Gamma radiation observed in space has been associated with lightning flashes in thunderstorms. These special flashes do not appear to be the large and energetic positive ground flashes that also produce sprites. Considerations of gamma ray attenuation in air indicate that such flashes may not produce gamma radiation at sufficient altitude to enable their escape to space. High-altitude intracloud lightning, most prevalent in the tropics where the tropopause is also high, may be a necessary source.
 Eighty years ago, Wilson [1925, 1929] anticipated two thunderstorm-related phenomena well in advance of their recent discovery. One was the expectation that lightning flashes with exceptional charge transfer to ground would be capable of ionizing the middle atmosphere, a phenomenon now recognized as sprites [Sentman and Wescott, 1993; Lyons, 1994]. The second was the expectation that the large potential differences in thunderclouds (10–100 MV) would provide for runaway electrons and ultimately gamma rays, at cloud top. BATSE satellite observations had shown an association between gamma rays and disturbed weather [Fishman et al., 1994] and a link between gamma rays and lightning [Inan et al., 1996]. Recent satellite observations [Smith et al., 2005] have confirmed the presence of terrestrial gamma rays, and complementary ground-based electromagnetic observations [Cummer et al., 2005] confirm their association with lightning flashes. A current puzzlement is why the exceptional lightning flashes responsible for sprites do not coincide with the lightning flashes that appear to send gamma rays to space. This study is concerned with a possible resolution to this puzzle.
2. RHESSI Satellite Observations of Gamma Rays
 Numerous bursts of gamma rays emanating from the atmosphere below the RHESSI (Reuven Ramaty High Energy Solar Spectroscopic Imager) satellite have been documented by Smith et al. . Figure 1 shows the global distribution of events detected in the time interval March 2002 to October 2005 This global map is broadly consistent with the global distribution of lightning [Christian et al., 2003], though the tropical belt (±23°) is preferentially emphasized, with North America and other extratropical regions with prevalent lightning rather sparsely represented in gamma ray events. The three tropical “chimneys” are discernible, with evidence for African dominance in areal density, consistent with earlier lightning comparisons [Williams and Sátori, 2004].
 The gamma ray energy spectra at satellite altitude [Smith et al., 2005] show mean energies of ∼2 MeV, with a sustained tail to over 20 MeV, an appreciable fraction of the potential differences known to be present in thunderclouds [Marshall and Stolzenburg, 2001]. The number of detected gamma rays per RHESSI event is quite modest—about 30 photons, with indications that a strong majority of events are within a factor of two of the detection threshold.
 On the basis of comparisons of observed RHESSI photon spectra and Monte Carlo simulations, Dwyer and Smith  have recently inferred a source altitude for the gamma rays of 15–21 km. This finding is consistent with the main results in the present work.
3. Candidate Lightning Flashes for RHESSI Gamma Rays
 The gross electrical structure of ordinary thunderclouds [Williams, 2001a] and mesoscale convective systems [Shepherd et al., 1996; Williams and Yair, 2006] are reasonably well established, as are the common lightning flashes occurring therein. Figure 2 illustrates four well-recognized flash types in their parent thunderstorms, all initial candidates for producing gamma rays at satellite altitude. Roughly 90% of all cloud-to-ground lightning flashes exhibit negative polarity (Figure 2a), lowering charge from the lower terminal of the prevalent positive thunderstorm dipole [Rakov and Uman, 2003]. The other 10% of ground flashes transfer positive charge to ground and are of two types—flashes from the upper charge reservoir (near cloud top) of a tilted dipole in cumulonimbus clouds (Figure 2b), and the so-called “spider” flashes in laterally extended stratiform precipitation (Figure 2c) in which the predominant positive charge reservoir is near cloud base (4–5 km) [Shepherd et al., 1996; Williams, 1998, 2001b; Lyons et al., 2003]. The tilted positive dipole is frequently linked pictorially and in theoretical models [Bell et al., 1995; Pasko et al., 1995, 1996, 1997; Inan, 2002] with the energetic sprite-producing positive ground flashes, but observations supporting the prevalence of Figure 2b related to sprite formation are scant. Indeed, detailed VHF radio maps of lightning flashes do not show Figure 2b as a prevalent lightning type at all (P. Krehbiel, personal communication, 2004). Numerous observations [Boccippio et al., 1995; Williams, 1998; Lyons et al., 2003; Williams and Yair, 2006] make a stronger link with the mesoscale structure in Figure 2c as the configuration most often responsible for sprites. A key distinction in the present study is the height above ground of the positive charge reservoir for the respective ground flash. Following observations by Lyons et al. , the extraordinary charge moments of such flashes [Huang et al., 1999; Hu et al., 2002] are generally attributed to the laterally extended positive charge reservoir (Figure 2c) rather than to its exceptional height (Figure 2b).
