Universal and local time variations deduced from simultaneous

RADIO SCIENCE, VOL. 46, RS5003, doi:10.1029/2011RS004663, 2011

Universal and local time variations deduced from simultaneous Schumann resonance records at three widely separated observatories A. P. Nickolaenko,1 E. I. Yatsevich,1 A. V. Shvets,1 M. Hayakawa,2 and Y. Hobara2 Received 20 January 2011; revised 27 May 2011; accepted 13 June 2011; published 15 September 2011.

[1] A technique is applied to experimental Schumann resonance intensity that separates the universal (UT) and local time (LT) variations. Two orthogonal horizontal magnetic field components were recorded simultaneously at the observatories of Moshiri, Japan (44.4°N, 142.2°E), Lehta, Russia (64.4°N, 34°E), and West Greenwich, Rhode Island, United States (41.6°N, 71.6°W). We use the cumulative magnetic field power integrated over the first three Schumann resonance modes. Diurnal variations were averaged over a month for the period from August 1999 to December 2001 at each site. These records were combined to obtain estimates for the UT daily patterns of the global thunderstorm activity. Diurnal variations of particular months repeat year after year, indicating that space‐time distributions of global thunderstorms are annually replicated with minor deviations. Another technique, based on geometric averaging of records, was used to obtain alternative estimates of the global thunderstorm intensity. Results acquired with both techniques showed an outstanding similarity. Citation: Nickolaenko, A. P., E. I. Yatsevich, A. V. Shvets, M. Hayakawa, and Y. Hobara (2011), Universal and local time variations deduced from simultaneous Schumann resonance records at three widely separated observatories, Radio Sci., 46, RS5003, doi:10.1029/2011RS004663.

1. Introduction [2] The dielectric shell bounded by the conducting Earth and lower ionosphere is an electromagnetic resonator. Global electromagnetic resonance (frequency band from 4 to 40 Hz) was predicted by Schumann [1952], and it is referred to as Schumann resonance (SR). The survey of SR studies might be found in extensive literatures [see, e.g., Barr et al., 2000; Nickolaenko and Hayakawa, 2002; Pasko, 2006, and references therein]. The signal of global electromagnetic (Schumann) resonance is originated from planetary thunderstorms, therefore the intensity of resonance oscillations reflects the present state of lightning activity worldwide. [3] Much attention was directed to resolving the inverse electromagnetic problem based on the SR data. The success was achieved for the discrete pulses (Q‐bursts) arriving at an observer from the single powerful strokes [see, e.g., Nickolaenko and Hayakawa, 2002; Pasko, 2006, and references therein]. A modest success was obtained in approaches based on the records of continuous SR background formed by pulses arriving at a rate ∼100 events per second [Ando et al., 2005; Füllekrug and Fraser‐Smith, 1997; Fraser‐ Smith et al., 1991; Nickolaenko et al., 1998; Shvets et al., 1 Usikov Institute for Radio‐Physics and Electronics, National Academy of Science of the Ukraine, Kharkov, Ukraine. 2 Department of Electronic Engineering, University of Electro‐ Communications, Tokyo, Japan.

Copyright 2011 by the American Geophysical Union. 0048‐6604/11/2011RS004663

2009, 2010], i.e., in obtaining characteristics of regular global thunderstorm activity. The objective of the present work is developing of relatively simple techniques for obtaining robust estimates of the global thunderstorm activity based on monitoring of the global electromagnetic (Schumann) resonance. More complicated approaches to the inverse problem aim to study variations of the source position and distribution of thunderstorms over the globe [e.g., Shvets et al., 2009, 2010]. We pursue a simpler objective here and discuss relevant processing procedures. [4] In the SR band, only the TEM wave propagates in the Earth‐ionosphere cavity. It has the nonzero vertical electric and horizontal magnetic field components. The latter is measured via its two orthogonal projections HNS and HEW. Each field component is presented formally in the frequency domain as a product of the source current moment and a function of the source‐observer distance (SOD). The latter is written as an expansion into a series of Legendre polynomials. Each term in the series is a resonance mode having specific frequency characteristic and distance dependence. [5] The field power at a fixed frequency is directly proportional to the source intensity (the level of thunderstorm activity). Thunderstorms cover the globe, and their distribution and intensity may vary in time, so that the observed field power also varies. A problem arises of separating signal changes due to alterations in the source intensity from those caused by its motion in respect to the observer. The distance dependence is associated with the modal structure of resonance field so that a moving source of constant

