Sprite lightning heard round the world by Schumann resonance methods



[1] Electromagnetic transients have been recorded at the Massachusetts Institute of Technology field station in West Greenwich, Rhode Island, coinciding with sprite-producing lightning flashes in northern Australia, at a distance of 16.6 Mm. Single-station Schumann resonance methods have been used to locate the parent lightning flashes and to evaluate their vertical charge moments. The charge moment thresholds for sprite production are consistent with similar measurements with identical methods made at considerably closer range (∼2 Mm). The use of a uniform model for the Earth-ionosphere waveguide can produce systematic errors in the source-receiver distance, of the order of 1 Mm. Further analysis of the observations has shown an important role for the day-night asymmetry of the waveguide in causing the systematic error, by lending appreciable asymmetry to the short and long paths of propagation round the world.

1. Introduction

[2] Sprites are electrical discharges in the mesosphere induced by energetic lightning flashes in the troposphere. First confirmed optically in 1989 in North America [Franz et al., 1990] and extensively investigated in the Great Plains of the United States [Lyons, 1994, 1996; Sentman et al., 1995], the interest in this phenomenon quickly spread worldwide [Williams, 2001]. In November 1997, sprites were first reported in Australia [Dowden et al., 1997; Hardman et al., 2000]. Their findings lay the foundation for the present study.

[3] The transient excitation of the Earth's Schumann resonances is now a well-recognized accompaniment of sprite lightning [Boccippio et al., 1995; Huang et al., 1999; Williams, 2001], and ELF methods are seeing increased use as a diagnostic for these events [Hobara et al., 2001, 2006; Sato and Fukunishi, 2003; Hayakawa et al., 2004; Williams et al., 2006]. The global nature of the phenomenon provides special incentive to examine very distant Australia events that are well documented by Hardman et al. [2000].

[4] These events are close to 16.6 Mm in distance, substantially greater than events previously analyzed within the same continent [Huang et al., 1999; Lyons et al., 2003] with Schumann resonance methods. The main goals of this study are threefold: to further verify the global detection capability of sprites from a single measurement station, to explore the hypothesis that the day-night asymmetry is responsible for systematic errors in the source-receiver distance on the basis of a uniform cavity model, and to provide further quantitative tests of the C. T. R. Wilson hypothesis for sprite initiation.

[5] Refinements in the criteria for sprite initiation in the mesosphere by lightning in the troposphere have been implemented [Williams, 2001] since the publication of Huang et al. [1999], following the original ideas of Wilson [1925]. Figure 1 shows the revised values for lightning charge moment change required to initiate sprites by conventional breakdown as a function of altitude. These computations employ a realistic variation of air density and also include the image effect of the conductive ionosphere. For a sprite initiation height of 75 km [Stanley, 2000], the critical charge moment is 750 C-km. This value will play an important role in the interpretations of the observations to be presented in section 3.

Figure 1.

Criteria for sprite initiation in the vertical charge moment of a lightning flash, based on work by Wilson [1925] but including the effects of electrostatic images in the ionosphere and an accurate profile for air density.

2. Methodology

[6] The optical observations of sprites 400–500 km southwest of Darwin, Australia, in a mesoscale convective system just east of the Kimberly Plateau, are described in detail by Hardman et al. [2000]. Information from that study suggests that the mesoscale convective system producing these sprites has a diameter of 300–400 km, an intermediate size among MCSs worldwide. The storm's position shown in the satellite imagery is 16.6 Mm from the Rhode Island ELF receiver. A Hamamatsu model 3100 image intensifier on a Hamamatsu C3507 black and white CCD camera was used, with recording on a S-VHS video tape deck. The peak optical response of this system lay in the 600–670 nm range. A photomultiplier tube was also used for the sprite observations near Darwin [Bähr et al., 2000], with absolute timing better than 1 ms.

[7] As far as the distant electromagnetic observations are concerned, Massachusetts Institute of Technology has operated a field station in West Greenwich, Rhode Island, for monitoring Schumann resonances since 1994. The measurement equipment and data processing methods used in this study are identical to those described by Huang et al. [1999] and so will be reviewed only briefly.

