The characteristics of thunderstorms that produce terrestrial gamma-ray flashes (TGFs) observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) are determined using climatological and meteorological data. RHESSI observed TGFs follow diurnal, seasonal, and geographic patterns that are very similar to those of thunderstorms confirming, in part, that these events are directly connected to thunderstorm activity. The TGF producing thunderstorms are shown to be closely associated with tall (ranging from 13.6 km to 17.3 km) tropical thunderstorm systems, a finding that is consistent with theoretical expectations from models of relativistic breakdown that relate the source region to the spectral signatures observed by RHESSI. Unlike sprites, there appears to be no predilection for TGFs to occur with large thunderstorm complexes. Rather, TGF producing thunderstorms are shown to range in areal extent by several orders of magnitude. Analysis of a single TGF event within the Mozambique Channel indicates an elevated mixed phase (both liquid water and ice present) level of approximately 6 km which is consistent with the climatological findings.
 Satellite observed terrestrial gamma-ray flashes (TGFs) from the Burst and Transient Source Experiment (BATSE) and the Reuven Ramaty High-Energy Solar Scectroscopic Imager (RHESSI) are well documented [e.g., Fishman et al., 1994; Smith et al., 2005]. Using Monte Carlo simulations of runaway breakdown, Dwyer and Smith  estimated the source altitude of these TGFs were between 15 and 21 km and thus suggested that thunderstorm tops might be the source region. Observed TGFs have been directly associated with specific lightning events [Inan et al., 2006; Cummer et al., 2005] and have been related to large thunderstorm systems [e.g., Fishman et al., 1994; Huang et al., 2005]. There is also evidence that TGFs emanate from source regions near and above thunderstorm top [Williams et al., 2006; Østgaard et al., 2008; N. Østgaard et al., Production altitude, initial distributions and time delays for TGFs when instrumental deadtime effects are treated properly, paper presented at Chapman Conference, AGU, University Park, Pa.] and associated with positive intracloud discharges [Stanley et al., 2006; Williams et al., 2006]. Here we further establish and provide a more direct link between RHESSI observed TGFs and thunderstorm systems and then examine what we believe to be relevant characteristics of the TGF producing thunderstorms and the TGF thunderstorm environment. The data used for this investigation are first presented followed by a global analysis of the TGF events that includes both their temporal and geographical distributions. An analysis of the ambient buoyancy and cloud top height are also presented for the global data set. A subset of “single storm” TGF events (29) is then selected for analysis. Finally, a case study for a single TGF event that occurred within the Mozambique Channel is presented.
2. Supporting Data
2.1. Meteorological Observations and Analyses
 Given that radiosonde data can be geographically sparse in locations where these events are frequent, global atmospheric reanalysis products are used in lieu of the radiosonde data. The reanalysis data are also used to generate seasonal averages of atmospheric fields that are not provided by the radiosondes. Two sets of atmospheric analyses are used here: (1) the National Centers for Environmental Prediction (NCEP)-National Center for Atmospheric Research (NCAR) reanalysis [Kistler et al., 2001] and (2) the European Center for Medium Range Weather Forecasts' (ECMWF) Interim analysis (ERA-Interim) which is an extension and improvement in the 40-year analysis product (ERA-40) [Uppala et al., 2005]. These analysis systems directly assimilate radiosonde data as well as a multitude of other in situ and remotely sensed data sets. Here, the radiosonde data is used when available to help determine thunderstorm top altitude as these data have greater vertical resolution than the global analyses. The horizontal resolution of the NCEP-NCAR reanalysis and ERA-Interim products are provided at 2.5° and 1.5°, respectively, though the analyses are conducted at higher resolution. The ERA-Interim grid resolution is depicted in Figure 1 with a hypothetical RHESSI footprint and a convective season GOES visible image in the Florida region. The analyses contain data on constant pressure levels, at the surface and top of atmosphere. Also available are derived meteorological indices, vertically integrated quantities, etc.
2.2. Satellite-Based Remote Sensing Systems
 The primary remote sensing data used herein are infrared radiances from geostationary satellites and include the following sources for worldwide coverage: GOES-9, GOES-10, GOES-12, GMS, Meteosat-5, Meteosat-7, and MTSAT. Infrared radiances are also obtained from the low-Earth-orbit Tropical Rainfall and Measurement Mission (TRMM) [Theon, 1993; Kummerow et al., 1998] satellite for a case study. The infrared radiances are used to obtain estimates of cloud top temperature for thunderstorm systems as well as for the determination of thunderstorm size using thunderstorm anvil size as a proxy. TRMM data are also used to obtain estimates of cloud liquid water and cloud ice for both seasonal periods and a case study. The TRMM vertical resolution for these data is 0.5 km between the surface and 4.0 km, 1.0 km up to 6.0 km, 2.0 km up to 10.0 km, and 4.0 km up to 18.0 km. Climatological TRMM Lightning Imaging Sensor (LIS) and Optical Transient Detector Data (OTD) global diurnal flash rate estimates provided by the Global Hydrology Resource Center, Marshall Space Flight Center, NASA are also used to compare to TGF diurnal occurrence rates.