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intensity provides alterations in the field power at a fixed frequency. [6] Two schemes were suggested to reduce the impact of source motion on the signal power. The first one implied monitoring at an “intermediate” frequency of 11 Hz. Intensity of electromagnetic field at this frequency positioned between the first and the second SR modes (8 and 14 Hz) is insensitive to the source distance [Fraser‐Smith et al., 1991]. The second scheme applies the field intensity integrated over a few adjacent modes. Cumulative field intensity in the frequency band of the three first SR modes also demonstrates the minor distance dependence [Sentman and Fraser, 1991; Füllekrug and Fraser‐Smith, 1997; Nickolaenko, 1997; Nickolaenko et al., 1998; Nickolaenko and Hayakawa, 2002, 2007]. Thus, “intermediate” and cumulative resonance intensities reflect the thunderstorm activity in a better way than individual modes, however, they still contain source distance effects. [7] We use in the present study the integrated SR intensity as a measure of the global thunderstorm activity. In particular, the integration is held over the first three resonance modes. [8] A technique was suggested by Sentman and Fraser [1991] that resolves the universal time (UT) and the local time (LT) factors involved in the SR, provided that signals were simultaneously recorded at a pair of widely separated points (see below). This technique was tested and further developed by Pechony and Price [2006] and Nickolaenko and Hayakawa [2007], and it was applied to the annual experimental data collected at Lehta and Moshiri sites. A conclusion was made that the local time modulations arise predominantly from the source‐receiver geometry, while the UT modulations are driven by changes in the global thunderstorm intensity. [9] In the present work we treat the long‐term data from three observatories and exploit the same concept, which is based on the following assumptions. [10] 1. SR intensity P(tU, l) at a site with the east longitude l and the UT tU is a product of a universal function U(tU) that depends on the UT only and the local modulating function L(tL) that varies in the LT: PðtU ; Þ ¼ U ðtU Þ  LðtL Þ

ð1Þ

[11] 2. The LT (hr) is related to the UT and the longitude l (radians) in the following way: tL ¼ tU þ 

12 

ð2Þ

[12] 3. The LT modulating function L(tU) is a complex periodic function of time with a period of 24 h. The following Fourier expansion is valid for it at the particular latitude lk: L k ðt U Þ ¼ 1 þ

N X

An  expfinWðtU þ lk Þg

ð3Þ

n¼1

Here An are the complex amplitudes, n in the number of Fourier harmonic, “longitude” lk = lk 12  is measured in hr, is in 1/hr. and the Earth rotation velocity W = 2 24

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[13] 4. We accept that the average of local modulation function is equal to unity, and only the real parts Re{L (tU)} have a physical meaning. [14] The diurnal component of 24 h period corresponds to the complex amplitude A1. Its semi‐diurnal term (12 h period) is characterized by the complex amplitude A2. Higher order terms are taken into account up to A5 amplitude. [15] We use the monthly averaged diurnal variations of SR intensity defined for particular interval tU 2 [1, 24 h], so that the time series contain 24 points. Therefore, the Fourier expansion might be used of N ≤ 8, and we apply N = 5 in computations. Since experimental data do not contain abrupt changes similar to a delta‐function, the complex amplitudes An decrease with the harmonic number: jAn j2 ! 0 when n ! N

ð4Þ

[16] Intensities P1(tU) = P (tU, l1), P2(tU) = P (tU, l2), and P3(tU) = P(tU, l3) were monitored by three observatories at l1, l2, and l3. The geographic coordinates of sites were: Lehta (64.4°N, 34°E), Moshiri (44.4°N, 142.2 E), and Rhode Island (41.6°N, −71.6°E). There are three possible pairs of observatories, and each pair provides the following identity [Nickolaenko and Hayakawa, 2007]:     ln Pk =Pp ¼ lnðLk Þ  ln Lp  A1 fexp½iWðtU þ lk Þ  exp½iWðtU þ lk Þg þ A2 fexp½i2WðtU þ lk Þ  exp½i2WðtU þ lk Þg þ . . .    ¼ A1 expðitU WÞ expðiWlk Þ  exp iWlp    þ A2 expð2iWtU Þ expð2iWlk Þ  exp 2iWlp þ . . . ð5Þ

where indices k and p correspond to the k‐th and p‐th observatory. For instance, the Lehta‐Moshiri pair corresponds to k = 1 and p = 2, Lehta–Rhode Island implies k = 1 and p = 3, and Moshiri–Rhode Island means that k = 2 and p = 3. [17] It is obvious that a ratio of cumulative field intensities recorded at two sites does not depend on the source power. Only distance dependence remains in such a ratio, which allows for finding coefficients of the relevant series (3). We tested workability and accuracy of approach by resolving the model problems, and this supplementary material is placed in Appendix A.

