Schumann resonances

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Animation of Schumann resonance in Earth's atmosphere.

The Schumann resonances (SR) are a set of spectrum peaks in the extremely low frequency (ELF) portion of the Earth's electromagnetic field spectrum. Schumann resonances are global electromagnetic resonances, excited by lightning discharges in the cavity formed by the Earth's surface and the ionosphere.

Description[edit]

This global electromagnetic resonance phenomenon is named after physicist Winfried Otto Schumann who predicted it mathematically in 1952. Schumann resonances occur because the space between the surface of the Earth and the conductive ionosphere acts as a closed waveguide. The limited dimensions of the Earth cause this waveguide to act as a resonant cavity for electromagnetic waves in the ELF band. The cavity is naturally excited by electric currents in lightning. Schumann resonances are the principal background in the electromagnetic spectrum[1] beginning at 3 Hz and extend to 60 Hz,[2] and appear as distinct peaks at extremely low frequencies (ELF) around 7.83 (fundamental),[3] 14.3, 20.8, 27.3 and 33.8 Hz.[1][4]

In the normal mode descriptions of Schumann resonances, the fundamental mode is a standing wave in the Earth–ionosphere cavity with a wavelength equal to the circumference of the Earth. This lowest-frequency (and highest-intensity) mode of the Schumann resonance occurs at a frequency of approximately 7.83 Hz, but this frequency can vary slightly from a variety of factors, such as solar-induced perturbations to the ionosphere, which comprises the upper wall of the closed cavity.[citation needed] The higher resonance modes are spaced at approximately 6.5 Hz intervals,[citation needed] a characteristic attributed to the atmosphere's spherical geometry. The peaks exhibit a spectral width of approximately 20% on account of the damping of the respective modes in the dissipative cavity. The 8th partial lies at approximately 60 Hz.[citation needed]

Observations of Schumann resonances have been used to track global lightning activity. Owing to the connection between lightning activity and the Earth's climate it has been suggested that they may also be used to monitor global temperature variations and variations of water vapor in the upper troposphere. It has been speculated that extraterrestrial lightning (on other planets) may also be detected and studied by means of their Schumann resonance signatures. Schumann resonances have been used to study the lower ionosphere on Earth and it has been suggested as one way to explore the lower ionosphere on celestial bodies. Effects on Schumann resonances have been reported following geomagnetic and ionospheric disturbances. More recently, discrete Schumann resonance excitations have been linked to transient luminous eventssprites, elves, jets, and other upper-atmospheric lightning. A new field of interest using Schumann resonances is related to short-term earthquake prediction.

History[edit]

In 1893, George Francis FitzGerald noted that the upper layers of the atmosphere must be fairly good conductors. Assuming that the height of these layers is about 100 km above ground, he estimated that oscillations (in this case the lowest mode of the Schumann resonances) would have a period of 0.1 second.[5] Because of this contribution, it has been suggested to rename these resonances as Schumann–FitzGerald resonances.[6] However FitzGerald's findings were not widely known as they were only presented at a meeting of the British Association for the Advancement of Science, followed by a brief mention in a column in Nature.

Hence the first suggestion that an ionosphere existed, capable of trapping electromagnetic waves, is attributed to Heaviside and Kennelly (1902).[7][8] It took another twenty years before Edward Appleton and Barnett in 1925,[9] were able to prove experimentally the existence of the ionosphere.

Although some of the most important mathematical tools for dealing with spherical waveguides were developed by G. N. Watson in 1918,[10] it was Winfried Otto Schumann who first studied the theoretical aspects of the global resonances of the earth–ionosphere waveguide system, known today as the Schumann resonances. In 1952–1954 Schumann, together with H. L. König, attempted to measure the resonant frequencies.[11][12][13][14] However, it was not until measurements made by Balser and Wagner in 1960–1963[15][16][17][18][19] that adequate analysis techniques were available to extract the resonance information from the background noise. Since then there has been an increasing interest in Schumann resonances in a wide variety of fields.

