Notice: Wiley Online Library will be unavailable on Saturday 27th February from 09:00-14:00 GMT / 04:00-09:00 EST / 17:00-22:00 SGT for essential maintenance. Apologies for the inconvenience.
 We estimated locations and rates of sprite occurrences on a global scale using 1–100 Hz ELF magnetic field waveform data obtained at Syowa station in Antarctica and Onagawa observatory in Japan. From the ELF data obtained in a period between June 19, 2001 and January 20, 2002, we identified 715,500 events of transient Schumann resonances (SRs). The locations and polarizations of these parent cloud-to-ground (CG) discharges were determined by a triangulation method. The charge moments of these CG discharges were calculated with a normal mode expansion model of SR waves. From these results and the empirical sprite initiation probability reported by Hu et al. , the global occurrence rate of sprites is estimated to be about 720 events/day on average. It is also found that the active regions of sprite occurrences are located in North and South America, Africa and South-East Asia.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 Since the first image of a transient luminous event called “sprite” appearing above thunderclouds was captured by Franz et al. , optical observations of sprites have been intensively carried out around the world. However, locations suitable for optical observations of sprites are limited in the world. Moreover, opportunities to capture sprites depend on local weather conditions at optical observation sites during the nighttime. Due to these reasons, global occurrence rates of sprites have not been determined.
 Electromagnetic waves in the frequency range less than 60 Hz excited by cloud-to-ground (CG) discharges can propagate globally with low attenuation rates inside the Earth-ionosphere cavity. Interferences of these globally propagating waves result in cavity resonances known as Schumann resonances (SRs). Consequently, these waves can be used to monitor global lightning activities [Füllekrug and Constable, 2000; Füllekrug et al., 2002]. Occasionally, transient SR bursts excited by extremely intense CG discharges are observed above the level of background SR signals. Recent observations of SRs by Boccippio et al.  and Sato et al.  revealed that occurrences of sprites and transient SRs are highly correlated. A method to estimate the charge moments of sprite-inducing CG discharges from SR data was developed by Huang et al. . They showed that the charge moments of sprite-inducing CG discharges are 200–2000 C·km. The probability of the sprite initiation as a function of charge moments of positive CG (+CG) discharges was estimated by Hu et al. . They suggested that this sprite initiation probability and the charge moment estimation derived from SR data enable us to estimate the global occurrence rate of sprites.
 Recently, it is suggested that sprites would chemically change the concentration of NOx and HOx in the mesosphere and lower thermosphere [Hiraki et al., 2002]. Since these chemical products may lead to an impact on the global cooling or heating in the middle atmosphere, it is particularly important to determine global occurrence locations and rates of sprites.
 In this study we have estimated the locations and rates of sprites on a global scale using 1–100 Hz ELF magnetic field waveform data obtained at Syowa station (69.0°S, 39.6°E in geographical coordinates) in Antarctica and at Onagawa observatory (38.4°N, 141.5°E) in Japan. The global occurrence rate of sprites has been estimated to be ∼720 events/day on average and that the active regions of sprite occurrences are located in North America and South-East Asia in summer of the northern hemisphere, and South America and Africa in summer of the southern hemisphere.
2. Observation System and Data
 In order to measure magnetic field perturbations in the frequency range of 1–100 Hz in the geomagnetic north-south (H-component) and east-west (D-component) directions, two orthogonal search coil magnetometers with pre-amplifiers were installed at West Ongul Island located ∼5 km southwest from Syowa station [Sato et al., 2003]. Output signals from these sensors are amplified by a main amplifier with a gain of 38 dB and are transmitted to Syowa station at East Ongul Island by a PCM telemeter. The telemetry signals are converted from digital to analog signals and are amplified again by a digital-to-analog (D/A) converter with a gain of 12 dB in a PCM decoder. Then, these analog signals and the IRIG-E time code of a GPS receiver are recorded continuously by a 16-bit analog-to-digital (A/D) converter with a sampling rate of 400 Hz. All these data are stored on DVD-RAM. This system has a stable flat sensitivity of 96 mV/pT for the frequency range of 2–90 Hz and the cutoff frequencies of the high-pass and low-pass filters inside the main amplifier are 1.0 Hz and 100 Hz, respectively.
 The same observation system has been installed at Onagawa observatory in Japan. In this system, signals from search coil sensors are transmitted though 200-m signal cables to the main amplifier and are amplified with a gain of 46 dB. In order to reject power line noises, three notch filters are used. The central rejection frequency of these filters is 50, 100, and 150 Hz with an attenuation of −60 dB and a Q-factor of ∼2. The sensitivity of this system is 60 mV/pT in the frequency range of 2–90 Hz except for the frequencies of these notch filters.
 We have analyzed ELF magnetic field waveform data obtained at Syowa and Onagawa in the period between June 19, 2001 and January 20, 2002. During this period ELF data are available for 154 days since there are some data gaps at each observation site. We have defined the time period from June to August 2001 as summer, from September to November 2001 as fall, and from December 2001 to January 2002 as winter, respectively.
