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Frequency dependence of atmospheric noise intensity from 1 to 1000 kHz at low and medium latitudes
Journal of Atmosphericand TerrestrialPhysics, 1969, Vol. 31, pp. 135 to 144. PergamonPreen. Printed in NorthernIre land
Frequency dependence of atmospheric noise intensity from 1 to 1000 kHz at low and medium latitudes B. SCHXNIN~ Observatory
for Ionospheric (Received
and G. CUMME Research,
Ktihlungsborn,
GDR
2 1 June 1968)
Summary-During June/July 1964, atmospheric noise has been measured in the frequency ranges 1 to 200 kHz (daytime) and 1 to 1000 kHz (night-time) on board a trade ship in the Mediterranean and Red Sea and at Zanzibar. The frequency dependence of noise level during daytime is in rough agreement with the frequency dependence of the attenuation rate in the earth-ionosphere wave guide. 1.
INTR~DUOTI~N
As A PART of the IQSY programme of the Observatory for Ionospheric Research at Ktihlungsborn, atmospheric noise measurements were made on board a trade ship on a route to East Africa in June and July 1964. LAUTER et aZ. (1966, 1967) have already reported the variations of the mean diurnal behaviour of atmospheric noise at different VLF and ELF frequencies with respect to the latitude. In the present contribution, the frequency dependence of atmospheric noise intensity in the ranges l-200 kHz (daytime) and l-1000 kHz (night-time) between 35’N and 6% (Mediterranean, Red Sea, Zanzibar) is analyzed. In the range 1-15 kHz, the atmospherics have been recorded by magnetic tape using a broad band receiver. From the records, the frequency dependence of fieldstrength was determined by a VLF analyzator (3 dB bandwidth = 200 Hz). Above 15 kHz, the diurnal variation of atmospheric noise at different frequencies was measured by a superhet * the output of which was connected with a pen recorder. A 35 m L-antenna was used, the frequency dependent effective height of which was measured by comparison with loop antennae (GL~~DE et al., 1965). 2. RESULTS Measured frequency distributions of atmospheric noise intensity on different parts of the ship route are presented in Figs. l-5. Striking similarity is present between distributions at different latitudes with respect to main features of the frequency dependence of noise intensity and its diurnal variations. An intensity minimum exists around 2.5 kHz, whereas a maximum is found around 10 kHz. As to be seen, the slopes below and above the minimum are nearly equal, if a logarithmic frequency scale is used. The location of the minimum shows a clear diurnal variation between 2.0 and 3.3 kHz, which can be seen from Fig. 6. Obviously, the variation width increases with latitude. At medium and high latitudes, the mean value is clearly greater than at low latitudes. At all latitudes, the diurnal frequency variation of the intensity minimum shows a considerable time advance with respect to local mean time. * 3 dB bandwidth
=
500 Hz. 135
B. SCHININQand G. CUMME
136 Figs. 1-5.
01
Frequency dependence of integrated atmospheric noise intensity E,,,. intensities refer to an unique 3 dB-bandwidth of .~r250 Hz.
1 !
2
(/Ii
4
6
8
10
I
’
//
20
40
f,
60
80
60
80
I
IO’
1”
I 400
200
400
All
!I 600800
600
800
kc/s
3
presence tioned
an has
minimum
a
near
above (cf. example
been by guide 1957a, WATT, 1957; et 1967). and derived minimum 3-4 and maximum 7 10 using formula by (experimental minimum kHz, 7-13 whereas et al.derive the frequency values l-3 kHz for the minimum and 7-13 kHz for the maximum (experimental results: minimum
Frequency dependence of atmospheric noise intensity from 1 to 1000 kHz
137
64
Frequency dependence of atmospheric noise intensity, IO*-20°N,
r
Red Sea
~~~~~~~”
32
\
l\ 24
~
l ---.
l’
lY
l
‘i
/ -.
,kyQ\ ‘\-
i
\,
/*
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j \
l\
d
<. %
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-%b k
.
08.30\
8
1.x
z
5&\, J\
LMT 1400
iil
),“1;!;/ 2
4
6
8
10
20
“4’+,&‘?l
\\ LtiT
00 LMl “‘\‘,\ -’ 1;:
00.40
---.--45
f,
63
60
io
200
400
LMT !i b@OBO@
ktiz
Fig. 3
Frequewy dependence of atmospheric nwe intensity, O”-IO”N, Coast of ‘Somolto I9.6.- 22.6.64
--L’
I#
I 4
6
8
10
40
20 f,
Fig.