 The most common lightning flash globally, and particularly in the tropics [Mushtak et al., 2005], is the intracloud flash bridging upper positive and lower negative charge (Figure 2d). This lightning type is characterized by vertical charge moments in the 20–200 Coulomb-kilometers (C-km) range [Koshak, 1991]. The higher tropopause confined to the tropical belt (±23°) [Wallace and Hobbs, 1977] allows the possibility for the upward negative ends of the lightning flash to extend to 16 km or higher, in contrast with the behavior in Figure 2c.
 Which of these flash types can be linked physically with gamma rays? Cummer et al.  have recently documented 26 lightning flashes closely associated with RHESSI satellite-detected gamma rays with ELF/VLF electromagnetic methods. Inan et al.  had earlier documented a lightning flash which produced gamma rays detected by the BATSE satellite [Fishman et al., 1994]. None of the flashes in either study had a polarity consistent with the negative ground flash in Figure 2a, which can therefore be rejected as a source. The three remaining candidates (Figures 2b, 2c, and 2d) all involve upward progressing negative leaders.
 An important and surprising finding by Cummer et al.  is the absence of large moment changes in the lightning flashes associated with the RHESSI gamma rays. The mean vertical charge moment (49 C-km) is more than an order of magnitude less than the threshold shown necessary for sprite occurrence [Huang et al., 1999; Hu et al., 2002]. The sprite-producing positive ground flashes with exceptional charge moments (>500 C-km) have been clearly identified as the most energetic flashes on the planet. The null results of Cummer et al.  on gamma ray links with this exceptional lightning type have been corroborated more recently by numerous other global electromagnetic searches for coincident lightning flashes with large charge moments.
 What diagnostics on the lightning causal to gamma radiation are available with ELF methods? The polarity of the lightning is readily determined from the initial excursion of the vertical electric field. The vertical charge moment is accessible with calibrated ELF measurements [Huang et al., 1999] with a typical sensitivity below the threshold for sprites (∼500 C-km). (The vast majority of lightning flashes have moment changes substantially smaller than this, and are lost from detection in the Schumann resonance “background”.) The distinction between intracloud and cloud-to-ground lightning flashes is more problematic with ELF observations alone. Numerous ELF stations are now operational with the capabilities here described, including Hungary, Israel, Japan and the United States. An additional VLF network with coverage over Africa and the Americas has also been used in this study.
 Observations in the lower ELF region at the Nagycenk Observatory in Hungary [Sátori et al., 1996] have revealed no significant lightning transients coincident with 84 gamma ray events documented with the RHESSI satellite in July and August 2004 and from February to June 2005. Timing comparisons have been made at the millisecond level.
 ELF observations by Tel Aviv University in the Negev Desert of Israel [Price and Melnikov, 2004] for eight RHESSI events have disclosed one case (26 April 2004; 15:05:12.337 UT) for which an ELF transient was detected within 1 s (the time resolution of the ELF observations) of a RHESSI event, and located consistently with the satellite position. This lightning flash showed positive polarity, and a charge moment of 150 C-km, well below the threshold recognized for sprite occurrence [Huang et al., 1999; Hu et al., 2002].
