Radio Science

Long-term observations of Schumann resonances at Modra Observatory



[1] The paper presents a summary of more than 4 years of continuous Schumann resonance (SR) monitoring of the vertical electric component at Modra Observatory. Principal parameters (peak frequency, amplitude, and quality factor) are determined for four resonances from 7 to 30 Hz, i.e., for modes one through four. Attention is also given to the less frequently compiled mode four. The resonance parameters are computed from 48 daily measurements and are represented as the mean monthly values for each time of the detection. Fitting of spectral peaks by Lorentz function is the main method used in data postprocessing. Diurnal, seasonal variations and the indication of interannual variations of these parameters (especially peak frequency) are discussed. The results are compared with other observatory measurements. Our observations confirm that variations in peak frequency of the lower-SR modes can be attributed mainly to the source-observer distance effect.

1. Introduction

[2] The Schumann resonances (SR)—electromagnetic oscillations in the resonator formed by the Earth's surface and the lower ionospheric layers—represent an important geophysical phenomenon, which can be used for monitoring mean global tropospheric thunderstorm activity by measuring natural ELF continuous (noise background) signals. Williams [1992] demonstrated some correlation between the first SR mode amplitude and the tropical land surface temperature anomaly on the El Niño–Southern Oscillation timescale. The global lightning activity, which is the principal excitation source of SR, is concentrated mostly in three tropical land regions: South America, Africa, and the maritime continents (Indonesia).

[3] If frequency dependence of the natural electromagnetic background noise is approximated by Lorentz functions, the spectral properties of each SR mode can be defined by three main parameters, namely peak (center) frequency, peak amplitude and quality factor (inversely proportional to the line half width). The time variations of the main parameters result from complex interplay of changes (temporal and spatial) of lightning foci intensities and changes of lower ionosphere state (above all, from its conductivity and density profile, which is also influenced by solar activity). Conductivity of the Earth's surface is considered infinite, so its influence on SR parameters can be neglected. The disentangling of such a complicated causal chain requires, first of all, accumulation of data for the longest possible time intervals; finding the most adequate method of data processing in terms of physics is no less important.

[4] The aim of the paper is to identify various types of frequency variations on different timescales. Four types of diurnal frequency patterns were identified by Sátori [1996]. It was concluded therein that the main cause of the frequency variations of the first and the second mode is the source migration between the northern and the southern hemispheres. Sátori and Zieger [2003] dealt with the areal variations of lightning activity on different timescales deduced from the variations of SR daily frequency range (DFR). They found that the annual variation of DFR shows an 11-year solar cycle modulation.

[5] Melnikov et al. [2004] studied the influence of solar terminator passages on SR parameters. They concluded that the terminator effect (TE) is more pronounced in amplitudes of higher-order SR modes. The other parameters were investigated only for the first mode. Furthermore, the TE was found stronger in the morning than in the evening and in winter than in summer.

2. Observatory Site and Hardware Description

[6] The Astronomical and Geophysical Observatory of the Faculty of Mathematics, Physics and Informatics, Comenius University, is located in the Western Carpathians (17.27°E, 48.37°N, 530 m above the sea level) at a place practically free of permanent settlements. The nearest inhabited place is approx. 1.5 km away with no powerful electric equipment. Nevertheless, the observatory site is still far from the ideal mostly because of the surrounding vegetation. Thus a circle of 50 m in diameter clear of trees was formed around the ball antenna. Unfortunately, the clearance was not large enough to get rid of all disturbances. The most pronounced disturbing signals in the electric data were those caused by wind jittering of the surrounding trees and vegetation.

[7] Monitoring of the vertical electric field component has been performed in our observatory since October 2001. Five spectral peaks were detected when meteorological conditions were favorable. Until December 2005 there were practically no interruptions except for the cases when the measuring hardware or software was being updated. Monitoring of the magnetic field SR components is still in the experimental phase.