2. Data Processing [18] An important feature of natural electromagnetic signals is their random nature. The meaningful results are obtained only after averaging of spectra. Stable SR spectra are usually obtained by averaging elementary spectra of 10 s samples during 5 or 10 min. To remove natural and man‐ made interference, the elementary spectra are inspected and selected for integration over an hour to provide the well‐ known spectral patterns. The spectra “spoiled” by interference are expelled. Since vertical electric antennae are sensitive to local weather conditions, our of SR data are based on the records of magnetic fields. [19] As a result, typical experimental data set contains hourly averaged selected spectra. When turning to the

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cumulative field power, we find that a regular daily pattern is revealed after averaging data over a month period. Therefore initial data used in this study implied the preliminary selection of spectra with pronounced resonance patterns and averaging of data, which provides the monthly averaged 24 h daily variations of cumulative horizontal magnetic field intensity. Even such an approach did not eliminate the data loss: the experimental results for July were missing. [20] SR was monitored simultaneously at three field sites, and we treat the data collected from August 1999 to December 2001. The cumulative intensity P = (HNS)2 + (HEW)2 of the horizontal magnetic field component was derived from the records of HNS and HEW fields and integrated over the first three resonance modes. Thus, functions Pk(tU) were obtained that we use in the further analysis. [21] The unknown complex amplitudes An were found from equation (5) for each pair of sites by multiplying both sides by exp (−inWtU) and integrating over 24 h:   dtU ln Pk =Pp expðinWtU Þ 1 0    An ¼ 24 expðinWlk Þ  exp inWlp R24

obtain the universal diurnal variations U1(tU) and U2(tU). One obtains two functions for a particular pair of sites: ð8aÞ

U2 ðtU Þ ¼ P2 ðtU Þ=L2 ðtU Þ:

ð8bÞ

[26] Thus two “independent” estimates are obtained for the hourly average global thunderstorm activity. Three dual sets of SR records provide six U(tU) patterns, and we can derive the average universal pattern hUk(tU)i and its standard deviation. Meanwhile, the factors L(tL) usually reflect diurnal motion of global thunderstorms in respect to the observatory pair. [27] An alternative signal processing scheme was suggested by Nickolaenko and Hayakawa [2007] based on the geometric averaging of original records. There are three “dual” estimates:

[22] One obtains the following relation for the denominator of equation (6) after introducing the intermediate longitude lkp = (lk + lp)/2 and the longitude partition Dlkp = (lk − lp)/2.

G1;2 ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PðtU ; 1 Þ  PðtU ; 2 Þ / U1;2 ðtU Þ

ð9aÞ

G1;3 ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PðtU ; 1 Þ  PðtU ; 3 Þ / U1;3 ðtU Þ

ð9bÞ

G2;3 ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PðtU ; 2 Þ  PðtU ; 3 Þ / U2;3 ðtU Þ

ð9cÞ

and a single “triple” estimate G3 ðtU Þ ¼

[23] Equation (6) for n = 1 corresponds to equation (8) of Sentman and Fraser [1991] who associated the UT factor U(tU) with the global thunderstorm activity and the LT functions L(tL) with the ionosphere height above the observatory (ionosphere day‐night asymmetry). Model computations by Pechony and Price [2006] demonstrated that L(tL) function predominantly reflects the source‐receiver distance. In particular, positions of the minima and maxima of L(tL) function for different pairs vary in accord with the source‐ receiver geometry and its amplitude disagrees with the “day‐night” interpretation [Pechony and Price, 2006]. The idea of source proximity becomes evident when applying a higher number of terms in the Fourier series (3). In particular, a narrow late night–early morning peak appears in the L(tL) pattern, which contradicts the ionosphere height variations [Nickolaenko and Hayakawa, 2007]. [24] We demonstrate below that separating the UT and LT terms provides sound and convincing results. The U(tU) functions represent the global thunderstorm intensity. The L(tL) variations usually allow for the interpretation in terms of source‐observer distance, provided that that the lightning activity (field sources) is assembled within a single area. Sophisticated thunderstorm distributions in space might result in complicated L(tL) functions (see Appendix A), while the recovered U(tU) terms continue to replicate the thunderstorm intensity. [25] Functions L1(tL) and L2(tL) are coincident in the local time, and they depend on the particular couple of sites. LT factors are used in equation (1) as functions of UT to

U1 ðtU Þ ¼ P1 ðtU Þ=L1 ðtU Þ

and

ð6Þ

      expðinWlk Þ  exp inWlp ¼ 2i sin nWDkp exp inWlkp ð7Þ

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p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 PðtU ; 1 Þ  PðtU ; 2 Þ  PðtU ; 3 Þ / U1;2;3 ðtU Þ

ð10Þ

of the current global thunderstorm intensity. The physical background of this procedure is rather simple: when thunderstorms approach one observatory, they simultaneously retreat from the other. Therefore, the product of SR intensities becomes less dependent on the source distance, or on the L functions. We demonstrate below that geometric averaging is an efficient tool for estimating the global thunderstorm activity.

3. Separating the LT and UT Components [28] We discuss in this section the results of separating the UT functions from those varying in the LT. Our major goal is obtaining the UT functions, which correspond to the global thunderstorm activity. Figure 1 depicts the “initial” intensities P(tU) recorded at three field sites. The year/moth from August 1999 to December 2001, with data missing in a few months, is shown on the abscissa. Daily variations of P(tU) records are shown on the ordinate in arbitrary units. In fact, initial data were the field intensity measured in pT2, but these particular units are inappropriate since we evaluate changes of the global thunderstorm activity, which might be characterized by the relative or arbitrary units. [29] Lehta data are shown by blue lines, and the red and green lines correspond to Moshiri and Rhode Island data. The plot is composed of 29 vertical strips separated by vertical dotted lines. Each strip shows the monthly averaged UT variations recorded at every field site.

