**4. Megi-Induced NIKE**

#### **4. Megi-Induced NIKE** *4.1. Temporal Variation and Spatial Distribution*

*4.1. Temporal Variation and Spatial Distribution* Figure 6 illustrates the depth-integrated NIKE from 18 October to 1 November with an interval of 2 days, from which the evolution of Megi-induced NIWs is detected. At 00:00 on 18 October when Megi's center did not enter the SCS (Figure 1), slight NIKE was found to the west of Luzon Island (Figure 6a). At 00:00 on 20 October, when Megi's center was at 117.3°E, 17.2°N in the SCS, Megi-induced NIKE reached 10–20 kJ/m<sup>2</sup> and was mainly concentrated in two zones to the north and south of typhoon Megi, respectively (Figure 6b). From 22 to 26 October, strong NIKE with several hot spots exceeding 35 kJ/m<sup>2</sup> appeared along Megi's wake (Figure 6c–e). It should be noted that Megi had left the SCS Basin before 12:00 on 22 October and finally dissipated on 24 October, which means that the strongest NIKE appeared several days after the passage of Megi rather than under its influence. Thereafter, strong NIKE scattered (mainly westward propagated) and the NIKE along Megi's wake quickly damped to below 10 kJ/m<sup>2</sup> after 30 October (Figure 6f–h). According to [53], the ocean's response to a typhoon in the northern hemisphere usually exhibits rightward biased features, i.e., larger sea surface temperature cooling, greater currents and deeper mixed layer appear to the right of the typhoon track. As shown in Figure 6, Megi-induced NIWs also exhibited apparent rightward biased features: the NIKE to the right of Megi's wake was stronger than that to the left. Figure 6 illustrates the depth-integrated NIKE from 18 October to 1 November with an interval of 2 days, from which the evolution of Megi-induced NIWs is detected. At 00:00 on 18 October when Megi's center did not enter the SCS (Figure 1), slight NIKE was found to the west of Luzon Island (Figure 6a). At 00:00 on 20 October, when Megi's center was at 117.3◦ E, 17.2◦ N in the SCS, Megi-induced NIKE reached 10–20 kJ/m<sup>2</sup> and was mainly concentrated in two zones to the north and south of typhoon Megi, respectively (Figure 6b). From 22 to 26 October, strong NIKE with several hot spots exceeding 35 kJ/m<sup>2</sup> appeared along Megi's wake (Figure 6c–e). It should be noted that Megi had left the SCS Basin before 12:00 on 22 October and finally dissipated on 24 October, which means that the strongest NIKE appeared several days after the passage of Megi rather than under its influence. Thereafter, strong NIKE scattered (mainly westward propagated) and the NIKE along Megi's wake quickly damped to below 10 kJ/m<sup>2</sup> after 30 October (Figure 6f–h). According to [53], the ocean's response to a typhoon in the northern hemisphere usually exhibits rightward biased features, i.e., larger sea surface temperature cooling, greater currents and deeper mixed layer appear to the right of the typhoon track. As shown in Figure 6, Megi-induced NIWs also exhibited apparent rightward biased features: the NIKE to the right of Megi's wake was stronger than that to the left. *J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 8 of 17

**Figure 6.** Depth-integrated NIKE (shading, unit: kJ/m<sup>2</sup> ) at 00:00 on (**a**) 18, (**b**) 20, (**c**) 22, (**d**) 24, (**e**) 26, (**f**) 28 and (**g**) 30 October and (**h**) 1 November 2010. Orange curves denote the track of typhoon Megi and the black plus indicates the position of mooring UIB6. The gray curve represents the 1000 m isobath. **Figure 6.** Depth-integrated NIKE (shading, unit: kJ/m<sup>2</sup> ) at 00:00 on (**a**) 18, (**b**) 20, (**c**) 22, (**d**) 24, (**e**) 26, (**f**) 28 and (**g**) 30 October and (**h**) 1 November 2010. Orange curves denote the track of typhoon Megi and the black plus indicates the position of mooring UIB6. The gray curve represents the 1000 m isobath.

