In this contribution, we investigate the seasonal variation of multi-muon events observed by the
NO𝜈A Near Detector (ND) at Fermilab, using the general-purpose Monte Carlo code FLUKA-
CERN to simulate the transport and interaction of the air-shower particles in the atmosphere and
other media. Our atmospheric model uses air densities for Winter and Summer averaged profiles
calculated from the temperature and geopotential information at 37 pressure levels given by the
European Center for Medium-Range Weather Forecasts (ECMWF) datasets in situ. Our FLUKA
geometry model also includes a layered underground approximated to match the NO𝜈A ND and its
location. We compare our simulation results with the measured seasonal flux modulation of multi-
muon events by the NO𝜈A ND. For the first time, we were able to describe the multi-muon excess
in Winter over Summer quantitatively and its dependence on the multi-muon event multiplicity,
as observed by NO𝜈A. Finally, we compare our results for the muon flux at the surface and
underground detector level obtained from FLUKA simulations with the previous work from other
authors based on CORSIKA simulations. We try to understand the reasons for the discrepancy by
nearly a factor of four between the results of two Monte Carlo codes.