Basic theory[edit]

Lightning discharges are considered to be the primary natural source of Schumann resonance excitation; lightning channels behave like huge antennas that radiate electromagnetic energy at frequencies below about 100 kHz.[20] These signals are very weak at large distances from the lightning source, but the Earth–ionosphere waveguide behaves like a resonator at ELF frequencies and amplifies the spectral signals from lightning at the resonance frequencies.[20]

In an ideal cavity, the resonant frequency of the n-th mode f_{n} is determined by the Earth radius a and the speed of light c.[11]

f_{n} =\frac{c}{2 \pi a}\sqrt{n(n+1)}

The real Earth–ionosphere waveguide is not a perfect electromagnetic resonant cavity. Losses due to finite ionosphere electrical conductivity lower the propagation speed of electromagnetic signals in the cavity, resulting in a resonance frequency that is lower than would be expected in an ideal case, and the observed peaks are wide. In addition, there are a number of horizontal asymmetries – day-night difference in the height of the ionosphere, latitudinal changes in the Earth's magnetic field, sudden ionospheric disturbances, polar cap absorption, variation in the Earth radius of +/- 11 km from equator to geographic poles, etc. that produce other effects in the Schumann resonance power spectra.

Measurements[edit]

Today Schumann resonances are recorded at many separate research stations around the world. The sensors used to measure Schumann resonances typically consist of two horizontal magnetic inductive coils for measuring the north-south and east-west components of the magnetic field, and a vertical electric dipole antenna for measuring the vertical component of the electric field. A typical passband of the instruments is 3–100 Hz. The Schumann resonance electric field amplitude (~300 microvolts per meter) is much smaller than the static fair-weather electric field (~150 V/m) in the atmosphere. Similarly, the amplitude of the Schumann resonance magnetic field (~1 picotesla) is many orders of magnitude smaller than the Earth's magnetic field (~30–50 microteslas).[21] Specialized receivers and antennas are needed to detect and record Schumann resonances. The electric component is commonly measured with a ball antenna, suggested by Ogawa et al., in 1966,[22] connected to a high-impedance amplifier. The magnetic induction coils typically consist of tens- to hundreds-of-thousands of turns of wire wound around a core of very high magnetic permeability.

Dependence on global lightning activity[edit]

From the very beginning of Schumann resonance studies, it was known that they could be used to monitor global lightning activity. At any given time there are about 2000 thunderstorms around the globe.[23] Producing ~50 lightning events per second,[24] these thunderstorms create the background Schumann resonance signal.

Determining the spatial lightning distribution from Schumann resonance records is a complex problem: in order to estimate the lightning intensity from Schumann resonance records it is necessary to account for both the distance to lightning sources as well as the wave propagation between the source and the observer. The common approach is to make a preliminary assumption on the spatial lightning distribution, based on the known properties of lightning climatology. An alternative approach is placing the receiver at the North or South Pole, which remain approximately equidistant from the main thunderstorm centers during the day.[25] One method not requiring preliminary assumptions on the lightning distribution[26] is based on the decomposition of the average background Schumann resonance spectra, utilizing ratios between the average electric and magnetic spectra and between their linear combination. This technique assumes the cavity is spherically symmetric and therefore does not include known cavity asymmetries that are believed to affect the resonance and propagation properties of electromagnetic waves in the system.

Diurnal variations[edit]

The best documented and the most debated features of the Schumann resonance phenomenon are the diurnal variations of the background Schumann resonance power spectrum.

A characteristic Schumann resonance diurnal record reflects the properties of both global lightning activity and the state of the Earth–ionosphere cavity between the source region and the observer. The vertical electric field is independent of the direction of the source relative to the observer, and is therefore a measure of global lightning. The diurnal behavior of the vertical electric field shows three distinct maxima, associated with the three "hot spots" of planetary lightning activity: 9 UT (Universal Time) peak, linked to the increased thunderstorm activity from Southeast Asia; 14 UT peak associated with the peak in African lightning activity; and the 20 UT peak resulting for the increase in lightning activity in South America. The time and amplitude of the peaks vary throughout the year, reflecting the seasonal changes in lightning activity.

"Chimney" ranking[edit]

In general, the African peak is the strongest, reflecting the major contribution of the African "chimney" to the global lightning activity. The ranking of the two other peaks – Asian and American – is the subject of a vigorous dispute among Schumann resonance scientists. Schumann resonance observations made from Europe show a greater contribution from Asia than from South America. This contradicts optical satellite and climatological lightning data that show the South American thunderstorm center stronger than the Asian center.,[24] although observations made from North America indicate the dominant contribution comes from South America. The reason for such disparity remains unclear, but may have something to do with the 60 Hz cycling of electricity used in North America (60 Hz being a mode of Schumann Resonance). Williams and Sátori[27] suggest that in order to obtain "correct" Asia-America chimney ranking, it is necessary to remove the influence of the day/night variations in the ionospheric conductivity (day-night asymmetry influence) from the Schumann resonance records. On the other hand, such "corrected" records presented in the work by Sátori et al.[28] show that even after the removal of the day-night asymmetry influence from Schumann resonance records, the Asian contribution remains greater than American. Similar results were obtained by Pechony et al.[29] who calculated Schumann resonance fields from satellite lightning data. It was assumed that the distribution of lightning in the satellite maps was a good proxy for Schumann excitations sources, even though satellite observations predominantly measure in-cloud lightning rather than the cloud-to-ground lightning that are the primary exciters of the resonances. Both simulations – those neglecting the day-night asymmetry, and those taking this asymmetry into account, showed same Asia-America chimney ranking. As for today, the reason for the "invert" ranking of Asia and America chimneys in Schumann resonance records remains unclear and the subject requires further, targeted research.

