We present simulation results of the vertical structure of Large Scale Traveling Ionospheric Disturbances (LSTIDs) during synthetic geomagnetic storms. These data are produced using a one-way coupled SAMI3/GITM model, where GITM (Global Ionosphere Thermosphere Model) provides thermospheric information to SAMI3 (SAMI3 is Another Model of the Ionosphere), allowing the production and propagation of LSTIDs. We show simulation results which demonstrate that the traveling atmospheric disturbances (TADs) generated in GITM propagate to the topside ionosphere in SAMI3 as LSTIDs. The speed and wavelength (900 m/s and 10º-20º latitude) are consistent with LSTID observations in storms of similar magnitudes. We demonstrate the LSTIDs reach altitudes beyond the topside ionosphere with amplitudes of <5% over background which will facilitate the use of plasma measurements from the topside ionosphere to supplement measurements from GNSS in the study of TIDs. Additionally, we demonstrate the dependence of the characteristics of these TADs and TIDs on longitude.