60
--. 80
IO
200
..400
I
’
600
800
ktiz 4
1-3 kHz, maximum 6-9 kHz). The above mentioned observed frequencies (minimum 2+0-3.3 kHz, maximum around 10 kHz) are well within those results. The ratio of the intensity maximum and the minimum shows a statistical distribution, which is demonstrated by Fig. 7. This diagram contains all low latitude results (6’S to 35”N). During daytime, the ratio is greater than during night, which is in accordance with theoretically calculated attenuation factors. The distance scale at the bottom of Fig. 7 is based upon theoretical considerations on daytime propagation, which will be described in Section 3.3. Above 10 kHz, the intensity decreases with increasing frequency, the slope of
Frequency atmospheric
dependence of noise intensity Zonzibor
O'-iO"S, 22.6-29.6.64
)’
f,
kHz
Fig. 6 LMT 0
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4
8
6
.. .
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IO
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-
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.
_. -xX.X25_
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:
.
.
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.
.
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._p;--.
-
Gulf of Aden 15.6.-19.6.64 . 2.7.-12.7.64
O--IO-N _
_
_:
. 8°C
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. . -%-.g .
. ‘i_
Coast of Somalia 19.6-22.6.64 29.6-2.7.64
.
---F-d.
l
I.5
I
.
.
_
l. ’ c;._;; . .
. .
30.-40.N Mediterranean 1.6-8.6.64 . 16.7.-23.7.64
. :,?_ <. .
o.- I0.S Zonr,bar - 22.6-29.6.64
Daily frequency variation of the intensity minimum of atmosphorio noise near 2.6 kHz at different geographical latitudes. 138
Frequency
139
dependence of atmospheric noise intensity from 1 to 1000 kHz 20 Log 6 1
go-
8
E,,(max)/E,,(min)
IO
12
14
16
=L , II3
20
dB 22
24
26
(35”N-6”s) June/July 1964 doy: 14.00-16.00 LMT night: 21.00-01.00 LMT
800 Distance
1000 1200 p. km (daytime
I I 1400 1600 propagation)
Fig. 7. Probability distributions of the ratio of the intensity maximum near 10 kHz and the minimum near 2.5 kHz for daytime and night-time conditions at low latitudes. The distances p, indicated at the lower abscissa, have been calculated using equation (3) with A(f) from the mean curve in Fig. 9b.
the distribution curve being steeper during daytime. Averaging the daytime distributions for low latitudes, a frequency dependence f-” is found between 20 and 100 kHz. During daytime, n = 2.14 whereas during night n = 1.28. The difference results from the smaller night-time attenuation at higher frequencies. 3. ANALYSIS OF RESULTS The lightning generated noise propagates through the Earth-ionosphere wave guide, where it suffers frequency dependent attenuation. For analysis of measurement results, knowledge of both the original electromagnetic spectrum of the lightning source and the attenuation factor is necessary.
3.1 The source spectrum The lightning spectrum has been described completely by KIMPARA (1963)and HORNER and BRADLEY (1964).A mean curve is given in Fig. 8. 3.2 Attenuation formula (l-100kHz) Noise measurements in this frequency range have been interpreted and MAXWELL (1957) using a formula derived by WAIT (1956, 1957a):
Ed =
&f
0.4 . 1()44w/2.109
1000km KG? I 8000 km.
by WATT
(1)
B. SCH;~NIXG and G. CUMME
140
-120
64-
Relative
power
NT,dB,
of the lightning
-
104
--96
-08 l
0
I
,
2
Measured intensity EO”,dB above Zanzibar (6”S), 22.6.-29.6.64 14.00 LMT Left ordinate
/
3
I [II/l/ 4
56
, 810
IpV/m
-a0
-
,
,
20
30
1 I[1111 40 5060
f,
dB
a0 100
,
,
,
1 lllll
200
300
500
72
8001000
kHz
Fig. 8. Comparison of the frequency dependence of relative lightning intensity near the source and the measured intensity at low latitudes in the frequency range l-200 kHz.