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Figure 1. Integrated Schumann reson (SR) intensity observed in horizontal magnetic field at three observatories. Lehta data are shown by blue curve; the red and green colors correspond to Moshiri and Rhode Island. The plot is composed of 29 vertical strips separated by vertical dotted lines. Each strip shows the monthly averaged UT diurnal variations recorded at every field site. The gaps in a plot correspond to absence of particular experimental data. [30] We note that the integrated SR intensity of Figure 1 reflects the thunderstorm activity: the well‐known variations on the annual and diurnal scales are recognized here. In particular, one can recognize African‐American peak on thunderstorm intensity combined with its decrease over the Pacific (early hours of the UT day). Frequency integration inhibited the modal structure in the distance dependence of field power, so that initial P(tU) data represent the global thunderstorm activity in a much better way than the intensities of separate resonance modes [Nickolaenko and Hayakawa, 2002]. [31] Pronounced seasonal/diurnal variations in Figure 1 occur at a “podium” present in records of all three observatories, i.e., the diurnal curve is elevated over the abscissa and never reaches the zero level. This vertical shift regarded as “podium,” originates from the “inappropriate” thunderstorm activity distributed over the whole globe and causing the depolarized SR signals at an observatory [Yatsevich et al., 2006, 2008]. [32] Figure 2 shows the LT factors L(tL) derived for each pair of sites by using equation (3). Data presentation is similar to that of Figure 1: the same 29 vertical strips, each presenting the diurnal L(tL) pattern for a particular month. The top plot depicts the monthly averaged diurnal variations L(tL) for the Lehta‐Moshiri pair. The middle and bottom plots correspond to Moshiri–Rhode Island and Lehta–Rhode Island pair. Gaps in curves correspond to incomplete data when a particular observatory was not working. One may observe that curve (sometimes rather complicated) of the local functions depends on the pair. For example, the pattern from February to May 2000 for Lehta‐Moshiri pair contains two to three diurnal peaks, which are almost invisible in the plots derived for the Lehta–Rhode Island and Moshiri– Rhode Island pair. Simultaneously, the range of daily variations is very stable, and the patterns tend to have a similar

shape for same months of different years. Such a behavior implies that LT variations correspond to a repeatable physical process. [33] After obtaining factors L(tL) for every month, we computed the UT factors from equations (8a) and (8b). As a result, each pair of sites provides a pair of Uk(tU) = Pk(tU)/ Lk(tU) estimates, which are collected in Figure 3. We regard Uk(tU) and Up(tU) functions as “recovered” patterns. These functions form six estimates of the global thunderstorm activity. We show relevant data in Figure 3 in the same fashion: 29 strips containing the 24 h daily variations. [34] Three vertically separated panels contain paired plots in Figure 3. The top panel depicts the Lehta‐Moshiri results. The red line shows the UT variations U1(tU) = P1(tU, lMo)/ L1(tU) pertinent to the Moshiri‐Lehta base. The blue curve depicts the Lehta U2(tU) function found similarly from the Lehta P2(tU, lLht) data. The middle plot in Figure 3 shows results for the Moshiri–Rhode Island observatories. The red line is the Moshiri UT variations U3(tU) and the green line demonstrate the Rhode Island U4(tU) function. The bottom plot depicts results for the Lehta–Rhode Island data sets. The blue line depicts the Lehta UT variations U5(tU), and the green line demonstrates the Rhode Island U6(tU) function. [35] As one may see, all six UT patterns have much in common. They show distinct and similar variations on both diurnal and seasonal scales. Contributions from different global thunderstorm centers might be recognized in the plots, but mutual deviations are also obvious. [36] The signal decomposition into UT and LT components retains the “podium” in the global lightning activity: diurnal patterns are elevated over the abscissa. Moreover, both the “podium” height and the amplitude range of diurnal variations vary in accord: both simultaneously grow or reduce. Six “individual” plots of Figure 3 are separate estimates for the global thunderstorm intensity. We now can

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Figure 2. LT factors L(tL) for particular pairs of SR records. Each graph is composed of 29 vertical strips separated by vertical dotted lines. The top plot depicts the monthly averaged diurnal variations L(tL) for the Lehta‐Moshiri pair. The middle and bottom plots correspond to Moshiri–Rhode Island and Lehta– Rhode Island pairs.

