After more than seven years of data taking with the full IceCube detector triggering at an average rate of 2.15 kHz, a sample of half a trillion muon events is available for analysis. The extreme temperature variations in the stratosphere together with the high data rate reveal features on both long and short time scales with unprecedented precision. In this paper we report an analysis in terms of the atmospheric profile for production of muons from decay of charged pions and kaons. We comment on the implications for seasonal variations of neutrinos, which are presented in a separate paper at this conference.