[8] The vertical electric and the horizontal (two-component) magnetic field are measured with an analog bandwidth extending from 3 Hz to 120 Hz. Electromagnetic transients produced by energetic lightning flashes worldwide are digitized on the basis of a trigger threshold (11.6 μA/m) in the azimuthal magnetic field. The frequency domain versions of these events, which all exhibit well-defined Schumann resonance structure, are used in conjunction with the normal mode equations of the Earth-ionosphere waveguide [Wait, 1992] to extract the distance to the event using the well-known wave impedance method [Kemp, 1971; Kemp and Jones, 1971; Burke and Jones, 1995], with refinements to be discussed in section 4. Given the distance, the lightning source property (vertical current moment and charge moment) of the lightning flash may be extracted. The assumption that the lightning charge transfer is short in comparison to the round-the-world light time (130–150 ms) enables the extraction of the charge moment directly from the current moment in the frequency domain [Sentman, 1996].

[9] A refinement of the standard magnetic bearing technique [Kemp, 1971] is used to establish the great circle path linking lightning source and receiver. The great circle together with the distance enables the determination of the latitude and longitude of the flash. These methods are currently automated for digital data recorded in Rhode Island [Huang et al., 1999].

3. Results

[10] The videotapes used in the Australian sprite study [Hardman et al., 2000] were first replayed and the sprite events reexamined. The results are summarized in Table 1, where the “UT sprite time” is taken as the (corrected) time stamp on the video frame with the brightest image (see Figures 2 and 3 for examples). Excellent agreement with Hardman et al. [2000] was found for the event times for the sprites on the videotapes. Of the 36 events listed in Table 1 of Hardman et al., one sprite event (1253:45.690 UT) could not be found, one event (1446:41.000 UT) appears to be a meteor trail rather than a sprite, and a third event (1529:08.010 UT) is a questionable sprite. Two additional sprites were also identified on tape (at 1223:45.620 UT and 1321:20.17 UT), one of which (1321:20.17 UT) was also associated with an electromagnetic transient in Rhode Island. Overall, this leaves 35 verified optical sprites.

Figure 2.

Nine sprites in Australia with corresponding ELF triggers in Rhode Island. The video frames with brightest imagery were selected.

Figure 3.

Nine sprites in Australia without corresponding ELF triggers in Rhode Island. The video frames with brightest imagery were selected.

Table 1. Rhode Island ELF Detections of Australian Sprite Lightning 26 November 1997a
EventLocal EstimatesRemote (ELF) Estimates
UT Sprite TimeVertical Extent, kmUT Arrival TimeLatitude, degLongitude, degDistance, MmBearing, degCharge Moment, C-km
  • a

    PD, poorly determined; N/A, not available.

  • b


71249:00.310381249:00.473PDPDPDPD+660 (?)

[11] All Schumann resonance receiving equipment in Rhode Island was functioning reliably during the sprite observations documented near Darwin, Australia, by Hardman et al. [2000] on 26 November 1997. The adjusted list of sprite times was compared with the Rhode Island digital archive of transients with a search procedure for trigger times within ±500 ms of the sprite times. Nineteen successful intersections were found and processed following methods outlined in the previous section. These 19 events are listed in Table 1. Included in Table 1 are the video sprite times (the frame of the brightest image), the ELF trigger times in Rhode Island, the ELF estimated source-receiver distances, the vertical extents of the video sprite images also derived from results of Hardman et al. [2000], the electrical polarity of the parent cloud-to-ground lightning flash (positive, in all reliably determined cases), and a brief description of the sprite.

[12] The Rhode Island arrival times are GPS time stamped and so are judged to be absolutely accurate to better than 1 ms. The video camera times in Australia were not absolutely accurate, but a photomultiplier tube was also aimed at the sprites and had GPS time stamping. Table 2 shows a subset of the sprite events in Table 1 whose peak optical intensity was captured with absolute accuracy. The time differences between the optical times in Australia and the arrival times in Rhode Island are tightly distributed in the range of 66 to 73 ms. These times are consistent with waveguide propagation over the 16.6 Mm distance between the satellite-observed storm in Australia and the Rhode Island receiver at the reduced light speed characteristic of the Schumann resonance band (v/c ∼ 0.8), or 69 ms. This comparison suggests that the peak sprite brightness is not delayed appreciably from the peak current (return stroke) of the parent lightning ground flash. One of the return strokes in a sprite lightning was recorded by Kattron, the Australian Lightning Network provider, with a time of 1438:08.949 UT. The corresponding ELF arrival time in Rhode Island for this event (from Table 1) is 1438:09.017 UT, representing a delay of 68 ms. This result, though for only one event, is consistent with the results shown in Table 2 and the simple calculation for ELF propagation delay. (It should also be noted that the current polarity report from Kattron was negative, in contrast to the consistent positive polarity determination from Rhode Island for all of these events. Kattron expressed no confidence, however, in the polarity determination at this extended range from their network at higher (southern) latitude in Australia.)

