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Keywords:

  • Schumann resonance;
  • ELF;
  • diurnal variations

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ELF Instruments
  5. 3. Observations
  6. 4. Theory
  7. 5. Discussion and Summary
  8. Acknowledgments
  9. References

[1] Schumann resonances (SR) are resonant electromagnetic waves in the Earth-ionosphere cavity, induced primarily by lightning discharges, with a fundamental frequency of about 8 Hz and higher-order modes separated by approximately 6 Hz. The SR are made up of the background signal resulting from global lightning activity and extremely low frequency (ELF) transients resulting from particularly intense lightning discharges somewhere on the planet. Since transients within the Earth-ionosphere cavity due to lightning propagate globally in the ELF range, we can monitor and study global ELF transients from a single station. Data from our Negev Desert (Israel) ELF site are collected using two horizontal magnetic induction coils and a vertical electric field ball antenna, monitored in the 5–40 Hz range with a sampling frequency of 250 Hz. In this paper we present statistics related to the probability distribution of ELF transients and background noise in the time domain and its temporal variations during the day. Our results show that the ELF signal in the time domain follows the normal distribution very well. The σ parameter exhibits three peaks at 0800, 1400, and 2000 UT, which are related to the three main global lightning activity centers in Asia, Africa, and America, respectively. Furthermore, the occurrence of intense ELF events obeys the Poisson distribution, with such intense events occurring every ∼10 s, depending on the time of the day. We found that the diurnal changes of the σ parameter are several percent of the mean, while for the number of intense events per minute, the diurnal changes are tens of percent about the mean. We also present the diurnal changes of the SR intensities in the frequency domain as observed at our station. To better understand the diurnal variability of the observations, we simulated the measured ELF background noise using space observations as input, as detected by the Optical Transient Detector (OTD). The most active center which is reflected from both ELF measurements and OTD observations is in Africa. However, the second most active center on the basis of ELF measurements appears to be Asia, while OTD observations show that the American center is more active than the Asian center. These differences are discussed. This paper contributes to our understanding of the origin of the SR by comparing different lightning data sets: background electromagnetic radiation and optical emission observed from space.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ELF Instruments
  5. 3. Observations
  6. 4. Theory
  7. 5. Discussion and Summary
  8. Acknowledgments
  9. References

[2] Worldwide lightning activity is produced by about 2000 active thunderstorms around the globe [Ogawa et al., 1966], generating dozens of lightning discharges per second. Brooks [1925] was the first to estimate the global flash rate on the basis of human observations and estimated a rate of 100 flashes per second. Nowadays advanced space-based tools like the Optical Transient Detector (OTD) allow us to understand the spatial and temporal distribution of lightning around the globe [Christian et al., 2003]. Another important tool for the study of global lightning activity is the electromagnetic radiation emitted by lightning.

[3] Each individual lightning discharge radiates radio noise over a wide frequency range, although the main interest of our research is in the lower ELF band, below 50 Hz. The advantage of this frequency band is the low attenuation rate of electromagnetic (EM) waves propagating within the Earth-ionosphere waveguide. Therefore, by observing the electromagnetic signals in both the time and frequency domains, one can deduce the behavior of global lightning activity from a single observation station.

[4] It is known that there are three main centers of global lightning activity in Africa, Central and South America and South Eastern Asia [Uman, 1969; International Telecommunication Union, 1990]. Furthermore, lightning activity occurs mainly in the summer hemisphere, moving from one hemisphere to the other during the annual cycle.

[5] Since Schumann's prediction about the existence of the Earth-ionosphere cavity eigenfrequencies [Schumann, 1952], it was realized that Schumann resonance (SR) field power variations are related to global thunderstorm activity [Holzer, 1958; Raemer, 1961; Balser and Wagner, 1962; Rycroft, 1963]. Therefore spectral SR measurements became a convenient tool for studying global lightning activity [Sentman and Fraser, 1991; Nickolaenko and Rabinowicz, 1995; Sátori, 1996]. This is done by tracking the parameters of the SR modes: amplitude, frequency and quality factor, which are determined by the temporal and spatial distribution of global lightning [Nickolaenko et al., 1998; Heckman et al., 1998; Belyaev et al., 1999]. Long-term measurements of SR enable us to understand diurnal changes, seasonal and interannual tendencies of global lightning activity [Füllekrug and Fraser-Smith, 1997; Sátori and Zieger, 1999; Price and Melnikov, 2004].

