Narrow (~1–2 s) infrasound pulses that followed, with ~11 to ~50 s delays, rapid changes of electrostatic field were observed by a microbarometer array in the Czech Republic during thunderstorm activity. A positive pressure fluctuation (compression phase) always preceded decompression; the compression was usually higher than the decompression. The angles of arrival (azimuth and elevation) were analyzed for selected distinct events. Comparisons of distances and azimuths of infrasound sources from the center of microbarometer array with lightning locations determined by the European Cooperation for Lighting Detection lightning detection network show that most of the selected events can be very likely associated with intracloud (IC) discharges. The preceding rapid changes of electrostatic field, their potential association with IC discharges, and high-elevation angles of arrival for near infrasound sources indicate that an electrostatic mechanism is probably responsible for their generation. It is discussed that distinguishing the relative role of thermal and electrostatic mechanism is difficult and that none of the published models of electrostatic production of infrasound thunder can explain the presented observations precisely. A modification of the current models, based on consideration of at least two charged layers, is suggested. Further theoretical and experimental investigations are however needed to get a better description of the generation mechanism.
 Two different mechanisms were proposed to explain audible and infrasound acoustic waves generated by lightning discharges. It is generally accepted [e.g., Holmes et al., 1971; Pasko, 2009; Assink et al., 2008; Farges and Blanc, 2010] that a strong heating of lightning channel causes a rapid expansion [Few, 1969], which is responsible for the audible part of thunder. Power spectral measurements, however, indicate that another mechanism might be responsible for the infrasound part [Holmes et al., 1971], especially in the case of intracloud (IC) discharges. Wilson  pointed out that the pressure inside a charged region in the cloud must be less than the pressure outside because of a mutual repulsion of the charged water droplets. Consequently, a sudden reduction of the electrostatic field within a thundercloud that follows a lightning discharge should produce a low-frequency (infrasonic) acoustic wave.
Dessler  elaborated Wilson's idea and showed that if the principal infrasonic signal comes from a flat horizontal charged layer, then this signal will be beamed nearly straight up and down so that it can be detected only by instruments placed directly above or below the charged region. This model suggests that a rarefaction pulse (decompression) is detected first, possibly followed by a compression (positive pulse). The spectral peak should occur within the range 0.2–2 Hz. Similar results were also obtained for a cylindrical charged volume with length longer than its radius except that sound is radiated perpendicular to the cylinder axis, and the amplitude will fall with the distance. The reported measurements [e.g., Bohannon et al., 1977; Balachandran, 1983], contrary to this theoretical prediction, showed that the waveform is usually characterized by an initial compression followed by a rarefaction; at the same time the multipoint measurements located the infrasound source in the cloud above the sensor array. It means that the infrasound signals did not come from the vertical portion of the cloud-to-ground (CG) discharge where channel heating is the strongest [Bohannon et al., 1977]. Considering the electrostatic mechanism, Bohannon et al.  suggested that the observed, initial positive pressure wave could be caused by a rapid (~0.5 s) intensification of the electric field (charging) just prior to discharge. Pasko  recently performed numerical simulations based on linearized equations of acoustics and demonstrated that growth of charge density in a thundercloud prior to lightning discharge on the time scales on the order of 2 to 6 s is sufficient to explain the initial compression (the longer the charging times, the lower the initial compression according to his results). Another explanation for the observed initial compression was proposed by Few , who considered that a lightning discharge decreases the electric field in the part of the charged volume by charge transport (probably positive coronal streamers) at supersonic speeds in a collision-dominated gas. This charge transport (current) produces a slight heating of the volume, leading to a positive pressure perturbation. Few  also estimated that the ratio of positive to negative pressure perturbation should be ~0.4.
 Various authors tried to reconstruct the geometry of lightning channels using microphone arrays [e.g., Few, 1970; Few and Teer, 1974; Arechiga et al., 2011] by determining the angle of propagation of the predominant acoustic signal received by the array. It was discussed that accuracy of source localization depends on the knowledge of wind and temperature along the ray trajectories. Infrasound emissions have not been conclusively located by the same manner [Johnson et al., 2011]. MacGorman et al.  performed acoustic reconstruction of thunder sources from several thunderstorms and showed that they are dispersed in vertical and horizontal directions inside a thundercloud, the horizontal extent being significantly larger than the vertical extent.
 This paper presents simultaneous measurements of electrostatic electric field and infrasound on the ground surface, provides information on lightning location using the EUCLID (European Cooperation for Lightning Detection) network, and gives estimates of locations of infrasound thunder sources based on the technique described by Johnson et al. . Possible mechanisms for conversion of electrostatic energy to infrasound are also discussed.
 The infrasound and electrostatic measurements were carried out in Panska Ves, located about 60 km northward from Prague, Czech Republic. In addition to local measurements, information from EUCLID is used to identify lightning discharges which caused or could cause individual observed infrasound thunder.
