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 ~ National Lightning Safety Institute ~

Section 5.1.3

Determining the Probability of Lightning Striking a Facility

By R.T. Hasbrouck, PE
National Lightning Safety Institute
Revised 4/18/04

One objective of a facility lightning hazard mitigation study is to determine the likelihood of its being struck by lightning. In this article, actual site-specific lightning strike data is used to calculate probability.

Estimating Probability

The probability of lightning striking a particular object situated on the earth (ground) is found by multiplying the object’s lightning-attractive area by the local ground-flash density (lightning strikes to ground per km2 per year). The following example considers a low structure surrounded by 12 tall, grounded metal light poles.

Caveats: It must be understood that calculations used for determining strike probability are based upon empirical relationships, generally accepted by the research community as reasonably representing the lightning phenomenon. The method presented here provides a reasonable estimate but should not be considered the “final word.” Other, more complicated geometric methods can be used but, considering the capricious nature of lightning, it is unlikely they would provide significantly improved results.

A complete cloud-to-ground lightning event, referred to as a flash, consists of one or more return strokes. Return strokes are high-peak-amplitude (tens to hundreds of thousands of amperes) current pulses, each lasting for a few hundred microseconds. Analysis of a large quantity of lightning flash data shows the average number of strokes (multiplicity) per negative (the most common type of lightning) flash to be between three and four. Approximately 25% of all negative flashes also exhibit several hundred amperes of continuing current during an interval lasting hundreds of milliseconds following at least one return stroke. In a given flash, consecutive return strokes may strike the ground within several meters of each other, or as far apart as eight km. Analysis of data (as reported by Dr. Phil Krider) indicates that flashes exhibit a “random walk,” having a mean interstroke distance of 1.8 km. Ground-flash density data used in this paper is based upon the first stroke of each flash—detected by the National Lightning Detection Network (see below)—regardless of stroke amplitude or flash multiplicity. The author is unaware of any strike probability estimates that take into account the area encompassed by a multi-stroke flash and/or the current-amplitude distribution of strokes in the flash. Finally, note that the statistically less frequent positive lightning flash usually consists of a single stroke having average and maximum peak amplitudes that are significantly higher than for negative lightning. It is accompanied by continuing current and has a total duration as long as one to two seconds.

Cumulative Probability

Lightning Attractive Area

If the earth’s surface beneath a storm cloud were perfectly flat, lightning could be expected to strike any point on the earth with equal probability. For example, if an area of 0.1 km2 experiences a ground-flash density of one flash per km2 per year, the probability of its being struck is 0.1 in any given year (a return frequency of 10 years per flash). However, a conductive object that is taller than the surrounding area exhibits a lightning attractive area greater than the ground surface area it occupies. The probability of its being struck is a function of its ground surface area, height, and the striking distance between the tip of the downward-moving stepped leader and the object (Ref. 1). For negative lightning, the stepped leader is a negatively charged channel that travels in discrete jumps from cloud to Earth.

Striking distance, the stepped leader’s final jump to the conductive object, varies with the amount of charge carried by the channel. (Note: For the sake of simplicity, striking distance calculations don’t take into account upward-moving, positively-charged streamers. These streamers emanate from conductive objects under the influence of the stepped leader’s strong electric field—much as hairs rise up toward a statically charged comb held over one's head.) Since the magnitude of this charge also determines return-stroke peak-current amplitude, greater striking distances are associated with larger amplitude return strokes, i.e., they jump farther to reach the object (Ref. 2). Thus, for a given ground surface area and object height, the maximum lightning-attractive area will be associated with the stroke having the largest peak amplitude.

Ground-Flash Density

In the United States, actual cloud-to-ground lightning strike data is detected and archived by the National Lightning Detection Network (NLDN). Global Atmospherics, Inc. (GAI—Tucson, AZ) analyzes the data and produces ground-flash density maps for user-specified areas. The map used for this study was based upon 29,207 negative and positive flashes—five years (1990–1994) of site-specific data—detected in an area of 1.3 x 104 km2. The average overall flash density was 0.45 flashes/km2/yr, ranging from < 0.25 to < 0.5 flashes/km2/yr within a 4-km radius of the facility.

The following should be taken into account when considering the GAI data. NLDN detection efficiency (DE)—i.e., the percentage of all lightning flashes that were detected and recorded—improved over the five-year period during which our data was acquired. Initially, DE was reported as 65–70%; the currently (1995) stated value is 85–90% (for Ipk > 5 kA). Assuming a five-year DE average of 75% (considered by GAI to be a reasonable estimate) gives a corrected facility flash-density range of < 0.33 to < 0.67. The median value of 0.5 flashes/km2/yr was used for our probability calculations.

Two points regarding this value of ground-flash density should be kept in mind. It is based upon only five years (1990–95) of actual NLDN data—the network was quite new at the time this study was carried out. Analysis of data collected since that time probably would indicate a different value, although it seems doubtful that it would differ by very much. Significantly different values of ground-flash density are found in other parts of the country. However, even locations relatively close to the area studied could have notably different values because of variations in topography. That is one of the benefits of NLDN data, the ability to identify differences between wide-area flash-density estimates, and site-specific values.

