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Radio atmospheric signal

August 25, 2023

A radio atmospheric signal or sferic (sometimes also spelled "spheric") is a broadband electromagnetic impulse that occurs as a result of natural atmospheric lightning discharges. Sferics may propagate from their lightning source without major attenuation in the Earth–ionosphere waveguide, and can be received thousands of kilometres from their source. On a time-domain plot, a sferic may appear as a single high-amplitude spike in the time-domain data. On a spectrogram, a sferic appears as a vertical stripe (reflecting its broadband and impulsive nature) that may extend from a few kHz to several tens of kHz, depending on atmospheric conditions.

A frequency vs. time plot (spectrogram) showing several whistler signals amidst a background of sferics as received at Palmer Station, Antarctica on August 24, 2005.

Sferics received from about 2,000 kilometres' distance or greater have their frequencies slightly offset in time, producing tweeks.

When the electromagnetic energy from a sferic escapes the Earth-ionosphere waveguide and enters the magnetosphere, it becomes dispersed by the near-Earth plasma, forming a whistler signal. Because the source of the whistler is an impulse (i.e., the sferic), a whistler may be interpreted as the impulse response of the magnetosphere (for the conditions at that particular instant).

Introduction Edit

A lightning channel with all its branches and its electric currents behaves like a huge antenna system from which electromagnetic waves of all frequencies are radiated. Beyond a distance where luminosity is visible and thunder can be heard (typically about 10 km), these electromagnetic impulses are the only sources of direct information about thunderstorm activity on the ground. Transients electric currents during return strokes (R strokes) or intracloud strokes (K strokes) are the main sources for the generation of impulse-type electromagnetic radiation known as sferics (sometimes called atmospherics).[1] While this impulsive radiation dominates at frequencies less than about 100 kHz, (loosely called long waves), a continuous noise component becomes increasingly important at higher frequencies.[2][3] The longwave electromagnetic propagation of sferics takes place within the Earth-ionosphere waveguide between the Earth's surface and the ionospheric D- and E- layers. Whistlers generated by lightning strokes can propagate into the magnetosphere along the geomagnetic lines of force.[4][5] Finally, upper-atmospheric lightning or sprites, that occur at mesospheric altitudes, are short-lived electric breakdown phenomena, probably generated by giant lightning events on the ground.

Source properties Edit

Basic stroke parameters Edit

In a typical cloud-to-ground stroke (R stroke), negative electric charge (electrons) of the order of Q ≈ 1 C stored within the lightning channel is lowered to the ground within a typical impulse time interval of τ = 100 μs . This corresponds to an average current flowing within the channel of the order of J ≈ Q⁄τ = 10 kA . Maximum spectral energy is generated near frequencies of f ≈ 1⁄τ = 10 kHz ,[6] or at wavelengths of λ = c⁄f ≈ 30 km (where c is the speed of light). In typical intracloud K-strokes, positive electric charge of the order of Q ≈ 10 mC in the upper part of the channel and an equivalent amount of negative charge in its lower part neutralize within a typical time interval of τ ≈ 25 μs . The corresponding values for average electric current, frequency and wavelength are J ≈ 400 A , f ≈ 40 kHz , and λ ≈ 7.5 km . The energy of K-strokes is in general two orders of magnitude weaker than the energy of R-strokes.[7]

The typical length of lightning channels can be estimated to be of the order of ℓ ≈ 1/4λ = 8 km for R-strokes and ℓ ≈ 1/2λ = 4 km for K-strokes. Often, a continuing current component flows between successive R-strokes.[1] Its "pulse" time typically varies between about 10–150 ms , its electric current is of the order of J ≈ 100 A , corresponding to the numbers of Q ≈ 1–20 C , f ≈ 7–100 Hz and λ ≈ 3–40 Mm . Both R-strokes as well as K-strokes produce sferics seen as a coherent impulse waveform within a broadband receiver tuned between 1–100 kHz. The electric field strength of the impulse increases to a maximum value within a few microseconds and then declines like a damped oscillator.[8][9] The orientation of the field strength increase depends on whether it is a negative or a positive discharge

The visible part of a lightning channel has a typical length of about 5 km. Another part of comparable length may be hidden in the cloud and may have a significant horizontal branch. Evidently, the dominant wavelength of the electromagnetic waves of R- and K-strokes is much larger than their channel lengths. The physics of electromagnetic wave propagation within the channel must thus be derived from full wave theory, because the ray concept breaks down.