2.1 Infrasound Measurements
 The infrasound measurements were done by a microbarometer array. The array consists of three differential microbarometers (MBs) equipped with an infrasound sensor ISGM03 of Russian production (http://en.ntcgi.ru/index.php/products/isgm03m) with a flat response in the frequency range from ~0.02 to ~4 Hz and differential sensitivity of ~80 mV/Pa. The sensor was calibrated and tested at Commisariat á l'Energie Atomique (CEA), Arpajon, France, and showed in the frequency range given above a good agreement with devices used in the network of the Comprehensive Nuclear Test Ban Treaty. In the Czech Republic, this sensor has been used in studies of infrasound triggered by earthquakes [Laštovička et al., 2010; Chum et al., 2012]. A more detailed description of the sensor and a discussion related to its sensitivity to vibrations can be found in the report about simultaneous infrasonic and seismic observations by Laštovička et al. . The measured pressure fluctuations were recorded in a dynamic range ~ ±25 Pa, sampled at 25 Hz, and stored with 16 bit resolution in data loggers, from where the data were regularly downloaded via Internet connection. GPS receivers were used to time stamp the acquired data in data loggers. Each microbarometer sensor is equipped with four hoses to reduce wind noise. Additionally, each hose branches at a ~2.3 m length, and continues as two ~2.3 m separate hoses. There are altogether eight porous ends in the hosing system that are approximately equidistantly distributed around the sensor. The three microbarometers (MB1: 50.5286N, 14.5663E; MB2: 50.5284N, 14.5690E; and MB3: 50.5269N, 14.5674E) form approximately an equilateral triangle with ~200 m side, and represent, thus, a minimum configuration to determine the angle of arrival of an acoustic (infrasound) wave. The method of data analysis will be described in section 3. The array configuration is drawn at the top right corner in Figure 3.
2.2 Electrostatic Measurements
 An electric field mill (Boltek, Electric Field Monitor EFM-100) with response time ~0.1 s was deployed about 20 m from the microbarometer MB3 to measure the vertical component of the atmospheric electrostatic field Ez. A differential analogue output of the electric field mill was acquired by the identical data acquisition system (data logger) as was used for the microbarometers. The data were stored with a 16 bit resolution and sampling frequency of 25 Hz. The signal was attenuated in such a way that the saturation levels correspond to the electric field intensity of ±6.6 kV/m. An example of a simultaneous measurement of electric field Ez and pressure fluctuations recorded by MB1 is presented in Figure 1. The Ez is positive for downward electric field intensity. Thus, during fair weather conditions, when fair weather current density of ~2 pA/m2 flows from the ionosphere to the ground [Rycroft et al., 2000], Ez is ~100 V/m.
2.3 Lightning Detection Network EUCLID
 The full EUCLID network consists of about 150 sensors contributing to the detection of lightning over the European area. Each sensor detects the electromagnetic signal emitted by the lightning return stroke in the frequency range from 10 to 350 kHz and sends the raw data to a central analyzer. GPS receivers are used for precise time stamping. For each lightning stroke, the main parameters are calculated and recorded, namely the time of the event, the impact point (latitude and longitude), the peak current, and polarity. The accuracy of lightning location is about 200 m for cloud-to-ground (CG) discharges for which the network was mainly developed. As for the intracloud (IC) discharges, the accuracy might be in the same range for predominantly vertically oriented channels, considering the projection of the vertically oriented channel at ground surface as the striking point. It will be definitely worse, better to say undefined, for horizontal IC discharges. Generally, it is not possible to approximate the discharge location by a single point on the ground surface for IC, and the given coordinates will be likely the location of a peak of radiated field projected on ground surface.
 A detection efficiency (DE) is a key performance parameter of a lightning location system and is defined as the percentage (or fraction) of discharges (of any given type) that are reported by the lightning location system. A typical negative cloud-to-ground flash is composed of three to five strokes, and flash DE is typically higher than stroke DE as a flash is reported (detected), if at least one of the strokes (first or subsequent) in a multistroke flash is detected [Diendorfer, 2010]. EUCLID uses similar technology as NLDN (National Lightning Detection Network) in the United States, and the strokes are grouped into flashes using a spatial and temporal clustering algorithm [Cummins et al., 1998].
