If γ is larger than 1, the resonance becomes adiabatic, but if it is small, resonance becomes non-adiabatic. The change of adiabaticity mainly occurs at H-resonance owing to the shock propagation. When the shock wave reaches the H-resonance, the density gradient becomes large and the value of γ decreases. This leads to a change of survival probability of neutrinos. Since the resonance point is inversely proportional to the neutrino energy, this effect appears from low-energy side and moves toward high-energy side according to the shock wave prop- agation. As shock wave propagates outward, the density at the shock front decreases and the resonance condition is satisfied for higher energy neutrinos. The expected event number of the neutrinos in a water Cherenkov detector can be ex- pressed as where N is the detection number of neutrinos, E$_{e}$ is the energy of electron or positron, E$_{ν}$ is the energy of neutrino, N$_{tar}$ is the target number, η$_{(}$$_{E}$$_{e}$$_{)}$ is the efficiency of the detector, d is the distance from the supernova, d $^{2}$N$_{ν}$ dE$_{ν}$dt is the neutrino spectrum, and σ ( E$_{ν}$ ) is the cross section as a function of the neutrino energy [59]. We assumed a supernova at the center of Milky Way ( d =10 kpc), and we neglected the Earth effect [60]. We assume the detection at SK and SNO. The mass of SK is 32000 ton and the solvent is pure water. SK mainly detects the ¯ ν$_{e}$ events with the reaction ¯ ν$_{e}$ + p → e $^{+}$+ n . The event number is obtained by integrating over the angular distribution of the events. As for the efficiency of the detector, we assumed as follows for simplicity: η$_{(}$$_{E}$$_{e}$$_{)}$ = 0 for E$_{e}$ < 7 MeV and η$_{(}$$_{E}$$_{e}$$_{)}$ = 1 for E$_{e}$ ≥ 7 MeV in accordance with SK Phase II [61]. The finite energy resolution of the detector was neglected here. The ¯ ν$_{e}$ and ν$_{e}$ events are evaluated taking account of the following four reactions, C. Detection of Supernova Neutrinos d $^{2}$N dE$_{e}$dt = N$_{tar}$ η$_{(}$$_{E}$$_{e}$$_{)}$ 1 4 πd 2 d $^{2}$N$_{ν}$ dE$_{ν}$dt σ ( E$_{ν}$ ) dE$_{ν}$ dE$_{e}$ , (8) ¯ ν$_{e}$ + p → e + + n , (9) ν$_{e}$ + e − → ν$_{e}$ + e $^{−}$, (10) ¯ ν$_{e}$ + e − → ¯ ν$_{e}$ + e $^{−}$, (11) ν$_{x}$ + e − → ν$_{x}$ + e $^{−}$. (12) 9