3. Lightning Locations and Charge Moments
 First, we have selected transient SR events from the ELF magnetic field data. From the Syowa ELF waveform data transient SR events that exceed the continuous SR background noise level by seven standard deviations are selected. On the other hand, transient SR events that exceed background noise level by three standard deviations are selected from Onagawa ELF waveform data. The typical effective amplitude of these seven and three standard deviations become equally ∼20 pT. If time differences between the onset times of transient events at Syowa and Onagawa are within ±60 ms, these transient events are selected for further analysis. Figure 1(a) shows sample waveform plots of the D-component magnetic field data obtained at Syowa and Onagawa for the time interval 1651:38.76–39.56 UT on August 12, 2001. These waveforms characterized by an impulsive onset and following damping oscillations are typical transient SR events that satisfy the above criterions. Using the H- and D-component data, the powers of the horizontal magnetic field are derived as
and are plotted in Figure 1(b) for the time interval 1651:38.96–39.16 UT. From this figure the time difference between the peak of the Syowa power and that of the Onagawa power is determined, as indicated by dt in Figure 1(b).
 In the next step, the locations and polarizations of CG discharges inducing the selected transient SR events are determined. Since the propagation mode of SR waves is the quasi-transverse electromagnetic (quasi-TEM) mode, a great circle corresponding to the propagation path becomes perpendicular to the polarization axis. It is possible to estimate the polarization axis of the transient SR wave from Lissajous plots using the horizontal magnetic field data. Figure 2(a) shows the waveforms of the H- and D-component magnetic field for the transient SR event observed at Onagawa shown in Figure 1(a). By using the data points between t1 and t2, a Lissajous plot is obtained as shown in Figure 2(b). A solid line corresponds to a Lissajous curve derived from the horizontal magnetic field data, while a dashed line with arrows shows the direction of propagation path. We have also estimated the propagation path of the transient SR event at Syowa in this manner. In this transient event the SR waves were detected at Syowa first (see Figure 1(b)). Thus, we can determine one of the two intersections of the two great circles as a candidate location of the parent CG discharges. Further, we perceive the difference of the wave arrival time dt and draw one more great circle. If SR waves propagated from any point on this great circle with a propagation velocity of 0.8c as suggested by Füllekrug and Constable , the difference of wave arrival time between Syowa and Onagawa becomes dt. Thus, additional two intersections are determined. Finally, the gravity center of a triangle formed by these three intersections is considered as the most probable CG location. Then, we can identify the polarization of the parent CG discharge (positive for this event). We have analyzed all of 715,500 transient SR events with this method and have estimated CG locations and polarizations automatically.
Table 1 shows the occurrence numbers of oceanic and continental CG discharges in the period between June 19, 2001 and January 20, 2002. It is found that the occurrence number of negative CG (−CG) discharges over oceanic region is higher than that of +CG discharges. On the other hand, the occurrence number of +CG over continental region is higher than that of −CG.
Table 1. Occurrence Number of +CG and −CG
 Similar to the models of Burke and Jones  and Huang et al. , complex current moment spectra can be obtained by using the frequency-dependent normal mode expansion model for the magnetic field as,
where Idlobs(f) is the complex current moment spectrum, Hφ(f) is the complex power spectrum of the observed magnetic field data, RE = 6378 km is the radius of the Earth, h0 = 80 km is the height of the ionospheric reflection boundary, m is the order of the harmonics, Pm1(cosθ) is the Legendre polynomials of order m and first degree, and θ is the angular distance between the CG discharge and the receiver. The complex eigenvalue ν that describes the propagation and dissipation characteristics is derived from the equation (5) shown in Ishaq and Jones . For the estimation of charge moments, we assume the lightning current moment as an exponential form in time domain. The complex current moment spectrum is obtained by the Fourier transform of the current moment waveform, as shown in equation (3).
Here the parameter τ corresponds to the decay time constant of the lightning currents. This theoretical current moment spectrum Idl(f) is fitted to the current moment spectrum Idlobs(f) which is estimated experimentally. Best fitting parameters of I0dl and τ are obtained using the least-squares method. Then, charge moments are estimated from (I0dl)·τ = (I0τ)·dl = Qdl.
 Using the Syowa magnetic field data, we have estimated the charge moments of CG discharges inducing transient SRs for the period between June 19, 2001 and January 20, 2002, as shown by shaded bars in Figure 3. It is found that 50.9% of these +CG events have charge moments between 200 and 600 C·km and that the average charge moment is estimated to be 686 C·km. For the -CG events, 53.7% of these events have charge moments between −200 and −600 C·km and the average charge moment is estimated to be −632 C·km. It should be noted that the distribution of charge moments is symmetrical for the +CG and −CG events.