 Based on ground-truth data from lightning to an instrumented tower in Austria, the flash detection efficiency of EUCLID was determined to be higher than 98% for CG flashes and 85% stroke detection efficiency for all strokes and 99% for strokes with peak currents above 10 kA. No reliable data for the DE of the EUCLID network for IC discharges are available. Prentice and Mackerras  showed that the ratio z of IC flashes to CG flashes varies from storm to storm, and they also found an empirical relationship between the ratio z and latitude. According to their study, the ratio z decreases with increasing latitude, and it is z ~ 2.26 for the latitude of 50.5 (latitude of our observation). Over the continental United States, Boccippio et al.  determined an overall IC to CG ratio of 2.6 to 2.9 based on the NASA Optical Transient Detector (OTD) data and the U.S. National Lightning Detection Network (NLDN). In Poland, Paweł et al.  reported the ratio z ~ 5. We calculated the number of IC to CG discharges detected by EUCLID for the period of May 2012 to August 2012 in the considered region of a circular area of radius 40 km around the infrasound monitoring site and obtained the ratio z ~ 2.6. We note that this value is close to values given by Prentice and Mackerras  and Boccippio et al.  rather than the value given by Paweł et al. . Admitting that EUCLID could miss some weak IC discharges (expecting that the real ratio is somewhere between values given by the authors mentioned above) and recalling high detection efficiency for all CG flashes, we roughly estimate the DE for IC lightning to be in the range from about 70% to 80%.
3 Observation and Data Analysis
 Figure 1 shows 26 min of measurement of vertical component Ez of electrostatic field (Figure 1a) and infrasound signal (Figure 1b) recorded by MB1 in the frequency range from 0.25 to 3 Hz (zero-phase Butterworth filter of 8-order was used) during significant storm activity on 20 June 2012 from 22:27 to 22:53 UT. This interval was chosen because Ez experienced a number of rapid changes indicating nearby lightning activity as will be seen later when discussing Figure 4. The rapid changes of Ez are marked by vertical lines in Figure 1a. Solid green lines are used for positive changes of Ez, and dashed red lines mark the negative changes. Importantly, narrow distinct pulses that followed (after ~14 to ~47 s) the rapid changes of Ez are registered in the infrasound record, and it is anticipated that these infrasound pulses could be associated to individual lightning discharges. We selected altogether nine distinct narrow pulses that correlated well for all three microbarometer records. The selected pulses are marked by grey columns at the bottom of Figure 1b and named by letters “a” to “i”. A zoomed inspection of these distinct pulses shown in Figure 2 reveals that the pulses are mostly bipolar (an interference of various frequencies or waves is sometimes observed) and that the compression always precedes the decompression. The largest fluctuations are observed within ~1 s. Another point which is worth mentioning and which can be seen in Figure 1b or Figure 2 is that the absolute value of the compression is approximately the same (or slightly larger, ~20%) than the absolute value of the rarefaction in most cases. The frequency band from 0.25 to 3 Hz was selected on the basis of spectral analysis of the selected pulses. The spectral content differed from case to case, but the dominant peak (or peaks) of spectral intensity occurred in this band. The spectral analysis is, however, reliable only up to ~4 Hz; for higher frequencies, the sensitivity of the microbarometers used falls. It is worth noting that the observed frequency range 0.25–3 Hz is very similar to the frequency range (0.2–2 Hz) predicted theoretically by Dessler  for infrasound produced by the electrostatic mechanism.
 Figure 3 shows a spatial distribution of lightning flashes around the infrasound array as detected by the EUCLID network. Only discharges located within the radius of 40 km from the array center are displayed. In total, 127 flashes were detected in this area on 20 June 2012 from 22:27:00 to 22:53:00. Diamonds represent CG discharges, and circles represent IC discharges. If a positive current was detected, a “+” sign is drawn inside these symbols. Times of discharges are indicated by the color of the symbols as shown by the color bar on the right-hand side. It is obvious that a thunderstorm activity with a relatively large number of strokes occurred in the vicinity of infrasound array and presents, thus, convenient conditions for simultaneous infrasound and electric field measurements. The array arrangement (section 2.1) is drawn in the grey box located at the top right corner. (Note that the scales for the map of lightning distribution and the array arrangement are different)
 Figure 4 presents the distances (Figure 4a) of lightning discharges detected by the EUCLID network from the center of the microbarometer array (50.5280N, 14.5676E), and computed azimuths (Figure 4b) to these discharges for the same time period as displayed in Figures 1 and 3. Different symbols distinguish different types of lightning discharges. Blue diamonds represent the CG lightning whereas magenta circles mark the IC discharges. A “+” sign is drawn inside these symbols if a positive current is detected by EUCLID. Green and red vertical lines show times when the positive and negative rapid changes of electric field Ez were detected (compare with Figure 1a). Figure 5 shows a detailed view on the rapid changes of Ez (dashed magenta line) for three different events. A statistical analysis of all the rapid changes (mostly positive) presented in Figures 1a and 4 shows that their mean duration is 0.19 s with a standard deviation of 0.15 s and maximum duration about 0.8 s. Figure 5 also shows that the infrasound pulses are observed with different time delays after the rapid changes of Ez (~14 s for event c, ~47 s for event g, and ~11 s for event n presented in the bottom plot). These time delays are used to determine distances of the infrasound sources (~4.7 km for event c, ~15.7 km for event g, and ~3.7 km for event n). The event “n” represents an example of observations from other thunderstorms which are shortly discussed at the end of this section. As can be seen in Figure 4a, the rapid changes of Ez (mostly positive) correspond relatively well with the detection of nearby lightning discharges (approximately for distances smaller than 20 km). The lightning flashes were usually detected at the start of rapid changes of Ez. This is particularly true for flashes, when EUCLID reports that the flash is composed of one stroke. It should be stressed that the time resolution of electric field measurement (~0.1 s) does not distinguish the individual strokes within the lightning flash.