Electric channel current Edit

The channel of a R stroke can be considered as a thin isolated wire of length L and diameter d in which negative electric charge has been stored. In terms of electric circuit theory, one can adopt a simple transmission line model with a capacitor, where the charge is stored, a resistance of the channel, and an inductance simulating the electric properties of the channel.[10] At the moment of contact with the perfectly conducting Earth surface, the charge is lowered to the ground. In order to fulfill the boundary conditions at the top of the wire (zero electric current) and at the ground (zero electric voltage), only standing resonant waves modes can exit. The fundamental mode which transports electric charge to the ground most effectively, has thus a wavelength λ four times the channel length L. In the case of the K stroke, the lower boundary is the same as the upper boundary.[7][10] Of course, this picture is valid only for wave mode 1 (λ/4 antenna) and perhaps for mode 2 (λ/2 antenna), because these modes do not yet "feel" the contorted configuration of the real lightning channel. The higher order modes contribute to the incoherent noisy signals in the higher frequency range (> 100 kHz).

Transfer function of Earth–ionosphere waveguide Edit

Sferics can be simulated approximately by the electromagnetic radiation field of a vertical Hertzian dipole antenna. The maximum spectral amplitude of the sferic typically is near 5 kHz. Beyond this maximum, the spectral amplitude decreases as 1/f if the Earth's surface were perfectly conducting. The effect of the real ground is to attenuate the higher frequencies more strongly than the lower frequencies (Sommerfeld's ground wave).

R strokes emit most of their energy within the ELF/VLF range (ELF = extremely low frequencies, < 3 kHz; VLF = very low frequencies, 3–30 kHz). These waves are reflected and attenuated on the ground as well as within the ionospheric D layer, near 70 km altitude during day time conditions, and near 90 km height during the night. Reflection and attenuation on the ground depends on frequency, distance, and orography. In the case of the ionospheric D-layer, it depends, in addition, on time of day, season, latitude, and the geomagnetic field in a complicated manner. VLF propagation within the Earth–ionosphere waveguide can be described by ray theory and by wave theory.[11][12]

When distances are less than about 500 km (depending on frequency), then ray theory is appropriate. The ground wave and the first hop (or sky) wave reflected at the ionospheric D layer interfere with each other.

At distances greater than about 500 km, sky waves reflected several times at the ionosphere must be added. Therefore, mode theory is here more appropriate. The first mode is least attenuated within the Earth–ionosphere waveguide, and thus dominates at distances greater than about 1000 km.

The Earth–ionosphere waveguide is dispersive. Its propagation characteristics are described by a transfer function T(ρ, f) depending mainly on distance ρ and frequency f. In the VLF range, only mode one is important at distances larger than about 1000 km. Least attenuation of this mode occurs at about 15 kHz. Therefore, the Earth–ionosphere waveguide behaves like a bandpass filter, selecting this band out of a broadband signal. The 15 kHz signal dominates at distances greater than about 5000 km. For ELF waves (< 3 kHz), ray theory becomes invalid, and only mode theory is appropriate. Here, the zeroth mode begins to dominate and is responsible for the second window at greater distances.

Resonant waves of this zeroth mode can be excited in the Earth–ionosphere waveguide cavity, mainly by the continuing current components of lightning flowing between two return strokes. Their wavelengths are integral fractions of the Earth's circumference, and their resonance frequencies can thus be approximately determined by fm ≃ mc/(2πa) ≃ 7.5 m Hz (with m = 1, 2, ...; a the Earth's radius and c the speed of light). These resonant modes with their fundamental frequency of f1 ≃ 7.5 Hz are known as Schumann resonances.[13][14]

Monitoring thunderstorm activity with sferics Edit

About 100 lightning strokes per second are generated all over the world excited by thunderstorms located mainly in the continental areas at low and middle latitudes.[15][16] In order to monitor the thunderstorm activity, sferics are the appropriate means.