Table 2. Photomultiplier Tube Times on Sprite Lightning Events Near Darwin, Australia, on 26 November 26 1997 Versus ELF Arrival Times in West Greenwich, Rhode Island, United States
EventUT Sprite TimeELF Arrival TimeTime Difference, ms

[13] Figure 2 shows video images of sprites recorded in Australia for nine of the lightning flashes for which Schumann resonance analysis was possible on the electromagnetic transients detected in Rhode Island. By way of contrast, Figure 3 shows examples of nine sprites for which no ELF triggers were obtained in Rhode Island. In both cases, the brightest images for each sprite event were selected. There is some evidence here that the bigger, brighter sprites were more likely to be associated with lightning that triggered the Rhode Island system.

[14] Figure 4 shows selected ELF waveforms for the first three of the sprite-producing lightning in Table 1. The waveform shapes are remarkably similar from event to event, and the signal-to-noise ratio is clearly large despite the great distance of propagation. Evidence for the “W” type waveforms discussed by Burke and Jones [1995] and Ogawa and Komatsu [2007] is apparent here. The current moment (IdS) spectra for all the sprite-producing events have been computed and the least squares slopes of log (amp IdS) versus log f plots have been evaluated as a measure of the “redness” of the source spectra. The mean slope for 19 events was found to be −0.41, significantly larger than the mean value for thousands of flashes (−0.24) with positive polarity observed worldwide from Rhode Island, but without any verification of sprites [Williams et al., 2007]. Despite the red nature of these source spectra, there was no obvious tendency for the fundamental Schumann resonance mode near 8 Hz to dominate for these events, as with the classical “Q bursts” [Ogawa et al., 1967.]

Figure 4.

ELF waveforms for selected sprite events, remarkably well matched, event to event. Magnetic Lissajous patterns are shown on top, illustrating departures from linear polarization that are attributable to the asymmetry of the real Earth-ionosphere waveguide. All measured field components are shown. The “W” structure of these waveforms noted elsewhere by Ogawa and Komatsu [2007] is apparent and can be interpreted as the first (short-path) and second (long-path) arrivals of EM energy from the lightning flash round the world from the receiver.

[15] Figure 5 shows a plot of sprite size (maximum vertical dimension, based on the video imagery and documented in Table 1) versus vertical charge moment based on the Schumann resonance analysis. The bigger, brighter events tend to be associated with larger charge moments, and the charge moments have a strong tendency to exceed the threshold predicted for dielectric breakdown at 75 km altitude. (Unfortunately, neither the absolute heights of the sprites nor the sprite initiation altitudes are available from Hardman et al. [2000], and so we assume here an initiation height based on high-speed video analysis in another study [Stanley, 2000].)

Figure 5.

Charge moments for sprite-producing lightning flashes in Australia versus their maximum vertical extents. Sprites with greater vertical extents tend to be associated with larger charge moments. The charge moments tend to be larger than the 750 C-km value deemed necessary for initiation at 75 km altitude.

[16] Figure 6 shows a map of all ELF sources located by Schumann resonance analysis methods based on a uniform model of the Earth-ionosphere cavity. These locations (most between 15.4 and 15.8 Mm distance; see Table 1) fall systematically short (by 0.8 Mm or more) of the location of the mesoscale convective system at 16.6 Mm shown in satellite imagery of Hardman et al. [2000]. The explanation for this systematic ranging error is the subject of the next section.

Figure 6.

Ground-true geographical position of the parent storm and its apparent locations estimated from ELF transients listed in Table 1. The sizes of the stars indicate observation subperiods: small, 1100–1300 UT; medium, 1300–1400 UT; large, 1400–1500 UT.

