Earth-Ionosphere Cavity Resonator - Ultra and Extremely Low Frequency Electromagnetic Fields - page 126

more than 250-350 C km, that is beyond its mean value, the ratio between C CG
occurrence rate and CG occurrence rate increases in a gradual manner. Consider-
ing, as an example, the charge moment distribution for lightning flashes located in
Africa (Williams et al. 2007 ), one can find that the ratio of the positive lightning
number to negative lightning number changes from 1:7 to more than 10,asthe
lightning charge moment increases from 500 to 2;000 C km. It is of interest at this
point to compare the contribution of C CG and CG global lightning activities to
the excitation of the Schumann resonances.
It is obvious from Fig. 3.8 that in the low-frequency band and, in particular, in
the range of the Schumann resonances, the spectral density m.!/ of the current
moment generated by CG return stroke is a slowly varying function of frequency.
In this frequency region Eq. ( 3.8 ) can be simplified to the following equation:
m.!/ D MF .!/ D l I 3

:

I 4
! 4 i! ! 3 C

(4.50)

Here the parameters I 3 and I 4 determine the magnitude of the low-frequency portion
of the lightning spectrum, ! 3 and ! 4 are inverse time parameters which define
the total duration of the signal, l is approximately equal to the maximal lightning
channel length, and ! D 2f . In the frequency range of the first Schumann
resonances, that is f D 7-22 Hz, the function ( 4.50 ) varies within 20 %. In the
subsequent discussion we will neglect this change; that is, the function F.!/ is
considered as a constant in the frequency range of interest.
From Eq. ( 3.6 ) for the stroke current, it is clear that the function ( 4.50 ) describes
the long-lasting CC (continuing current) that immediately follows the CG peak
current. In this picture the CC makes a considerable contribution to ULF/ELF region
and thus can play a significant role in the generation of Schumann resonances.
According to Ballarotti et al. ( 2005 ), only 28 % of the strokes in CG flash are
followed by some kind of CC whereas almost every C CG lightning is accompanied
by the CC that can reach a value of about I p D 5-10 kA for periods up to
p D 5-10 ms (Brook et al. 1982 ). Typically the CCs last for ten to hundreds of
milliseconds (Rakov and Uman 2003 ). So large a CC may result in the extraordinary
large charge transfer of the order of tens coulombs. The low-frequency spectrum of
the C CG lightning can be written similarly to Eq. ( 4.50 ) where one should replace

the parameter I 3 =! 3 C I 4 =! 4 by the mean parameter I p =! p ! p p .
The charge moment distributions for hundreds of thousands of positive and
negative lightning flashes have been measured over the globe including world
thunderstorm centers located in Africa, North and South America (e.g., see Williams
et al. 2007 ). In practice, with decreasing charge moment the lightning waveforms
overlap in such a way that individual flashes cannot be resolved (Füllekrug et al.
2002 ). So, the empirical distribution of the distant flashes is bounded from below by
the magnitude about 50 C km (Williams et al. 2007 ). In this study we do not come
close to exploring the statistical distributions of the lightning parameters in any
detail, since we focus on a rough estimate based on the mean parameters of the CG