Influence of the day-night asymmetry[edit]

In the early literature the observed diurnal variations of Schumann resonance power were explained by the variations in the source-receiver (lightning-observer) geometry.[15] It was concluded that no particular systematic variations of the ionosphere (which serves as the upper waveguide boundary) are needed to explain these variations.[30] Subsequent theoretical studies supported the early estimations of the small influence of the ionosphere day-night asymmetry (difference between day-side and night-side ionosphere conductivity) on the observed variations in Schumann resonance field intensities.[31]

The interest in the influence of the day-night asymmetry in the ionosphere conductivity on Schumann resonances gained new strength in the 1990s, after publication of a work by Sentman and Fraser.[32] Sentman and Fraser developed a technique to separate the global and the local contributions to the observed field power variations using records obtained simultaneously at two stations that were widely separated in longitude. They interpreted the diurnal variations observed at each station in terms of a combination of a diurnally varying global excitation modulated by the local ionosphere height. Their work, which combined both observations and energy conservation arguments, convinced many scientists of the importance of the ionospheric day-night asymmetry and inspired numerous experimental studies. However, recently it was shown that results obtained by Sentman and Fraser can be approximately simulated with a uniform model (without taking into account ionosphere day-night variation) and therefore cannot be uniquely interpreted solely in terms of ionosphere height variation.[33]

Schumann resonance amplitude records show significant diurnal and seasonal variations which in general coincide in time with the times of the day-night transition (the terminator). This time-matching seems to support the suggestion of a significant influence of the day-night ionosphere asymmetry on Schumann resonance amplitudes. There are records showing almost clock-like accuracy of the diurnal amplitude changes.[28] On the other hand there are numerous days when Schumann Resonance amplitudes do not increase at sunrise or do not decrease at sunset. There are studies showing that the general behavior of Schumann resonance amplitude records can be recreated from diurnal and seasonal thunderstorm migration, without invoking ionospheric variations.[29][31] Two recent independent theoretical studies have shown that the variations in Schumann resonance power related to the day-night transition are much smaller than those associated with the peaks of the global lightning activity, and therefore the global lightning activity plays a more important role in the variation of the Schumann resonance power.[29][34]

It is generally acknowledged that source-observer effects are the dominant source of the observed diurnal variations, but there remains considerable controversy about the degree to which day-night signatures are present in the data. Part of this controversy stems from the fact that the Schumann resonance parameters extractable from observations provide only a limited amount of information about the coupled lightning source-ionospheric system geometry. The problem of inverting observations to simultaneously infer both the lightning source function and ionospheric structure is therefore extremely underdetermined, leading to the possibility of nonunique interpretations.

The "inverse problem"[edit]

One of the interesting problems in Schumann resonances studies is determining the lightning source characteristics (the "inverse problem"). Temporally resolving each individual flash is impossible because the mean rate of excitation by lightning, ~50 lightning events per second globally, mixes up the individual contributions together. However, occasionally there occur extremely large lightning flashes which produce distinctive signatures that stand out from the background signals. Called "Q-bursts", they are produced by intense lightning strikes that transfer large amounts of charge from clouds to the ground, and often carry high peak current.[22] Q-bursts can exceed the amplitude of the background signal level by a factor of 10 or more, and appear with intervals of ~10 s,[26] which allows to consider them as isolated events and determine the source lightning location. The source location is determined with either multi-station or single-station techniques, and requires assuming a model for the Earth–ionosphere cavity. The multi-station techniques are more accurate, but require more complicated and expensive facilities.