[8] The electric field SR component was picked up by a capacitive (ball) antenna (height 5 m, effective capacitance about 50 pF). The preamplifier (input impedance about 500 Mohm, electrometric vacuum tube as the input stage) with a gain of about 85 dB, was located immediately at the antenna base. 50-Hz analog filters and three-channel 24 bit ADC followed (also for the magnetic component data). The signal samples were collected every half hour for 5 min 27.7 s (65536 samples taken with 200 Hz sampling frequency) and subsequently stored in a PC.

[9] Man-made disturbing signals (much more pronounced in the magnetic than in the electric component), especially the 16.67 Hz signal from the Austrian Railways drive system, were frequently observed in the electrical component spectrum, but mostly with lower amplitude.

3. Data Processing

[10] Each sequence of digitized data was subjected to digital filtering by TISEAN package [Hegger et al., 1999] for reducing the rest of the 50 Hz peak by a bank of notch filters. Moreover, the low-frequency noise was occasionally suppressed by a high-pass filter with a cutoff frequency of 4.5 Hz. The data were then transformed by standard Hamming window.

[11] In the second step, the DFT spectrum of the whole sequence of the data samples was computed. To obtain amplitude spectra, the square roots of the spectral coefficients were given at output. The frequency resolution was 3.05 mHz. (These spectra in the frequency interval 5–45 Hz are given in real time at A typical example of the electric component spectrum is given in Figure 1a. One of the “most fortunate” magnetic component spectra recorded is shown in Figure 1b.

Figure 1.

(a) Typical raw spectrum of the electrical component taken at Modra Observatory at 1000 UT, 5 February 2006, under very favorable conditions (clear sky, no wind) and (b) raw spectrum of the magnetic component from 19 July 2005, 2115 UT (sensor direction E–W). The narrow line at 16.67 Hz is due to the driving frequency of the Austrian Railways. The level of man-made disturbances is often higher.

[12] The principal parameters for the first four modes (peak frequency fi, quality factor Qi and relative peak amplitude Ai) were obtained by least squares fitting of spectra by the sum of four Lorentz functions. The theoretical peak frequencies from a simple uniform ionosphere model [Bliokh et al., 1977] were taken as necessary starting guesses of frequencies. Some tests were carried out in which the Prony algorithm [Lawrence, 1987] was implemented to get initial frequency guesses. This version of the fitting code was discarded as unnecessary. The GSL library ( was finally implemented in the fitting code using the Lorentzians and LSM.

[13] The initial guess for a mode amplitude was taken as half the maximum amplitude within definite frequency interval around the corresponding peak and initial Q factors were set to 1.0 for each mode. The fitting procedure was normally terminated if the sum of the squared differences between the input and the fitted spectrum was smaller than the prescribed value. In most cases, the fitting process finished successfully after 20–50 iterations.

[14] In calm weather, the low-frequency wing of the first peak has a small amplitude. Suppression of f−1 noise floor by including the fifth Lorentzian centered at 2.5–3 Hz (suggested by Melnikov et al. [2004]) was not used because it could not substantially change the overall picture of time variations of the mode parameters.

[15] The results of fitting were considered reliable only if the quality factor (Q) was between 1.0 and 15.0 and the difference between the peak frequency obtained and the initial guess was not greater than 3.0 Hz. If, for some data set, the fitting algorithm convergence was not achieved in 1000 iterations or some values of parameters were clearly unphysical (e.g., negative amplitude, or Q factor outside the above mentioned interval, or the peak frequency too different from the initial guess) for at least one mode, the whole data sequence was completely discarded. No data clipping was used.

4. Overview of the Results

[16] For each complete year there should be 48 × 365 = 17520 data sequences (for 5.5 min every half hour). However, some of them were missing as a result of low antenna sensitivity (mostly during winter months at heavy snow or icing), sometimes due to the hardware experiments and repairs. If the result of spectrum fitting was unreliable (as described in the previous paragraph), the corresponding data sequence was completely abandoned. This happened mostly in 2003, where one can observe two continuous data gaps, and in 2004, where scattered cases occur. The above blanks constitute at most 15% of the total observation time. In all graphs the time displayed is in UT.