[6] Williams [1992] suggested that SR parameters may be used to monitor planetary temperatures (linked to SR through the lightning flash rate, which increases nonlinearly with temperature). More recently [Price, 2000; Price and Asfur, 2006] suggested to monitor global upper tropospheric water vapor changes with SR (water vapor and lightning activity are closely linked through thunderstorms). If it is possible to monitor global temperature and water vapor changes through SR records from a single station, SR may be a convenient and a low-cost tool for global climate change observations. Since ELF transients represent the most intense lightning flashes, tracking their statistics may supply additional information regarding thunderstorm variability on all spatial and temporal scales [Huang et al., 1999; Hobara et al., 2006].

[7] In this paper we focus on the diurnal statistics of ELF transients, together with the background SR diurnal variations. In section 2 we describe the observation system and data acquisition. In section 3 we present results from our ELF observations in the time and frequency domains. In section 4 we present theoretical calculations, using OTD lightning data as input to the simulated model, in order to simulate the ELF measurements. In section 5 we analyze and discuss the implications of the results.

2. ELF Instruments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ELF Instruments
  5. 3. Observations
  6. 4. Theory
  7. 5. Discussion and Summary
  8. Acknowledgments
  9. References

[8] The ELF instruments used in this study are located at Tel-Aviv University's astronomical observatory near the town of Mitzpe-Ramon (MR) in the Negev Desert, far away from industrial activity which produces different kinds of ELF interferences (50 Hz power supply lines). The station has two horizontal magnetic induction coils for receiving the magnetic field in the north-south direction (Hns) and the east-west direction (Hew) and one vertical electrical ball antenna for receiving Er [Price et al., 1999; Price and Melnikov, 2004]. The three components of the electromagnetic field are sampled at 250 Hz, with a notch filter at 50 Hz in use. The raw time series data are saved in 5-min files, with all analysis performed during postprocessing. In this paper we present results for the magnetic field components only. Each magnetic coil is calibrated using our calibration coil by driving a current of 1 μA that induces a uniform magnetic field with amplitude of 93 pT to the “receiving coil,” enabling us to calculate the system spectral response. This allows us to obtain the SR intensity in units of pT in the time domain or pT2/Hz in the frequency domain. In Figure 1a we present a time series for one of the magnetic field coils (Hns) during 5 min. The signal consists of background noise caused by global lightning activity, with amplitude of 3–5 pT, together with intense transients from individual powerful lightning discharges, with amplitudes of tens of picotesla. Figure 1b presents the dynamic spectrum of Figure 1a, using 256 samples per FFT (∼1 s) with a moving window of 128 samples (∼0.5 s). The dominant SR mode at 8 Hz can be observed, with some higher modes at 14 Hz and 20 Hz. The intense transients show up clearly in the dynamic spectrum as enhancements of the SR spectra.

image

Figure 1. (a) Time series of Hns, background noise and intense transients and (b) its dynamic spectrum, Schumann resonance (8, 14, and 20 Hz), and transients' signatures.

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3. Observations

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ELF Instruments
  5. 3. Observations
  6. 4. Theory
  7. 5. Discussion and Summary
  8. Acknowledgments
  9. References

3.1. Time Domain

[9] Statistical analysis of the ELF signal in the time domain reveals that the magnetic field data follow the normal distribution very well, between 1% and 99%. Figure 2a shows the distribution of ELF amplitudes for the Hns component (Figure 1a). In blue are the measured counts for specific magnetic field amplitude, while in red is the normal (Gaussian) distribution fit where its parameters μ (mean) and σ (variance) were estimated on the basis of the observed data. Figure 2b shows a normal probability plot. The plot has the sample data displayed with pluses. On the plot is superimposed a line joining the first and third quartiles of the data. This line is extrapolated out to the ends of the sample to help evaluate the linearity of the data. For a normal distribution the plot will appear linear. The curvature introduced at the extremes shows that the most intense events deviate from the normal distribution.

image

Figure 2. (a) Histogram of Hns in blue and the normal distribution (μ and σ were estimated) in red. (b) Normal probability plot.

