  Large mass ice/water Cherenkov experiments, optimized to detect low energy
(1-20 GeV) atmospheric neutrinos, have the potential to discriminate between
normal and inverted neutrino mass hierarchies. The sensitivity depends on
several model and detector parameters, such as the neutrino flux profile and
normalization, the Earth density profile, the oscillation parameter
uncertainties, and the detector effective mass and resolution. A proper
evaluation of the mass hierarchy discrimination power requires a robust
statistical approach. In this work, the Toy Monte Carlo, based on an extended
unbinned likelihood ratio test statistic, was used. The effect of each model
and detector parameter, as well as the required detector exposure, was then
studied. While uncertainties on the Earth density and atmospheric neutrino flux
profiles were found to have a minor impact on the mass hierarchy
discrimination, the flux normalization, as well as some of the oscillation
parameter (\Delta m^2_{31}, \theta_{13}, \theta_{23}, and \delta_{CP})
uncertainties and correlations resulted critical. Finally, the minimum required
detector exposure, the optimization of the low energy threshold, and the
detector resolutions were also investigated.