Transient luminous events research[edit]

It is now believed that many of the Schumann resonances transients (Q bursts) are related to the transient luminous events (TLEs). In 1995 Boccippio et al.[35] showed that sprites, the most common TLE, are produced by positive cloud-to-ground lightning occurring in the stratiform region of a thunderstorm system, and are accompanied by Q-burst in the Schumann resonances band. Recent observations[35][36] reveal that occurrences of sprites and Q bursts are highly correlated and Schumann resonances data can possibly be used to estimate the global occurrence rate of sprites.[37]

Global temperature[edit]

Williams [1992][38] suggested that global temperature may be monitored with the Schumann resonances. The link between Schumann resonance and temperature is lightning flash rate, which increases nonlinearly with temperature.[38] The nonlinearity of the lightning-to-temperature relation provides a natural amplifier of the temperature changes and makes Schumann resonance a sensitive "thermometer". Moreover, the ice particles that are believed to participate in the electrification processes which result in a lightning discharge[39] have an important role in the radiative feedback effects that influence the atmosphere temperature. Schumann resonances may therefore help us to understand these feedback effects. A strong link between global lightning and global temperature has not been experimentally confirmed as of 2008.

Upper tropospheric water vapor[edit]

Tropospheric water vapor is a key element of the Earth’s climate, which has direct effects as a greenhouse gas, as well as indirect effect through interaction with clouds, aerosols and tropospheric chemistry. Upper tropospheric water vapor (UTWV) has a much greater impact on the greenhouse effect than water vapor in the lower atmosphere,[40] but whether this impact is a positive, or a negative feedback is still uncertain.[41] The main challenge in addressing this question is the difficulty in monitoring UTWV globally over long timescales. Continental deep-convective thunderstorms produce most of the lightning discharges on Earth. In addition, they transport large amount of water vapor into the upper troposphere, dominating the variations of global UTWV. Price [2000][42] suggested that changes in the UTWV can be derived from records of Schumann Resonances.

On other planets and moons[edit]

The existence of Schumann-like resonances is conditioned primarily by two factors:

  1. A closed, planetary-sized spherical[dubious ] cavity, consisting of conducting lower and upper boundaries separated by an insulating medium. For the earth the conducting lower boundary is its surface, and the upper boundary is the ionosphere. Other planets may have similar electrical conductivity geometry, so it is speculated that they should possess similar resonant behavior.
  2. A source of electrical excitation of electromagnetic waves in the ELF range.

Within the Solar System there are five candidates for Schumann resonance detection besides the Earth: Venus, Mars, Jupiter, Saturn and its biggest moon Titan. Modeling Schumann resonances on the planets and moons of the Solar System is complicated by the lack of knowledge of the waveguide parameters. No in situ capability exists today to validate the results.

Venus[edit]

The strongest evidence for lightning on Venus comes from the impulsive electromagnetic waves detected by Venera 11 and 12 landers. Theoretical calculations of the Schumann resonances at Venus were reported by Nickolaenko and Rabinowicz [1982][43] and Pechony and Price [2004].[44] Both studies yielded very close results, indicating that Schumann resonances should be easily detectable on that planet given a lightning source of excitation and a suitably located sensor.

Mars[edit]

In the case of Mars there have been terrestrial observations of radio emission spectra that have been associated with Schumann resonances.[45] The reported radio emissions are not of the primary electromagnetic Schumann modes, but rather of secondary modulations of the nonthermal microwave emissions from the planet at approximately the expected Schumann frequencies, and have not been independently confirmed to be associated with lightning activity on Mars. There is the possibility that future lander missions could carry in situ instrumentation to perform the necessary measurements. Theoretical studies are primarily directed to parameterizing the problem for future planetary explorers.

Detection of lightning activity on Mars has been reported by Ruf et al. [2009].[45] The evidence is indirect and in the form of modulations of the nonthermal microwave spectrum at approximately the expected Schumann resonance frequencies. It has not been independently confirmed that these are associated with electrical discharges on Mars. In the event confirmation is made by direct, in situ observations, it would verify the suggestion of the possibility of charge separation and lightning strokes in the Martian dust storms made by Eden and Vonnegut [1973][46] and Renno et al. [2003].[47] Martian global resonances were modeled by Sukhorukov [1991],[48] Pechony and Price [2004][44] and Molina-Cuberos et al. [2006].[49] The results of the three studies are somewhat different, but it seems that at least the first two Schumann resonance modes should be detectable. Evidence of the first three Schumann resonance modes is present in the spectra of radio emission from the lightning detected in Martian dust storms.[45]

Titan[edit]

It was long ago suggested that lightning discharges may occur on Titan,[50] but recent data from Cassini–Huygens seems to indicate that there is no lightning activity on this largest satellite of Saturn. Due to the recent interest in Titan, associated with the Cassini–Huygens mission, its ionosphere is perhaps the most thoroughly modeled today. Schumann resonances on Titan have received more attention than on any other celestial body, in works by Besser et al. [2002],[51] Morente et al. [2003],[52] Molina-Cuberos et al. [2004],[53] Nickolaenko et al. [2003][54] and Pechony and Price [2004].[44] It appears that only the first Schumann resonance mode might be detectable on Titan.