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[10] To further study only the intense ELF transients (Q bursts), with values 5σ above the background noise (∼15 pT), thousands of files were analyzed (hundreds of hours of raw data). It was found that the number of intense events obeys the Poisson distribution (Figure 3), thus the parameter of the Poisson distribution λ was estimated for every 5-min file. The λ parameter is the mean number of intense events that arrive in a 5-min interval and enables us to estimate how often such event occurs (Figure 3a, blue). To examine the validity of the Poisson distribution a random vector was generated (named “Theory”) and plotted in red.

image

Figure 3. (a) Distribution of the number of intense events per file for Hns in blue and a random vector distributed by estimated Poisson parameter λ in red. (b) Quantile-quantile plot of measured and theoretical vectors.

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[11] Figure 3b shows the sample quantiles of intense events versus theoretical quantiles from the Poisson distribution (blue versus red data points in Figure 3a). Since the plot is almost linear, our assumption regarding the distribution is justified. The λ parameter was estimated for every file with 99.9% confidence intervals in order to evaluate the goodness of the fit. The mean and variance was also evaluated for each data file and found to be highly correlated (for an ideal Poisson distribution the mean and variance are equal). Files with more than 60 intense events occurred when there were high levels of local man-made noise or close thunderstorms, which leads to the excursion from the Poisson distribution.

[12] For each 5-min file we have estimated the normal distribution parameter σ and calculated the number of intense events per file. Data files were analyzed every hour from February until October 2004 and a total number of 4320 files were processed. Hence, for every hour, some 180 files were analyzed to obtain the diurnal behavior of these parameters. Figure 4 presents hourly averaged diurnal variations in σ and the number of transients, for both Hns and Hew.

image

Figure 4. Diurnal changes parameters for Hns (a) σ and (b) intense events and for Hew (c) σ and (d) intense events.

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[13] Each horizontal magnetic field sensor is sensitive to waves arriving from directions normal to its axis. Therefore, because of the position of the observation station in Mitzpe-Ramon (30°N, 34°E), the major regions of thunderstorm activities are well separated (see Figure 5). Furthermore, waves from Southeast Asia arrive from the east and are detected primarily by the north-south magnetic induction coil, with maximum activity around 0800 UT. From the Americas the EM waves come primarily from the west, with maximum activity around 2000 UT. Waves from Africa arrive primarily from the south and therefore are detected by the east-west magnetic induction coil, with the maximum activity around 1400 UT.

image

Figure 5. ELF observation station in Mitzpe-Ramon (MR) and the general direction to the main global lightning activity centers: Southeast Asia, central Africa, North America, and South America.

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[14] The normal distribution parameter σ is determined by the variance of the background noise level: increased lightning activity leads to increased values of the σ parameter. In Figure 4a, the diurnal change of the σ parameter for Hns shows three maxima at 0800–0900, 1200–1300 and 1700–1800 UT which marked with arrows, representing the three major “hot spots.” The African chimney is less obvious since the north-south coil is sensitive mainly to the other two regions. The Asian chimney looks more powerful than the American chimney, although only slightly larger.

[15] Figure 4b presents the diurnal change in the number of intense events above 15 pT. In Figure 4b the Asian center dominates the number of ELF transients, with Africa following, and the Americas in third place. The mean number of intense events arrived to the Hns sensor every 5 min during 0800 UT is ∼32 while during 2000 UT is ∼24. Since the north-south coil is sensitive to pulses arriving from Asia and America we can deduce that an intense event occur every ∼10 and ∼12 s, respectively and disregard from the number for Africa during 1400 UT since this coil is not sensitive to pulses arrive almost in parallel to its axis. The values of σ show moderate variability compared to the number of intense events. While the values of σ at 0800 UT are 1% greater than its values at 2000 UT, the number of intense events is more prominent by 30%.

