1  2  3  4  5  6 sin $^{2}$2 $_{13}$=10 -2 inverted hierarchy  1  2  3  4  5 6  0  2  4  6  8 10 Time [s] sin $^{2}$2 $_{13}$=10 -5 1  2  3  4  5 6 R  SK sin $^{2}$2 $_{13}$=10 -3 1  2  3  4  5 6 sin $^{2}$2 $_{13}$=10 -4  2.1  2.2  2.3  2.4  2.5  2.6 sin $^{2}$2 $_{13}$=10 -4  2.1  2.2  2.3  2.4  2.5  2.6 sin $^{2}$2 $_{13}$=10 -3  2.1  2.2  2.3  2.4  2.5  2.6 sin $^{2}$2 $_{13}$=10 -2 normal hierarchy  2.1  2.2  2.3  2.4  2.5  2.6  0  2  4  6  8  10 Time [s] sin $^{2}$2 $_{13}$=10 -5 R  SNO FIG. 9: Time-dependent ratios of the events of high-energy neutrinos (20 MeV < E$_{ν}$ < 60 MeV) t o those of low-energy neutrinos (5 MeV < E$_{ν}$ < 20 MeV) for the SK and SNO detectors for various mixing angles of sin $^{2}$2 θ$_{13}$ = 10 − $^{2}$, 10 − $^{3}$, 10 − 4 and 10 − 5 from top to bottom panel. Left panels are the ratio R$_{SNO}$ ( t ) for normal hierarchy, and right panels are the ratio R$_{SK}$ ( t ) in 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. 34