Comment on “Sprite lightning heard round the world by Schumann resonance methods” by E. R. Williams, V. C. Mushtak, R. Boldi, R. L. Dowden, and Z.-I. Kawasaki

Authors


[1] The interpretation of experimental Schumann resonance data presented by Williams et al. [2007] is discussed. We demonstrate that time delay of the model ELF pulse is in excellent agreement with their records conditioned by the geometrical source-observer distance, thus suggesting the day-night transition in their paper being unnecessary. Besides, we show that the terminator effect could not be detected in their particular experiment owing to a long propagation path, a particular orientation of terminator, and the ‘extremely red’ spectra of the field source.

[2] Since the pioneer work by Ogawa et al. [1966], Q-bursts are used for global detection and location of powerful lightning discharges. A spectral technique was developed by Jones [1970a, 1970b] and used by Kemp and Jones [1971], Kemp [1971], Lazebny and Nickolaenko [1976], and Burke and Jones [1992]. Correct stroke location in the Schumann resonance (SR) band was verified and the accuracy was 1–2 Mm for global distances [Boccippio et al., 1998; Füllekrug et al., 2000]. The paper by Williams et al. [2007] (hereinafter referred to as Paper I) directly compares the red sprites observed in Australia with simultaneous Q-bursts recorded in the USA at a distance of 16.6 Mm. The authors demonstrate that ELF pulses are connected with red sprites by presenting convincing experimental data: these indicate the correct source-observer distance (SOD) with the above mentioned accuracy.

[3] However, they are not satisfied with their results and try to attribute the SOD deviations to the impact of the day-night asymmetry of the Earth-ionosphere waveguide. Validity of such an interpretation is dubious since their experimental data agree with computations in the model of a uniform cavity as seen in Figure 1a.

Figure 1.

(a) Waveforms, (b) spectra of the electric field of a Q-burst arriving from 15.6 and 16.6 Mm distances, and (c) spectra of normalized wave impedance for these distances.

[4] There is no problem to readily compute the pulse waveforms shown in Figure 1a [Nickolaenko and Hayakawa, 2002; Nickolaenko et al., 2004] and to find that the arrival time of the direct wave is τ = 68.8 ms for the ‘geometrical’ SOD of 16.6 Mm. The 69 ms delay is mentioned in Paper I. Experimental data listed in Table 2 of Paper I provide the average time delay of 68.1 ms, which perfectly matches with the computations for the distance D = 16.6 Mm (see Figure 1a).

[5] The distance found from the spectra is 15.6 Mm in Paper I. We suspect that the problem lies in the wave impedance technique applied to too great SODs. An application of the average oscillation period dF of the wave impedance ∣W(f)∣ was suggested by Bliokh et al. [1980] as an alternative to the algorithm developed by Kemp and Jones [1971]. The idea was that the average period dF is found with the Fourier transform of ∣W(f)∣ function in the whole receiver band. Thus, we can reduce the effect of the SR background, which is significant at maxima and minima of the ∣W(f)∣ because either E(f) or H(f) spectra reach their minima here, as seen in the lower plot in Figure 1.

[6] Finding dF for great SODs is obscured by slow variations of the ∣W(f)∣ function. As is shown in Figure 1c, the first peak of ∣W(f)∣ occurs at 40 or 33 Hz (D = 16.6 or D = 15.6 Mm correspondingly). The average periods are 37 Hz and 28 Hz. The accuracy in estimating the period dF cannot be high: only 3–4 oscillations fall into the receiver 120 Hz bandwidth. This is why ‘calibrating curves’ dF(D) usually end when D ≤ 15 Mm [Nickolaenko and Hayakawa, 2002]. In addition, there are ‘dynamic’ minima (not shown in the plot) around 60 Hz relevant to notch filters in every channel.

[7] Reality is even worse. The authors note the ‘red’ spectrum of the source with the slope of −0.41. Hence, the initial pulse/background ratio of ∼10 becomes ∼4 at 80 Hz (the second maximum of ∣W∣). Higher peaks of the wave impedance are influenced by the SR background, and we expect reduction in the accuracy in estimating SODs.

[8] An additional ‘independent’ estimate of distance would help in this situation. The distance could be found from the mutual delay between direct and antipodal pulses of the signal W-waveform [see Ogawa and Komatsu, 2007]. Unfortunately, the subpulses are not resolved experimentally as is shown in Figure 4 of Paper I, which might be conditioned by the frequency response of equipment, or by the ‘red’ spectrum of the field source, or by both of them. At any rate, this pulse merging indicates an additional problem in experimental finding of the large SOD. It is worth noting that systematic distance departures are within the standard error of 1–2 Mm established by Boccippio et al. [1998] with the same equipment whose measurements were performed close in time and with the same technique, although applied for the strokes from a smaller range.