Measurements of Schumann resonances at only a few stations around the world can monitor the global lightning activity fairly well.[14] One can apply the dispersive property of the Earth–ionosphere waveguide by measuring the group velocity of a sferic signal at different frequencies together with its direction of arrival. The group time delay difference of neighbouring frequencies in the lower VLF band is directly proportional to the distance of the source. Since the attenuation of VLF waves is smaller for west to east propagation and during the night, thunderstorm activity up to distances of about 10,000 km can be observed for signals arriving from the west during night time conditions. Otherwise, the transmission range is of the order of 5,000 km.[17]

For the regional range (< 1,000 km), the usual way is magnetic direction finding as well as time of arrival measurements of a sferic signal observed simultaneously at several stations.[18] Presumption of such measurements is the concentration on one individual impulse. If one measures simultaneously several pulses, interference takes place with a beat frequency equal to the inversal average sequence time of the pulses.

Atmospheric noise Edit

The signal-to-noise ratio determines the sensibility and sensitivity of telecommunication systems (e.g., radio receivers). An analog signal must clearly exceed the noise amplitude in order to become detectable. Atmospheric noise is one of the most important sources for the limitation of the detection of radio signals.

The steady electric discharging currents in a lightning channel cause a series of incoherent impulses in the whole frequency range, the amplitudes of which decreases approximately with the inverse frequency. In the ELF-range, technical noise from 50–60 Hz, natural noise from the magnetosphere, etc. dominates. In the VLF-range, there are the coherent impulses from R- and K-strokes, appearing out of the background noise.[19] Beyond about 100 kHz, the noise amplitude becomes more and more incoherent. In addition, technical noise from electric motors, ignition systems of motor cars, etc., are superimposed. Finally, beyond the high frequency band (3–30 MHz) extraterrestrial noise (noise of galactic origin, solar noise) dominates.[2][3]

The atmospheric noise depends on frequency, location and time of day and year. Worldwide measurements of that noise are documented in CCIR-reports.[a][20]

See also Edit

Footnotes Edit

  1. ^ The acronym CCIR stands for Comité Consultatif International des Radiocommunications (International Consultation Committee on Radio Communications).