2.3. Lightning Data
 The very low frequency (VLF) based World Wide Lightning Location Network (WWLLN) [Lay et al., 2004] data were used to help identify single storm cases in which a specific thunderstorm can be associated with a RHESSI identified TGF event. The selection criteria for these cases include the following: (1) at least five WWLLN strikes occur within 20 min and 600 km of the RHESSI at the TGF observation time (i.e., within the large RHESSI footprint) and (2) the RMS distance from the WWLLN strikes to the average WWLLN strike position is less than 100 km. The WWLLN absolute location accuracy is roughly 20 km [Lay et al., 2004].
3.1. Diurnal Variation of RHESSI Observed TGFs
 RHESSI identified TGF event times for 805 TGFs from March 2002 through December 2007 are converted to local solar time (LST) to determine the diurnal distribution of the TGFs. In addition, TGFs are also geographically segregated into oceanic-based, coastal-based, and land- based events determined by the location of RHESSI at the event time. Coastal events are defined to be within 200 nautical miles (370 km) of the coastline. Figure 2a shows the diurnal TGF trend. While the RHESSI location may be significantly different from the actual TGF source location given its large footprint, the number of oceanic cases is substantially less than that in either coastal regions or over land. The diurnal minimum and maximum in TGFs near 1200 LST and 1700 LST, respectively, are consistent with the diurnal variation of thunderstorms reported by Dai  as is the scarcity of oceanic events and the large amplitude of the diurnal cycle for land-based thunderstorms. Diurnal lightning flash (in-cloud and cloud-to-ground) rate estimates from a 5 year combined TRMM LIS and OTD detectors are also included in Figure 2a. The TRMM diurnal flash rate product is provided on a 2.5° grid at hourly time resolution. The data were spatially averaged over the full horizontal extent of the grid for each hour to produce an average flash rate for each hourly time interval.
 Although the diurnal variation between TGFs and the global lightning flash rates is well correlated, it appears as if the number of TGFs during the 0000 to 1000 LST time period may be disproportionately large. In an effort to examine this issue, the relative abundance of TGFs as compared to the diurnal lightning curve is calculated in two ways here. For both methods the number of observed TGFs per hour are converted into a daily fraction. For the first method, the hourly values of the mean diurnal curve between 35 N and 35 S are converted into fractions of the daily total. The fractional hourly TGF values are then divided by the fractional LIS/OTD lightning values and constitute the scaled TGF-lightning ratios. The second method addresses issues associated with geographic variations in the diurnal cycle. In this method, for each TGF location, the LIS/OTD diurnal hourly values are scaled by their daily total. These scaled hourly values are then averaged for the full set of TGFs. Both of these scaled TGF-lightning ratios indicate a higher efficiency for TGF production between the hours 0300 and 0900 LST (Figure 2). The second method shows a lower diurnal amplitude in the scaled TGF-lightning ratio, suggesting that some of the diurnal signal may be explained by the geographical distribution of TGFs. Using a similar scaling approach for addressing geographical diurnal variations of TGFs, Hazelton  noted that coastal zones had a higher TGF-to-lightning ratio than either land or ocean zones. An important caveat for these diurnal scalings is that the combination of a large RHESSI footprint and coarse resolution of the LIS/OTD diurnal climatology data set may produce an erroneous diurnal cycle, especially where flash density gradients are high. For example, TGFs over land but in proximity of the coastline might be incorrectly identified as oceanic thus biasing in the inferred diurnal signal.
3.2. Geographic Distribution of RHESSI Observed TGFs
 The geographic distribution of 805 RHESSI identified TGF events from 2002 to 2007 are shown in Figure 3. TGF occurrences are frequent near coastlines, large islands, peninsulas, and isthmuses in the tropics where low level atmospheric convergence is often enhanced and promotes thunderstorm development. Although TGF occurrence over the oceans is generally low, they are more frequent over Oceania where many island systems are present. TGFs also frequently occur over central and southern Africa and from Southeast Asia to northwest Australia. The TGF distribution is well correlated with global lightning distributions [e.g., Christian et al., 2003] with the exception of regions where the RHESSI spacecraft's ability to observe TGFs is limited such as in the vicinity of the Southern Atlantic Anomaly (SAA). This explains the dearth of TGF observations in regions of high lightning frequency over South America.