Since the landing of the Huygens probe on Titan's surface in January 2005, there have been many reports on observations and theory of an atypical Schumann resonance on Titan. After several tens of fly-bys by Cassini, neither lightning nor thunderstorms were detected in Titan's atmosphere. Scientists therefore proposed another source of electrical excitation: induction of ionospheric currents by Saturn's co-rotating magnetosphere. All data and theoretical models comply with a Schumann resonance, the second eigenmode of which was observed by the Huygens probe. The most important result of this is the proof of existence of a buried liquid water-ammonia ocean under few tens of km the icy subsurface crust.[55][56][57][58]

Jupiter and Saturn[edit]

Jupiter is one planet where lightning activity has been optically detected. Existence of lightning activity on that planet was predicted by Bar-Nun [1975][59] and it is now supported by data from Galileo, Voyagers 1 and 2, Pioneers 10 and 11 and Cassini. Saturn is also confirmed to have lightning activity.[60] Though three visiting spacecraft – Pioneer 11 in 1979, Voyager 1 in 1980 and Voyager 2 in 1981, failed to provide any convincing evidence from optical observations, in July 2012 the Cassini spacecraft detected visible lightning flashes, and electromagnetic sensors aboard the spacecraft detected signatures that are characteristic of lightning. Little is known about the electrical parameters of Jupiter and Saturn interior. Even the question of what should serve as the lower waveguide boundary is a non-trivial one in case of the gaseous planets. There seem to be no works dedicated to Schumann resonances on Saturn. To date there has been only one attempt to model Schumann resonances on Jupiter.[61] Here, the electrical conductivity profile within the gaseous atmosphere of Jupiter was calculated using methods similar to those used to model stellar interiors, and it was pointed out that the same methods could be easily extended to the other gas giants Saturn, Uranus and Neptune. Given the intense lightning activity at Jupiter, the Schumann resonances should be easily detectable with a sensor suitably positioned within the planetary-ionospheric cavity.

See also[edit]

References[edit]