References Edit

  1. ^ a b Uman, M. A. (1980), The Lightning Discharge, New York: Academic Press
  2. ^ a b Lewis, E. A. (1982), "High frequency radio noise", in Volland, H. (ed.), CRC Handbook of Atmospherics, vol. I, Boca Raton, Florida: CRC Press, pp. 251–288, ISBN 9780849332265
  3. ^ a b Proctor, D. E. (1995), "Radio noise above 300 kHz due to Natural Causes", in Volland, H. (ed.), Handbook of Atmospheric Electrodynamics, vol. I, Boca Raton, Florida: CRC Press, pp. 311–358, ISBN 9780849386473
  4. ^ Hayakawa, M. (1995), "Whistlers", in Volland, H. (ed.), Handbook of Atmospheric Electrodynamics, vol. II, Boca Raton, Florida: CRC Press, pp. 155–193
  5. ^ Park, C. G. (1982), "Whistlers", in Volland, H (ed.), CRC Handbook of Atmospherics, vol. II, Boca Raton, Florida: CRC Press, pp. 21–77, ISBN 0849332273
  6. ^ Serhan, G. L.; et al. (1980), "The RF spectra of first and subsequent lightning return strokes in the ℓ ≈ 100 km range", Radio Science, 15 (108), doi:10.1029/RS015i006p01089
  7. ^ a b Volland, H. (1995), "Longwave sferics propagation within the atmospheric waveguide", in Volland, H. (ed.), Handbook of Atmospheric Electrodynamics, vol. II, Boca Raton, Florida: CRC Press, pp. 65–93
  8. ^ Lin, Y.T.; et al. (1979). "Characterization of lightning return stroke electric and magnetic fields from simultaneous two-station measurements". J. Geophys. Res. 84 (C10): 6307. Bibcode:1979JGR....84.6307L. doi:10.1029/JC084iC10p06307.
  9. ^ Weidman, C.D.; Krider, E. P. (1979). "The radiation field wave forms produced by intracloud lightning discharge processes". J. Geophys. Res. 84 (C6): 3159. Bibcode:1979JGR....84.3159W. doi:10.1029/JC084iC06p03159.
  10. ^ a b Volland, H. (1984), Atmospheric Electrodynamics, Berlin: Springer
  11. ^ Wait, J. R. (1982), Wave Propagation Theory, New York: Pergamon Press
  12. ^ Harth, W. (1982), "Theory of low frequency wave propagation", in Volland, H. (ed.), CRC Handbook of Atmospherics, vol. II, Boca Raton, Florida: CRC Press, pp. 133–202, ISBN 0849332273
  13. ^ Polk, C. (1982), "Schumann resonances", in Volland, H. (ed.), CRC Handbook of Atmospherics, vol. I, Boca Raton, Florida: CRC Press, pp. 111–178, ISBN 9780849332265
  14. ^ a b Sentman, D. D. (1995), "Schumann resonances", in Volland, H. (ed.), Handbook of Atmospheric Electrodynamics, vol. I, Boca Raton, Florida: CRC Press, pp. 267–295, ISBN 9780849386473
  15. ^ Vonnegut, B. (1982), "The physics of thundercloudes", in Volland, H (ed.), CRC Handbook of Atmospherics, vol. I, Boca Raton, Florida: CRC Press, pp. 1–22, ISBN 9780849332265
  16. ^ Williams, E. R. (1995), "Meteorological aspects of thunderstorms", in Volland, H. (ed.), Handbook of Atmospheric Electrodynamics, vol. I, Boca Raton, Florida: CRC Press, pp. 27–60, ISBN 9780849386473
  17. ^ Grandt, C. (1992), "Thunderstorm monitoring in South Africa and Europe by means of VLF sferics", J. Geophys. Res., 97 (D16): 18215, Bibcode:1992JGR....9718215G, doi:10.1029/92JD01623
  18. ^ Orville, R. E. (1995), "Lightning detection from ground and space", in Volland, H. (ed.), Handbook of Atmospheric Electrodynamics, vol. I, Boca Raton, Florida: CRC Press, pp. 137–149, ISBN 9780849386473
  19. ^ Fraser-Smith, A. C. (1995), "Low-frequency radio noise", in Volland, H. (ed.), Handbook of Atmospheric Electrodynamics, vol. I, Boca Raton, Florida: CRC Press, pp. 297–310, ISBN 9780849386473
  20. ^ Spaulding, A. D. (1995). "Atmospheric noise and its effects on telecommunication system performance". In Volland, H. (ed.). Handbook of Atmospheric Electrodynamics. Vol. I. Boca Raton, Florida: CRC Press. pp. 359–395. ISBN 9780849386473.