3.3. Seasonal Migration of RHESSI Observed TGFs
 Given their correlation to tropical thunderstorms, it should be expected that TGFs will follow the seasonal migration of deep convection. Two seasons are focused on here: (1) December–January–February (DJF) representing the southern hemisphere summer and (2) June–July–August (JJA) representing the northern hemisphere summer. The NCEP-NCAR reanalysis monthly sea level pressure data are averaged over 30 seasons to provide a representation of the mean lower tropospheric global weather patterns. In addition, TRMM monthly averaged cloud liquid water content, in the 10 to 14 km layer, was seasonally averaged over 9 available years to identify zones where liquid water is being lofted high by atmospheric convection. The TRMM cloud liquid water estimates are scaled by a RHESSI detection efficiency factor (Figure 4) that accounts for the exposure time and sensitivity of the instrument [Grefenstette et al., 2009]. The decreased sensitivity of the RHESSI detector due to high background noise levels in the SAA accounts for the low scaling factors in that region. The DJF and JJA RHESSI TGFs are shown to seasonally migrate along with the predominant tropical convergence zones, mainly the intertropical convergence zone (ITCZ, the solid gray lines in Figure 5). The TGFs are embedded within regions where the scaled 10–14 km liquid water content is relatively high, indicating the TGFs are occurring in zones of deep tropical convection. Seasonal averages of the scaled TRMM 10–14 km cloud liquid water and cloud ice content were performed to assess mixed phase potential which is important for cloud electrification. Scaled cloud ice content for JJA (Figure 6) is found to be prevalent in regions where TGFs are not observed, such as along the ITCZ in the Atlantic and Pacific Oceans. However, in these regions, cloud liquid water is low, underscoring the importance of the mixed phase.
3.4. Convective Available Potential Energy
 A common meteorological measure of thunderstorm potential is the convective available potential energy (CAPE). CAPE is a measure of the buoyancy available for convective updrafts. Estimates of CAPE for 805 RHESSI TGF events between 2002 and 2007 were obtained from the ERA-Interim atmospheric analysis data set. Given the large RHESSI footprint, the CAPE values do not necessarily reflect conditions at the true TGF location. To provide a baseline for comparison, CAPE estimates corresponding to the times of the RHESSI TGF events were obtained from random tropical locations between 30°N and 30°S which includes the large majority of observed TGFs. The expectation is that CAPE from the TGF locations will, on average, be higher than the tropical background. Figure 7 indicates that the distribution of CAPE values near TGF locations is in fact shifted toward higher values of CAPE as compared to the tropical background. A number of TGF events appear to be associated with little or no CAPE, but these may be cases where the CAPE at the RHESSI location may not be representative of the actual TGF location. Also, convectively active regions may have areas that have been cooled by thunderstorm downdrafts and thus have little or no CAPE.
3.5. Outgoing Infrared Thermal Flux
 Similar to the analysis of CAPE, the ERA-Interim analyses are used to evaluate the outgoing atmospheric infrared flux. The expectation is that the outgoing infrared flux values will be shifted toward lower values at RHESSI identified TGF locations because thunderstorms anvils, which emit at relatively cold temperatures, would be more likely at these locations. Indeed, the outgoing flux is shown (Figure 8) to be shifted to lower values for the RHESSI TGF locations as compared to randomly selected locations in the tropics, indicating the RHESSI satellite is, at the very least, observing regions with high level cloudiness (e.g., thunderstorm anvils). For perspective, estimates of outgoing infrared radiation from tropical thunderstorms have been shown to range between approximately 80 and 180 Wm−2 with a peak near 125 Wm−2 [Eitzen and Xu, 2005]. Because the RHESSI position may be offset from the actual TGF producing thunderstorm by as much as 600 km, the RHESSI location can be in regions with lower cloud tops or no cloud at all. Thus estimates of outgoing infrared radiation at these locations are expected to be shifted toward higher (warmer) values. Also, small thunderstorms will not be well resolved in the analysis products and will likely be biased warm.