Here E, = Vertical electric field strength at distance d (km) from the source, which is assumed to be a vertical electric dipole E, = “Effective radiated field at one mile from the source (usually expressed in V/m)” f = frequency, kHz A(f) = frequency dependent attenuation factor, dBjlOO0 km. A transmitter (vertical electric dipole) with power N, (kW) standing on ideally conducting flat earth produces at a distance p (km) the vertical fieldstrength, mV/m
Substituting
this for E, (p = 1 mile = l-61 km) into (l), we get E, = 1862/N,
+f
0.4 . 1pm.mo4*
(3)
Here
E, = Vertical electric field strength (?nv/m) at distance p (km) from transmitting vertical electric dipole = transmitting power, kW p = distance, km f = frequency, kHz A(f) = frequency dependent attenuation N,
factor, dB/lOOO km
Frequency dependence of atmospheric noise intensity from 1 to 1000 kHz 3.3
141
Comparison between theory and measurement at Zanzibar
The primarily emitted atmospheric radio noise spectrum was assumed to be X&j’) (in kW kHz-l), as presented in Fig. 8. This is a mean distribution of different curves given by A. Kimpara (1963). Recently, MAXWELL (1967) has described a range, which comprises many lightning spectra (given by different authors). The
a A ( f 1-A (15 KHz)
1000km 1500 km 2000km
xwell,
upper
limit
I f,
kHr
Fig. 9. Frequency dependence of attenuation rate A. (a) A(f) - A(15 k=), (b) A(f) The upper and lower limits (full lines) have been taken from I1IJlyiwE~ (1967). The other curves (dashed lines) have been caloulated from source spectrum, observed spectrum and distance, which is indicated as a parameter.
above quoted spectrum is situated near the upper border of this range, It shows the often confirmed l/f-dependence at frequencies above 15 kHz. From the W&IO thunders~rm distribution (1956), the situation of the noise sources relatively to the observation site is most clear for the Zanzibar measurements during June. During daytime, the main atmospheric noise source region was 1000-2000 km NW from the observation site. For calculating theoretical noise spectra, knowledge of the frequency dependent attenuation rate A is necessary. A-values as given by different authors show a relatively broad spread (Fig. 9b). Therefore, the reverse procedure has been adopted, i.e., the variation of A with frequency has been calculated from the observed variation of fieldstrength with frequency by aid of equation (3). Relative values have been calculated, for the absolute source intensity is unknown. As to be seen from Fig. 9a, A varies within the expected limits if p is between 1000 and 2000 km.
B. SCHLNINUand G. CUMME
142
MAXWELL (1967) refers to the relatively
broad limits of A(f) in connection with the influence of location, time of day, season, sunspot cycle etc. Regarding daytime values of different authors, A(f) seems to be situated mainly in the upper half of the range given by Maxwell for f < 10 kHz, whereas above 10 kHz A(f) may even surpass the upper limit given here (see WATT, MAXWELL (1957) and additional references). Therefore, p values between 1500 and 1000 km are probable. This is in reasonable agreement with the source distance range 1000 to 2000 km according to
36
4 0 -4
1
I 20
30
II 40
50
I
I
I
I
I
70
100
200
390
400
f,
kHz
I 500
Fig. 10. Comparison of observed frequency dependence of atmospheric intensity (2) with theoretical values (full lines) in the frequency range 50-200 Source distances for theoretical curves are indicated. All values have normalized to equal intensity at f = 50 IrHz. For explanation see Section
noise kHz. been 3.3.
the WMO thunderstorm distribution, for the influence of the nearer sources upon the observed spectrum is stronger. Adding a constant value to A(f) - A(15 kHz) at p = 1200 km, an A(f) curve has been constructed according to the limits given by Maxwell (Fig. 9b). The attenuation maximum near 2.5 kHz corresponds to the observed intensity minimum near this frequency. An intensity minimum between 2 and 4 kHz has also been p I 3000 km); WATT, observed by other authors (e.g., ALPERT et al. (1967; MAXWELL (1956)).