External links Edit

August 25, 2023
radio, atmospheric, signal, radio, atmospheric, signal, sferic, sometimes, also, spelled, spheric, broadband, electromagnetic, impulse, that, occurs, result, natural, atmospheric, lightning, discharges, sferics, propagate, from, their, lightning, source, witho. A radio atmospheric signal or sferic sometimes also spelled spheric is a broadband electromagnetic impulse that occurs as a result of natural atmospheric lightning discharges Sferics may propagate from their lightning source without major attenuation in the Earth ionosphere waveguide and can be received thousands of kilometres from their source On a time domain plot a sferic may appear as a single high amplitude spike in the time domain data On a spectrogram a sferic appears as a vertical stripe reflecting its broadband and impulsive nature that may extend from a few kHz to several tens of kHz depending on atmospheric conditions A frequency vs time plot spectrogram showing several whistler signals amidst a background of sferics as received at Palmer Station Antarctica on August 24 2005 Sferics received from about 2 000 kilometres distance or greater have their frequencies slightly offset in time producing tweeks When the electromagnetic energy from a sferic escapes the Earth ionosphere waveguide and enters the magnetosphere it becomes dispersed by the near Earth plasma forming a whistler signal Because the source of the whistler is an impulse i e the sferic a whistler may be interpreted as the impulse response of the magnetosphere for the conditions at that particular instant Contents 1 Introduction 2 Source properties 2 1 Basic stroke parameters 2 2 Electric channel current 3 Transfer function of Earth ionosphere waveguide 4 Monitoring thunderstorm activity with sferics 5 Atmospheric noise 6 See also 7 Footnotes 8 References 9 External linksIntroduction EditA lightning channel with all its branches and its electric currents behaves like a huge antenna system from which electromagnetic waves of all frequencies are radiated Beyond a distance where luminosity is visible and thunder can be heard typically about 10 km these electromagnetic impulses are the only sources of direct information about thunderstorm activity on the ground Transients electric currents during return strokes R strokes or intracloud strokes K strokes are the main sources for the generation of impulse type electromagnetic radiation known as sferics sometimes called atmospherics 1 While this impulsive radiation dominates at frequencies less than about 100 kHz loosely called long waves a continuous noise component becomes increasingly important at higher frequencies 2 3 The longwave electromagnetic propagation of sferics takes place within the Earth ionosphere waveguide between the Earth s surface and the ionospheric D and E layers Whistlers generated by lightning strokes can propagate into the magnetosphere along the geomagnetic lines of force 4 5 Finally upper atmospheric lightning or sprites that occur at mesospheric altitudes are short lived electric breakdown phenomena probably generated by giant lightning events on the ground Source properties EditBasic stroke parameters Edit In a typical cloud to ground stroke R stroke negative electric charge electrons of the order of Q 1 C stored within the lightning channel is lowered to the ground within a typical impulse time interval of t 100 ms This corresponds to an average current flowing within the channel of the order of J Q t 10 kA Maximum spectral energy is generated near frequencies of f 1 t 10 kHz 6 or at wavelengths of l c f 30 km where c is the speed of light In typical intracloud K strokes positive electric charge of the order of Q 10 mC in the upper part of the channel and an equivalent amount of negative charge in its lower part neutralize within a typical time interval of t 25 ms The corresponding values for average electric current frequency and wavelength are J 400 A f 40 kHz and l 7 5 km The energy of K strokes is in general two orders of magnitude weaker than the energy of R strokes 7 The typical length of lightning channels can be estimated to be of the order of ℓ 1 4 l 8 km for R strokes and ℓ 1 2 l 4 km for K strokes Often a continuing current component flows between successive R strokes 1 Its pulse time typically varies between about 10 150 ms its electric current is of the order of J 100 A corresponding to the numbers of Q 1 20 C f 7 100 Hz and l 3 40 Mm Both R strokes as well as K strokes produce sferics seen as a coherent impulse waveform within a broadband receiver tuned between 1 100 kHz The electric field strength of the impulse increases to a maximum value within a few microseconds and then declines like a damped oscillator 8 9 The orientation of the field strength increase depends on whether it is a negative or a positive dischargeThe visible part of a lightning channel has a typical length of about 5 km Another part of comparable length may be hidden in the cloud and may have a significant horizontal branch Evidently the dominant wavelength of the electromagnetic waves of R and K strokes is much larger than their channel lengths The physics of electromagnetic wave propagation within the channel must thus