Abstract
All what we know about neutrinos with high confidence fits well the three-neutrino paradigm: 3 massive and mixed neutrinos with interactions described by the Standard Model. The paradigm is challenged by possible existence of new neutrino species - sterile neutrinos and new (“nonstandard”) interactions. The big unknowns include the type of neutrino mass ordering (hierarchy) and value of the CP-violation phase. Possibilities to determine these unknowns using the astrophysical and atmospheric neutrinos are described. Future large under-ice/water detectors of the atmospheric neutrinos PINGU and ORCA, have good chance to determine the hierarchy first. The hierarchy can also be established from analysis of Galactic supernova neutrino bursts. Although it is believed that the CP phase will be measured using accelerator neutrinos, a possibility should be explored to determine the phase using atmospheric neutrinos and upgrades of PINGU and ORCA with low energy threshold, Eth = (0:5 1) GeV.
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