V. Shostak

Far-field-current relationship based on the TL model for lightning return strokes to elevated strike objects

New general expressions relating lightning return stroke currents and far radiated electric and magnetic fields are proposed, taking into account the effect of an elevated strike object, whose presence is included as an extension to the transmission line (TL) model. Specific equations are derived for the case of tall and electrically short objects. The derived expressions show that, for tall structures (when the round-trip propagation time from top to bottom within the tower is greater than the current zero-to-peak risetime), the far field is enhanced through a factor with respect to an ideal return stroke initiated at ground level. The enhancement factor can be expressed in terms of the return stroke wavefront speed v, the speed of light in vacuum c, and the current reflection coefficient at the top of the elevated strike object. For typically negative values of this top reflection coefficient, lightning strikes to tall towers result in a significant enhancement of the far electromagnetic field. Expressions relating the far electromagnetic field and the return stroke current are also presented for electrically short towers and for very long return stroke current wavefronts. For the case of return strokes initiated at ground level (h=0), these expressions represent a generalization of the classical TL model, in which the reflections at the ground are now taken into account. We describe also simultaneous measurements of return stroke current and its associated electric and magnetic fields at two distances related with lightning strikes to the 553-m-high Toronto Canadian National (CN) Tower performed during 2000 and 2001. The derived expressions for tall strike objects are tested versus obtained sets of simultaneously measured currents and fields associated with lightning strikes to the CN Tower, and a reasonable agreement is found. Additionally, it is shown that the peak of the electromagnetic field radiated by a lightning strike to a 553-m-high structure is relatively insensitive to the value of the return stroke velocity, in contrast to the lightning strikes to ground.

Simultaneous measurement of lightning parameters for strokes to the Toronto Canadian National Tower

Successful simultaneous measurements of significant parameters for lightning strikes to the Canadian National (CN) Tower in Toronto have been performed since the summer of 1991. Three 10-bit 10-ns computer-controlled double-channel digitizers, with long segmented memory, have simultaneously captured the current derivative at the CN Tower and the corresponding electric and magnetic fields 2.0 km north of the tower. Lightning flashes to the tower were videotaped from two mutually perpendicular directions for the purpose of constructing a three-dimensional image of the lightning path. Furthermore, the return stroke velocity, a parameter also needed for the analysis of lightning radiation models, has been measured by a computer-controlled photodiode system. In this paper all relevant parameters for a CN Tower lightning stroke, observed on August 17, 1991, are shown and analyzed.

On the Current Peak Estimates Provided by Lightning Detection Networks for Lightning Return Strokes to Tall Towers

The peak current estimation of lightning detection networks for strikes to tall towers is discussed in this paper. Such systems are sometimes calibrated using return-stroke current data obtained by means of rocket-triggered lightning or instrumented towers of relatively short height. However, for strikes to electrically tall towers, they tend to overestimate the return-stroke current peak. In this case, in fact, the associated radiated electromagnetic fields, from which the return-stroke current is estimated, experience a significant enhancement with respect to the field that would be radiated if the same return stroke was initiated at ground level or on a short tower. Two approaches to correct the current estimates of a lightning detection network for a lightning strike to a tall tower are discussed and applied to the current measurements obtained at the CN Tower in Toronto in the summer of 2005, for which estimates were available from the North American Lightning Detection Network (NALDN). It is shown that correcting the NALDN estimates using the so-called tower factor obtained from theoretical studies results in an excellent estimation of lightning current peaks.

Lightning strikes to elevated structures: influence grounding conditions on currents and electromagnetic fields

This paper presents an analysis of lightning return strokes to tall structures. The interaction of lightning with a tall structure is modeled using the antenna theory. The finite ground conductivity as well as the buried grounding system of the tall structure are taken into account in the analysis. It is shown that the current waveform, in sections of the tower close to ground, is somewhat affected by a finite ground conductivity. However, for sections further up the tower, it is not significantly influenced. Furthermore, our simulations show that some fine structure associated with current waveforms measured on the Toronto CN tower can be attributed to the finite ground conductivity. It is also shown that the current path down the tower structure is notably subjected to the skin effect. The current distribution along the buried grounding structure of the tower is also presented, illustrating the dispersion effect as a function of the ground conductivity. Finally, the lightning return-stroke generated electric and magnetic fields computed at a distance of 2 km from the tower are presented. It is shown that some late-time subsidiary peaks are smoothed out by the effect of the propagation along a finitely-conducting ground.

Radiated Fields From Lightning Strikes to Tall Structures: Effect of Upward-Connecting Leader and Reflections at the Return Stroke Wavefront

An extension of the engineering return-stroke models for lightning strikes to tall structures that takes into account the presence of possible reflections at the return-stroke wavefront and the presence of an upward-connecting leader is presented. Based on the approach proposed by Shostak et al., closed-form, iterative solutions for the current distribution along the channel, and the strike object are derived. Simulation results for the magnetic fields are compared with experimental waveforms associated with lightning strikes to the CN Tower (553 m). It is shown that taking into account the reflections at the return-stroke wavefront results in better agreement with the fine structure of the magnetic-field waveforms. Moreover, the obtained results are in better agreement with experimental observations, reproducing both the early narrow undershoot and the far-field zero crossing. The results also suggest that the typical double-peak response of the radiated fields from tall structures might be due to the combined effect of upward-connecting leaders and reflections at the return-stroke wavefront.