be derived from full wave theory because the ray concept breaks down Electric channel current Edit The channel of a R stroke can be considered as a thin isolated wire of length L and diameter d in which negative electric charge has been stored In terms of electric circuit theory one can adopt a simple transmission line model with a capacitor where the charge is stored a resistance of the channel and an inductance simulating the electric properties of the channel 10 At the moment of contact with the perfectly conducting Earth surface the charge is lowered to the ground In order to fulfill the boundary conditions at the top of the wire zero electric current and at the ground zero electric voltage only standing resonant waves modes can exit The fundamental mode which transports electric charge to the ground most effectively has thus a wavelength l four times the channel length L In the case of the K stroke the lower boundary is the same as the upper boundary 7 10 Of course this picture is valid only for wave mode 1 l 4 antenna and perhaps for mode 2 l 2 antenna because these modes do not yet feel the contorted configuration of the real lightning channel The higher order modes contribute to the incoherent noisy signals in the higher frequency range gt 100 kHz Transfer function of Earth ionosphere waveguide EditSferics can be simulated approximately by the electromagnetic radiation field of a vertical Hertzian dipole antenna The maximum spectral amplitude of the sferic typically is near 5 kHz Beyond this maximum the spectral amplitude decreases as 1 f if the Earth s surface were perfectly conducting The effect of the real ground is to attenuate the higher frequencies more strongly than the lower frequencies Sommerfeld s ground wave R strokes emit most of their energy within the ELF VLF range ELF extremely low frequencies lt 3 kHz VLF very low frequencies 3 30 kHz These waves are reflected and attenuated on the ground as well as within the ionospheric D layer near 70 km altitude during day time conditions and near 90 km height during the night Reflection and attenuation on the ground depends on frequency distance and orography In the case of the ionospheric D layer it depends in addition on time of day season latitude and the geomagnetic field in a complicated manner VLF propagation within the Earth ionosphere waveguide can be described by ray theory and by wave theory 11 12 When distances are less than about 500 km depending on frequency then ray theory is appropriate The ground wave and the first hop or sky wave reflected at the ionospheric D layer interfere with each other At distances greater than about 500 km sky waves reflected several times at the ionosphere must be added Therefore mode theory is here more appropriate The first mode is least attenuated within the Earth ionosphere waveguide and thus dominates at distances greater than about 1000 km The Earth ionosphere waveguide is dispersive Its propagation characteristics are described by a transfer function T r f depending mainly on distance r and frequency f In the VLF range only mode one is important at distances larger than about 1000 km Least attenuation of this mode occurs at about 15 kHz Therefore the Earth ionosphere waveguide behaves like a bandpass filter selecting this band out of a broadband signal The 15 kHz signal dominates at distances greater than about 5000 km For ELF waves lt 3 kHz ray theory becomes invalid and only mode theory is appropriate Here the zeroth mode begins to dominate and is responsible for the second window at greater distances Resonant waves of this zeroth mode can be excited in the Earth ionosphere waveguide cavity mainly by the continuing current components of lightning flowing between two return strokes Their wavelengths are integral fractions of the Earth s circumference and their resonance frequencies can thus be approximately determined by fm mc 2pa 7 5 m Hz with m 1 2 a the Earth s radius and c the speed of light These resonant modes with their fundamental frequency of f1 7 5 Hz are known as Schumann resonances 13 14 Monitoring thunderstorm activity with sferics EditAbout 100 lightning strokes per second are generated all over the world excited by thunderstorms located mainly in the continental areas at low and middle latitudes 15 16 In order to monitor the thunderstorm activity sferics are the appropriate means Measurements of Schumann resonances at only a few stations around the world can monitor the global lightning activity fairly well 14 One can apply the dispersive property of the Earth ionosphere waveguide by measuring the group velocity of a sferic signal at different frequencies together with its direction of arrival The group time delay difference of neighbouring frequencies in the lower VLF band is directly proportional to the distance of the source Since the attenuation of VLF waves is smaller for west to east propagation and during the night thunderstorm activity up to distances of about 10 000 km can be observed for signals arriving from the west during night time conditions Otherwise the transmission range is of the order of 5 000 km 17 For the regional range lt 1 000 km the usual way is magnetic direction finding as well as time of