Inserting A(f) into equation (3) and using the primary spectrum NT(f), the intensity ratio EmsX/Eminof the maximum intensity near 10 kHz and the minimum intensity near 2.5 kHz can be calculated as a function of distance. In Fig. 7, the observed distribution of Emax/Emin is presented for all measurements between 6”s and 35”N (Zanzibar to Mediterranean) and the corresponding p values are indicated at the bottom side scale. For any alteration of the above mentioned mean value p = 1200 km causes the same alteration of the p values belonging to Emax/Emin,and propagation in different directions with respect to the Earth’s magnetic field (i.e., with different A values)
Frequency
dependence of atmospheric noise intensity from 1 to 1000 kHz
143
cont~bu~d to the me~~ement points of Fig. 7, the bottomside scale should be used only as an indicator of the order of magnitude of source distances. During night, the attenuation is lower, producing smaller spectrum curve slopes. The noise sources are not only placed in the 1000-2000 km distance range, and it is difficult to define a mean distance. Therefore the above described method of analyzing the noise spectra has not been applied. With respect to the frequency range 50-200 kHz, VOLLAND (1964) has given an at~nuation formula similar to that of klaxwell, A(f) being proportional tofO.6:
(4) Here IE,l = Vertical electric field strength (mV/m) at distance p (km) from transmitting vertical electric dipole 2 /&Jo/= vertical electric fieldstrength at distance p from transmitter, if both transmitter and receiver stand on an ideally conducting flat earth p = distance, km 0 = p/W, R = radius of the Earth (the factor y’(B,%in 0) accounts for the curved earth) 3, = vacuum wavelength, km h, = height of sharply bounded equivalent ionosphere above the earth, (70 km during daytime, 90 km at night-time) A Buf = attenuation factor; AAu’ = O*OOlPduring daytime, AAu’ = 0.0009 at night-time. Inserting equation (2) into equation (4), we get [B’,l = 3602/(X,)
- J J s-f
a e-AAdpa-o’6
(5)
with @,I = vertical electric fieldstrength frnV/~~,)at distance p (km) from transmitting vertical electric dipole iV, = transmitted power, kW for the other symbols see text below equation (4). There has been some discussion regarding the way of deducing that formula and especially the correctness of the flat-earth-approximation used therein. From the observed noise spectra, it seems likely that the attenuation may be described by a formula of this kind. Thus, noise spectra have been calculated from source spectrum and distance, using Volland’s Formula. The results have been normalized to equal intensity at f = 50 kHz and are presented together with the experimental result in Fig. 10. Except the relatively low intensity at 100 kHz, the observed values indicate distances between 1500 and 2500 km. Enlarging the attenuation rate in Volland’s Formula by a factor 1.3 would give the same curves as in Fig. 10, belonging to distances smaller by a factor O-75. Then the observed values would indicate distances similar to those taken of the WMO thunderstorm distribution. With respect to the uncertainty of A values in general, this variation seems not too large.
B. SCE_&NINU and G. CUMME
144
Ae~~o~Z~ge~~t-~e oxpedition measurement form a part of the GDR IQSY programmo, which was sponsored and supported finanoi&~y by the ~ation~komi~ee fiir Geodijsie und Geophysik der DDR (NKGG). REFERENCES A.LPERT,JA.,L.,FLIGIZLD. &and MICHAILOVA G.A. GLADE P.,MEVENBUR~ D.and SCH~NINCB. HoRNERF.~~~BRADLEYP.A. KIZPARAA. LAVTERE.A.,SC~NINUB.~~~WEISSJ. LAUTERE.A.~~~SCI&NINUB.
1967
J. Atmosph. Terr. Phys., 29, 29.
1965
Zs. f. Meteorologic, 18, 1.
1964 1963 1968 1966
J. Atrnosph. Terr. Phys. 26, 1155. Proc. Res. Inst. Atmosph. 11, 1. 2s. f. Meteorolog~e (In press.). Schriftenreihe des NKGG, Reihe 11, Heft 3, 95.
MAXWELL E.L. VOLLAND H. WAIT J.R. WAIT J. R. WAIT J.R. ~A~A.D.~~~~~AX~LL~. L. WMO (WORLD IMETEOR~L~C~ICAL ORQANIZATION),GXNEVA
1967 1964 1956 1957a 19573 1957 1956
Rad. Xci. 2, 637. Nachr.-Techn. 2s. 12, 641. NBS Rep. 6022. Proc. IRE 45, 760. Proe. IRE 45, 768. Proc. IRE 45, 787. World Distribution of Thunderstorm Days, PA. 2, Tables of Marine Data and World Maps, No. 21.
1967 1956 1964 1967
J. Atmosph. Terr. Phys. 29, 803. Nature, Load. 177, 930. J. Atmosph. Terr. Phys. 20, 1015. IEE-Conf. on M.F., L.F. and V.L.F. Radio Propagation, London Sth-10th Nov. 1967, 204. Electromagnetio Waves inStratijed Media, Vol. 3, Pergamon Press, Oxford.
Ad&tionaZ references CHALLINOR R.A. CHAP~N F.W.und CRO0MD.L. J0NxD.L.
WAIT
J. R.
MAOARIO R.C.V.
1962
Frequency dependence of atmospheric noise intensity from 1 to 1000 kHz at low and medium latitudes B. SCHXNIN~ Observatory
for Ionospheric (Received
and G. CUMME Research,
Ktihlungsborn,
GDR
2 1 June 1968)
Summary-During June/July 1964, atmospheric noise has been measured in the frequency ranges 1 to 200 kHz (daytime) and 1 to 1000 kHz (night-time) on board a trade ship in the Mediterranean and Red Sea and at Zanzibar. The frequency dependence of noise level during daytime is in rough agreement with the frequency dependence of the attenuation rate in the earth-ionosphere wave guide. 1.
