Monte Carlo simulations of the runaway breakdown of air are used to calculate the spectra of terrestrial gamma‐ray flashes (TGFs), which are then compared with RHESSI and CGRO/BATSE observations. It is found that the recent RHESSI spectrum is not consistent with a source altitude above 24 km but can be well fit by a source in the range of 15–21 km, depending upon the electric field geometry of the source. Because 15 km is not unusual for the tops of thunderstorms, especially at low latitudes, and is lower than typical minimum sprite altitudes, the RHESSI data imply that thunderstorms and not sprites may be the source of these TGFs. On the other hand, the soft energy spectrum seen in some BATSE TGFs is inconsistent with such large atmospheric depths, indicating that there may exist two distinct sources of TGFs, with altitudes below 21 km and above 30 km.