 The time intervals of the selected infrasound events are indicated by grey columns marked by letters “a” to “i” in Figure 4a (their width is exaggerated). Heights of these columns represent the distances of infrasound sources from the microbarometer array center that were calculated from the time differences between the observations of the selected infrasound events and detections of corresponding (preceding) changes of Ez. The accuracy of determination of these distances depends on the width of the selected narrow pulses and on the knowledge of the sound speed along the trajectory of infrasound wave packets. We estimate that it is ~0.5 km. An average sound speed of 337 m/s (corresponds to ~282 K) along the infrasound ray trajectories was assumed. The real wind and temperature fields are unknown. As can be seen from the height of the grey columns displayed in Figure 4a, the infrasound sources were only ~5 km distant for the events a, b, c, and d, whereas they were more than 15 km away for the events f and g. Comparing these distances (heights of grey columns) with the distances of preceding (~14 to 47 s) lightning discharges, we can associate the infrasound narrow pulses to the detected lightning discharge for events a, b, e, g, f, and h, whereas for the events c, d, and i, this association is impossible or problematic. It is also worth mentioning that the positive IC discharges can probably be associated with the individual infrasound narrow pulses for events a, b, and e, and a couple of negative IC and CG discharges with events f, g, and h. It is also interesting to compare the sign of the rapid changes of Ez with the type of corresponding detected discharges. If a negative charge flows up in the case of a near IC discharge, then EUCLID assigns a positive current, and an increase of Ez will be expected since the negative charge is moved away or reduced. This might be observed, e.g., for the IC discharges preceding the event b. When a negative charge flows down in a negative CG discharge, then EUCLID shows a negative current, and again a positive change of Ez is expected since the negative charge is removed from the cloud. This is observed, e.g., for CG discharges at 22:33 UT. So the current polarity for near discharges and signs of corresponding rapid changes of Ez shown in Figure 4a are consistent.
 To confirm or discard a potential association between the observed infrasound signals and the detected lightning discharges, it is very useful to estimate the angles of arrival (azimuth and elevation) for the individual infrasound signals (selected events). To do this, we follow an approach described by Johnson et al.  which is based on a search of horizontal slowness components for a presumed plane wave, applied on the measured infrasound signals (in the frequency range 0.25 to 3 Hz in our case). Horizontal slowness components sx (positive eastward) and sy (positive northward) correspond to the inverse of vx and vy components of apparent horizontal velocity and have units of meters per second. For an acoustic (infrasound) wave, the slowness components must satisfy the equation
where cs is the sound velocity and sz is the vertical component of the slowness. The procedure is then based on calculating the energy map W(sx, sy) from pressure fluctuations recorded by an array consisting of N elements (N = 3 in our case) in a time window Δt centered at the time of the given infrasound event for different values of slowness components sx and sy according to the relation (2)
where pn is the pressure measured by the n-th array element at a given time, and Δxn, Δyn, and Δzn are the Cartesian coordinates of n-th array element relative to the center of the array. We neglected the vertical differences Δzn and used Δt = 4 s in our case. It is usual to normalize this energy map. Following Johnson et al. , we normalize the map as
where Wunc is a measure of uncorrelated energy estimated as the average value of W(sx, sy) obtained for impossibly large slowness values sx and sy, 1/cs2 < sx2 + sy2 that do not correspond to acoustic (infrasound) waves. In our case, we computed the W(sx, sy) map for the values of slowness components sx and sy from −4.6 km/s to 4.6 km/s with a 0.2 km/s step and considered cs = 0.337 km/s. The normalized energy (coherence) maps C(sx, sy) have the advantage of making it possible to identify multiple coherent sources and naturally provide the information about the uncertainties of the source localization.
