  The proposed PINGU project (Precision IceCube Next Generation Upgrade) is
expected to collect O(10^5) atmospheric muon and electron neutrino in a few
years of exposure, and to probe the neutrino mass hierarchy through its imprint
on the event spectra in energy and direction. In the presence of nonnegligible
and partly unknown shape systematics, the analysis of high-statistics spectral
variations will face subtle challenges that are largely unprecedented in
neutrino physics. We discuss these issues both on general grounds and in the
currently envisaged PINGU configuration, where we find that possible shape
uncertainties at the (few) percent level can noticeably affect the sensitivity
to the hierarchy. We also discuss the interplay between the mixing angle
theta_23 and the PINGU sensitivity to the hierarchy. Our results suggest that
more refined estimates of spectral uncertainties are needed in next-generation,
large-volume atmospheric neutrino experiments.