3.6. Single Storm Data Set Analysis
 Given what appears to be overwhelming evidence here and in past studies that RHESSI observed TGFs are associated with thunderstorms, an analysis is conducted to better understand the characteristics of TGF producing thunderstorm systems. The subset of single storm events described earlier (section 2.3) is analyzed to provide estimates of storm size and storm height. The subset contains 29 events that are distributed globally throughout the tropics and thus provides a representative geographic sampling of TGFs.
 The height of TGF producing thunderstorms is estimated using the cloud top temperature obtained from the geostationary satellites. Thunderstorm height is determined using proximity radiosonde data by converting the minimum observed satellite brightness temperature to a height estimate assuming that the cloud top is in approximate thermal equilibrium with the atmosphere. Atmospheric analyses were used in lieu of radiosonde data for five cases in which no proximity radiosonde data were available. Sherwood et al.,  have shown that cloud top estimates from GOES IR data can be biased low by as much as 2.0 km for deep convection with an average underestimate of approximately 1.0 km. Cloud top height estimates for the TGF producing thunderstorms (Figure 9) ranged from a 13.6 km to 17.3 km with an average of 15.3 km without accounting for bias. The range in heights is consistent with the theoretical estimates previously noted by Dwyer and Smith , though this does not preclude the possibility that TGF sources were actually from lower sources. But, the dropoff in the number cases when cloud top heights fall below 15.0 km may indicative of a threshold whereby TGFs are not observable by the RHESSI. This is especially relevant considering evidence that the frequency of deep convective systems in the tropics peaks between 12.0 and 14.0 km [Eitzen and Xu, 2005].
 The areal extent of TGF producing thunderstorms is evaluated using cloud top area (i.e., anvil). Here, the anvil is defined by the area where cloud top temperature is −60°C or less, though other temperature criteria can be used [e.g., McAnelly and Cotton, 1989]. The cloud top area for the single storm cases (Figure 10) spans several orders of magnitude ranging from 400 km2 (in an isolated thunderstorm off the coast of El Salvador) to 111,100 km2 (in a large monsoonal thunderstorm system in the Himalayas) with an average size of 26,500 km2. TGF producing thunderstorms that are observed by the RHESSI are not exclusively limited to larger convective systems, although larger systems may be more likely to have a TGF observed. These results are consistent with the observation that TGF-related lightning flashes are not associated with large charge moment changes [Cummer et al., 2005] in contrast to sprite producing large mesoscale convective systems [Lyons et al., 2008].
3.7. Case Study of TGF Producing Thunderstorm
 A case from the single storm data set was also observed by an overpass of the TRMM satellite within an hour of the TGF event. The TGF was observed by RHESSI over the Mozambique Channel on 2354 UTC 31 December 2004. TRMM passed over this storm approximately 55 min following the TGF event. The WWLN identified location and the position of the RHESSI relative to the TRMM observed cloud top temperatures are shown in Figure 11. Profiles of cloud liquid water content and cloud ice content for a vertical cross section through the thunderstorm complex are shown in Figure 12. Several regions with elevated mixed phase, when compared to the seasonal freezing level average of 4.75 km in this vicinity [Harris et al., 2000], are evident between 6 and 8 km, indicating the potential for cloud electrification at relatively high altitude. But, these fields could have evolved significantly in the 55 min delay between the observed TGF and TRMM overpass time. As discussed previously, the seasonal aspects of TGFs indicate a tendency for TGF producing thunderstorms to occur in regions where mixed phase cloud extends high into the troposphere. Although this case falls into that category, it is not conclusive with a single case that this is a necessary condition for TGFs to be observable by the RHESSI.
 Analysis of in situ and remotely sensed meteorological data indicates that RHESSI detected TGFs are both spatially and temporally correlated with tropical thunderstorm systems further establishing the link between the two. The ambient buoyancy and outgoing infrared radiation associated with TGF producing thunderstorms are substantially different than that obtained from randomly selected tropical locations. Analysis of individual thunderstorms from the subset of single storm events indicates average cloud top heights near 15 km, which is consistent with theoretical expectations. TGF producing thunderstorm area spans several orders of magnitude ranging from small isolated thunderstorms to large mesoscale convective complexes. A case study using TRMM data was observed to have an elevated mixed phase region which may indicate, along with climatological data, that the charging mechanisms may occur at high altitudes for these TGF producing thunderstorms.
 This work was supported by the NSF grant ATM 0607885. This work also reflects contributions from personnel no longer associated with the project, including Kathryn Shontz, Evelyn Rivera, and Dan Tyndall. TRMM data were made available by the Global Hydrology Resource Center.
 Amitava Bhattacharjee thanks Thomas Gjesteland and another reviewer for their assistance in evaluating this paper.