  1. ^ a b MacGorman, W. D. Rust, W. David Rust. "The electrical nature of storms". Page 114.
  2. ^ Handbook of atmospheric electrodynamics, Volume 1 By Hans Volland. Page 277.
  3. ^ Rusov, V.D. (2012). "Can Resonant Oscillations of the Earth Ionosphere Influence the Human Brain Biorhythm?". arXiv:1208.4970 [physics.gen-ph]. Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Ukraine
  4. ^ Recent advances in multidisciplinary applied physics By A. Méndez-Vilas. Page 65.
  5. ^ G. F. FitzGerald, “On the period of vibration of electrical disturbances upon the Earth,” Br. Assoc. Adv. Sci., Rep. 63, 682 (1893)
  6. ^ J. D. Jackson, Examples of the zeroth theorem of the history of science, American Journal of Physics, Vol. 76, No. 8, pp. 704–719, August 2008
  7. ^ O. Heaviside (1902). "Telegraphy, Sect. 1, Theory". Encyc. Brit.10th ed.. . London 9: 213–218. 
  8. ^ A.E. Kennelly (1902). "On the elevation of the electrically-conducting strata of the earth's atmosphere". Electrical world and engineer 32: 473–473. 
  9. ^ Appleton, E. V. , M. A. F. Barnett (1925). "On Some Direct Evidence for Downward Atmospheric Reflection of Electric Rays". Proceedings of the Royal Society. Series A, Containing Papers of a Mathematical and Physical Character 109 (752): 621–641. Bibcode:1925RSPSA.109..621A. doi:10.1098/rspa.1925.0149. 
  10. ^ Watson, G.N. (1918). "The diffraction of electric waves by the Earth". Proceedings of the Royal Society. Ser.A 95: 83–99. 
  11. ^ a b Schumann W. O. (1952). "Über die strahlungslosen Eigenschwingungen einer leitenden Kugel, die von einer Luftschicht und einer Ionosphärenhülle umgeben ist". Zeitschrift und Naturfirschung 7a: 149–154. Bibcode:1952ZNatA...7..149S. 
  12. ^ Schumann W. O. (1952). "Über die Dämpfung der elektromagnetischen Eigenschwingnugen des Systems Erde – Luft – Ionosphäre". Zeitschrift und Naturfirschung 7a: 250–252. Bibcode:1952ZNatA...7..250S. 
  13. ^ Schumann W. O. (1952). "Über die Ausbreitung sehr Langer elektriseher Wellen um die Signale des Blitzes". Nuovo Cimento 9 (12): 1116–1138. doi:10.1007/BF02782924. 
  14. ^ Schumann W. O. and H. König (1954). "Über die Beobactung von Atmospherics bei geringsten Frequenzen". Naturwiss 41 (8): 183–184. Bibcode:1954NW.....41..183S. doi:10.1007/BF00638174. 
  15. ^ a b Balser M. and C. Wagner (1960). "Measurement of the spectrum of radio noise from 50 to 100 c/s". J.Res. NBS 64D: 415–418. doi:10.6028/jres.064d.050. 
  16. ^ Balser M. and C. Wagner (1960). "Observations of Earth–ionosphere cavity resonances". Nature 188 (4751): 638–641. Bibcode:1960Natur.188..638B. doi:10.1038/188638a0. 
  17. ^ Balser M. and C. Wagner (1962). "Diurnal power variations of the Earth–ionosphere cavity modes and their relationship to worldwide thunderstorm activity". J.G.R 67 (2): 619–625. Bibcode:1962JGR....67..619B. doi:10.1029/JZ067i002p00619. 
  18. ^ Balser M. and C. Wagner (1962). "On frequency variations of the Earth–ionosphere cavity modes". J.G.R 67 (10): 4081–4083. Bibcode:1962JGR....67.4081B. doi:10.1029/JZ067i010p04081. 
  19. ^ Balser M. and C. Wagner (1963). "Effect of a high-altitude nuclear detonation on the Earth–ionosphere cavity". J.G.R 68: 4115–4118. doi:10.1029/jz068i013p04115. 
  20. ^ a b Volland, H. (1984). Atmospheric Electrodynamics. Springer-Verlag, Berlin. 
  21. ^ Price, C., O. Pechony, E. Greenberg (2006). "Schumann resonances in lightning research". Journal of Lightning Research 1: 1– 15. 
  22. ^ a b Ogawa, T., Y. Tanka, T. Miura, and M. Yasuhara (1966). "Observations of natural ELF electromagnetic noises by using the ball antennas". J. Geomagn. Geoelectr 18: 443– 454. doi:10.5636/jgg.18.443. 
  23. ^ Heckman S. J., E. Williams, (1998). "Total global lightning inferred from Schumann resonance measurements". J. G. R. 103(D24): 31775–31779. Bibcode:1998JGR...10331775H. doi:10.1029/98JD02648. 
  24. ^ a b Christian H. J., R.J. Blakeslee, D.J. Boccippio, W.L. Boeck, D.E. Buechler, K.T. Driscoll, S.J. Goodman, J.M. Hall, W.J. Koshak, D.M. Mach, M.F. Stewart, (2003). "Global frequency and distribution of lightning as observed from space by the Optical Transient Detector". J. G. R. 108(D1): 4005. Bibcode:2003JGRD..108.4005C. doi:10.1029/2002JD002347. 