 ELF observations by Tohoku University [Sato and Fukunishi, 2003] in Japan have been associated with thirty RHESSI events. For about half of these cases, the ELF signal is too small to make charge moment estimates. For the other half of the events, the charge moments are less than 100 C-km, and hence substantially smaller than the sprite initiation threshold. All of these thirty events were well timed (at the 10–20 ms level of accuracy) with RHESSI cases, indicative of lightning events. They furthermore showed positive polarity, consistent with lightning origins with ascending negative leaders.
 ELF observations at Moshiri, Hokkaido, Japan (44.29°N, 142.2°W) [Hobara et al., 2001; Ando et al., 2005] for 41 RHESSI events in the 3-month period November 2004 to January 2005 indicate no significant related ELF transients. Event comparisons were made at the millisecond level.
 Electromagnetic observations in West Greenwich, Rhode Island at MIT's Schumann resonance station showed no triggered events, following procedures detailed by Huang et al. , for eight RHESSI events in January 2005. Event comparisons were made at the millisecond level.
 VLF observations by the University of Connecticut using a network of VLF receivers in the African continent [Chronis and Anagnostou, 2003] have revealed three possible lightning events associated with RHESSI gamma rays, among 54 satellite detections checked for 2003 and 78 events for 2004. Two of these events showed a timing offset with RHESSI of less than one millisecond, as with some comparisons of Cummer et al. . Unfortunately, neither charge moment estimates nor polarities are available for these events. The sparsity of the “finds” is however indirect evidence that the source strengths for the parent lightning events are not exceptional.
 These collective results from several different locations worldwide cast substantial doubt on Figure 2c as a source for satellite-detected gamma rays.
 Given the substantial observational evidence against the prevalence of Figure 2b in the literature, the only remaining lightning candidate for gamma rays is Figure 2d. This intracloud scenario is further substantiated by observations with the Los Alamos Sferic Array (LASA) [Stanley et al., 2006] that provide evidence for intracloud flashes with source altitudes of 12–16 km. No ground flashes have been identified in association with RHESSI events in the latter study.
 The remainder of this paper is concerned with an explanation for why intracloud flashes may be necessary for the satellite-detected gamma rays.
4. Gamma Ray Survival From Thunderstorm to Satellite
 The interaction of gamma rays with atmospheric air and their attenuation with distance have been studied extensively [Gray, 1972; Glasstone and Dolan, 1977]. Figure 3 summarizes the results on mass attenuation coefficient over a range of energies appropriate to the problem at hand. For gammas in the MeV range, Compton scattering and the transfer of photon energy to kinetic energy of electrons is the dominant loss mechanism. Multiplication of the mass absorption coefficient by the density of air gives the reciprocal e-folding distance for photon flux. These distances h(E) for air at mean sea level are depicted on the right-hand axis in Figure 2. Specific e-folding lengths are 120 m for 1 MeV, 220 m for 3 MeV and 380 m for 10 MeV gamma rays [Glasstone and Dolan, 1977], all distances small in comparison with the scale height for density in the atmosphere (7000 m). This scale comparison places a strong constraint on the transfer of gamma rays from lightning in thunderstorms to the altitude of the RHESSI satellite (550–600 km).
 The results in Figure 3 can be used to estimate the gamma flux at satellite altitude for an arbitrary height of origin. Air density varies inverse exponentially with altitude as
where ρo = 1.2 kg/m3 and H = 7000 m. The total atmospheric mass per unit area between the source height ZS and the satellite altitude (550–600 km, many tens of scale heights and so effectively, infinity) is the integral of (1):
The upward gamma ray flux at satellite altitude, F∞, is exponentially attenuated from its initial value FS at the height of origin ZS according to
where the e-folding length as a function of photon energy h(E) is obtained from Figure 3. This reduces to a nondimensional ratio
The strong dependence of satellite-observed flux on the source height is evident in this simple analytical treatment. Numerical results for the flux ratio are shown in Figure 4 for three gamma ray energies.
