  We discuss the neutrino mass hierarchy determination with atmospheric
neutrinos in PINGU (Precision IceCube Next Generation Upgrade), based on a
simulation with the GLoBES software including the full three flavor framework
and parameter degeneracy, and we compare it to long-baseline experiment
options. We demonstrate that the atmospheric mass hierarchy sensitivity depends
on the achievable experiment properties and we identify the main targets for
optimization, whereas the impact of a large number of tested systematical
errors turns out to be small. Depending on the values of theta_23, delta, and
the true hierarchy, a 90% CL to 3sigma discovery after three years of operation
seems conceivable. We also emphasize the synergy with existing beam and reactor
experiments, driven by NOvA, such as the complementary coverage of the
parameter space. Finally, we point out that a low intensity neutrino beam with
a relatively short decay pipe could be used to determine the mass hierarchy
with a sensitivity comparable to the LBNE experiment irrespective of the
directional resolution of the detector.
