# Implications of GNSS-Inferred Tropopause Altitude Associated with Terrestrial Gamma-ray Flashes
## 2 Data and Methodology  
In this work, we adopt the TGF observations from three space-borne missions: the RHESSI project from April 2006 to November 2013 [2], Fermi Gamma-ray Burst Monitor (GBM) from August 2008 to December 2019 [4; 5], and Insight Hard X-ray Modulation Telescope (Insight-HXMT) from July 2017 to September 2019 [29]. We use the quality-controlled temperature profiles from the following four missions and time periods: SAC-C (Scientific Applications Satellite C, [30]) from March 2006 to August 2011, COSMIC (Formosa Satellite Mission 3/Constellation Observing System for Meteorology, Ionosphere, and Climate, [26]) from April 2006 to present, GRACE (Gravity Recovery and Climate Experiment, [31]) from March 2007 to November 2017, TerraSAR-X [32] from February 2008 to present, MetOp-A (October 2007-December 2019), and MetOp-B (February 2013-December 2019) [33; 34; 35]. All data are available from the University Corporation for Atmospheric Research (UCAR) Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) Data Analysis and Archive Center (CDAAC) and are provided at 0.1 km vertical resolution from the surface to about 40 km altitude. SAC-C and TerraSAR-X acquire up to 250 daily occultations (temperature profiles), MetOp-A and B provide about 630-680 daily occultations, while GRACE retrieves about 150-200 occultations and COSMIC provides up to 2500 occultations per day, respectively. The observations from the TGF detectors and GNSS-RO are required to be within 300 km and \(\pm\)3 h of each other [28], resulting in 1917 TGF-related GNSS-RO temperature profiles. The spatial relationship between TGFs and associated lightning has been confined typically within 300 km based on the space-borne TGF detection and ground-based broadband spheric measurements [36; 37]. The authors of [36] found that the majority (about 75% for TGF-associated lightning discharges located with three or more stations) of TGFs are detected within 300 km of the associated lightning, and the authors of [38] attributed half of 2188 TGFs located within 300 km range from the associated lightning discharge. Tropopause altitudes are calculated for each GNSS-RO profile by employing the WMO temperature lapse rate tropopause definition [39], which defines the primary tropopause as the lowest altitude level at which the lapse rate is \(\leq\)2 \({}^{\circ}\)C km\(-1\) and the average lapse rate between that level and any higher levels within 2 km remains less than 2 \({}^{\circ}\)C km\(-1\). This definition relates directly to the static stability of the atmosphere and has been used widely in atmospheric convection studies. The WMO definition allows for additional tropopauses to be defined if, above the primary tropopause, \"the average lapse rate between any level and all higher levels within 1 km exceeds 3 \({}^{\circ}\)C km\(-1\), then a secondary tropopause is defined by the same criterion.\" The profiles that have a secondary tropopause are defined as double tropopause events [25; 40]. To avoid false tropopause identification and boundary layer inversions, the algorithm is applied only to altitudes above 5 km at the pole and 10 km at the equator according to \(7.5+2.5\cos(2\varphi)\) km, where \(\varphi\) is the latitude. The temperature profiles are time-averaged to construct a gridded monthly climatology with a 5\({}^{\circ}\)\(\times\) 5\({}^{\circ}\) latitude-longitude resolution. This climatology is adopted to compare with the profiles in the vicinity of TGF-producing thunderstorms to identify anomalous temperature behavior \(T_{Anomaly}\). \[T_{Anomaly}(i)=T_{TGF}(i)-T_{Clim}(i) \tag{1}\]  
where i is the altitude varying from 0 km to 39.9 km with 0.1 km vertical resolution, \(T_{TGF}\) is the average temperature profile associated with TGF flashes within a 5\({}^{\circ}\)\(\times\) 5\({}^{\circ}\) bin, and \(T_{Clim}\) is the temperature climatology for the same bin. We require these gridded temperatures, containing more than three GNSS-RO profiles.