4. Global Sprite Occurrence Rate
 In order to estimate the global sprite occurrence rate from the charge moment distribution shown in Figure 3, we considered the results from Hu et al.  concerning the empirical sprite initiation probability due to +CG discharges. That is, the global sprite occurrence rate is estimated by multiplying this sprite initiation probability by the +CG charge moment distribution derived from Syowa ELF data. Open bars in Figure 3 represent the estimated sprite occurrence rates. It is found that the number of sprite events is estimated to be 110,375 (32.3% of the detected +CG events). Seasonal variations of the charge moments and the sprite occurrence rates are summarized in Table 2. The average sprite occurrence rates in the summer, fall and winter seasons are estimated to be 684, 733, and 741 events/day, respectively. Thus, the average sprite occurrence rate during this period is estimated to be 719 events/day.
Table 2. Seasonal Variations of Charge Moments and Sprite Occurrence Rates
Charge Moment (C·km)
 From the CG locations derived from the Syowa and Onagawa ELF data and the occurrence rates of sprites, we can make global maps of the sprite occurrence regions, as shown in Figure 4. In this figure the occurrence rate is displayed by a blue-to-red color code with a 2° × 2° spatial resolution. The global maps of the sprite occurrence rate in the summer, fall and winter seasons are shown in Figure 4(a), 4(b), and 4(c), respectively. Note that a great circle indicated by the symbol “‡‡‡” (the latitudinal width of this region is roughly ∼600 km) represents the region where CG locations can not be determined because the difference of wave arrival time dt becomes 0. It is obvious that the high occurrence regions of sprites are concentrated in the major lightning source regions. In the summer season, sprite occurrence rates are higher in the northern hemisphere than in the southern hemisphere with large enhancements in North America and South-East Asia, as shown in Figure 4(a). On the other hand, these rates are higher in the southern hemisphere in the winter season with large enhancements in South America and Africa, as shown in Figure 4(c). It is also estimated that sprites occur with rates of ∼113 and ∼190 events/day in North America (region-I in Figure 4(a)) and South-East Asia (region-II in the same figure) in the summer season, respectively, while they occur with a rate of ∼240 events/day in Africa (region-III in Figure 4(c)) in the winter season.
5. Discussion and Summary
 As listed in Table 2, the global occurrence rate of sprites is estimated to be ∼720 events/day on average. Note that this average occurrence rate of sprites is a minimum value since we have selected only very strong transient SR events from Syowa and Onagawa ELF waveform data. If we also analyze transient SR events below the threshold levels, the occurrence rate of sprites would increase considerably. However, the small charge moment sprites that could be missed in this analysis are typically quite small and dim. In terms of any large-scale impact of sprites, it is likely that the ∼720 bigger events per day would dominate any effect.
 The errors in determining CG locations with triangulation depend on the accuracy of the bearing angle derived from the Lissajous plot and the difference of wave arrival time dt. We have estimated a mean accuracy in triangulation as ∼1.6 Mm. This value is derived from not only the 16 sprite events observed by ground-based optical instruments simultaneously with ELF transients but also 78 lightning events detected by the LIS sensor onboard the TRMM satellite. Note that this error does not appear to be geographically random and may shift the entire regions rather than simply scatter the data points.
 In the study of Hu et al.  the charge moment distribution of +CG discharges, which was estimated by observing a small number of storms in Europe, is used to estimate the sprite initiation probability. However, it is uncertain if one can consider this charge moment distribution as a representative of all storms around the world. This may affect our estimation of global sprite occurrence rate. Moreover, sprite initiation probability by −CG has not been carried out yet. We need more accurate charge moment distribution of both +CG and −CG discharges to deduce reliable empirical sprite initiation probabilities that enable us to estimate global sprite occurrence locations and rates.
 It should be noted that the charge moment distribution shown in Figure 3 is differ from that reported by Füllekrug et al. . They showed that the most frequent values for both +CG and −CG events is >1000 C·km, whereas our results show such large values to be at the tail of the distribution. This difference might be caused by the underestimate of charge moment values since we assumed the time scale of lightning currents to be shorter than that of SRs and used equation (3). For CG events with very long continuing currents equation (3) should not be applied to the estimation of charge moments. As a future work, we will develop a method to estimate charge moments more accurately.
 Finally, the major findings in this study are summarized as follows: 1) average charge moments for −CG and +CG discharges inducing transient SRs are estimated to be −632 C·km and 686 C·km, respectively, 2) 32.3% of the detected +CG events produce sprites, 3) average sprite occurrence rate of sprites is estimated to be 684, 733, and 741 events/day in the summer, fall and winter seasons, respectively, 4) active regions of sprite occurrences are located in North America and South-East Asia in summer, while in the equatorial regions in fall and in Africa and South America in winter.
 The ELF magnetic field observations at Syowa station were carried out as part of the 41st and 42nd Japanese Antarctic Research Expedition programs. We acknowledge Dr. M. Kikuchi, Profs. H. Yamagishi and N. Sato at National Institute of Polar Research. We also acknowledge Dr. T. Sakanoi and Mr. T. Tamura for their assistance to operate ELF observation system at Onagawa observatory.