  25. ^ Nickolaenko, A.P. (1997). "Modern aspects of Schumann resonance studies". J.a.s.t.p. 59: 806–816. doi:10.1016/s1364-6826(96)00059-4. 
  26. ^ a b Shvets A.V. (2001). "A technique for reconstruction of global lightning distance profile from background Schumann resonance signal". J.a.s.t.p. 63: 1061–1074. doi:10.1016/s1364-6826(01)00024-4. 
  27. ^ Williams E. R., G. Sátori (2004). "Lightning, thermodynamic and hydrological comparison of the two tropical continental chimneys". J.a.s.t.p. 66: 1213–1231. doi:10.1016/j.jastp.2004.05.015. 
  28. ^ a b Sátori G., M. Neska, E. Williams, J. Szendrői (2007). "Signatures of the non-uniform Earth–ionosphere cavity in high time-resolution Schumann resonance records". Radio Science. in print. 
  29. ^ a b c Pechony, O., C. Price, A.P. Nickolaenko (2007). "Relative importance of the day-night asymmetry in Schumann resonance amplitude records". Radio Science. in print. 
  30. ^ Madden T., W. Thompson (1965). "Low-frequency electromagnetic oscillations of the Earth–ionosphere cavity". Rev. Geophys. 3 (2): 211. Bibcode:1965RvGSP...3..211M. doi:10.1029/RG003i002p00211. 
  31. ^ a b Nickolaenko A. P. and M. Hayakawa (2002). Resonances in the Earth–ionosphere cavity. Kluwer Academic Publishers, Dordrecht-Boston-London. 
  32. ^ Sentman, D.D., B. J. Fraser (1991). "Simultaneous observations of Schumann Resonances in California and Australia – Evidence for intensity modulation by the local height of the D region". Journal of geophysical research 96 (9): 15973–15984. Bibcode:1991JGR....9615973S. doi:10.1029/91JA01085. 
  33. ^ Pechony, O., C. Price (2006). "Schumann Resonances: interpretation of local diurnal intensity modulations". Radio Sci. 42 (2): RS2S05. Bibcode:2006RaSc...41.2S05P. doi:10.1029/2006RS003455. 
  34. ^ Yang H., V. P. Pasko (2007). "Three-dimensional finite difference time domain modeling of the diurnal and seasonal variations in Schumann resonance parameters". Radio Science 41 (2): RS2S14. Bibcode:2006RaSc...41.2S14Y. doi:10.1029/2005RS003402. 
  35. ^ a b Boccippio, D. J., E. R. Williams, S. J. Heckman, W. A. Lyons, I. T. Baker, R. Boldi (1995). "Sprites, ELF transients, and positive ground strokes". Science 269 (5227): 1088–1091. Bibcode:1995Sci...269.1088B. doi:10.1126/science.269.5227.1088. PMID 17755531. 
  36. ^ Price, C., E. Greenberg, Y. Yair, G. Sátori, J. Bór, H. Fukunishi, M. Sato, P. Israelevich, M. Moalem, A. Devir, Z. Levin, J.H. Joseph, I. Mayo, B. Ziv, A. Sternlieb (2004). "Ground-based detection of TLE-producing intense lightning during the MEIDEX mission on board the Space Shuttle Columbia". G.R.L. 31: L20107. doi:10.1029/2004GL020711. 
  37. ^ Hu, W., S. A. Cummer, W. A. Lyons, T. E. Nelson (2002). "Lightning charge moment changes for the initiation of sprites". G.R.L. 29 (8): 1279. Bibcode:2002GeoRL..29h.120H. doi:10.1029/2001GL014593. 
  38. ^ a b Williams, E.R. (1992). "The Schumann resonance: a global tropical thermometer". Science 256 (5060): 1184–1186. Bibcode:1992Sci...256.1184W. doi:10.1126/science.256.5060.1184. PMID 17795213. 
  39. ^ Williams, E.R. (1989). "The tripole structure of thunderstorms". J. G. R. 94: 13151–13167. Bibcode:1989JGR....9413151W. doi:10.1029/JD094iD11p13151. 
  40. ^ Hansen, J., A. Lacis, D. Rind, G. Russel, P. Stone, I. Fung, R. Ruedy, J., Lerner (1984). "Climate sensitivity: Analysis of feedback mechanisms". Climate Processes and Climate Sensitivity, J.,E. Hansen and T. Takahashi, eds.. AGU Geophys. Monograph 29: 130–163. doi:10.1029/gm029p0130. 
  41. ^ Rind, D. (1998). "Just add water vapor". Science 28 (5380): 1152–1153. doi:10.1126/science.281.5380.1152. 
  42. ^ Price, C. (2000). "Evidence for a link between global lightning activity and upper tropospheric water vapor". Letters to Nature 406 (6793): 290–293. doi:10.1038/35018543. PMID 10917527. 
  43. ^ Nickolaenko A. P., L. M. Rabinowicz (1982). "On the possibility of existence of global electromagnetic resonances on the planets of Solar system". Space Res. 20: 82–89. 