[17] As follows from the processing of our data, the amplitude changes over long time intervals were not very reliable because the ball antenna sensitivity was strongly influenced by the weather conditions (the changes of antenna-ground resistance). Moreover, the preamplifier was repeatedly upgraded and subjected to experiments, so its frequency response was deliberately changed. Since reliable and precise sensitivity calibration of capacitive ELF antenna is a very difficult process [Nickolaenko et al., 1996], it was omitted, although relative calibration for crude checking of amplitude-frequency function was performed several times.

[18] It is worth mentioning that the curves in Figures 2, 3, 4, 5, and 6were smoothed by Bézier spline (minimal integral curvature), which might obscure sharper data changes in shorter intervals.

Figure 2.

Monthly averaged diurnal variations of the first-mode amplitude for 2001–2005. Because of the amplifier modifications in some cases, the amplitudes in graphs are nonnormalized. Years 2001 (dash-dotted line), 2002 (dashed line), 2003 (thin dotted line), 2004 (thick dotted line), and 2005 (solid line); see also the legend in Figure 3.

Figure 3.

Monthly averaged diurnal variations of the first-mode frequency in the years 2001–2005. Note analogical patterns in different years in all months except some peculiarity in May.

Figure 4.

Monthly averaged diurnal variations of the second-mode frequency in the years 2001–2005. For the point and line types, see the legend in Figure 3.

Figure 5.

Same as Figure 4 but for the third mode.

Figure 6.

Same as Figure 4 but for the fourth mode.

4.1. Diurnal Variations

[19] Figure 2 shows the average diurnal variations in the first-mode amplitude (nonnormalized) for each month between October 2001 and December 2005. In some cases the amplitude is out of range. In general, the diurnal amplitude variation exhibits its maximum mostly at around 1500–1600 UT, which coincides with the maximum lightning activity of the African source. The difference against the well-known Carnegie curve (with the maximum at about 1800 UT) is profoundly explained by Williams and Sátori [2004]. The relative increase of SR amplitudes in evening hours (2000–2100 UT) in several months is attributable to the increase of lightning activity in the Amazon region [Williams and Sátori, 2004]. However, the overall amplitude of the signal from the Amazon source is low as our site lies at about 90° angular distance from this source in the nodal region for both the first and the third EZ modes. The characteristic SR amplitude pattern changes between November and February because of the migration of lightning activity regions and the lightning activity in the maritime continent.

[20] In Figures 3–6 the averaged frequencies of the first to fourth modes are given for each month/year of observation. The values shown are the means in the fixed half hour from all the days of month quoted. All the times shown are in UT.

[21] The diurnal frequency variation pattern of each mode was predominantly determined by the source-observer geometry. The overall pattern seen in the whole years corresponds to the annual transition from the “winter-type” to the “summer-type” diurnal frequency variation. In January, the minimum frequency occurs at about 11 LT, while at this time in June–July the first-mode frequency exhibits its maximum.

[22] The difference between the maximal and minimal frequencies, the so-called diurnal frequency range (DFR), depends on the size of the active thunderstorm region. Figure 3 shows that the first-mode DFR is maximal during December–January while it is much narrower in April and August.

[23] The second-mode DFR is also broadest in winter months and nearly zero in May–July, although no significant “phase reversal” at the equinoxes (as for the first mode) occurs.

[24] The diurnal variation pattern of higher modes is an increasingly humped curve as the number of nodal lines grows with the growing mode number. For the third mode there is a secondary maximum in frequency at about 1100–1200 UT, which is more distinctive in winter, during summer months (May–July) this feature looks like an “inflexion point.” The maximum of the fourth-mode frequency around noon persists all the year and thus cannot be considered as secondary. The broadest DFR (of about 1.1 Hz at equinoxes) is clearly visible in the third mode.

[25] If we consider the nth mode excited by a linear current source [Nickolaenko and Hayakawa, 2002], the angular distribution of vertical electric (Er) field amplitude is given by appropriate linear combination of spherical harmonics Yn(m). The weights of individual harmonics depend on the excitation current direction and on boundary conditions. The angular spacing of nodal lines for all harmonics of the same order equals π/n. Naturally, because of the finite area of the source, the nodal lines are smeared out; yet, in general, their pattern persists. Thus one should rather speak about “nodal valleys.” For the third and fourth modes this spacing is approximately equal to the distance between the observation point and the equatorial Africa lightning focus [Sátori and Zieger, 1996]. Therefore, as the instantaneous center of lightning activity shifts around the globe, different spatial harmonics of the field become preferable from the observer's point of view.