INTR~DUOTI~N
As A PART of the IQSY programme of the Observatory for Ionospheric Research at Ktihlungsborn, atmospheric noise measurements were made on board a trade ship on a route to East Africa in June and July 1964. LAUTER et aZ. (1966, 1967) have already reported the variations of the mean diurnal behaviour of atmospheric noise at different VLF and ELF frequencies with respect to the latitude. In the present contribution, the frequency dependence of atmospheric noise intensity in the ranges l-200 kHz (daytime) and l-1000 kHz (night-time) between 35’N and 6% (Mediterranean, Red Sea, Zanzibar) is analyzed. In the range 1-15 kHz, the atmospherics have been recorded by magnetic tape using a broad band receiver. From the records, the frequency dependence of fieldstrength was determined by a VLF analyzator (3 dB bandwidth = 200 Hz). Above 15 kHz, the diurnal variation of atmospheric noise at different frequencies was measured by a superhet * the output of which was connected with a pen recorder. A 35 m L-antenna was used, the frequency dependent effective height of which was measured by comparison with loop antennae (GL~~DE et al., 1965). 2. RESULTS Measured frequency distributions of atmospheric noise intensity on different parts of the ship route are presented in Figs. l-5. Striking similarity is present between distributions at different latitudes with respect to main features of the frequency dependence of noise intensity and its diurnal variations. An intensity minimum exists around 2.5 kHz, whereas a maximum is found around 10 kHz. As to be seen, the slopes below and above the minimum are nearly equal, if a logarithmic frequency scale is used. The location of the minimum shows a clear diurnal variation between 2.0 and 3.3 kHz, which can be seen from Fig. 6. Obviously, the variation width increases with latitude. At medium and high latitudes, the mean value is clearly greater than at low latitudes. At all latitudes, the diurnal frequency variation of the intensity minimum shows a considerable time advance with respect to local mean time. * 3 dB bandwidth
=
500 Hz. 135
B. SCHININQand G. CUMME
136 Figs. 1-5.
01
Frequency dependence of integrated atmospheric noise intensity E,,,. intensities refer to an unique 3 dB-bandwidth of .~r250 Hz.
1 !
2
(/Ii
4
6
8
10
I
’
//
20
40
f,
60
80
60
80
I
IO’
1”
I 400
200
400
All
!I 600800
600
800
kc/s
3
presence tioned
an has
minimum
a
near
above (cf. example
been by guide 1957a, WATT, 1957; et 1967). and derived minimum 3-4 and maximum 7 10 using formula by (experimental minimum kHz, 7-13 whereas et al.derive the frequency values l-3 kHz for the minimum and 7-13 kHz for the maximum (experimental results: minimum
Frequency dependence of atmospheric noise intensity from 1 to 1000 kHz
137
64
Frequency dependence of atmospheric noise intensity, IO*-20°N,
r
Red Sea
~~~~~~~”
32
\
l\ 24
~
l ---.
l’
lY
l
‘i
/ -.
,kyQ\ ‘\-
i
\,
/*
\
j \
l\
d
<. %
16-m-
-%b k
.
08.30\
8
1.x
z
5&\, J\
LMT 1400
iil
),“1;!;/ 2
4
6
8
10
20
“4’+,&‘?l
\\ LtiT
00 LMl “‘\‘,\ -’ 1;:
00.40
---.--45
f,
63
60
io
200
400
LMT !i b@OBO@
ktiz
Fig. 3
Frequewy dependence of atmospheric nwe intensity, O”-IO”N, Coast of ‘Somolto I9.6.- 22.6.64
--L’
I#
I 4
6
8
10
40
20 f,
Fig.
60
--. 80
IO
200
..400
I
’
600
800
ktiz 4
1-3 kHz, maximum 6-9 kHz). The above mentioned observed frequencies (minimum 2+0-3.3 kHz, maximum around 10 kHz) are well within those results. The ratio of the intensity maximum and the minimum shows a statistical distribution, which is demonstrated by Fig. 7. This diagram contains all low latitude results (6’S to 35”N). During daytime, the ratio is greater than during night, which is in accordance with theoretically calculated attenuation factors. The distance scale at the bottom of Fig. 7 is based upon theoretical considerations on daytime propagation, which will be described in Section 3.3. Above 10 kHz, the intensity decreases with increasing frequency, the slope of
Frequency atmospheric
dependence of noise intensity Zonzibor
O'-iO"S, 22.6-29.6.64
)’
f,
kHz
Fig. 6 LMT 0
2
4
8
6
.. .