[16] In Figures 4c and 4d, the diurnal change of the σ parameter and number of intense events above 15 pT are given for the east-west magnetic component (Hew). There is one clear maximum at 1300–1400 UT due to the sensitivity of the east-west sensor to signals arriving from Africa. The mean number of intense events arriving from Africa to the Hew sensor every 5 min around 1400 UT is ∼44, so we can deduce that an intense event occur every ∼7 s. Here we disregard the number for Asia and America since this coil is not sensitive to pulses arrived from its directions.

[17] Once more the values of σ show moderate variability compared to the number of intense events. While the values of σ at 1400 UT are 30% greater than its values at other hours during the day, the number of intense events at 1400 UT is 230% greater than at other times of the day.

[18] The source current amplitudes are frequently represented by lognormal distributions. The probability that the peak current of a return stroke equation image exceeds the median current equation image is given by [Galejs, 1972]

  • equation image

where m is the median value of log equation image. The physical meaning of our results is that the tail of the distribution is more sensitive to the global lightning activity than the mean values. While variations during the day are minor for the common amplitudes which occur often, the number of intense discharges which occur rarely changes significantly. We should also mention that the low sampling frequency does not allow us to distinguish between every two adjacent lightning discharges since its mean duration is about 10 ms (assuming uniform global rate of 100 flashes per second) and our system time period is 25 ms (limited by instrumental bandwidth 40Hz), resulting in interference between numerous EM waves arriving simultaneously.

3.2. Frequency Domain

[19] Figure 6 presents the observed dynamic spectrum in the ELF band below 30 Hz, showing the diurnal changes of the Schumann resonance modes at 8, 14 and 20 Hz, both for Hns and Hew. In Figure 7 are plotted the diurnal behavior of each mode shown in Figure 6. In Figure 7a, the fundamental SR mode at 8Hz for Hns shows two prominent peaks at 0800 and 2000 UT produced by lightning in Southeast Asia and the Americas, respectively. The Asian chimney appears to be more powerful than the American chimney. The maximum is wider at 0800 UT than at 1400 UT, implying that the quality factor of the Earth-ionosphere cavity at 0800 UT is lower than at 2000 UT. In Figure 7b (Hns second mode) the most powerful peak is at 1400 UT relative to the two other peaks. Although the north-south induction coil is less sensitive to signals arriving from the direction closely normal to its axis (Africa), the modal structure of the waveguide attenuates the second SR mode at 14Hz when the source region and the observation station are separated by 10,000 km. Figure 7c presents the diurnal change of the third SR mode. Here too, Africa dominates the diurnal cycle of the Hns component. In Figures 7d–7f we present the three SR modes for Hew. The most active thunderstorm center on the globe can clearly be seen at 1400 UT because of its natural dominance, together with the sensitivity of the east-west induction coil to signals arriving from Africa.

image

Figure 6. Dynamic spectrum of signals in the SR band based on ELF measurements for (a) Hns and (b) Hew.

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image

Figure 7. Diurnal changes of Schumann resonance modes based on ELF measurements in Israel for Hns at (a) 8 Hz, (b) 14 Hz, and (c) 20 Hz and for Hew at (d) 8 Hz, (e) 14 Hz, and (f) 20 Hz.

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4. Theory

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ELF Instruments
  5. 3. Observations
  6. 4. Theory
  7. 5. Discussion and Summary
  8. Acknowledgments
  9. References

[20] To understand our observations we carried out simulations using input with the OTD satellite lightning data. This space-based instrument was specifically designed to optically detect and locate lightning discharges as it orbits the Earth [Christian et al., 2003]. The OTD hourly averaged data from 1995 to 2000 are freely available at the Web site of GHCC (http://thunder.msfc.nasa.gov/otd/). We used spatial resolution bins of 1° × 1°, so the globe is divided to 181 rows and 360 columns and each cell of the matrix contains the flash density per squared km per year. As a first step we present the spatial and temporal distribution of lightning sources observed by OTD (Figure 8). The three main “hot spots” revealed by the OTD are in Asia (0700–0800 UT), Africa (1300–1400 UT) and the Americas (1700–2000 UT), at distances of 8000 km, 4000 km and 11000 km from Israel (Figure 8a), and azimuths of 90, 200 and 280°–320° from Israel (Figure 8b).

image

Figure 8. Spatial and temporal distribution of lightning sources based on OTD observations: (a) distances from Israel and (b) azimuths from Israel. Units of color are flashes per km2 per year.

