  We investigate the precision with which the supernova neutrino spectra can be
reconstructed in water Cherenkov detectors, in particular the large scale
Hyper-Kamiokande and Super-Kamiokande. To this aim, we consider quasi-thermal
neutrino spectra modified by the Mikheev-Smirnov-Wolfenstein effect for the
case of normal ordering. We perform three 9 degrees of freedom likelihood
analyses including first inverse-beta decay only, then the combination of
inverse beta decay and elastic scattering on electrons and finally a third
analysis that also includes neutral scattering neutrino-oxygen events. A tenth
parameter is added in the analyses to account for the theoretical uncertainty
on the neutral current neutrino-oxygen cross section. By assuming a 100\%
efficiency in Hyper-Kamiokande, we show that one can reconstruct the electron
antineutrino average energy and pinching parameter with an accuracy of
$\sim2\%$ and $\sim7\%$ percent respectively, while the antineutrino integrated
luminosity can be pinned down at $\sim3\%$ percent level. As for the muon and
tau neutrinos, the average energy and the integrated luminosity can be measured
with $\sim7\%$ precision. These results represent a significant improvement
with respect Super-Kamiokande, particularly for the pinching parameter defining
the electron antineutrino spectra. As for electron neutrinos, the determination
of the emission parameters requires the addition of supplementary detection
channels.