“>
IO
77 .<.
x -
g-*_-
I
I2
1
x
14
_
_X
16
1
1
.a x.J? X 3 -X‘ X
22
20
is
/
/
j
1
. f ? .h_?_.
.‘I
r.x
24
1
’
3
.?A.
3.5
-
-
-
_
_
-#.
-
+-;A
_.._
x l.
_, North Sea
20.5-30.5.64 26.7-8.8.64
40’-50.N Channel Gulf of Biscaya X 30.5-1.6.64 . 23.7-25.7.64
.
_. -xX.X25_
50’-60’N Boltlc.
7(~
F . ..
0 _t.-•.
_.-
. . . . -._.. ri._ . .
. -
-
.
. _._..----.._x
. - _
p*
=.
*
l
-
35
E .
2.5’---
0 *_
.
-
‘-Lo-- *.
:
.
.
20.-30.N Red Sea
.
.
-
)i
k”,‘,- 20&N ..
+
._p;--.
-
Gulf of Aden 15.6.-19.6.64 . 2.7.-12.7.64
O--IO-N _
_
_:
. 8°C
.
_p....--
. . -%-.g .
. ‘i_
Coast of Somalia 19.6-22.6.64 29.6-2.7.64
.
---F-d.
l
I.5
I
.
.
_
l. ’ c;._;; . .
. .
30.-40.N Mediterranean 1.6-8.6.64 . 16.7.-23.7.64
. :,?_ <. .
o.- I0.S Zonr,bar - 22.6-29.6.64
Daily frequency variation of the intensity minimum of atmosphorio noise near 2.6 kHz at different geographical latitudes. 138
Frequency
139
dependence of atmospheric noise intensity from 1 to 1000 kHz 20 Log 6 1
go-
8
E,,(max)/E,,(min)
IO
12
14
16
=L , II3
20
dB 22
24
26
(35”N-6”s) June/July 1964 doy: 14.00-16.00 LMT night: 21.00-01.00 LMT
800 Distance
1000 1200 p. km (daytime
I I 1400 1600 propagation)
Fig. 7. Probability distributions of the ratio of the intensity maximum near 10 kHz and the minimum near 2.5 kHz for daytime and night-time conditions at low latitudes. The distances p, indicated at the lower abscissa, have been calculated using equation (3) with A(f) from the mean curve in Fig. 9b.
the distribution curve being steeper during daytime. Averaging the daytime distributions for low latitudes, a frequency dependence f-” is found between 20 and 100 kHz. During daytime, n = 2.14 whereas during night n = 1.28. The difference results from the smaller night-time attenuation at higher frequencies. 3. ANALYSIS OF RESULTS The lightning generated noise propagates through the Earth-ionosphere wave guide, where it suffers frequency dependent attenuation. For analysis of measurement results, knowledge of both the original electromagnetic spectrum of the lightning source and the attenuation factor is necessary.
3.1 The source spectrum The lightning spectrum has been described completely by KIMPARA (1963)and HORNER and BRADLEY (1964).A mean curve is given in Fig. 8. 3.2 Attenuation formula (l-100kHz) Noise measurements in this frequency range have been interpreted and MAXWELL (1957) using a formula derived by WAIT (1956, 1957a):
Ed =
&f
0.4 . 1()44w/2.109
1000km KG? I 8000 km.
by WATT
(1)
B. SCH;~NIXG and G. CUMME
140
-120
64-
Relative
power
NT,dB,
of the lightning
-
104
--96
-08 l
0
I
,
2
Measured intensity EO”,dB above Zanzibar (6”S), 22.6.-29.6.64 14.00 LMT Left ordinate
/
3
I [II/l/ 4
56
, 810
IpV/m
-a0
-
,
,
20
30
1 I[1111 40 5060
f,
dB
a0 100
,
,
,
1 lllll
200
300
500
72
8001000
kHz
Fig. 8. Comparison of the frequency dependence of relative lightning intensity near the source and the measured intensity at low latitudes in the frequency range l-200 kHz.
