the design of the receivers are discussed and case studies of five cloud flashes are presented. Cloud flashes could be classified into two types according to the rates at which they emitted pulses in the VHF part of the radio spectrum. One class radiated pulses at rates that approximated 103 pulses per second when received in bandwidths of 10 MHz. These pulses were often nearly rectangular in form, lasted approximately 1 ms on average, and occurred in synchronism with pulses received at HF and at UHF. The second class emitted much shorter pulses (median durations of 0.2 to 0.4 ms were measured) at higher rates typically 105 pulses per second, and pulses were generally not in synchronism with those received at other radio frequencies. Diameters of the channels occupied by radio sources varied from 100 m to several hundred meters, and were enlarged by the extents of the sources themselves. It was possible to measure the principal extents of many individual sources active during low-pulse-frequency cloud flashes. Average sizes near 300 m were measured for low-pulse-frequency flashes, and sizes near 60 m were estimated for sources active during high-pulse-frequency flashes. It was found that pulses originated in regions near streamer tips, and that pulses were associated with initial ionization. First streamers progressed at speeds that ranged from 0.9 × 105 m/s to 2.1 × 105 m/s except for one extensive, positive flash that moved at 5 × 105 m/s for the first few kilometers. We define a positive flash as being one which conducts excess positive charge in the same direction as that in which the streamer progresses. Subsequent discharges along paths that had been ionized previously seldom radiated much noise but noise was radiated by channels that were several tens of milliseconds old, and then we measured streamer speeds that were at least an order of magnitude higher than first streamer speeds. Relatively few cloud flashes were found to have been oriented vertically. Most were horizontal and often consisted of several streamers that extended from a common origin. Measurements of electric field change were used to estimate quantities of charge involved. These estimates were made by adopting various models for the distribution of charge along the known paths, and the quantities were not greatly dependent on the form of the distribution. Most estimates yielded line densities near 10−3 C m−1. Only one of the cloud discharges had been a positive flash. Trains of band-limited noise which lasted for times that ranged approximately from 10 μs to about 1.5 ms were also emitted by lightning flashes of all kinds, but in cloud flashes this type of noise, which was distinctly different from the pulsed emission, occurred more frequently and with longer durations during the J-type portions or final stages of cloud flashes. It accompanied streamers which progressed at speeds near 107 m/s, often accompanied K changes, which were usually delayed after the start of this noise by tens of microseconds, and the streamers that caused the noise were positive streamers, with the single exception of one train which was found to have been due to a negative streamer that formed near the origin of an extensive, positive cloud flash. There was evidence that events that produced this noise sometimes triggered dart leaders and recoil streamers and most sources of this band-limited noise were located near the origins of the flashes, and streamers which caused the noise served also to discharge the origins but not usually by way of the paths formed by first streamers. The principal results of this work are listed at the end of the paper.

VHF radio pictures of cloud flashes

Observations of lightning discharges in winter thunderstorms were made during 1972/73 and 1973/74 at Unoke near Kanazawa. The main characteristics observed are as follows.

On Lightning Discharges in Winter Thunderstorm

The atmospheric electric conductivity and potential gradient were measured aboard the Icebreaker "Fuji", an antarctic observation ship, during her test cruise around the Japan Islands in October 1966. The electric conductivity was found to vary with distance from the coastline, reflecting the effect of atmospheric pollution extending from land sources over the ocean by diffusion. Analysis of the data obtained shows that the conductivity was determined almost uniquely as a function of distance from the coastline when the weather was clear.

/pdf/the-extension-of-air-pollution-from-land-over-ocean-as-3qhzv7glr4.pdf

The Extension of Air Pollution from Land over Ocean as Revealed in the Variation of Atmospheric Electric Conductivity

Remarkable Characteristics of Cloud-to-Ground Discharges Observed in Winter Thunderstorms in Hokuriku Area, Japan

冬の雷放電について;冬の雷放電について;On Lightning Discharges in Winter Thuderstorms

The nature of ground discharge has been investigated using the data of electric field measurement, thunder recording, flash photographing, etc. The height of charge center neutralized by a return stroke was found not to increase with the stroke order in contrast with the report given by Malan and Schonland, instead the stroke channel was often found to progress laterally successively. The existence of a continuing discharge process between and after return stroke has been verified in agreement with the report given by Malan, and Kitagawa et al. The charge neutralized by return strokes in a ground discharge is, on the average, smaller than that neutralized by a cloud discharge. However this does not always mean that the total charge neutralized by a ground discharge is smaller than that of a cloud discharge, because a ground discharge is often accompanied by a continuing discharge process neutralizing considerable amount of negative charge. A new leader stroke which is proposed by us has the structure of corona-like streamers on the top part of the stroke channel. If the electrical structure of a thundercloud in South Africa is the same as that in Japan, the charge height reported by Malan and Schonland seems to be too high and should be reduced to a smaller value.

Tosio Takeuti

Papers

On Lightning Discharges in Winter Thunderstorm

The Extension of Air Pollution from Land over Ocean as Revealed in the Variation of Atmospheric Electric Conductivity

Remarkable Characteristics of Cloud-to-Ground Discharges Observed in Winter Thunderstorms in Hokuriku Area, Japan

冬の雷放電について;冬の雷放電について;On Lightning Discharges in Winter Thuderstorms

Studies on Thunderstorm Electricity