> trated in the deep SCS Basin where the water depth is greater than 1000 m (the gray curve in Figure 6), although typhoon Megi passed over both the deep SCS basin and shallow continental shelf and slope in the northern SCS. To investigate the possible cause of this phenomenon, Figure 7 illustrates several snapshots of meridional currents of NIWs along 118°E on 24 October. Similar results can be found at other meridional sections on the adjacent several days. From Figure 7, we can detect that the continental slope in the northern SCS is supercritical to Megi-induced NIWs, i.e., the topographic slope (the black solid lines in Figure 7) is apparently larger than that of NIWs. In other words, the NIWs impinging on the continental slope in the northern SCS would be reflected to the SCS Basin. However, due to the complex vertical pattern of NIWs shown in Figure 7, the reflection of NIWs is not visible. Therefore, we adopted the same method as [42,43] to separate the NIWs propagating in different directions. Figure 8 shows an example at 00:00 on 24 October. The NIW component with *m*>0 (*m* represents the vertical wavenumber) dominates over that with *m*<0, suggesting that the energy of Megi-induced NIWs mainly propagated downward, which is consistent with the above analysis and general features of typhooninduced NIWs [49–51]. For the same *m*, the NIW component with *l*>0 (*l* represents the horizontal wavenumber) is comparable to that with *l*<0, suggesting that the northwardpropagating and southward-propagating NIWs had comparable intensity. In order to study whether Megi-induced NIWs reflected on the continental slope, attention should be paid to the northward–downward (*l*>0 and *m*>0) and southward–downward (*l*<0 and *m*>0) components (Figure 8b,d). According to Figure 8b, two northward–downward-propagating beams impinged on the continental slope in the northern SCS, which radiated from the surface at 19–20.5°N (positive sign) and 20.5–22°N (negative sign), respectively. At the same time, two southward–downward-propagating beams were found to radiate from the continental slope with different signs (Figure 8d). To demonstrate that the two southward–downward-propagating beams are the reflected beams of the two northward– downward-propagating ones, a simple ray tracing model [54,55] is adopted to qualitatively illustrate the propagating paths of NIWs. Given that reflection occurred in a small region near the continental slope in the northern SCS, the beta effect of Coriolis frequency and the influence of background currents were not taken into consideration. The ray trac-

ing model [54,55] is described as

It is interesting to find from Figure 6 that Megi-induced NIKE was mainly concentrated in the deep SCS Basin where the water depth is greater than 1000 m (the gray curve in Figure 6), although typhoon Megi passed over both the deep SCS basin and shallow continental shelf and slope in the northern SCS. To investigate the possible cause of this phenomenon, Figure 7 illustrates several snapshots of meridional currents of NIWs along 118◦ E on 24 October. Similar results can be found at other meridional sections on the adjacent several days. From Figure 7, we can detect that the continental slope in the northern SCS is supercritical to Megi-induced NIWs, i.e., the topographic slope (the black solid lines in Figure 7) is apparently larger than that of NIWs. In other words, the NIWs impinging on the continental slope in the northern SCS would be reflected to the SCS Basin. However, due to the complex vertical pattern of NIWs shown in Figure 7, the reflection of NIWs is not visible. Therefore, we adopted the same method as [42,43] to separate the NIWs propagating in different directions. Figure 8 shows an example at 00:00 on 24 October. The NIW component with *m* > 0 (*m* represents the vertical wavenumber) dominates over that with *m* < 0, suggesting that the energy of Megi-induced NIWs mainly propagated downward, which is consistent with the above analysis and general features of typhooninduced NIWs [49–51]. For the same *m*, the NIW component with *l* > 0 (*l* represents the horizontal wavenumber) is comparable to that with *l* < 0, suggesting that the northwardpropagating and southward-propagating NIWs had comparable intensity. In order to study whether Megi-induced NIWs reflected on the continental slope, attention should be paid to the northward–downward (*l*>0 and *m* > 0) and southward–downward (*l* < 0 and *m* > 0) components (Figure 8b,d). According to Figure 8b, two northward–downwardpropagating beams impinged on the continental slope in the northern SCS, which radiated from the surface at 19–20.5◦ N (positive sign) and 20.5–22◦ N (negative sign), respectively. At the same time, two southward–downward-propagating beams were found to radiate from the continental slope with different signs (Figure 8d). To demonstrate that the two southward–downward-propagating beams are the reflected beams of the two northward– downward-propagating ones, a simple ray tracing model [54,55] is adopted to qualitatively illustrate the propagating paths of NIWs. Given that reflection occurred in a small region near the continental slope in the northern SCS, the beta effect of Coriolis frequency and the influence of background currents were not taken into consideration. The ray tracing model [54,55] is described as