 Figure 6 shows the normalized energy maps C(sx, sy) for the nine selected events marked “a” to “i”. The horizontal and vertical axes correspond to negative values of sx and sy. Therefore, red and yellow regions in the maps indicate the directions to infrasound sources from the array center. The values of C(sx, sy) obtained for the unrealistically large slowness values (1/cs2 < sx2 + sy2) and values C(sx, sy) < 0 are not displayed (white color in the maps). Solid black circular lines correspond to the elevation angles of 0°, 30°, and 60°. The largest circle (elevation of 0°) represents the equality 1/cs2 = sx2 + sy2. Dashed black lines show different azimuths with 30° step (northward to the top and eastward to the right). The calculated azimuths to infrasound sources displayed in Figure 6 by red and yellow colors are also schematically shown in Figure 4b as grey columns. The azimuths could not be determined for the events a and b since the infrasound arrived from very high elevation angles from all possible azimuths, so the grey columns were sketched from −180° to 180° for these events. It is interesting to compare the distances of infrasound sources displayed in Figure 4a and the C(sx, sy) maps shown in Figure 6. We observe large values of C(sx, sy) for high-elevation angles, indicating that the waves propagated from above, for events a, b, c, d, and i. These events correspond to relatively near infrasound sources (~5–7 km in Figure 4a). For the more distant sources (events f, g, and h), the infrasound waves propagated practically horizontally (very low elevation angles) and arrived from azimuth range of ~30° to ~60°. At the same time, the azimuths of the associated lightning discharges (IC and CG) are in the range of 50° to 57° for these events (Figure 4b). In the case of the event h, there are more discharges that occurred at about the same time, but an inspection of the data reveals that the azimuths of two closest discharges (IC and CG) that can potentially be associated with event h are 50.5° and 50.6°. These values are again consistent with the back azimuth detected by the infrasound array (Figure 6h).
 It is also useful to look at the cases when no detected lightning discharge can be associated to the observed infrasound narrow pulses, namely at the events d and i. We see that the infrasound arrived from high-elevation angles in these cases. So it is probable that the sources could be assigned to IC activity not detected by the EUCLID network. It is interesting that EUCLID detected nine lightning discharges that occurred within ~0.46 s and preceded the event i. None of these detected discharges can, however, be associated with this event because of large distances of these detections (~15 km and larger). Note also that the back azimuths of these detected discharges vary greatly. Thus, a very complicated lightning activity took place around Panska Ves at that time, and it is likely that a near IC lightning was not detected by the EUCLID network or that the uncertainty in the location of IC discharges with large horizontal extent is very large (~10 km). We also note that IC discharges are often linked with CG discharges as shown in Figure 4; both types are observed almost simultaneously.
 To summarize our observations, the infrasound narrow pulses for which the analysis shows high-elevation angles of arrival (infrasound propagating from above) can either be associated with IC discharges (e.g., events a and b), or no corresponding discharge was detected for them (e.g., events i and d). The infrasound narrow pulses that propagated approximately from the horizon (events f, g, and h) could be associated to pairs of IC and CG discharges that occurred practically simultaneously and at almost identical locations. We also analyzed additional eight infrasound narrow pulses from other thunderstorms occurring on other days (22 May, 11 June, 1 July, and 2 July 2012), and in all these eight cases, there was either an IC discharge (three cases) or IC and CG discharges (one case) that could be associated to the infrasound event, or no suitable discharge was detected (four cases). A preceding rapid change of Ez was observed in all analyzed cases. One example from 2 July 2012 is given in the bottom plot in Figure 5. This record also presents the smallest time delay (~11 s) that we have observed between the rapid change of Ez and corresponding infrasound signal (we only consider events where the related infrasound pulses can be clearly identified). The slowness analysis shows elevation angles from ~60° to ~70° and back azimuths from ~45° to ~90° for this case. No lightning discharge (likely an IC discharge) that could be associated to this event was detected by EUCLID.
 The plots presented in Figure 5 also show that the signal recorded by MB3 (blue lines) is more noisy, compared to the signals from MB1 or MB2. This is because the MB3 is located in an open place, whereas the MB1 and MB2 are more or less sheltered by trees. Blockages that were later found in some hoses could also contribute to the higher noise level of the MB3. That might partially deteriorate the accuracy of the direction analysis presented in Figure 6. The fact that back azimuths to the distant causative lightning are within confidence intervals of direction analysis for infrasound sources, however, shows that this problem cannot qualitatively change the results of the presented analysis.
4 Relation to Previous Reports and Discussion of Electrostatic Mechanism
 Unlike the recent papers by Assink et al.  and by Farges and Blanc , this study does not deal with the evolution of back azimuths of infrasound sources during a thunderstorm passage and their comparison with the evolution of azimuths and distances to lightning discharges detected by a lightning detection network. We focus on the analysis of the infrasound pulses from thunderstorm that occurred almost overhead, nevertheless, similarly to the reports above, we have found a correspondence between locations of infrasound sources and lightning for distant discharges (~15 km). Assink et al.  discarded the possibility of pulses starting by compression with electrostatic mechanism and IC discharges considering the electrostatic model by Dessler  that predicts rarefaction pulses coming first. Farges and Blanc  did not consider IC discharges since the Météorage network used in their study did not report IC discharges. This report focuses on the relation between selected distinct infrasound narrow pulses and potentially associated lightning discharges. Our observations show that the distinct infrasound pulses were observed with specific time delays (used for estimates of distances to infrasound sources) after the rapid changes of electrostatic field Ez. Most of the distinct infrasound narrow pulses can be associated with IC discharges, and we also discuss models of electrostatic mechanism (this section).