[26] For both horizontal magnetic field components (Hθ, Hϕ), the angular field amplitude distribution is different [Nickolaenko and Hayakawa, 2002]. The appropriate linear combination is composed of the terms proportional to (Yn(m)/sin θ) in the former case and (∂Yn(m)/∂θ) in the latter. Therefore the mode preferences and their diurnal changes can be entirely different.

[27] On the basis of our observations, typical diurnal frequency variations (in patterns and magnitude of DFR) can be mainly, though not solely, attributed to changes in source-observer geometry and area of source regions. For each of the four seasons, there is a distinctive diurnal frequency pattern, as well as a different DFR [Sátori, 2003].

4.2. Combined Diurnal, Seasonal, and Interannual Variations

[28] Figures 7, 8, and 9 in gray/colour show a combination of diurnal and annual variations from January 2002 to December 2005 as pseudo-three-dimensional maps. In Figure 7 there are maps for the first and second modes, the maps for modes three and four are depicted in Figure 8. The maps of amplitudes and Q factors for 2005 are depicted for all investigated modes in Figure 9. The hours of the day (in UT) are marked along the vertical axis while the days of the year are shown along the horizontal axis. The data for modes one through four are arranged from top to bottom. The white points or areas represent the missing, unreliable or out-of-range data. The black curves in maps of amplitude show the times of local sunrises and sunsets on the ground, the terminator passages.

Figure 7.

Diurnal-seasonal frequency variations of (left) the first mode and (right) the second mode. The black triangles show the onsets of the most prominent solar proton events.

Figure 8.

Same as Figure 7 but for (left) the third mode and (right) the fourth mode.

Figure 9.

Diurnal-seasonal variations of (left) amplitude and (right) quality factor for the year 2005 and for (top to bottom) modes one to four. The times of sunrises and sunsets (terminator lines) are marked by black lines. The black triangles show the onsets of the most prominent solar proton events.

[29] The diurnal frequency variations from Figures 3–6 seem to be visible also in maps in Figures 7–8. Unfortunately, the “map form” cannot show them in detail. Concerning the seasonal types (patterns) in the first and second mode, discovered by Sátori and Zieger [2003], their characteristics and distinctive appearance are not in contradiction with our observations. However, the duration of individual phases seems to vary slightly from year to year.

[30] In the second mode, interannual variations of the patterns are less visible. The transition phases appear more diffuse. Since the global pattern of solar illumination is strictly repetitive from year to year, there must be another factor responsible for such variations.

[31] Considering the interannual variations, comparison between subsequent years 2001–2005 shows that diurnal variation of the fundamental-mode frequency repeats almost unchanged from year to year in winter. In summer, the interannual differences are greater. A similar tendency can be observed for the higher modes; even in winter months there is a monotonous interannual decrease of frequency. This decrease of the mean diurnal frequency level, which appears in all modes with the same sign, can be attributed to changes in ionospheric parameters (particularly to the decrease in conductivity of the lower ionosphere) due to the decline in solar activity. However our 4-year observation period is insufficient and allows only a preliminary conclusion on this point.

[32] The diurnal and seasonal variations of SR mode amplitudes (Figure 9) show some correlation with the changes of the ionospheric height and conductivity profile (as a result of the daily formation or disintegration of the ionospheric D layer).

[33] The overall daytime amplitude level is higher than the nighttime level; these levels are separated by terminator lines. The day-night amplitude contrast decreases with frequency (see Figure 9). Similarly, the daytime amplitude level in summer is higher than in winter. This type of SR amplitude variation is combined with the variation caused by successive onset of the lightning activity over the three principal tropical areas (see also Figure 2).