arrival measurements of a sferic signal observed simultaneously at several stations 18 Presumption of such measurements is the concentration on one individual impulse If one measures simultaneously several pulses interference takes place with a beat frequency equal to the inversal average sequence time of the pulses Atmospheric noise EditThe signal to noise ratio determines the sensibility and sensitivity of telecommunication systems e g radio receivers An analog signal must clearly exceed the noise amplitude in order to become detectable Atmospheric noise is one of the most important sources for the limitation of the detection of radio signals The steady electric discharging currents in a lightning channel cause a series of incoherent impulses in the whole frequency range the amplitudes of which decreases approximately with the inverse frequency In the ELF range technical noise from 50 60 Hz natural noise from the magnetosphere etc dominates In the VLF range there are the coherent impulses from R and K strokes appearing out of the background noise 19 Beyond about 100 kHz the noise amplitude becomes more and more incoherent In addition technical noise from electric motors ignition systems of motor cars etc are superimposed Finally beyond the high frequency band 3 30 MHz extraterrestrial noise noise of galactic origin solar noise dominates 2 3 The atmospheric noise depends on frequency location and time of day and year Worldwide measurements of that noise are documented in CCIR reports a 20 See also Edit1955 Great Plains tornado outbreak Cluster One a Pink Floyd track using sferics and dawn chorus as an overtureFootnotes Edit The acronym CCIR stands for Comite Consultatif International des Radiocommunications International Consultation Committee on Radio Communications References Edit a b Uman M A 1980 The Lightning Discharge New York Academic Press a b Lewis E A 1982 High frequency radio noise in Volland H ed CRC Handbook of Atmospherics vol I Boca Raton Florida CRC Press pp 251 288 ISBN 9780849332265 a b Proctor D E 1995 Radio noise above 300 kHz due to Natural Causes in Volland H ed Handbook of Atmospheric Electrodynamics vol I Boca Raton Florida CRC Press pp 311 358 ISBN 9780849386473 Hayakawa M 1995 Whistlers in Volland H ed Handbook of Atmospheric Electrodynamics vol II Boca Raton Florida CRC Press pp 155 193 Park C G 1982 Whistlers in Volland H ed CRC Handbook of Atmospherics vol II Boca Raton Florida CRC Press pp 21 77 ISBN 0849332273 Serhan G L et al 1980 The RF spectra of first and subsequent lightning return strokes in the ℓ 100 km range Radio Science 15 108 doi 10 1029 RS015i006p01089 a b Volland H 1995 Longwave sferics propagation within the atmospheric waveguide in Volland H ed Handbook of Atmospheric Electrodynamics vol II Boca Raton Florida CRC Press pp 65 93 Lin Y T et al 1979 Characterization of lightning return stroke electric and magnetic fields from simultaneous two station measurements J Geophys Res 84 C10 6307 Bibcode 1979JGR 84 6307L doi 10 1029 JC084iC10p06307 Weidman C D Krider E P 1979 The radiation field wave forms produced by intracloud lightning discharge processes J Geophys Res 84 C6 3159 Bibcode 1979JGR 84 3159W doi 10 1029 JC084iC06p03159 a b Volland H 1984 Atmospheric Electrodynamics Berlin Springer Wait J R 1982 Wave Propagation Theory New York Pergamon Press Harth W 1982 Theory of low frequency wave propagation in Volland H ed CRC Handbook of Atmospherics vol II Boca Raton Florida CRC Press pp 133 202 ISBN 0849332273 Polk C 1982 Schumann resonances in Volland H ed CRC Handbook of Atmospherics vol I Boca Raton Florida CRC Press pp 111 178 ISBN 9780849332265 a b Sentman D D 1995 Schumann resonances in Volland H ed Handbook of Atmospheric Electrodynamics vol I Boca Raton Florida CRC Press pp 267 295 ISBN 9780849386473 Vonnegut B 1982 The physics of thundercloudes in Volland H ed CRC Handbook of Atmospherics vol I Boca Raton Florida CRC Press pp 1 22 ISBN 9780849332265 Williams E R 1995 Meteorological aspects of thunderstorms in Volland H ed Handbook of Atmospheric Electrodynamics vol I Boca Raton Florida CRC Press pp 27 60 ISBN 9780849386473 Grandt C 1992 Thunderstorm monitoring in South Africa and Europe by means of VLF sferics J Geophys Res 97 D16 18215 Bibcode 1992JGR 9718215G doi 10 1029 92JD01623 Orville R E 1995 Lightning detection from ground and space in Volland H ed Handbook of Atmospheric Electrodynamics vol I Boca Raton Florida CRC Press pp 137 149 ISBN 9780849386473 Fraser Smith A C 1995 Low frequency radio noise in Volland H ed Handbook of Atmospheric Electrodynamics vol I Boca Raton Florida CRC Press pp 297 310 ISBN 9780849386473 Spaulding A D 1995 Atmospheric noise and its effects on telecommunication system performance In Volland H ed Handbook of Atmospheric Electrodynamics Vol I Boca Raton Florida CRC Press pp 359 395 ISBN 9780849386473 External links Edithttp www srh noaa gov oun wxevents 19550525 stormelectricity php Radio in Space and Time Whistler Sferics and Tweeks G Wiessala in RadioUser 1 2013 UK Retrieved from https en wikipedia org w index php title Radio atmospheric signal amp oldid 1117634487, wikipedia, wiki, book, books, library,

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