 The fact that we cannot associate infrasound narrow pulses with the individual lightning discharges for all the events is consistent with the work by [Johnson et al., 2011] who compared the locations of thunder obtained from an array of broadband microphones (signals filtered in 1–10 Hz and 4–40 Hz bandwidths were used in their study) and the localizations of very high frequency (VHF) radiation from New Mexico Lightning Mapping Array (LMA). They get a good spatial correlation between acoustic signals with discharge channels detected by the LMA for some events, whereas in several cases, thunder imaging identified regions of sound production which were not seen in the LMA record. Johnson et al.  conclude that the electromagnetic LMA sensors detect channel formation and fast current impulses, whereas the acoustic (infrasound) signals are probably generated by net charge transport and volume charging/discharging. It should be noted in this respect that long discharges can be missed by LMA. Arechiga et al.  investigated thunder produced by triggered lightning and showed that thunder sources can be accurately located using acoustic signals when compared with LMA locations of lightning channels.
 It is worth mentioning that investigations into lightning propagation and preliminary breakdown reveal that the horizontal branch of preliminary breakdown can have a size of several kilometers and can last up to several hundreds of milliseconds [Coleman et al., 2008 and references therein]. If the net charge transport is responsible for the generation of infrasound [Johnson et al., 2011], then the large horizontal extension of charge transport during preliminary breakdown will enlarge the volume from which the infrasound is produced, which could explain (together with the discussed accuracy and detection efficiency for IC discharges) that some causative IC discharges were missed by the EUCLID or located differently.
 The fact that the analyzed infrasound events could be potentially associated with IC lightning activity (if detected) is consistent with the previous work by Holmes et al. . They reported that power spectrum from IC discharges at frequencies below 10 Hz, contrary to CG discharges, is not consistent with a thunder production by a thermally driven expanding channel and suggested that the electrostatic mechanism, originally predicted by Wilson , could be responsible for the infrasound part of the spectrum. As mentioned in section 1, the model of electrostatic mechanism proposed by Dessler  differs from observations and that it predicts that a rarefaction pulse should be observed first. Few  and Pasko  therefore came with different modifications of Dessler's model. Few  suggested that electrical heating by streamer systems is responsible for the positive pressure perturbation that advances the rarefaction pulse. His calculations, however, predict that the ratio of positive to negative perturbation should be close to 0.4, whereas our measurements show that this ratio is mostly larger than 1. Pasko  followed the idea by Bohannon et al.  that a rapid intensification of electric field just prior to the discharge could explain the initial positive perturbation and concluded (based on modeling) that a substantial charge growth on the time scale of several seconds could explain the initial compression. Our ground-based measurements of the electrostatic field presented in Figure 1a and Figure 5, however, do not show significant fast intensifications before the lightning discharges that are seen as rapid changes of Ez in electrostatic measurement. Charging seems to be a more or less continuous process occurring on much larger time scales. An intensification of the absolute value of Ez, before the discharge (rapid change of Ez) on the time scale of seconds, is not observed (Figures 1 and 5) or seems to be much lower than needed by Pasko , who considered the charge intensification comparable with charge change during the discharge. We cannot exclude the possibility that the intense charging just before the discharges is shielded by a charged layer. Stolzenburg et al. , based on balloon measurements, reported that the charge structure inside the thunderstorm clouds can be relatively complicated; within convective updrafts, there are typically four charged regions at different altitudes, whereas six charged regions were typically observed outside the updrafts. A tripole structure is also often reported [Saunders, 2008 and references therein]. We, however, consider such an efficient shielding just before the discharge unlikely. We note that all the discharges are seen very well as rapid significant changes in our measurements.
