  The sensitivity of a huge underground water/ice Cherenkov detector, such as
PINGU in IceCube, to the neutrino mass hierarchy, the atmospheric mixing angle
and its octant, is studied in detail. Based on the event rate decomposition in
the propagation basis, we illustrate the smearing effects from the neutrino
scattering, the visible energy and zenith angle reconstruction procedures, the
energy and angular resolutions, and the muon mis-identification rate, as well
as the impacts of systematic errors in the detector resolutions, the muon
mis-identification rate, and the overall normalization. The sensitivity,
especially the mass hierarchy sensitivity, can be enhanced by splitting the
muon-like events into two channels, according to the event inelasticity. We
also show that including the cascade events can improve and stabilize the
sensitivity of the measurements.