Here E, = Vertical electric field strength at distance d (km) from the source, which is assumed to be a vertical electric dipole E, = “Effective radiated field at one mile from the source (usually expressed in V/m)” f = frequency, kHz A(f) = frequency dependent attenuation factor, dBjlOO0 km. A transmitter (vertical electric dipole) with power N, (kW) standing on ideally conducting flat earth produces at a distance p (km) the vertical fieldstrength, mV/m
Substituting
this for E, (p = 1 mile = l-61 km) into (l), we get E, = 1862/N,
+f
0.4 . 1pm.mo4*
(3)
Here
E, = Vertical electric field strength (?nv/m) at distance p (km) from transmitting vertical electric dipole = transmitting power, kW p = distance, km f = frequency, kHz A(f) = frequency dependent attenuation N,
factor, dB/lOOO km
Frequency dependence of atmospheric noise intensity from 1 to 1000 kHz 3.3
141
Comparison between theory and measurement at Zanzibar
The primarily emitted atmospheric radio noise spectrum was assumed to be X&j’) (in kW kHz-l), as presented in Fig. 8. This is a mean distribution of different curves given by A. Kimpara (1963). Recently, MAXWELL (1967) has described a range, which comprises many lightning spectra (given by different authors). The
a A ( f 1-A (15 KHz)
1000km 1500 km 2000km
xwell,
upper
limit
I f,
kHr
Fig. 9. Frequency dependence of attenuation rate A. (a) A(f) - A(15 k=), (b) A(f) The upper and lower limits (full lines) have been taken from I1IJlyiwE~ (1967). The other curves (dashed lines) have been caloulated from source spectrum, observed spectrum and distance, which is indicated as a parameter.
above quoted spectrum is situated near the upper border of this range, It shows the often confirmed l/f-dependence at frequencies above 15 kHz. From the W&IO thunders~rm distribution (1956), the situation of the noise sources relatively to the observation site is most clear for the Zanzibar measurements during June. During daytime, the main atmospheric noise source region was 1000-2000 km NW from the observation site. For calculating theoretical noise spectra, knowledge of the frequency dependent attenuation rate A is necessary. A-values as given by different authors show a relatively broad spread (Fig. 9b). Therefore, the reverse procedure has been adopted, i.e., the variation of A with frequency has been calculated from the observed variation of fieldstrength with frequency by aid of equation (3). Relative values have been calculated, for the absolute source intensity is unknown. As to be seen from Fig. 9a, A varies within the expected limits if p is between 1000 and 2000 km.
B. SCHLNINUand G. CUMME
142
MAXWELL (1967) refers to the relatively
broad limits of A(f) in connection with the influence of location, time of day, season, sunspot cycle etc. Regarding daytime values of different authors, A(f) seems to be situated mainly in the upper half of the range given by Maxwell for f < 10 kHz, whereas above 10 kHz A(f) may even surpass the upper limit given here (see WATT, MAXWELL (1957) and additional references). Therefore, p values between 1500 and 1000 km are probable. This is in reasonable agreement with the source distance range 1000 to 2000 km according to
36
4 0 -4
1
I 20
30
II 40
50
I
I
I
I
I
70
100
200
390
400
f,
kHz
I 500
Fig. 10. Comparison of observed frequency dependence of atmospheric intensity (2) with theoretical values (full lines) in the frequency range 50-200 Source distances for theoretical curves are indicated. All values have normalized to equal intensity at f = 50 IrHz. For explanation see Section
noise kHz. been 3.3.
the WMO thunderstorm distribution, for the influence of the nearer sources upon the observed spectrum is stronger. Adding a constant value to A(f) - A(15 kHz) at p = 1200 km, an A(f) curve has been constructed according to the limits given by Maxwell (Fig. 9b). The attenuation maximum near 2.5 kHz corresponds to the observed intensity minimum near this frequency. An intensity minimum between 2 and 4 kHz has also been p I 3000 km); WATT, observed by other authors (e.g., ALPERT et al. (1967; MAXWELL (1956)).