 The working hypothesis for this study is that upward propagating gamma rays originate in the high-field regions of upward moving negative leaders in lightning. Electrons are repelled at the negative end of the double-ended tree where they gain energy in a runaway process [e.g., Gurevich et al., 1992] that sends energy away from the lightning discharge. Leaders are highly conductive and hence capable of concentrating the potential differences available in a thundercloud over a relatively small scale. This scenario is based on a growing number of ground-based observations of X-ray/gamma ray [Moore et al., 2001; Dwyer et al., 2004a, 2004b, 2005], also in the vicinity of negative leaders, as illustrated in Figure 2a. The source altitude for the gamma radiation recently inferred by Dwyer and Smith  is consistent with a central role for the negative upper end of intracloud lightning flashes (Figure 2d).
 The calculations in Figure 4 illustrate the critical role of source altitude in allowing the escape of high-energy photons to space. The steep behavior of upward flux with source altitude is attributable to the smallness of the e-folding path lengths for gamma rays in comparison to the density scale height. For gamma ray energies near the mean value observed by RHESSI [Smith et al., 2005], a factor-of-three increase in source height ZS from 5 km to 15 km, reflecting a difference in source lightning type from Figures 2c to 2d, results in more than a five decade increase in flux at satellite altitude. At the maximum gamma ray energy found by Smith et al.  (10 MeV), the change in flux for the same threefold change in source height is still three orders of magnitude. Given the already marginal quantity of photons detected per event by RHESSI, this degradation in photon flux from sources deep in the troposphere could easily account for the absence of gamma ray detections from giant lightning flashes of the kind illustrated in Figure 2c (Cummer et al.  and the additional null results discussed here).
 The considerable sensitivity of upward gamma flux to source altitude may also offer an alternative explanation for the relative absence of RHESSI events in North America and other lightning-active extratropical regions, as illustrated in Figure 1. The tropopause height is a good indicator of maximum cloud tops for all but the most extreme thunderstorms (those that overshoot the tropopause by 1–5 km). In the tropics, where RHESSI events are notably more prevalent, the tropopause height is ∼16–17 km. At higher latitudes (i.e., North America), the summertime tropopause is distinctly lower, at 11–13 km, and this transition is fairly abrupt at the tropical boundary [Wallace and Hobbs, 1977] in Figure 1. According to Figure 4, the difference in gamma ray flux for lightning sources at the tropopause in these two latitude ranges is an order of magnitude for the mean observed gamma ray energy (2 MeV), and a factor of five for 10 MeV gammas at the high-energy limit.
 The conspicuous absence of sprite events linked with RHESSI gamma ray events in the collective observations could in principle be caused by the rarity of sprites within the satellite field of view. This suggestion appears unlikely. Current estimates of the global sprite rate [Sato and Fukunishi, 2003; Y. Takahashi, personal communication, 2005] are 10–100 times greater than the global terrestrial gamma ray event rate (∼50 per day, Smith et al. ). The estimated mean wait time for RHESSI to have a sprite within its field is of view is 30–60 min, far shorter than the total viewing period to date (∼1300 days).
 The marginal number of photons (∼30) recorded in RHESSI events is a good indication by itself that many events are missed. This marginal photon yield is also consistent with the conclusion that the source region is in the upper troposphere/lower stratosphere, from which substantial attenuation is still present in the path to the satellite (Figure 4).