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4.1. Time Domain

[21] To interpret the relative magnitude of the different source regions we assumed that every flash detected by the OTD has the same amplitude (or charge moment). The electromagnetic wave in the SR band that propagates in the Earth-ionosphere waveguide exhibits an attenuation of 0.3 (dB/Mm). Since the main lightning activity centers are located at different distances from our ELF observation station we have implemented a loss of energy for each flash on the basis of the attenuation rate in order to eliminate the factor of distance. By calculating the contribution of each lightning source from the flash density detected by the OTD (Figure 8), we deduced the total relative amplitude as should be measured at our ELF station in MR and the projections to the north-south and east-west axis. Figure 9a presents the expected amplitude for the north-south coil. The American peak at 2000 UT is 40% larger than the Asian and African peaks at 0800 and 1400 UT, respectively, which are almost equal. Figure 9b presents the expected amplitude at the east-west coil. The African peak at 1400 UT is 80% larger than the American peak at 2000 UT while the Asian peak at 0800 UT is not visible.

image

Figure 9. Simulated magnetic field relative amplitude based on OTD observations for (a) Hns and (b) Hew.

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4.2. Frequency Domain

[22] In the ELF frequency range we can assume that for distances greater than 2000 km the quasi-transverse electromagnetic mode (q-TEM) is the only mode effectively radiated, while higher TEn and TMn modes are attenuated in the vicinity of the source. Since the main lightning activity centers are located more than 4000 km from our ELF observatory in Israel, it is sufficient to assume that the propagated waves in the Earth-ionosphere cavity consist of the radial electric field Er and the horizontal magnetic field Hϕ [Jones and Kemp, 1970]. In geocentric spherical polar coordinates {r, θ, ϕ} the magnetic field may be written in terms of zonal harmonic series:

  • equation image

where ω denotes the angular frequency; θ is the great circle angle from lightning to the observer; ɛ0 is vacuum permittivity; a is the radius of the Earth; h is the height of the ionosphere; Pn1(cosθ) is the associated Legendre function of degree n and order 1; υ is the modal eigenvalue related to the propagation constant of the Earth-ionosphere spherical shell cavity; and Idl(ω) is the vertical current moment of the lightning ground flash. In order to compute the zonal harmonic series we used a finite number of terms n = 300, constant ionospheric height h = 60 km, and propagation constant

  • equation image

[23] By the knowledge of the spatial distribution of lightning based on OTD data, we simulated the diurnal behavior of the ELF magnetic fields and their projections to the north-south and east-west axis. Since OTD provided only the flash density with no amplitude for each flash, we assumed that each individual stroke has the same charge moment.

[24] The simulated diurnal SR modes at 8, 14, 20, 26 Hz (Figure 10) are based on OTD input data (Figure 8) by assigning a time and distance to each flash. In Figure 11 are plotted the diurnal behavior of each mode shown in Figure 10. In Figure 11a, Hns, the American chimney at 8 Hz appears to be more powerful than the Asian one, in contrast with the findings of our ELF observations (Figure 7a). At 14 Hz, Figure 11b, the African peak becomes more prominent relative to the others, but the Americas are less powerful with respect to the Asian center, in contrast with the findings of our ELF measurements (Figure 7b). At 20 Hz, Figure 11c, the African peak increases more and the Americas are more powerful than the Asian center. In Figure 11d, Hew, the African center is the most dominant and becomes even more prominent for higher modes (Figures 11e and 11f), in agreement with the observations (Figures 7e and 7f).

image

Figure 10. Dynamic spectrum of signals in the SR band based on OTD observations for (a) Hns and (b) Hew.

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image

Figure 11. Diurnal changes of Schumann resonance modes based on OTD observations from space for Hns at (a) 8 Hz, (b) 14 Hz, and (c) 20 Hz and for Hew at (d) 8 Hz, (e) 14 Hz, and (f) 20 Hz.