$$\frac{dz}{dy} = \tan\alpha = \sqrt{\frac{\omega^2 - f^2}{N(z)^2 - \omega^2}}\tag{5}$$

where *y* and *z* are the local Cartesian coordinates (positive northward and upward, respectively), *α* is the slope of NIWs, *ω*, *f* and *N*(*z*) are the NIW, local Coriolis and buoyancy frequencies, respectively. In this study, *N*(*z*) was set as the averaged buoyancy frequency near the continental slope along 118◦ E, *f* was set to the value of the generation point at the surface and *ω* was determined through a series of trials. It is found that *ω* = 1.015*f* could lead to reasonable results, therefore, *ω* = 1.015*f* was adopted in the ray tracing model in this study. Figure 8b,d shows the ray tracing results. The two northward–downwardpropagating and two southward–downward-propagating beams mentioned above show good consistency with the ray tracing results, confirming the occurrence of reflection of NIWs at the supercritical continental slope in the northern SCS.

Based on the aforementioned analysis, it can be concluded that because the continental slope in the northern SCS is supercritical to Megi-induced NIWs, the NIWs impinging on the continental slope were reflected back and then trapped in the SCS Basin, which finally resulted in the concentrated NIKE in the deep SCS Basin (Figure 6). In addition, because mooring UIB6 was located on the continental slope in the northern SCS, the NIKE here was not very significant. This explains why the strongest typhoon in 2010, Megi, did not generate stronger NIWs than another typhoon, Meranti, at mooring UIB6 [37].

at the supercritical continental slope in the northern SCS.

 <sup>2</sup> <sup>2</sup> 22

 

*f*

*zN*

(5)

tan

*dy dz*

where *y* and *z* are the local Cartesian coordinates (positive northward and upward, respectively), *α* is the slope of NIWs, *ω*, *f* and *N*(*z*) are the NIW, local Coriolis and buoyancy frequencies, respectively. In this study, *N*(*z*) was set as the averaged buoyancy frequency near the continental slope along 118°E, *f* was set to the value of the generation point at the surface and *ω* was determined through a series of trials. It is found that *ω*=1.015*f* could lead to reasonable results, therefore, *ω*=1.015*f* was adopted in the ray tracing model in this study. Figure 8b,d shows the ray tracing results. The two northward–downward-propagating and two southward–downward-propagating beams mentioned above show good consistency with the ray tracing results, confirming the occurrence of reflection of NIWs

Based on the aforementioned analysis, it can be concluded that because the continental slope in the northern SCS is supercritical to Megi-induced NIWs, the NIWs impinging on the continental slope were reflected back and then trapped in the SCS Basin, which finally resulted in the concentrated NIKE in the deep SCS Basin (Figure 6). In addition, because mooring UIB6 was located on the continental slope in the northern SCS, the NIKE here was not very significant. This explains why the strongest typhoon in 2010, Megi, did

not generate stronger NIWs than another typhoon, Meranti, at mooring UIB6 [37].

**Figure 7.** Meridional currents of NIWs (shading, unit: m/s) along 118°E at(**a**) 00:00, (**b**) 06:00, (**c**) 12:00 and (**d**) 18:00 on 24 October. The gray shading in each subfigure indicates the topography. The black solid line in each subfigure indicates the approximate topographic slope. **Figure 7.** Meridional currents of NIWs (shading, unit: m/s) along 118◦ E at(**a**) 00:00, (**b**) 06:00, (**c**) 12:00 and (**d**) 18:00 on 24 October. The gray shading in each subfigure indicates the topography. The black solid line in each subfigure indicates the approximate topographic slope. *J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 10 of 17

**Figure 8.** NIWs propagating in different directions along 118°E at 00:00 on 24 October. Note that *l* and *m* represent the horizontal and vertical wavenumbers, respectively; *l*>0 (*l*<0) corresponds to NIWs propagating northward (southward) and *m*<0 (*m*>0) corresponds to NIWs propagating upward (downward). The gray shading in each subfigure indicates the topography. In (**b**) and (**d**), the black solid and dashed curves represent the ray tracing results. **Figure 8.** NIWs propagating in different directions along 118◦ E at 00:00 on 24 October. Note that *l* and *m* represent the horizontal and vertical wavenumbers, respectively; *l* > 0 (*l* < 0) corresponds to NIWs propagating northward (southward) and *m* < 0 (*m* > 0) corresponds to NIWs propagating upward (downward). The gray shading in each subfigure indicates the topography. In (**b**,**d**), the black solid and dashed curves represent the ray tracing results.