4. Theoretical Interpretation of Results

[17] The global location procedure used in this study is based on the single-mode theory of ELF propagation within a spherically symmetrical waveguide approximating the real Earth-ionosphere cavity. The reasons for the limitations in accuracy of locating the lightning events parental to sprites (with the major accent made on the distance deviations), and the possible ways of improving this accuracy, are the subjects of this section.

[18] Following the approach suggested by Kemp and Jones [1971], the source-observer angular distance θ0 is estimated from the transient's wave impedance defined as the ratio of the spectra of the vertical electric and horizontal magnetic components:

equation image

In a spherically symmetrical model of the waveguide, the wave impedance is expressed via the Legendre and associated Legendre functions [Burke and Jones, 1995]:

equation image

where θ0 is the observer's angular position in the {r, θ, ϕ} spherical coordinate system with the θ axis centered on the source, a is the Earth's radius, ɛ0, is the permittivity of free space, and v(f) is the propagation problem's zeroth eigenvalue related to such more traditional propagation parameters as the phase velocity vPHASE(f) and attenuation rate α(f) via simple algebraic relationships [Galejs, 1972; Mushktak and Williams, 2002].

[19] Computations show that both the modulus and argument of the wave impedance, considered in the frequency domain, have a quasiperiodical structure with a quasi-period Δf that, in any spherically symmetrical waveguide, is uniquely related to the source-observer distance. Various forms of this relationship have been suggested and applied since the publication of the pioneering work by Kemp and Jones [1971], the simple formulae proposed by Burke and Jones [1995] or by Nickolaenko and Hayakawa [2002] as characteristic examples. In this study, a more complicated calibration curve (Figure 7) has been used, a curve computed on the basis of Ishaq and Jones's [1977] expressions for vPHASE(f) and α(f) that are considered to be representative for a spherically symmetrical model of the waveguide at lower ELF [Mushktak and Williams, 2002]. All of these results are in numerical agreement at the level of a few tenths of Mm, and the selection of one over the others does not provide a solution to the systematic ranging error (∼1 Mm) encountered in this study.

Figure 7.

Calibration plot: source-observer distance estimate versus the quasi-period of the wave impedance.

[20] The storm in Australia responsible for the sprite-producing lightning (Table 1) was reported to have an almost fixed geographical position of approximately 16.5°S, 129°E, its relatively slow NW motion having only small effect on the actual source-observer distance of about 16.6 Mm during the 4-hour observation period. Nevertheless, the ELF distance estimates show a pronounced tendency to increase with time (Figure 8) over the 4-hour period of the sprite observations, which suggests a change in the propagation conditions not accounted for in the spherically symmetrical model. An obvious candidate for the factor responsible for this tendency is the day/night asymmetry of the real Earth-ionosphere waveguide.

Figure 8.

Distance estimates versus universal time: results of estimating the source-observer distance from experimental and simulated quasi-periods of the wave impedance.

[21] To qualitatively understand the change in the ELF distance estimates, it is advisable to reformulate (2) via an asymptotic expression for the Legendre function [Abramowitz and Stegun, 1965]:

equation image


equation image

where the first exponentials in the nominator and the denominator can be interpreted as the “direct” (short-path) electric and magnetic waves, respectively, while the second exponentials mathematically represent the “around-the-globe” (long-path) waves whose interference with the “direct” ones produces the Schumann resonance phenomenon.

[22] For a spherically asymmetrical waveguide with the eigenvalue dependent on the angular coordinate, equation (3) can be reformulated into a WKB-like form:

equation image

with the propagation parameter ν(f; θ) integrated over the “direct” and “around-the-globe” paths.