 Our measurements are consistent with the electrostatic mechanism and with the previous studies in that sense that the analyzed infrasound narrow pulses occurred in the frequency band predicted by Dessler , as mentioned in section 3, and can be very likely associated with IC lightning activity [Holmes et al., 1971]. However, our simultaneous electrostatic and infrasound measurements do not fit exactly any model [Dessler, 1973; Few, 1985; Pasko, 2009] describing the electrostatic mechanism of infrasound production. So it is probable that all these models still need some modification. A detailed modeling is outside the scope of this experimental paper, but we would like to mention one mechanism which might be worth of further investigation, and which might contribute to the initial positive pressure pulse. All the mentioned models of electrostatic production of thunder considered only one flat (horizontal) charged layer, simplifying the problem to one dimension, and the electric field was determined only from this charged layer. The actual electric field E is, however, a superposition of electric fields from all charged layers. It is instructive to imagine a situation when a positive charge region is found just below the main negative charge region. Note that Saunders  reports that a positive charge can be merged into the negative charge region. The attraction between the negative charge region and positive charge region then produces a positive pressure fluctuation (situated below the negative pressure fluctuation) in a stationary solution at the interface of layers having the opposite charge. An estimate of the stationary solution can be easily found, following the approach by Pasko , by integrating the Gauss's law (4) and equation of motion (5), if we ignore the effects of gravity and consider only the vertical component of electric field for simplicity
where p1 is the pressure perturbation owing to electric forces, ρC is the charge density (including the sign), and ε0 is the permittivity of free space. The solution depends on charge distributions and boundary conditions (value of electric field just below the charged volume). We note that an electric field pointing upward was usually measured at the ground before occurrence of discharges. Figure 7 shows an example of solution to (4) and (5) for charge density that varies with height h in sinusoidal form (wavelength of 200 m was used for the lower positive charge region and wavelength of 400 m was used for the main negative charge region). In Figure 7, h = 0 at the bottom of the lower positive charge (estimated roughly ~4 km above the ground surface) and increases upward. The electric field Ev is positive upward (contrary to Ez in Figure 1a which is negative upward). The boundary conditions were set in such a way that p1 is zero at the bottom and top (at h = 0 and h = 300 m) of the considered height interval. The pressure perturbation p1 was obtained for electric field intensities that are comparable with those used by Pasko . According to equation (5), the pressure perturbation increases in the region where both the electric field and charge densities are positive (have the same sign) and decreases in the region where they have opposite signs. If the charge is removed during the lightning discharge, the pressure perturbation p1 (Figure 7c) that evolved during quasi-stationary conditions starts to propagate away. The time scale of the recorded perturbation can be obtained from the spatial scale of this quasi-stationary perturbation divided by the speed of sound. In the 1D approximation (variables only depend on height), the perturbation propagates up and down. In other words, the initial positive pressure perturbation is obtained for ground measurements without an assumption of fast charging before the discharge. Note that the shape of the pressure perturbation in Figure 7c resembles relatively well the basic shape of the measured distinct infrasound pulses presented, e.g., in Figure 2.
 There is still very little known about the charge distribution inside the thundercloud in 3D, but investigations [Stolzenburg et al., 1998; Saunders, 2008] show that charges can also differ in horizontal direction inside the thundercloud; the situation mainly being different in the updraft and outside the updraft region. So it is reasonable to expect that for a realistic thundercloud, the infrasound beam is not directed only strictly downward or upward as predicted from horizontally extended layers (1D approximation), but the source radiates in cones with diverging rays. The larger the horizontal extent of charge layers compared to their vertical size, and the less the horizontal gradients of charge density, the closer the situation is to the 1D approximation, and the less divergent are the infrasound rays. We also stress that the electric field intensities measured on the ground are significantly different from intensities reported in the cloud (more than one order).
 It should be mentioned that a similar shape (compression observed first) could also be caused by the thermal expansion. One way that could partially distinguish thermal expansion and electrostatic mechanism is spectral analysis. We rely in this respect on published reports [Holmes et al., 1971; Few, 1969] that state the thermal expansion should produce spectral peaks at frequencies typically from ~10 to ~100 Hz. Thus, a significant secondary peak at infrasound frequencies (below ~4 Hz) and the association with IC discharges (note that peak current for IC discharges is mostly smaller than for CG discharges) could indicate an electrostatic mechanism. Our analysis reveals that most of the energy for selected events was in the frequency range from ~0.25 to ~3 Hz. The frequency range of our measurements is however only up to ~4 Hz, so the upper limit of this frequency range should be considered with caution, and is not reliable. Another possible way for discerning between the two mechanisms of infrasound production could be a statistical analysis of infrasound amplitudes for near discharges. It is expected that IC discharges above the array will produce larger signal amplitudes in infrasound frequency range than close CG discharges (better to say than CG discharges at distances similar as the height of cloud base) if the electrostatic mechanism is dominant, and if the 1D approximation is applicable (infrasound rays from electrostatic mechanisms are expected to be less divergent than from thermal