  44. ^ a b c Pechony, O., C. Price (2004). "Schumann resonance parameters calculated with a partially uniform knee model on Earth, Venus, Mars, and Titan". Radio Sci. 39 (5): RS5007. Bibcode:2004RaSc...39.5007P. doi:10.1029/2004RS003056. 
  45. ^ a b c Ruf, C., N. O. Renno, J. F. Kok, E. Bandelier, M. J. Sander, S. Gross, L. Skjerve, and B. Cantor (2009). "Emission of Non-thermal Microwave Radiation by a Martian Dust Storm". Geophys. Res. Lett. 36 (13): L13202. Bibcode:2009GeoRL..3613202R. doi:10.1029/2009GL038715. 
  46. ^ Eden, H. F. and B. Vonnegut (1973). "Electrical breakdown caused by dust motion in low-pressure atmospheres: consideration for Mars". Science 180 (4089): 962–3. Bibcode:1973Sci...180..962E. doi:10.1126/science.180.4089.962. PMID 17735929. 
  47. ^ Renno N. O., A. Wong, S. K. Atreya, I. de Pater, M. Roos-Serote (2003). "Electrical discharges and broadband radio emission by Martian dust devils and dust storms". G. R. L. 30 (22): 2140. Bibcode:2003GeoRL..30vPLA1R. doi:10.1029/2003GL017879. 
  48. ^ Sukhorukov A. I. (1991). "On the Schumann resonances on Mars". Planet. Space Sci. 39 (12): 1673–1676. Bibcode:1991P&SS...39.1673S. doi:10.1016/0032-0633(91)90028-9. 
  49. ^ Molina-Cuberos G. J., J. A. Morente, B. P. Besser, J. Porti, H. Lichtenegger, K. Schwingenschuh, A. Salinas, J. Margineda (2006). "Schumann resonances as a tool to study the lower ionosphere of Mars". Radio Science 41: RS1003. Bibcode:2006RaSc...41.1003M. doi:10.1029/2004RS003187. 
  50. ^ Lammer H., T. Tokano, G. Fischer, W. Stumptner, G. J. Molina-Cuberos, K. Schwingenschuh, H. O. Rucher (2001). "Lightning activity of Titan: can Cassiny/Huygens detect it?". Planet. Space Sci. 49 (6): 561–574. Bibcode:2001P&SS...49..561L. doi:10.1016/S0032-0633(00)00171-9. 
  51. ^ Besser, B. P., K. Schwingenschuh, I. Jernej, H. U. Eichelberger, H. I. M. Lichtenegger, M. Fulchignoni, G. J. Molina-Cuberos, J. A. Morente, J. A. Porti, A. Salinas (2002). "Schumann resonances as indicators for lighting on Titan". Proceedings of the Second European Workshop on Exo/Astrobiology, Graz, Australia, September 16–19. 
  52. ^ Morente J. A., Molina-Cuberos G. J., Porti J. A., K. Schwingenschuh, B. P. Besser (2003). "A study of the propagation of electromagnetic waves in Titan’s atmosphere with the TLM numerical method". Icarus 162 (2): 374–384. Bibcode:2003Icar..162..374M. doi:10.1016/S0019-1035(03)00025-3. 
  53. ^ Molina-Cuberos G. J., J. Porti, B. P. Besser, J. A. Morente, J. Margineda, H. I. M. Lichtenegger, A. Salinas, K. Schwingenschuh, H. U. Eichelberger (2004). "Shumann resonances and electromagnetic transparence in the atmosphere of Titan". Advances in Space Research 33 (12): 2309–2313. Bibcode:2004AdSpR..33.2309M. doi:10.1016/S0273-1177(03)00465-4. 
  54. ^ Nickolaenko A. P., B. P. Besser, K. Schwingenschuh (2003). "Model computations of Schumann resonance on Titan". Planet. Space Sci. 51 (13): 853–862. Bibcode:2003P&SS...51..853N. doi:10.1016/S0032-0633(03)00119-3. 
  55. ^ Béghin, C., et al., 2007. A Schumann-like resonance on Titan driven by Saturn’s magnetosphere possibly revealed by the Huygens Probe, Icarus 191, 251-266.
  56. ^ Béghin, C., et al., 2009. New insights on Titan’s plasma-driven Schumann resonance inferred from Huygens and Cassini data, Planet. Space Sci., 57, 1872-1888.
  57. ^ Béghin, C., Hamelin, M., Sotin, C., 2010. Titan’s native ocean revealed beneath some 45 km of ice by a Schumann-like resonance, Comptes Rendus Geoscience, 342, 425-433.
  58. ^ Béghin, C., and 8 colleagues. Analytic theory of Titan’s Schumann resonance: Constraints on ionospheric conductivity and buried water ocean, Icarus, 218, 1028-1042, 2012.
  59. ^ Bar-Nun A. (1975). "Thunderstorms on Jupiter". Icarus 24: 86–94. Bibcode:1975Icar...24...86B. doi:10.1016/0019-1035(75)90162-1. 
  60. ^ http://www.ciclops.org/view_event/178/Lightning_Flashing_in_Daylight
  61. ^ Sentman D. D. (1990). "Electrical conductivity of Jupiter's Shallow interior and the formation of a resonant planetary-ionosphere cavity". Icarus 88: 73–86. Bibcode:1990Icar...88...73S. doi:10.1016/0019-1035(90)90177-B. 

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