 Given the extensive evidence that sprites are initiated by the electrostatic field of the energetic positive ground flashes [Pasko et al., 1995; Boccippio et al., 1995; Williams, 2001b; Hu et al., 2002], suggestions were raised about a possible electron runaway process near 70–75 km, in a vertical field favorable for upward acceleration of electrons [Chang and Price, 1995]. The available measurements [Huang et al., 1999; Hu et al., 2002] favor conventional breakdown at this altitude, and the huge avalanche lengths (hundreds of kilometers) expected theoretically in the runaway process in low-density air [Gurevich et al., 1992; Gurevich and Zybin, 2005] discourage a runaway process at this high altitude. On the basis of the foregoing, the expectation remains that the height of origin of the gamma rays associated with thunderstorms will be at lower altitude.
 One earlier case of a lightning-associated gamma ray burst with the BATSE satellite [Inan et al., 1996] also deserves some discussion, in light of the more recent findings by Cummer et al.  and in the present study. The VLF sferic of Inan et al.  for the event in question showed the weakest amplitude among 10 other lightning events shown, a result out of line with other evidence for sprite events [Huang et al., 1999]. The sferic polarity was consistent with a positive ground flash, but it was also consistent with the polarity of the intracloud lightning in Figure 2d. A weak “slow tail” signature was also evident, interpreted by Inan et al.  as a continuing current in a positive ground flash. In his classical theoretical analysis, Wait  argued that the slow tail could be explained by an impulsive lightning (without continuing current) and subsequent dispersion in the Earth-ionospheric waveguide. In summary, the evidence from this single event is not at variance with the idea here that the lightning type causal to gamma ray bursts is an intracloud flash.
 Some caveats deserve discussion in this study. The calculations presented in this paper are highly simplified. The reduction of gamma ray energy loss to a simple exponential e-folding process with a single length scale ignores the cascade of particle energy and momentum that is more accurately treated with a Monte Carlo technique [e.g., Dwyer, 2003; Torii et al., 2004; Dwyer and Smith, 2005]. The smaller the photon energy, the more important is the cascade from higher to lower energy, and the less meaningful are the simplified calculations presented here. For this reason, only gamma rays in the high-energy “tail” are treated in Figure 4. The one-dimensional assumption also ignores the probable localized origin of the gamma rays and their spreading during their escape through the atmosphere to the satellite. Nevertheless, the strong dependence of upward flux on the source altitude is expected to retain its validity and provide a plausible explanation for the absence of satellite-detected gamma rays originating from low-altitude lightning.
 Simple considerations of gamma ray attenuation in the atmosphere suggest a strong dependence of upward flux on source altitude. Assuming that gamma rays originate in the vicinity of negative lightning leaders, the escape of gammas to RHESSI satellite altitude is far more likely from the upper troposphere/lower stratosphere (15–21 km) than from the middle troposphere (5 km). These results afford an explanation for why the largest and most energetic lightning flashes in the troposphere have not been paired with satellite-observed gamma rays in available observations. The calculations also provide an explanation for the infrequence of gamma rays from lightning at extratropical latitudes, where the maximum altitude of lightning extent is reduced. The apparent absence of gamma rays at RHESSI satellite altitude from positive ground flashes is no guarantee that this kind of lightning did not produce them, but only that they were unable to escape the atmosphere to be detected.
 Discussions on this topic with B. Blake, S. Cummer, J. Dwyer, K. Eack, U. Ebert, A. Gurevich, C. Hogg, R. Holzworth, U. Inan, W. Lyons, T. Marshall, S. Mende, G. Milikh, V. Pasko, R. Roussel-Dupré, D. Sentman, X.-M. Shao, and M. Stanley are gratefully acknowledged. Valuable assistance with the analysis of the ELF observations in Hungary was provided by Veronika Barta and Miklós Balázs from Eötvös Loránd University. The sustained use of the Alton Jones Campus of the University of Rhode Island for MIT's ELF measurements, facilitated by T. Mitchell and his associates, is much appreciated. This study was supported by the Physical Meteorology section of the National Science Foundation on grant ATM-0003346.