Figure 3. UT functions U(tU) found for particular pairs of SR records. The top plot depicts the Lehta‐ Moshiri results. The red line here shows the Moshiri U1(tU) variations, and the blue curve depicts the Lehta U 2 (t U ) function found for the Moshiri‐Lehta pair. The middle plot shows results for the Moshiri–Rhode Island observatories. The red line is the Moshiri variation U3(tU) and the green line is the Rhode Island U4(tU) function. The bottom plots depict the Lehta–Rhode Island data. The blue line depicts the U5(tU) function for Lehta, and the green line demonstrates the Rhode Island U6(tU) function. All six patterns have much in common, and contributions from the global thunderstorm centers might be recognized in the plots. 5 of 12

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Figure 4. Average diurnal/seasonal variations of the global thunderstorm activity estimated by using U(tU) and G(tU) schemes. The plot contains 29 vertical strips corresponding to particular month separated by vertical dotted lines. The black line shows the average universal time functions hU(tU)i, and the red curve depicts the geometric average hG(tU)i. statistically process the U(tU) data and find the average diurnal variations hU(tU)i (the black line in Figure 4) and estimate its standard deviation: hU ðtU Þi ¼

6 1X U k ðt U Þ 6 k¼1

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 6 u1 X U ¼ t ½ U k ðt U Þ  hU ðt U Þi  2 5 k¼1

ð11Þ

ð12Þ

4. Geometric Averaging and Comparison With UT Factors [37] The alternative data processing technique implies the geometric averaging of initial records [Nickolaenko and Hayakawa, 2007]. We present in this section the results of this alternative scheme. We computed relevant patterns by using paired (the Lehta‐Moshiri, Lehta–Rhode Island, and Moshiri–Rhode Island sites) geometric averaging G1,2, G1,3, and G2,3 defined by equation (9) together with the “triple” geometric average equation (10). All the functions were averaged giving us the hG(tU)i variations. [38] After processing the experimental data, we obtain two estimates for the diurnal/seasonal variations of the global thunderstorm intensity. The first is based on the resolving of the LT and UT factors. The relevant hU(tU)i function is shown in Figure 4 by black line. Results of geometric averaging include four quantities, and their average hG(tU)i is shown in Figure 4 by red line. [39] The UT is shown along the abscissa in hr, and the intensity of thunderstorms is plotted on the ordinate in arbitrary units. As one may observe, two completely different techniques provide exceptionally consistent data: positions of the minima and the maxima practically coin-

cide, and the curves are very close. The two lines come so close together that sometimes they are not resolved in the plot. [40] Figure 5 surveys the universal diurnal patterns pertinent to four seasons of a year: winter (December, January, February, top plots), spring (March, April, May, second row of plots), summer (June, July, August, third row of plots), and autumn (September, October, November, bottom plots). Plots for individual months comprise the average diurnal variation hU(tU)i (curves with dots) and the hG(tU)i functions (smooth curves). Data for different years are collected in the same monthly panels demonstrating the interannual variability in the global thunderstorm intensity. The black curves correspond to 1999; the blue curves show 2000; and the red lines are the year 2001. It occurred that experimental data sets for July were always incomplete, so the relevant frame is empty. One may observe a close correspondence of estimates that we already noted when discussing Figure 4. [41] Processing of SR data results in distinct seasonal variations of thunderstorm intensity, while the diurnal variations are less pronounced. Intensity of global thunderstorms varies by a factor of 2 during the day. The summer activity exceeds that of the winter by a factor of about 3. It is interesting to note that daily patterns of a particular month repeat year after year thus indicating that diurnal change and the space‐time distributions of global thunderstorms for a given month are annually replicated with minor deviations [Nickolaenko et al., 1998]. Inter‐annual deviations (if any) are observed as vertical shift of curves, and such shifts are comparable with the range of twofold diurnal variations (compare, e.g., with Sátori et al. [2008]). Three distinct peaks in the diurnal curve associated with the global thunderstorm centers are but rarely observed in the U(tU) functions. [42] It is important to remind the reader that averaged hU(tU)i data and the geometrical average functions hG(tU)i were obtained directly from the ELF intensity driven by the

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electromagnetic radiation of the worldwide thunderstorm activity. Evaluation of the latter from the Schumann resonance records acquired at three widely separated observatories proved to be rather efficient as resonances collect and weight electromagnetic radiation from all lightning strokes in the natural way.

5. LT Factors

Figure 5. Global thunderstorm activity estimated by two techniques. Data range from 1999 to 2001. Curves with dots present the hU(tU)i function and the smooth curves show the geometric average hG(tU)i. The black, blue, and red curves correspond to years 1999, 2000, and 2001 correspondingly. Experimental data for July were incomplete, and the relevant frame is empty.

