influence of the shock wave on the spectra moves from the low-energy side to the high-energy side. The effect at later times is seen as a reduction of the high energy component of the neutrino spectrum. The influence of the shock wave in the case of sin $^{2}$2 θ$_{13}$ = 10 − 2 does not clearly appear in spectra for the same reason as discussed in the previous section. In the case of sin $^{2}$2 θ$_{13}$ = 10 − $^{5}$, the neutrino spectra with shock are not different from the spectra without shock. H-resonance is non-adiabatic even without the shock wave. We do not see any shock effects on the ¯ ν$_{e}$ spectra in inverted hierarchy. From Figure 5, the effect of shock wave appears in the spectra of ¯ ν$_{e}$ in the case of inverted hierarchy. The dependence of the ¯ ν$_{e}$ spectra on sin $^{2}$2 θ$_{13}$ is almost the same as the dependence of the ν$_{e}$ spectra in normal hierarchy. The spectrum of ν$_{e}$ at the surface of the supernova is written from Eq.(5) as The initial spectra are φ org ν$_{e}$ > φ org ν$_{x}$ in low energy side, and ( φ org ν$_{e}$ − φ org ν$_{x}$ ) is positive. Therefore, φ obs ν$_{e}$ increases when P is not 0. On the other hand, the initial spectra are φ org ν$_{e}$ < φ org ν$_{x}$ in high energy side, and ( φ org ν$_{e}$ − φ org ν$_{x}$ ) is negative. Therefore, φ obs ν$_{e}$ decreases when P is not 0. These increase and decrease appear in the observed neutrino spectra as the result from the influence of the shock wave. In the lower part of each panel, we can see this effect clearly. We note that the energy that satisfies φ org ν$_{e}$ = φ org ν$_{x}$ is about 18.7 MeV, and the energy that satisfies φ org ¯ ν$_{e}$ = φ org ν$_{x}$ is about 23.3 MeV. We discuss here the predicted event rates of the supernova neutrinos to be detected with SK in the manner described in section II C. The upper parts of each panel of Figure 6 show the expected energy-integrated event rates of ν$_{e}$ where the integrand in right hand side is the expected event number of neutrinos defined by Eq. (8), and E$_{th}$ are the threshold energies which are equal to 7 MeV and 5 MeV for SK and SNO detectors, respectively, as explained in section II C. Left and right panels of Figure 6 are for the cases of normal and inverted hierarchies, respectively. The lower part of dN dt ≡ ∫ ∞ E$_{th}$ d $^{2}$N dE$_{e}$dt dE$_{e}$, (18) φ SN ν$_{e}$ ( E$_{ν}$ ) = P ( E$_{ν}$ ) { φ org ν$_{e}$ ( E$_{ν}$ ) − φ org ν$_{x}$ ( E$_{ν}$ ) } + φ org ν$_{x}$ ( E$_{ν}$ ) . (17) C. Event rate of supernova neutrino 13