  Production of high-energy muons in cosmic-ray air showers, relevant for
underground detectors, depends on the properties of the primary cosmic ray as
well as the atmospheric temperature through the competition between decay and
re-interaction of charged pions and kaons. We present a parameterization of
muon production profiles based on simulations as a function of the primary
cosmic-ray energy, mass and zenith angle, the minimum energy for a muon to
reach the detector and an atmospheric temperature profile. We illustrate how
this can be used to calculate muon bundle properties such as multiplicity and
transverse size and their seasonal variations in the context of underground
measurements in coincidence with a surface detector which fixes the primary
cosmic-ray energy.
