Source Altitude of Energetic In-Cloud Pulses Inside Thunderstorms and Implication for the Intrinsic Brightness of Terrestrial Gamma-Ray Flashes

Upward Terrestrial Gamma-Ray Flashes (TGFs) are mainly produced during the upward propagating negative leaders inside thunderclouds. The exact source position of TGFs, which is crucial to understanding TGF source properties, is still unclear. The link between positive energetic in-cloud pulses (+EIPs) and TGFs provides us with a potential target to aim at. In this study, the low-frequency radio emissions of 75 +EIPs are analyzed to retrieve the source altitudes with an improved ray theory model. Furthermore, the meteorology contexts of +EIPs derived from the ground-based weather radars and satellite-based infrared cloud top temperature measurements are investigated. +EIPs are produced at 8.8-13.7 km, with an average of 11.3 km inside thunderclouds, and at an average of similar to 2.5 km below cloud tops. These altitudes indicate that a total number of 1.7 x 1016 to 2.6 x 1018 gamma ray photons with energy greater than 1 MeV are required for an EIP-TGF to be measured by spaceborne detectors.