Geoscience Reference
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Fig. 5.15 Sketch of model thunderstorm distribution around the ground-recording station, with
the location of the thunderstorm sites ( little circles ) and the station (the “house” in the center of
the picture) indicated. The thunderstorm sites are randomly distributed along the “equidistant”
circumferences so that the circumference radii are r n D r 1 n,wheren D 1;2;3;:::, and the mean
number density of the sites is approximately constant. Taken from Surkov et al. ( 2006 )
area with radius r n gives N=S 2= r 1 , which is a constant value as we have
assumed above. Hence r 1 can be expressed through the mean distance, h r i , between
the thunderstorms r 1 Dh r i .2=/ 1=2 .
In Figs. 5.16 and 5.17 we plot the spectra of the correlation function xx versus
frequency f D !=.2/. We have chosen the above parameters for the lightning
discharges as well as the ionospheric parameters for the nighttime conditions. The
spectrum due to four thunderstorms located on the first circumference with radius
r 1 D 550 km is shown in Fig. 5.16 with lines 1. The same but for r 1 D 400 km
is shown in Fig. 5.17 with lines 1. The mean number rate of lightning flashes
is chosen to be D 0:05 s 1 for each thunderstorm, that is a typical value for
the single thunderstorm center. The thunderstorm sites were randomly distributed
along the circumference with the help of a random-number generator. In making
the plots in Figs. 5.16 and 5.17 we have used two different random samplings of
the thunderstorm site distribution. In the next place we take into account the total
contribution of all the thunderstorms located on the first and second circumferences.
The areas occupied by these thunderstorms have the radii r 2 D 1;100 and 800 km,
respectively. The spectra due to these 12 thunderstorms are shown in Figs. 5.16
and 5.17 with lines 2. Moreover, each spectrum shown in these figures is related
to a certain area occupied by the thunderstorms, which make a contribution to the
spectrum. The spectra shown with lines 1-7 correspond to the area radii r D 0:55,
1:1, 1:65, 2:2, 3:3, 4:4, and 5:5 thousands km (Fig. 5.16 ) and r D 0:4, 0:8, 1:2,
1:6, 2:4, 3:2, and 4:0 thousands km (Fig. 5.17 ). Total number of the thunderstorms
restricted by the latest radius (line 7) is equal to 220.
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