Inserting A(f) into equation (3) and using the primary spectrum NT(f), the intensity ratio EmsX/Eminof the maximum intensity near 10 kHz and the minimum intensity near 2.5 kHz can be calculated as a function of distance. In Fig. 7, the observed distribution of Emax/Emin is presented for all measurements between 6”s and 35”N (Zanzibar to Mediterranean) and the corresponding p values are indicated at the bottom side scale. For any alteration of the above mentioned mean value p = 1200 km causes the same alteration of the p values belonging to Emax/Emin,and propagation in different directions with respect to the Earth’s magnetic field (i.e., with different A values)
Frequency
dependence of atmospheric noise intensity from 1 to 1000 kHz
143
cont~bu~d to the me~~ement points of Fig. 7, the bottomside scale should be used only as an indicator of the order of magnitude of source distances. During night, the attenuation is lower, producing smaller spectrum curve slopes. The noise sources are not only placed in the 1000-2000 km distance range, and it is difficult to define a mean distance. Therefore the above described method of analyzing the noise spectra has not been applied. With respect to the frequency range 50-200 kHz, VOLLAND (1964) has given an at~nuation formula similar to that of klaxwell, A(f) being proportional tofO.6:
(4) Here IE,l = Vertical electric field strength (mV/m) at distance p (km) from transmitting vertical electric dipole 2 /&Jo/= vertical electric fieldstrength at distance p from transmitter, if both transmitter and receiver stand on an ideally conducting flat earth p = distance, km 0 = p/W, R = radius of the Earth (the factor y’(B,%in 0) accounts for the curved earth) 3, = vacuum wavelength, km h, = height of sharply bounded equivalent ionosphere above the earth, (70 km during daytime, 90 km at night-time) A Buf = attenuation factor; AAu’ = O*OOlPduring daytime, AAu’ = 0.0009 at night-time. Inserting equation (2) into equation (4), we get [B’,l = 3602/(X,)
- J J s-f
a e-AAdpa-o’6
(5)
with @,I = vertical electric fieldstrength frnV/~~,)at distance p (km) from transmitting vertical electric dipole iV, = transmitted power, kW for the other symbols see text below equation (4). There has been some discussion regarding the way of deducing that formula and especially the correctness of the flat-earth-approximation used therein. From the observed noise spectra, it seems likely that the attenuation may be described by a formula of this kind. Thus, noise spectra have been calculated from source spectrum and distance, using Volland’s Formula. The results have been normalized to equal intensity at f = 50 kHz and are presented together with the experimental result in Fig. 10. Except the relatively low intensity at 100 kHz, the observed values indicate distances between 1500 and 2500 km. Enlarging the attenuation rate in Volland’s Formula by a factor 1.3 would give the same curves as in Fig. 10, belonging to distances smaller by a factor O-75. Then the observed values would indicate distances similar to those taken of the WMO thunderstorm distribution. With respect to the uncertainty of A values in general, this variation seems not too large.
B. SCE_&NINU and G. CUMME
144
Ae~~o~Z~ge~~t-~e oxpedition measurement form a part of the GDR IQSY programmo, which was sponsored and supported finanoi&~y by the ~ation~komi~ee fiir Geodijsie und Geophysik der DDR (NKGG). REFERENCES A.LPERT,JA.,L.,FLIGIZLD. &and MICHAILOVA G.A. GLADE P.,MEVENBUR~ D.and SCH~NINCB. HoRNERF.~~~BRADLEYP.A. KIZPARAA. LAVTERE.A.,SC~NINUB.~~~WEISSJ. LAUTERE.A.~~~SCI&NINUB.
1967
J. Atmosph. Terr. Phys., 29, 29.
1965
Zs. f. Meteorologic, 18, 1.
1964 1963 1968 1966
J. Atrnosph. Terr. Phys. 26, 1155. Proc. Res. Inst. Atmosph. 11, 1. 2s. f. Meteorolog~e (In press.). Schriftenreihe des NKGG, Reihe 11, Heft 3, 95.
MAXWELL E.L. VOLLAND H. WAIT J.R. WAIT J. R. WAIT J.R. ~A~A.D.~~~~~AX~LL~. L. WMO (WORLD IMETEOR~L~C~ICAL ORQANIZATION),GXNEVA
1967 1964 1956 1957a 19573 1957 1956
Rad. Xci. 2, 637. Nachr.-Techn. 2s. 12, 641. NBS Rep. 6022. Proc. IRE 45, 760. Proe. IRE 45, 768. Proc. IRE 45, 787. World Distribution of Thunderstorm Days, PA. 2, Tables of Marine Data and World Maps, No. 21.
1967 1956 1964 1967
J. Atmosph. Terr. Phys. 29, 803. Nature, Load. 177, 930. J. Atmosph. Terr. Phys. 20, 1015. IEE-Conf. on M.F., L.F. and V.L.F. Radio Propagation, London Sth-10th Nov. 1967, 204. Electromagnetio Waves inStratijed Media, Vol. 3, Pergamon Press, Oxford.
Ad&tionaZ references CHALLINOR R.A. CHAP~N F.W.und CRO0MD.L. J0NxD.L.
WAIT
J. R.
MAOARIO R.C.V.
1962