  We show that the temperatures of the emergent non-electron neutrinos and the
binding energy released by a galactic Type II supernova are determinable,
assuming the Large Mixing Angle (LMA) solution is correct, from observations at
the Sudbury Neutrino Observatory (SNO) and at Super-Kamiokande (SK). If the
neutrino mass hierarchy is inverted, either a lower or upper bound can be
placed on the neutrino mixing angle $\theta_{13}$, and the hierarchy can be
deduced for adiabatic transitions. For the normal hierarchy, neither can
$\theta_{13}$ be constrained nor can the hierarchy be determined. Our
conclusions are qualitatively unchanged for the proposed Hyper-Kamiokande
detector.
