Using a semi-analytic formulation, we study the varations of the atmospheric neutrino and muon fluxes calculated with the variations of a hadronic interaction model.
Considering the difference of the hadronic interaction model from the true one as variation of hadronic interaction model, we can estimate the the calculation error of the atmospheric neutrino flux by comparing of the atmospheric muon flux calculated and the observed one in a presition experiment.
We find a relation between the reconstruction residual of the observed muon flux and the error of the atmospheric neutrino flux prediction.
Then we studied the atmospheric muon flux at sevaral candidate of the observation site, Tsukuba (sea level), Mt. Norikura (2770m a.s.l.), Hanle India (4500m a.s.l.), and Balloon altitude ($\sim$ 32km a.s.l.) near South Pole, to ind a proper observation site for this study.
We find the muon flux observed at high mountain is most useful to reduce the error of the atmospheric neutrino flux