We use lightning sferics from the World Wide Lightning Location Network to identify storms near 362 Terrestrial Gamma‐ray Flashes (TGFs). The combined spectrum of TGFs with storms within 300 km of the sub‐satellite point is much harder than the spectrum of TGFs with more distant storms. When these data are compared with simulations of vertically oriented relativistic runaway breakdown, it is found that the most likely model has a source altitude of 15 km and a wide‐beam geometry. We find four associations of TGFs with individual sferics geolocated to positions more than 300 km from the sub‐satellite point and show that a narrow‐beam source at ≥21 km altitude is unlikely to produce the number of high energy photons in these TGFs.