[23] In the lower ELF region, because of the limited accuracy of asymptotic expression (2) and the equally limited validity of the path concept because of the global dimensions of the Fresnel zones [Bliokh et al., 1980], expressions (4) and (5) are not recommended for quantitative computations, but (5) qualitatively illustrates the change in the distance estimates with universal time. Indeed, with the day/night boundary shifting westward for about 60° during the 4-hour observation period, the day/night proportions in both “direct” and “around-the-globe” paths change considerably (see Table 3; in the interests of visual simplicity, the paths are computed assuming that the day/night boundary cuts the globe into two equal hemispheres, which is not the case in reality). This causes significant phase modifications in all the waves, and results in a change of interference conditions in both electric and magnetic components and, consequently, in a change of the quasiperiodical structure of the wave impedance that, in the present study, determines the distance estimate. In the beginning of the observation period, the source-observer configuration can be defined as maximally asymmetrical—the whole “direct” path is under nighttime conditions, while the “around-the-globe” path has almost daytime character (Table 3), which results in the maximum deviation of the ELF distance estimate (Figure 8). With time, both paths become more and more mixed, the configuration—less and less asymmetrical, and the distance estimates move closer to the ground-true value of 16.6 Mm [Hardman et al., 2000].

Table 3. Propagation Conditions and Results of TDTE Simulations Versus Universal Time
Universal TimeLocal ConditionsDirect Path, 16.6 MmAround-the-Globe Path, 23.4 MmTDTE Simulated Quasi-Period, HzSimulated Distance Estimate, Mm
SourceObserverDay Segment, MmNight Segment, MmDay Segment, MmNight Segment, Mm

[24] To interpret quantitatively the tendency in the observations for increasing distance with time, the two-dimensional telegraph equation (TDTE) method [Kirillov et al., 1997; Kirillov, 2002] has been applied, a method developed specifically for treating asymmetries of the real Earth-ionosphere waveguide in ELF computations. As the actual propagation parameters, the TDTE technique uses a pair of complex characteristic altitudes, HC(f; equation image) and HL(f; equation image), presenting in a condensed form the electrodynamic properties of two ionospheric layers responsible for ELF propagation as well as the spatial distribution of these properties in the spherical coordinate system {a; equation image } centered on the solar zenith axis. Since our own propagation model is at present only under construction, the daytime and nighttime frequency dependences of the phase velocity and attenuation rate has been adopted from the early, but still relevant, monograph by Galejs [1972], and recalculated into the characteristic altitudes.

[25] With the known, ground-true geographical location of the storm, the modulus of the wave impedance (1) has been TDTE computed for the observer's position in Rhode Island (USA) as a function of frequency and universal time, after which the simulated distance estimates has been obtained from the modulus' quasi-periods (Table 3) on the basis of the same calibration curve as that used in the experiment (Figure 7). The reasonable agreement between simulated and experimental dynamics of the distance estimates with universal time confirms that the day/night asymmetry, the only one modeled in simulations, is the major factor for both the underestimated and UT-dependent distance estimates. Consequently, a location procedure based on a theory that treats the day/night asymmetry is expected to improve considerably the distance accuracy.

[26] The distribution of the ELF locations relative to the storm's ground-true position (Figure 6) shows that the geographical displacements result not only from distance deviations, but also from bearing inaccuracies, also dependent on universal time. This phenomenon had first been observed as statistically significant variations with UT of the arrival direction of African transients observed at the Rhode Island ELF site [Huang, 1997], and then by Price et al. [2002] in a global United States–Israel location experiment with a known ground-true position of the parent storm. Phenomena of this nature had been theoretically simulated, on the basis of the TDTE technique, and interpreted by Mushtak and Williams [1997] and Mushtak et al. [2002] as a result of the magnetic field's refraction on the day/night boundary. An important implication is the corresponding change of the orientation of the polarization ellipse's major axis (the nonlinear polarization also caused by the day/night asymmetry) from its geometrically “right” direction. Neither effect is accounted for in the location procedure. Since the experimental procedure determines the bearing to the source in the time domain, while the TDTE technique operates in the frequency domain, an accurate qualitative comparison of theoretical simulations with the present experimental bearing deviations has not yet been implemented.

[27] In addition to the use of a more accurate propagation theory to minimize the bearing deviations suggested here, another instrumental solution [Price et al., 2002] has been suggested and successfully applied. The distinguishing feature of this location solution is determining the bearing to the parent lightning on the basis of the VLF (less vulnerable to the refraction effect) component of its electromagnetic signature, the distance location still based on the ELF component. This technique considerably improves the bearing accuracy without any additional theoretical contrivances, but it also has an obvious shortcoming: because of the stronger wave attenuation at VLF, a significant portion of smaller events could be lost from the analysis.