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5. Discussion and Summary

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ELF Instruments
  5. 3. Observations
  6. 4. Theory
  7. 5. Discussion and Summary
  8. Acknowledgments
  9. References

[25] In this paper we have demonstrated the ability of single station ELF observations to monitor the diurnal variability of global lightning activity centers. Understanding the SR observations at individual stations is essential for a better understanding of global lightning activity, the global electric circuit and climate change [Füllekrug and Fraser-Smith, 1997; Sátori and Zieger, 1999; Rycroft et al., 2000; Price, 2000]. The ELF signals in the time and frequency domains exhibit pronounced excursion on 0800, 1400 and 2000 UT correspondingly to the three major lightning activity centers in Southeast Asia, central Africa and the Americas, respectively, whose thunderstorm activity develops in the late afternoon.

[26] In the time domain, the amplitude of the background noise is about 3–5 pT and an intense ELF transient with amplitudes above 15 pT occurs every ∼10 s depending on the hour of the day. The diurnal changes in the number of intense events are an order of magnitude larger than the normal distribution parameter σ which represents the background noise level. Therefore we suggest that the number of intense events may act as a better indicator of diurnal thunderstorm activity in the main thunderstorm centers.

[27] The diurnal amplitude of measured ELF signals (σ) in the time domain was compared with the simulated relative amplitude using numerous lightning sources detected by the OTD as input. While the Asian chimney at 0800 UT is more prominent than the American chimney from ELF measurements (Hns component), the opposite was found from OTD observations. For the Hew component the African peak is dominant at 1400 UT both on ELF measurements and simulated values based on OTD observations.

[28] Furthermore, in the frequency domain, the eigenfrequencies of the Earth-ionosphere waveguide change during the day because of its modal structure responding to the changing locations of the global lightning centers. Here too ELF measurements from our single station were compared with simulations using OTD observations from space as input. As with the time domain analysis, the main three global lightning activity centers dominate the ELF power spectrum. Once again, for the Hns component, while the Asian chimney at 0800 UT is more prominent than the American chimney from ELF measurements, the opposite was found from OTD observations. For the Hew component the African peak is dominant at 1400 UT both on ELF measurements and simulated values based on OTD observations.

[29] The disagreements which were found between the ELF observations and simulations can possibly be explained by the following.

[30] 1. The OTD may be sensitive mainly to intracloud discharged since it detects the diffused light leaving cloud top. ELF measurements are most sensitive to cloud-to-ground discharges with dominant vertical radiation components from the lightning channel.

[31] 2. The OTD may have different sampling efficiencies/biases in Asia and the Americas. In the South American region the South Atlantic Anomaly (SAA) is known to produce false detections of lighting. On the other hand, could clouds over Asia be optically thicker than those over South America? This would lower the detection efficiency of Asian lightning by the OTD sensor.

[32] 3. The OTD provides flash density without specifying the amplitude for every event. Therefore we have assumed and implemented in time domain analysis and in the zonal harmonic series model the same charge moment for every lightning discharge. Storms in Asia and South America may have different charge moment distributions.

[33] 4. The terminator effect is propagation of waves through the day-night transition and the asymmetry of the ionosphere conductivity [Keefe et al., 1964; Sentman and Fraser, 1991; Melnikov et al., 2004]. At 0800 UT our observatory in Israel is located on the day side together with the active center for this period of time: Asia. At 2000 UT the observatory is located on the night side while the active center for this period of time, America, is located on the day side. Therefore, instead of a simple uniform ELF model, a more realistic model should be used with different daytime and nighttime ionospheric heights and a height-dependent conductivity distribution.

[34] 5. Near-field effects, lightning activity in the vicinity of our ELF observatory, some hundreds of km, may excite higher TE and TM modes than the basic q-TEM assumed. Future research will attempt to resolve these differences between the observed and simulated ELF diurnal variations.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ELF Instruments
  5. 3. Observations
  6. 4. Theory
  7. 5. Discussion and Summary
  8. Acknowledgments
  9. References

[35] This research was funded by the Israel Science Foundations grant 183/00-2. Construction, calibration, and operation of the Israeli station were made possible by the help of Boris Satarobinets, Michael Finkelstein, and David Shtibelman. We also thank the Wise Astronomical Observatory for access to their site for the SR measurements in Israel.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ELF Instruments
  5. 3. Observations
  6. 4. Theory
  7. 5. Discussion and Summary
  8. Acknowledgments
  9. References
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