To study the vertical distribution of Megi-induced NIKE, Figure 9 displays the NIKE at several depths at 00:00 on 24 October as an example. Similar results can be found on the adjacent several days, which are not shown. From Figure 9, we can find that strong NIKE mainly appeared in the upper ocean, especially near the surface. Megi-induced NIKE in the upper 200 m (the upper panels of Figure 9) was at least one order of magnitude stronger than that below 500 m depth (the lower panels of Figure 9). Moreover, there was a slight elevation of NIKE at 1000 m depth, whereas almost no enhancement was found at lower depths. This result suggests that Megi-induced NIWs could only reach an approximate depth of 1000 m in the SCS Basin. In addition, because NIWs are a kind of internal wave which can propagate in both horizontal and vertical directions, the patterns of Megi-induced NIKE at different depths were different. To study the vertical distribution of Megi-induced NIKE, Figure 9 displays the NIKE at several depths at 00:00 on 24 October as an example. Similar results can be found on the adjacent several days, which are not shown. From Figure 9, we can find that strong NIKE mainly appeared in the upper ocean, especially near the surface. Megi-induced NIKE in the upper 200 m (the upper panels of Figure 9) was at least one order of magnitude stronger than that below 500 m depth (the lower panels of Figure 9). Moreover, there was a slight elevation of NIKE at 1000 m depth, whereas almost no enhancement was found at lower depths. This result suggests that Megi-induced NIWs could only reach an approximate depth of 1000 m in the SCS Basin. In addition, because NIWs are a kind of internal wave which can propagate in both horizontal and vertical directions, the patterns of Megi-induced NIKE at different depths were different.

on 24 October 2010. Note that the range of colorbar for the upper and lower panels is different. Orange curves denote the

) at (**a**) 0, (**b**) 50, (**c**) 100, (**d**) 200, (**e**) 500, (**f**) 1000, (**g**) 2000 and (**h**) 3000 m depth at 00:00

**Figure 9.** NIKE (shading, unit: J/m<sup>3</sup>

track of typhoon Megi.

of Megi-induced NIKE at different depths were different.

**Figure 8.** NIWs propagating in different directions along 118°E at 00:00 on 24 October. Note that *l* and *m* represent the horizontal and vertical wavenumbers, respectively; *l*>0 (*l*<0) corresponds to NIWs propagating northward (southward) and *m*<0 (*m*>0) corresponds to NIWs propagating upward (downward). The gray shading in each subfigure indicates the

> To study the vertical distribution of Megi-induced NIKE, Figure 9 displays the NIKE at several depths at 00:00 on 24 October as an example. Similar results can be found on the adjacent several days, which are not shown. From Figure 9, we can find that strong NIKE mainly appeared in the upper ocean, especially near the surface. Megi-induced NIKE in the upper 200 m (the upper panels of Figure 9) was at least one order of magnitude stronger than that below 500 m depth (the lower panels of Figure 9). Moreover, there was a slight elevation of NIKE at 1000 m depth, whereas almost no enhancement was found at lower depths. This result suggests that Megi-induced NIWs could only reach an approximate depth of 1000 m in the SCS Basin. In addition, because NIWs are a kind of internal wave which can propagate in both horizontal and vertical directions, the patterns

topography. In (**b**) and (**d**), the black solid and dashed curves represent the ray tracing results.

**Figure 9.** NIKE (shading, unit: J/m<sup>3</sup> ) at (**a**) 0, (**b**) 50, (**c**) 100, (**d**) 200, (**e**) 500, (**f**) 1000, (**g**) 2000 and (**h**) 3000 m depth at 00:00 on 24 October 2010. Note that the range of colorbar for the upper and lower panels is different. Orange curves denote the track of typhoon Megi. **Figure 9.** NIKE (shading, unit: J/m<sup>3</sup> ) at (**a**) 0, (**b**) 50, (**c**) 100, (**d**) 200, (**e**) 500, (**f**) 1000, (**g**) 2000 and (**h**) 3000 m depth at 00:00 on 24 October 2010. Note that the range of colorbar for the upper and lower panels is different. Orange curves denote the track of typhoon Megi. *J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 11 of 17

The damping of NIKE is an important characteristic of typhoon-induced NIWs