[43] The LT factors accessible from integrated SR intensity carry information on the diurnal motion of thunderstorms. It would be interesting to compare these functions derived from the records of different pairs. Figure 6 presents the three different local L(tL) functions thus testing the validity of assumptions 1 and 2. By definition, see equation (3), the only distinction among the LT modulating functions is the temporal shift accounting for the longitude of site. The soundness of attribution of functions L(tL) to the source proximity is demonstrated in Appendix A where we process the model data and evaluate the accuracy of the “output” information on the postulated source intensity and on its motion around the globe. [44] Expectations of close similarity in the LT factors among all the pairs might not be satisfied. However, one may observe clear similarity of experimental curves in Figure 6: all of them have much in common and tend to reflect the idea of diurnal motion of a single source with respect to observation sites. The horizontal axis in Figure 6 is divided into monthly strips each showing 24 h LT. The plots show LT variations derived for Lehta‐Moshiri (blue curve), Lehta–Rhode Island (green line), and Moshiri– Rhode Island (red line) pairs. Gaps in plots correspond to incomplete data when at least one of three observatories did not work. [45] To characterize departures in L(tL) patterns, we performed statistical processing of data and depict its results in Figure 7. Here, the top plot shows the average local time

Figure 6. Comparison of LT modulation in local time. Abscissa is divided into monthly strips each showing 24 h LT. The green, blue, and red curves correspond to local time variations derived for the Lehta–Rhode Island, Lehta‐Moshiri, and Moshiri–Rhode Island pairs. 7 of 12

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Figure 7. Median LT variations. The top plot shows the average LT function hL(tL)i. The bottom plot depicts the normalized standard deviation sL/hL(tL)i. variations hL(tL)i and the bottom plot depicts the relevant standard deviation normalized by the average variation (in %). Deviations among the LT modulating functions are rather modest, and the typical value is about 10–15%. [46] The L(tL) factors typically have two maxima during the day. One can easily attribute these maxima to the thunderstorm proximity conditioned by motion of activity around the globe. The peaks correspond to times when thunderstorms approach the observatories or come close to their antipodes. However, such simple patterns are not always observed: the local factors for particular pairs may be of forms with different number of maxima for certain months. [47] To show such an example, we separately depict the September 2001 segment in Figure 8. The local time is shown on the abscissa in hr. Plots show three individual L(tL) functions. The one obtained for the Lehta‐Moshiri pair is shown in blue line, L(tL) for Moshiri–Rhode Island pair is red, and the green graph shows the data for Lehta–Rhode Island base. The thick black line with dots depicts the median hL(tL)i variation, and the vertical bars show its standard deviation or the accuracy of recovery (the highest standard deviation is about 10%). The blue line in Figure 8 (Lehta‐Moshiri pair) has a single peak positioned at 14 h LT, it has also the point of inflection around 9–10 h. Other curves have two peaks at 10–11 h and 17 h. The morning peak for the Moshiri–Rhode Island pair is higher than the afternoon maximum while the morning peak of the Lehta–Rhode Island L(tL) function is lower than that of the afternoon. Such a behavior implies that the LT modulation depends not only on the average source‐observer distance, but also on the spatial distribution of sources. [48] Bi‐modal local time variations are often obtained experimentally. Sometimes, the morning peak becomes more pronounced (the valley between two peaks is deeper), sometimes it almost merges with the afternoon peak. However, two peaks are always present, at least, in the present data set. In accordance with equation (7), the form of LT variation is governed by the intermediate longitude of

two observatories lm = (lk + lp)/2. This is why its position at the time axis alters for different pairs (see the model results in Appendix A). We present in Appendix A the model computations based on the realistic DMM‐OTD data (Diurnal Monthly Mean–Optical Transient Detector), which indicate that many peaks might appear in the L(tL) dependence. This occurred in particular for the Moshiri–Rhode Island pair in the month of September. The result is probably explained by a complex source‐observer geometry during this month.

6. Conclusion [49] Continuous simultaneous records of SR intensity were processed for the period of 2.5 years. Data were col-

Figure 8. LT modulating factors and standard deviations for September 2001. Blue, red, and green lines correspond to Lehta‐Moshiri, Moshiri–Rhode Island, and Lehta–Rhode Island pairs. The thick black line with dots depicts the median hL(tL)i variation, and the vertical bars show the standard deviation.

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Figure A1. Model data for the uniform Earth‐ionosphere cavity with a compact moving equatorial source (SRC) of varying intensity. The top plots correspond to the Lehta‐Moshiri pair. The middle plots show the Moshiri–Rhode Island and the bottom plots display the Lehta–Rhode Island data. The blue, red, and green curves show the integrated horizontal magnetic field intensity at Lehta, Moshiri, and Rhode Island. Initial paired data P(tU) are shown in the left plots. Owing to frequency integration, initial data are rather similar. The middle plots depicts the LT modulation factors L(tL). Obviously, these functions reflect the diurnal motion of thunderstorms around the globe. The right plots show the UT factors U(tU). Their high correspondence might be expected, as the source model is very simple. lected at three globally separated sites: in Japan, Russia, and United States. [50] Two techniques were applied that single out the UT variations as an estimate of the global thunderstorm intensity. Individual functions proved to be consistent thus indicating the robustness of the approach. The averaged estimates for the global lightning intensity are characterized by the standard deviation of ±10–15%. [51] The global thunderstorm intensity varies by a factor of 2 during the day. Its seasonal alterations may reach the factor of 3. Three distinct peaks associated with the global thunderstorm centers are rarely observed. The constant “podium” is always present in the global lightning intensity. [52] Daily patterns of a particular month repeat year after year with minor vertical shifts corresponding to interannual variations. [53] The LT variations are explained in terms of diurnal motion of the global lightning activity around the globe. However, situations are met with complicated local time modulations probably associated with sophisticated spatial distribution of sources.