[9] Paper I presents no convincing evidence that the 1 Mm deviation is significant and why this deviation must be attributed to the day-night asymmetry. We show below that a particular experimental setup excludes such an interpretation. Of course, the ionosphere is by 20–30 km higher on the night side of the globe causing, say, diurnal variations of VLF radio signals [Hayakawa et al., 1996]. The terminator effect was also reported for the ELF man-made radio signal [Bannister, 1999, and references therein]. However, in the particular case of SOD in the measurements of Paper I the terminator must vanish. Let us consider basic elements of the wave diffraction at the particular path 16.6 Mm long.

[10] Here we study the first Fresnel zone (FFZ), though it is not shown as a figure. One may observe that owing to large SODs, the whole planet falls within the FFZ at the lowest resonance modes (below 17 Hz frequency). Hence, the terminator effect is unimportant at these frequencies: the object is smaller than the FFZ. Even the FFZ of the fifth SR mode exceeds the half of the globe, so that an impact is problematic of a terminator even at this frequency. Also the FFZ at high ELF frequencies (n ≥ 10) might be embedded in the day or night hemispheres, so that one might have well-defined ambient day or ambient night propagation conditions for f ≥ 62 Hz.

[11] Spectra in Figure 1b show that a major part of the Q-burst energy is concentrated below that specific frequency even when the field source is ‘white’. The effect is conditioned by an interference of direct and antipodal waves and by wave attenuation increasing with frequency. Accounting for an ‘extremely red’ source makes the situation worse: the high frequency components of a pulse become negligible, while only these might be involved in the terminator effect. Thus, the day-night asymmetry becomes disabled in the particular case of remote strokes.

[12] The unimportance of terminator effect is clear from the propagation geometry during the particular observations (see Figure 2). The source and observer are denoted by dots of the global map shown in the Cartesian geographical coordinates. The FFZ of the SR modes n = 3, 5, 10, and 50 are depicted. The zone with n = 50 clearly surrounds the propagation path. ‘Sinusoidal’ lines extended from Northern to the Southern hemisphere are the morning and evening terminators, and relevant UT times are shown. The far right part of the map is in the day hemisphere, while the center of it remains in the night. The dawn terminator enters the smallest FFZ (n = 50) around 11:30 UT–the n = 50 path was in ambient night conditions until that time. The terminator crosses almost one half of the zone at 16 UT. Hence, one cannot expect a full scale effect even at 300 Hz frequency: incomplete changes occur in the propagation geometry, and only a portion of the total day-night modulation might be expected. As 300 Hz frequency is far beyond the receiver band, the particular effect could not be detected. The FFZ of frequencies detected by the receiver (n = 3, 5, and 10) have outlines providing insignificant changes in propagation geometry. Hence, minute alterations (if any) might be expected in the pulsed ELF radio signals. Besides, these should be separated from possible variations in the SR background, which is smaller only by a factor of 10 or so.

Figure 2.

Global position of the propagation path and FFZ corresponding to n = 3, 5, 10, and 50. Sinusoidal lines depict positions of the dawn and dusk terminator lines during the measurements of Paper I.

[13] The Fresnel zones should be applied instead of paths partition in Table 3 of Paper I, which in its present form corresponds to geometrical optics or to infinitely high frequency. The authors should consider areas of FFZ found in the day and night hemispheres, provided that the zones do not exceed the size of hemispheres. In the case of Paper I, the significant FFZs are comparable with the globe, and a substantial part of section 4 in Paper I is irrelevant. Figure 2 demonstrates that the day-night transition falls within the FFZ for frequencies below 17 Hz. Hence, the position and orientation of the terminator has a minute impact on SR. In other words, the integration in equation (5) in Paper I should be done over the whole Fresnel zone with the stable result regardless the terminator position for f < 17 Hz. Physically, the long distance propagation at lower SR modes occurs in an average ‘neither day nor night’ uniform cavity.

[14] The last, but not the least: as we observe from the map in Figure 2, the dawn terminator is almost perpendicular to the propagation path. Hence, modifications in the source bearing cannot arise: the wave is incident normally on the nonuniformity. Source bearing modifications might be sought at gliding incidence angles, which definitely was not the case of Paper I.

[15] We listed arguments and facts that allow us to make the following conclusion. The interpretation of experimental data in Paper I has no background and contains inconsistencies. Delays measured agree with the propagation in the uniform Earth-ionosphere cavity. ‘Terminator explanation’ is irrelevant to the geometry and disagrees with the essentials of wave diffraction. A combination of three factors eliminates the terminator effect from the recorded data: too long propagation path, a particular orientation of terminator, and the ‘extremely red’ spectra of the field source.

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