Return-Stroke Peak-Current Amplitude

Over a number of decades, researchers have measured and recorded a variety of lightning parameters, with much of the data resulting from strikes to tall, instrumented steel towers. Along with current rate of rise and total charge transfer, peak return-stroke current is considered to be one of lightning’s most significant threat parameters. For the generally accepted frequency distribution of peak currents for negative lightning, the first-percentile value, 200 kA (i.e., 99% of all lightning is of lower amplitude), is generally considered to constitute a severe negative stroke.

Although the NLDN detection efficiency is less than 100%, GAI reports that it is low-peak-current (i.e., < 5 kA) events that are missed. Thus, had all flashes been detected, the distribution of peak-current amplitudes would be expected to show a somewhat lower average value.

Facility Lightning Attractive Area

Since the twelve 32-meter-tall perimeter light poles for our study appeared to be likely lightning strike points—at least for large-amplitude flashes—they were used in calculating the facility's lightning-attractive area. For the sake of simplicity, structure height was not included in our equation. It is reasonable to expect that some low-amplitude strokes will bypass the poles and attach to the structure.

As previously discussed, attractive area must take into account the peak amplitude of return-stroke current. Thus, an attractive area must be calculated for each current amplitude. The following method for dealing with the distribution of return-stroke currents is attributed to the late J. Stahmann of Boeing/Kennedy Space Center (Ref. 3). Stahmann assigned return-stroke peak currents from a large body of available data to deciles—i.e., 10% of the total number of flashes being considered were placed into each of ten bins. The mean peak current per decile was then calculated.

Facility Strike Probability

Stahmann’s mean peak-current per decile values were used to find the per-decile attractive area. The effect of the tall light poles on attractive area (Aa) can be seen in Table 1. Although the surface area encompassed by the poles is 45*103 m2, the lightning-attractive area is 77*103 m2 for a 6-kA stroke and 171*103 m2 for a 112-kA stroke. The product of attractive area times ground-flash density provided per-decile probability, the sum of which gave a cumulative probability. The reciprocal of cumulative probability is the mean return period (average strike frequency). Our study determined that some point of the facility will be struck by lightning—of some amplitude—approximately once every 17 years.

Table 1. Cumulative Probability of Strike to Facility

 

Ipk

Ds

r

AA

Po

Pc

R

Decile #

(kA)

(m)

(m)

(m2)

 

 

(yr/fl)

1

6

33

33

76,764

3.8E-03

   

2

13

53

48

93,489

4.7E-03

   

3

18

65

56

101,496

5.1E-03

   

4

23

76

62

108,624

5.4E-03

   

5

28

88

68

115,399

5.8E-03

   

6

35

101

74

122,391

6.1E-03

   

7

45

118

81

130,658

6.5E-03

   

8

57

138

89

140,196

7.0E-03

   

9

77

168

99

153,061

7.6E-03

   

10

112

215

113

171,380

8.6E-03

6E-02

17

 

Area enclosed by light poles: l = 312 m, w = 144 m (l x w = 44,928) m2
h = height of poles above ground level = 32 m
Ipk = average peak return-stroke current per decile kA
Ds = lightning striking distance = 10 x Ipk0.65 m
r = radius of light pole's attractive area = (2 x Ds x h - h2)0.5 m
AA = attractive area/decile = (l + 2r) x (w + 2r) - 10 x [(4 - π)/4] x r2 m2
Fg = ground flash density = 0.5 {using GAI flash density analysis} fl/km2/yr
PO = strike probability/decile = AA x (0.1 x Fg) x 106  
PC = cumulative probability = Σ PO  
R = mean return period (i.e., average strike frequency) = 1/PC years/flash

Conclusion

Reasonable strike probability estimates can be made using site-specific, ground-flash density values that are based upon actual lightning data. Strike estimates are interesting, and although their results provide an indication of lightning strike return frequency, they should not be considered as absolutes. Perhaps their most useful function is to permit determination of the relative effects of changes made to a facility. Examples of such changes are: increased lightning-attractive area—either by extending the facility's surface dimensions and/or height (adding a vent stack or tower); placing an identical facility in a location having a significantly different ground-flash density.

References

1. Golde, R.H., "Protection of Structures Against Lightning," Proceedings of the Institute of Electrical Engineers, Vol. 115, No. 10, pp. 1523-1529, 1968.

2. Golde, R.H., "The Lightning Conductor," in Golde, Lightning, Vol. 2, p. 560, Academic Press, London, 1977 (the striking distance equation attributed to E.R. Love).

3. Stahmann, J.R., "Launch Pad Lightning Protection Enhancement by Induced Streamers," Boeing Aerospace Operations, Kennedy Space Center, Florida, September 1968.


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