expansion). Unfortunately, no narrow infrasound pulse has been associated with a near CG discharge. There is no near CG discharge located at the proper infrasound source distance for the selected events. The reexamination of data, however, indicates that infrasound responses at ~22:29:55 UT, ~22:33:51 UT, and ~22:41:29 UT (Figure 1b) can be associated with CG discharges (rapid changes of Ez) at 22:29:39.6 UT, 22:33:32.7 UT, and 22:41:06.8 UT (Figure 4a). It should be noted that the character of these infrasound responses is a little bit different from distinct narrow (quasi-bipolar) pulses that we selected before. There are more oscillations with comparable amplitudes around the main pulse. We are not sure if it is a real characteristic or just a wind perturbation. Figure 8a shows peak-to-peak amplitudes of pressure fluctuations both for the nine selected events marked in Figure 1b and for these three new events as a function of distance from the infrasound source. Magenta circles and blue diamonds are used for infrasound pulses associated with IC and CG discharges. Red asterisks mark infrasound pulses for which we have not found the causative discharge, and green squares represent infrasound pulses for which we could assign pairs of IC and CG discharges. Figure 8b represents an attempt to normalize the infrasound response on peak current of the discharges (the meaning of symbols is the same as in Figure 8a). This attempt should be considered with caution. First, we normalized the amplitudes of unassociated infrasound pulses (red asterisks) by a median value of all recorded IC discharges (7 kA). Second, we do not know the duration of the discharges, which also plays a role in the normalization [Assink et al., 2008]. For the distant sources, associated with IC and CG discharges, we assumed peak currents of IC discharges (green squares); additionally, we also plotted the amplitudes normalized by peak currents of CG discharges (blue diamonds) and IC discharges (magenta circles) for distances determined from the EUCLID detection. All the previous distances are estimated, as before, from the time delay between the infrasound response and related rapid change of Ez (which corresponds with the ~0.1 s precision with the time of particular discharge). Figures 8a and 8b show that the pressure amplitudes associated with IC discharges are usually higher than pressure amplitudes associated with CG discharges. Thus, we consider that our measurements support the electrostatic mechanism rather than the thermal expansion. A much larger amount of data is however needed to get statistically reliable information and to evaluate relative contributions of the thermal expansion and electrostatic mechanism on the infrasound production. We also cannot exclude that the relative contributions of electrostatic and thermal expansion mechanisms vary from thunderstorm to thunderstorm. We hope to address this question in the future. We also want to install basic meteorological measurements to have better information about the possible wind perturbation of the measurements since winds are the main source of uncertainties in infrasound studies.
 It is important to note that if a “double layer” (positive charge region just below the main negative charge region) is a dominant mechanism for infrasound thunder, then compression will be observed on the ground first, whereas a decompression will advance the positive perturbation above the main negative charge region (probably at a “sufficient” distance from a discharge channel in the case of IC discharge). Thus, such a mechanism could be potentially recognized in future multipoint experiments.
 Distinct infrasound narrow pulses (thunderbolts) in the frequency range from ~0.25 to ~3 Hz were observed by the microbarometer array. It should be noted that the sensitivity of microbarometers used falls for frequencies higher than 4 Hz. The pulses started by a compression phase and followed by a rarefaction. The ratio of positive to negative pressure fluctuations (absolute values) was close to 1 or slightly higher. All the distinct infrasound pulses were preceded by a rapid change of electrostatic field Ez measured on the ground (at the microbarometer array). Assuming that the change of electrostatic field is responsible for the infrasound production, or better to say corresponds with the time of infrasound production, we determined the distances of the infrasound sources from the array center for the selected distinct infrasound narrow pulses from the time delays between the infrasound pulses and preceding changes of Ez. For the near sources (~4.7 to 7 km), the infrasound thunder arrived from above or from high-elevation angles, whereas for the distant sources (~15 km), the infrasound propagated almost horizontally, and the estimated back azimuths were consistent with the azimuths to detected lightning.
 The frequency range of the selected narrow pulses, observed rapid changes of electrostatic field before the detections of infrasound narrow pulses, high-elevation angles of infrasound for near sources, and the fact that mostly IC discharges can be associated with the selected infrasound events support the hypothesis that an electrostatic mechanism is probably responsible for their production. It was however discussed that the presented measurements make it impossible to evaluate the relative contribution of thermal and electrostatic mechanism. None of the existing models of electrostatic mechanism [Dessler, 1973; Few, 1985; Pasko, 2009] fit our simultaneous infrasound and electrostatic observations precisely. We think that a modification of the existing models is still needed and that a consideration of two or more charged layers in theoretical models together with future multi-instrument and multipoint observations could help to contribute to clarification and more precise description of infrasound production. Calculations based on realistic charge distributions inside a thundercloud and realistic electric field intensities at the boundaries of the charged layers together with experimental measurements (infrasound, electrostatic, electromagnetic, radar, in situ, etc.) could contribute to a better understanding of infrasound production by the electrostatic mechanism.
 The support by the grant 205/09/1253, P209/12/2440 of the Grant Agency of the Czech Republic and seventh RF EU project ARISE 284387 are acknowledged. All member organizations of EUCLID are acknowledged for providing the lightning data.