[28] The efforts to improve the location accuracy are important not only to refine the geographical distribution of lightning sources, but also for more accurate estimation of their current moments. Indeed, in the TDTE formalism, the vertical electric field can be symbolically expressed as

equation image

where MS(f) is the spectrum of the source's current moment; and S, O, and SO indicate the factors dependent on the source-local, observer-local and global electrodynamic properties of the Earth-ionosphere waveguide. The day-to-night change in the lower characteristic altitude HC(f;O) amounts to 20–25% [Greifinger et al., 2005] and needs to be considered when estimating the current moment from the source's ELF signature. In contrast to the well-known position of the observer relative to the day/night transition, the conditions to be considered over the source (HL(f;S)HC−1(f;S), another 10–15% in the day/night change) are critically dependent on the accuracy of its location.

5. Discussion

[29] Electromagnetic energy from sprite lightning in Australia has been successfully detected at ELF in Rhode Island, USA, via a short great circle path over the western Pacific Ocean, Alaska, and North America, and over a long great circle path over the Atlantic and Indian Oceans. Consistent geographical locations are found for many sprite-parent lightning flashes (Table 1) on the basis of standard wave impedance analysis and a uniform model for the Earth-ionosphere cavity. Accurate timing for the short propagation path, documented in Table 2, shows excellent agreement with subluminal v/c values in the Schumann resonance frequency range.

[30] Bigger sprites in video imagery in Australia tend to be associated with larger charge moments estimated in Rhode Island (Figures 2 and 5), again on the basis of a uniform propagation model. Smaller, weaker sprites are generally caused by Australian lightning that was less likely to be detected with the amplitude-thresholded system in Rhode Island (Figure 3). The magnitude of the charge moments needed for sprites (following the C. T. R. Wilson criteria; see Figure 1) for these events far from the Rhode Island receiver (∼16.6 Mm) are in good agreement with values at closer range (∼2 Mm) [Huang et al., 1999; Lyons et al., 2003] with the same detection methods.

[31] All detected lightning flashes causal to sprites (Table 1) showed positive polarity in the initial excursion of the vertical electric field in Rhode Island (see Figure 4), consistent with thousands of other determinations in other studies [Williams et al., 2007]. The current moment spectra for these events are redder than a random collection of large positive events that may or may not have produced sprites [Williams et al., 2007]. These findings are consistent with the working hypothesis that sustained lightning currents (i.e., “continuing currents”) are needed to produce well-developed sprites, of the kind evident in Figure 2. Despite their red current moment spectra, these events do not fit the mold of the classical Q burst [Ogawa et al., 1967] with a strongly dominant fundamental (∼8 Hz) component in the frequency domain and clear evidence for several round-the-world “trips” in the time domain. The latter events may also produce sprites [e.g., Price et al., 2002], but also appear to occupy a category all their own.

[32] Telltale evidence for a problem with the uniform cavity model in this study is the underestimate of true distance using standard calibration curves (e.g., Figure 7), with an observed clustering of event locations short of the parent storm location (Figure 6). The interference between ELF waves going both directions round the world is fundamental in establishing the Schumann resonance phenomena. If these two paths are asymmetrical in propagation conditions, as Table 3 demonstrates, one can expect shortcomings with a uniform model. The systematic change of estimated source location over time (Figure 8), unattributable to the motion of the parent storm in Australia, is rather easily ascribed to the changing geometry of the day/night asymmetry of the ionosphere, relative to the source-receiver path (Table 3). This same asymmetry will affect the charge moments computed here on the basis of a uniform model, but these adjustments have not yet been studied in detail.

6. Conclusions

[33] Sprite lightning has been successfully detected and analyzed with Schumann resonance methods for numerous events documented independently with optical methods on the other side of the world. The interpretation of the observations supports the approximation of a uniform Earth-ionosphere cavity in calculating charge moments and locating events, but simultaneously verifies a departure from uniform cavity conditions in achieving accurate values for these quantities.


[34] Assistance in the analysis of these results from Everest Huang and Akash Patel at MIT, Simon Hardman, Craig Rodger, and John Bähr at Otago University, and Ken Ticehurst at Kattron (Australian Lightning Data Service) is much appreciated. Earle Williams acknowledges support from the Physical Meteorology Program of the U.S. National Science Foundation (ATM-0221215).