On the use of transmission line theory to represent a nonuniform vertically-extended object struck by lightning

In this study, we present an experimental validation of the transmission line representation of an elevated object struck by lightning. The experimental results are obtained using a reduced-scale model and injected signals with narrow pulse widths (down to 500 ps). The validation is performed using a reduced scale structure representing the Toronto CN Tower in Canada. Two models consisting, respectively, of 1-section and 3-section uniform transmission lines were considered for the comparison. It is shown that the 3-section model is able to accurately reproduce the obtained experimental data. The overall agreement between the 1-section model and the experimental results is also satisfactory, at least for the early-time response.

On the enhancement of radiated electric and magnetic fields associated with lightning return strokes to tall structures

We propose in this paper new expressions relating lightning return stroke currents and far radiated electric and magnetic fields, taking into account the presence of an elevated strike object. The derived expressions show that the presence of an elevated strike object enhances the radiated electromagnetic field. The enhancement with respect to a return stroke initiated at ground level is expressed simply through a factor equal to (1+c//spl nu/), where /spl nu/ and c are the return stroke speed and the speed of light, respectively. The computed results using the proposed expression are compared with sets of simultaneously-measured currents and fields associated with lightning strikes to the Toronto CN Tower, and a reasonable agreement is found.

Comparison of current characteristics of lightning strokes measured at the CN Tower and at other elevated objects

Since 1991, a broadband, high-resolution current measurement system has captured the lightning current derivative at the Toronto CN Tower. In this paper, extensive statistics (1992-2001) of CN Tower lightning current waveform parameters (maximum steepness and peak) are compared with waveform parameters of current recorded at other elevated objects, including rockets trailing conducting wires. The influence of the height of the struck object on waveform parameters is analyzed. The paper focuses on the comparison of CN Tower data with data from other tall structures as well as from rocket-triggered lightning facilities in Florida and New Mexico. The elevated structures used for the comparison include the two towers on Mount San Salvatore in Switzerland, the 160-m tower on Hoher Peissenberg Mountain in Germany and the New York Empire State Building. As the height of the elevated struck object increases, the conducted statistical analysis shows a decrease in the current wavefront steepness. The presented statistical results will assist in the establishment of a more sophisticates approach in designing protective measures against hazards of lightning, especially from lightning occurring at tall structures on in mountainous areas.

Analysis of lightning detection network data for selected areas in Canada

An analysis of Canadian Lightning Detection Network (CLDN) data recorded during years 2004 - 2006 is performed for two selected areas in Canada within a 20-km radius around two tall structures: the CN Tower (CNT, 553 m) in Toronto and the Superstack (SS, 380 m) in Sudbury. The explored lightning characteristics include stroke polarity, lake water or land termination (WT or LT), ground stroke densities Ngs, stroke peak currents (including values of I50%, I95%, I5%), distributions of parameters. The results show noticeable differences between characteristics of lightning terminated to lake water and land. In Toronto area (Ngs ≈ 3.24 strokes/(km2·year)), a commonly accepted feature, according to which positive strokes exhibit dominating peak currents in comparison to negative ones, is confirmed only for WT lightning (not close to the CNT), especially in the range of high currents. For LT lightning in the range of current amplitudes close to 50% values, the negative strokes are characterized by larger peaks (by more than 30%) with respect to positive ones. No positive strokes to water were recorded within 5 km near the CNT during the period of analysis. While WT events exhibit a lower Ngs than LT ones, they show larger peak currents. The Sudbury area, characterized by a lower lightning activity (Ngs ≈ 0.91 strokes/(km2·year)), shows the common relation between peak currents of positive and negative polarities (first are dominating). For the SS, the estimated number of upward lightning looks rather low: 0.47 strokes or 0.37 flashes per year. For the CNT, it is about 32 strokes or 14 upward flashes per year. Distributions of Ngs along the distance from the tall objects, beside the increased levels near object, contain dips next to object (up to 3 - 7 km).

Influence of the height of an elevated strike object on the enhancement of lightning radiated fields

We discuss in this paper the influence of the height of an elevated strike object on the magnitude of lightning radiated electric and magnetic fields. For the analysis, the transmission line (TL) return stroke model for the lightning channel is adopted and the strike object is represented by a uniform lossless transmission line. Analytical expressions derived recently by the authors for the radiated electric and magnetic fields are used to investigate the influence of the height of the elevated strike object Two specific cases of electrically-long and electrically-short strike objects are considered in the analysis. It is shown that, for both cases, the presence of a strike object results in an enhancement of the radiated electromagnetic field, compared to that of return strokes initiated at ground level. However, the enhancement is considerably larger for tall structures compared to short ones. The paper investigates additionally the effect of other parameters such as return stroke speed and reflection coefficients at the top and at the bottom of the strike object on the field enhancement.