  We explore the physics potential of multi-megaton scale ice or water
Cherenkov detectors with low ($\sim 1$ GeV) threshold. Using some proposed
characteristics of the PINGU detector setup we compute the distributions of
events versus neutrino energy $E_\nu$ and zenith angle $\theta_z$, and study
their dependence on yet unknown neutrino parameters. The $(E_\nu - \theta_z)$
regions are identified where the distributions have the highest sensitivity to
the neutrino mass hierarchy, to the deviation of the 2-3 mixing from the
maximal one and to the CP-phase. We evaluate significance of the measurements
of the neutrino parameters and explore dependence of this significance on the
accuracy of reconstruction of the neutrino energy and direction. The effect of
degeneracy of the parameters on the sensitivities is also discussed. We
estimate the characteristics of future detectors (energy and angle resolution,
volume, etc.) required for establishing the neutrino mass hierarchy with high
confidence level. We find that the hierarchy can be identified at $3\sigma$ --
$10\sigma$ level (depending on the reconstruction accuracies) after 5 years of
PINGU operation.
