  Observed since the 1950's, the seasonal effect on underground muons is a well
studied phenomenon. The interaction height of incident cosmic rays changes as
the temperature of the atmosphere changes, which affects the production height
of mesons (mostly pions and kaons). The decay of these mesons produces muons
that can be detected underground. The production of muons is dominated by pion
decay, and previous work did not include the effect of kaons. In this work, the
methods of Barrett and MACRO are extended to include the effect of kaons. These
efforts give rise to a new method to measure the atmospheric K/$\pi$ ratio at
energies beyond the reach of current fixed target experiments. These methods
were applied to data from the MINOS far detector. A method is developed for
making these measurements at other underground detectors, including OPERA,
Super-K, IceCube, Baksan and the MINOS near detector.