Appendix A [54] We demonstrate workability and accuracy of the processing technique by applying it to the model data

computed in the uniform Earth‐ionosphere cavity. Two source models are used. The first, the simple model is the compact source [Yatsevich et al., 2006, 2008]: the global thunderstorms occupy a compact area (15° radius) at the equator and move around the globe during the day. The source intensity appropriately varies in time. The source center is positioned at the point where tL = 17 h. The random lightning strokes are uniformly distributed in the above circular area, and their pulses form the Poisson random process. The latter means that “individual pulse intensities are summed” in the power spectra. [55] We computed the power spectra of the HEW and HNS field components at each observatory. These fields are the functions of frequency, the distance from the source center (and hence, functions of time) and of the source azimuth. To form the input data, we integrated the power spectra in the frequency band from 5 to 23 Hz. [56] Different observatories were used in preliminary computations including the idealistic three sites at the same latitude separated by 120° in longitude. But here, we show data obtained for Lehta, Moshiri, and Rhode Island observatories. The results are depicted in Figure A1 relevant to a single month registrations. The abscissa shows the UT tU 2 [1–24] hr. [57] The top plots in Figure A1 show the model data for the Lehta‐Moshiri pair. The middle plots corresponds to

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Figure A2. Comparison of postulated model compact source (SRC) intensity with the averaged hU(t U )i data. The red curve depicts postulated thunderstorm intensity. The black curve with dots and error bars shows the averaged function hU(tU)i and its standard deviation. The blue curve depicts temporal variations of geometric average hG(tU)i. Moshiri–Rhode Island pair, and the bottom plots display the Lehta–Rhode Island data. The blue, red, and green lines in Figure A1 correspond to Lehta, Moshiri, and Rhode Island. [58] The left plots show the initial paired data P(tU). One may observe that initial data are rather close to each other. This similarity confirms that the procedure of intensity averaging over three SR modes substantially reduces the distance dependence of the fields [e.g., Sentman and Fraser, 1991; Nickolaenko, 1997; Nickolaenko and Hayakawa, 2002]. Decomposition of patterns into the UT and LT functions improves the final results, as the right plots demonstrate. [59] The middle plots depict the LT modulation L(tL) derived from the initial data. One may observe that local modulations deviate for different pairs. Obviously, functions L(tL) reflect diurnal motion of thunderstorms around the globe: their peaks correspond to the closest proximity of compact source to the intermediate longitude lkp or to its antipode (lkp + p). [60] The right plots show “recovered” UT factors U(tU) = P(tU)/L(tU). The six daily patterns are presented in the right plots of Figure A1. High correspondence of U(tU) data might be expected, as the source model was very simple: a single compact moving “thunderstorm” of varying intensity. [61] Figure A2 shows the source intensity in detail. The red curve depicts the postulated thunderstorm activity as a function of UT. The black curve with dots and error bars shows the averaged recovered data hU(tU)i and relevant standard deviations. The blue curve depicts temporal variations of geometric average hG(tU)i. One may observe the reciprocity of all three curves. [62] We must remark here that hU(tU)i and hGtU)i patterns derived from the SR data cannot exactly coincide with the source intensity, as they were found from magnetic field intensity measured in (mA/m)2 or in (pT)2. The recovered source intensity must deviate from the postulated one by a conversion factor even in the case of an ideal reconstruction. To estimate this factor, we postulate that the average source intensity SA and the daily averaged function UA are equal:

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SA = UA. Thus we find the “normalizing” factor SA/UA = 0.87. The relevant source intensity is shown by the red curve in Figure 2. The blue, and black curves depict the recovered intensities, which match SA with ±5% deviations. [63] The second, more realistic source model that we used in tests is based on the Optical Transient Detector (OTD) data [Christian et al., 2003; Hayakawa et al., 2005; Nickolaenko et al., 2006a, 2006b]. We computed integrated Schumann resonance intensity in the uniform Earth‐ionosphere cavity by using the DMM (Diurnal Monthly Mean) maps of average global distribution of lightning flashes [Pechony and Price, 2006; Pechony, 2007; Pechony et al., 2007; Yatsevich et al., 2008]. DMM is a special processing of original OTD data [Pechony and Price, 2006; Pechony, 2007]. The raw orbital data collected during five years of OTD operation were used to obtain the monthly mean diurnal variations with hourly time resolution. Data for a given hour were averaged over all days in a month (for all five years). The procedure provides 24 maps of global lightning distribution: one for an hour. The single map (of 2.5° × 2.5° resolution) contains averaged information from ∼150 raw maps (see Pechony [2007] for details). We show the results obtained with the DMM‐OTD data for the month of September. [64] By using the DMM‐OTD source distribution, we computed fields arriving at three observatories from the lightning activity concentrated in a particular cell of the global map. The contribution from a cell was directly proportional to the number of optical flashes observed by OTD in this cell. Again, “intensities are summed” as the pulses form a Poisson process. After summing contributions from all cells, we obtain the SR power spectra as function of frequency at three field sites for 24 h of a day. The cumulative intensity of the horizontal components of magnetic field was found by integrating over the frequency band from 5 to 23 Hz. [65] Plots in Figure A3 survey the DMM‐OTD model data. The results are presented in the same fashion as in Figure A1. The rows of plots (from top to bottom) show computations for the Lehta‐Moshiri, Moshiri–Rhode Island, and Lehta–Rhode Island pairs. Again, the blue lines correspond to Lehta, the red curves are Moshiri, and the green lines depict the Rhode Island data. The left plots show “initial” integrated SR intensities P(tU). The “original” plots have much in common, although their similarity has reduced owing to a more complicated source model. It is interesting to note that SR intensity in the DMM‐OTD model distinctly shows three peaks, contributions from three global thunderstorm centers at South‐East Asia (∼9 h), Africa (∼15 h), and America (∼20 h), while the experimental data for September do not contain three distinct peaks (see Figure 5). [66] The middle plots in Figure A3 show the LT factors L(tL) derived for different pairs. The local modulations become outstandingly different from pair to pair. The L(tU) plot for the Moshiri–Rhode Island pair contains the “high frequency” (fifth) harmonic. In the case of a single compact source (the previous model) one can readily conclude that the L(tL) functions reflect diurnal motion of thunderstorms with respect to observatories: the higher peak is the closest distance, the smaller peak is the “antipodal” distance. Particular LT variations obtained in the DMM‐OTD source model do not allow for such an interpretation; the L(tL) plots are different for different pairs, and large number maxima

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Figure A3. The source (SRC) model based on OTD distribution of lightning flashes in September. The top plots correspond to the Lehta‐Moshiri pair. The middle plots show the Moshiri–Rhode Island pair, and the bottom plots display the Lehta–Rhode Island data. The blue, red, and green curves show the integrated horizontal magnetic field intensity at Lehta, Moshiri, and Rhode Island. The left plots show “initial” integrated SR intensities P(tU) at different sites. The DMM‐OTD model distinctly shows three global thunderstorm centers at South‐East Asia (∼9 h), Africa (∼15 h), and America (∼20 h). The middle plots depict the modulating factors L(tL) derived for different pairs. These functions became outstandingly different. Right plots depict the U(tU) factors, which are very close. indicates that interpretation in terms of source distance meets problems when the spatial distribution of activity incorporates many distinct thunderstorm centers. [67] Right plots in Figure A3 depict the U(tU) factors. These have much in common again. Contributions from three global thunderstorm centers are well pronounced and clearly resolved in the DMM‐OTD source model: one easily recognizes the peaks around 10, 14, and 20 h UT. The six daily patterns U(tU) of Figure A3 were statistically processed giving the average diurnal pattern hU(tU)i and the standard deviation s(tU). In addition, the geometric average was obtained hG(tU)i. The former is shown in Figure A4 by black line with dots and vertical error bars, and the latter is shown by blue line with dots. To equalize the thunderstorm intensity postulated with the Schumann resonance power, we demand that average values SDMM, and UA are equal SDMM = UA. Thus we obtain the “normalizing” coefficient SDMM/UA = 0.2175934. [68] The “normalized” intensity of model source is shown in Figure A4 by red line. As one may see, correspondence to the postulated intensity of hU(tU)i and hG(tU)i remains very high. It is almost as good as in case of a single compact source, however, the error corridor widens to approximately ±10%. [69] Model computations presented here drive to conclusion that the both separating techniques work efficiently, and accuracy of the recovered global thunderstorm intensity is rather high. The statistical error of measurements is correctly evaluated by the standard deviations among individual U(tU) functions.

[70] Concerning the LT variations, these functions are sensitive to the particular source‐observer geometry and to the positions of field sites with respect to the global thunderstorm centers. Therefore, the LT factors obtained from SR records should be treated with care.

Figure A4. The postulated OTD‐DMM source intensity (red line) and the recovered data. The black curve with dots and error bars shows the averaged function hU(tU)i and its standard deviation. The blue curve depicts temporal variations of geometric average hG(tU)i. Correspondence of estimates to the postulated source intensity is rather good: the error corridor is approximately ±10%.

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[71] Acknowledgments. Authors are grateful to E. R. Williams from Parsons Laboratory, MIT, who has kindly provided us with the ELF data from the Rhode Island observatory. We express our thanks to O. Pechony and C. Price for allowing us to use their DMM‐OTD model and for valuable remarks and suggestions that improved this paper. We thank unknown reviewers for helpful comments and recommendations.

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