[34] The Q factor variations are shown only in Figure 9. They appear to be rather chaotic and it seems to be impossible to extract any trend from them. However, some decrease around local noon is evident in the first mode. Yet, it is also evident that Q factor increases with mode number, which is in accordance with theoretical and observational results shown, e.g., by Sátori et al. [2005].

4.3. Observations of SPE

[35] The influence of short-term bursts of solar activity (through changes of the lower ionosphere state) on SR parameters has been unambiguously proved and discussed in numerous publications [e.g., McGlade et al., 2004; Roldugin et al., 2003]. We searched for the signatures of solar proton events (SPEs) and their respective X-ray bursts during the period of our observations. The intense solar flares, accompanied by strong SPEs of 28 October 2003 and 16 January 2005 were particularly promising candidates for some related short-term SR parameter changes (their onsets are marked in Figures 7 and 8 by black triangles). Nevertheless, no significant changes of any SR parameter can be surely attributed to them. This conclusion seems to be implied by the middle geomagnetic latitude of our site. For higher geomagnetic latitudes Roldugin et al. [2004] concluded and confirmed by observations that intense solar X-ray bursts slightly increase the first-mode resonance frequency (due to the ionization increase at higher altitudes). By contrast, the SPEs cause a more pronounced decrease in the first-mode resonance frequency at high latitudes.

5. Possible Theoretical Explanations

[36] Generally speaking, two principal mechanisms responsible for SR parameters variations can be considered: (1) variations in intensity or/and positions of prevalent lightning sources [Sátori and Zieger, 1996; Sátori, 2003; Sátori and Zieger, 2003; Ando et al., 2005] and (2) variations in lower ionosphere parameters (especially the height-conductivity profile) caused by regular variations in solar illumination (diurnal and seasonal cycles) [Melnikov et al., 2004; Price and Melnikov, 2004] and irregular variations in solar activity (mostly X-ray flares and Solar Proton Events) [McGlade et al., 2004].

[37] According to the three-dimensional FDTD analysis [Yang and Pasko, 2005; McGlade et al., 2004], for laterally homogenous ionosphere model, the increase in atmospheric conductivity at the heights above 60 km tends to shift the first mode resonance frequency upward. Analogical conductivity increase below this altitude results in reverse effect.

[38] More elaborate model calculations, taking into account the laterally inhomogeneous ionosphere [Otsuyama et al., 2003; Simpson and Taflove, 2004], qualitatively confirm the conclusions made from observations and simple models. In spite of this, the use of Transmission Line Method (TLM) for resonator parameter calculations seems to be very promising [Morente et al., 2003].

6. Conclusions

[39] The new experimental Schumann resonance facility at the Astronomical and Geophysical Observatory near Modra, western Slovakia, has proved its ability to detect and monitor the Schumann resonances with plausible time and frequency resolution on a permanent basis. Almost all measuring equipment and software codes have been designed and produced by the SR working group itself.

[40] The method of data acquisition and processing can provide principal SR mode parameters (peak frequencies, amplitudes and quality factors) for at least the first four SR modes. These data on electric component collected during more than four years of observations are analyzed and presented in various graphical forms.

[41] Measurements at Modra Observatory qualitatively confirm the overall pattern of diurnal and seasonal variations in SR frequencies as reported from other observatory sites (Mitzpe Ramon, Hollister, Silberborn and especially Nagycenk, which is closest to our site), although there are some differences in details discussed above.

[42] It was confirmed that the changes in source-observer distance are dominant for seasonal variations in diurnal pattern of the first-mode frequency. As we move from mode one to mode four, there is an increasing number of extremes of the diurnal frequency pattern and the DFR has a tendency to grow.

[43] The overall daytime amplitude level is higher than the nighttime level. The daytime amplitude level in summer is higher than in winter, which is in accordance with theoretical expectations.


[44] We would like to thank Ľ. Turňa and our observatory staff, especially D. Kalmančok, for their help in the construction of receiving equipment and antenna. The authors also thank G. Sátori for many useful recommendations on the topic of this paper. This work was supported by grant 1/2033/05 of the Slovak Scientific Grant Agency VEGA.