time and energy. We here define time-dependent ratio of the events of high-energy to low-energy neutrinos, R$_{x}$ ( t ) ≡ ∫ 60MeV 20MeV d $^{2}$N dE$_{e}$dt dE$_{e}$ ∫ 20MeV E$_{th}$ d $^{2}$N dE$_{e}$dt dE$_{e}$ , (20) where x refers to SK or SNO. Figure 9 shows this ratio R$_{x}$ ( t ) as a function of time. The values of sin $^{2}$2 θ$_{13}$ are 10 − $^{2}$, 10 − $^{3}$, 10 − 4 and 10 − 5 from top to bottom panels. Left panels are for normal hierarchy and right panels are for inverted hierarchy. Solid and dashed lines are the calculated results with and without shock wave, respectively. Note that the scale of each panel is different. First, we show R$_{SNO}$ ( t ) in normal hierarchy in left panels of Figure 9. The effect of shock wave is seen, but it is a very small effect of at most about 10 %. As for observed ν$_{e}$ spectrum in normal hierarchy, 70 % is the original ν$_{x}$ and 30 % is the original ν$_{e}$ in the non-adiabatic case, though almost 100 % is the original ν$_{x}$ in the adiabatic case. On the other hand, 70 % of the observed ν$_{e}$ is the original ¯ ν$_{e}$ and 30 % is the original ν$_{x}$ in inverted hierarchy. Moreover, the shock effect of ν$_{e}$ in normal hierarchy is washed out by neutral current and charged current of ¯ ν$_{e}$ because the target of neutrino detection is deuteron. Therefore, the variation of the event rate ratio is small in the normal hierarchy. There is, however, possibility of finding shock wave effect if much larger events are detected by the next generation detector. Second, we show R$_{SK}$ ( t ) in inverted hierarchy in right panels of Figure 9. The event rate ratio R$_{SK}$ ( t ) is constant in early times and strongly depends on sin $^{2}$2 θ$_{13}$ . It is 4.7 and 1.8 in the case of sin $^{2}$2 θ$_{13}$ = 10 − 3 and 10 − $^{5}$, respectively, at t = 0 s. The value of R$_{SK}$ ( t ) is large when sin $^{2}$2 θ$_{13}$ is large, because the H-resonance is adiabatic and the average energy of ¯ ν$_{e}$ is high. The small R$_{SK}$ ( t ) value is due to non-adiabatic state of H-resonance. When the shock wave effects are included and sin $^{2}$2 θ$_{13}$ is 10 − 3 (large), R$_{SK}$ ( t ) greatly changes with time. Although R$_{SK}$ ( t ) is 4.7 until 2 s, it decreases to ∼ 2, which is closer to the ratio in the case of non-adiabatic state in 4 - 8 s. This decrease is due to the change of the adiabaticity of H-resonance according to the shock propagation. The H-resonance is adiabatic before the shock arrival to the resonance. In contrast, the H-resonance is non-adiabatic while the shock wave propagates in the resonance, and R$_{SK}$ ( t ) approaches R$_{SK}$ ( t ) ∼ 1 . 8 which is the ratio in small sin $^{2}$2 θ$_{13}$ case (see the bottom panel). 18