*4.2. Damping*

*4.2. Damping*

The damping of NIKE is an important characteristic of typhoon-induced NIWs [31,32,34,37]. To investigate the damping of Megi-induced NIWs, Figure 10a illustrates the e-folding time of depth-integrated NIKE. It is interesting to find that the e-folding time of Megi-induced NIWs was site-dependent and varied from several days to approximate a month. Along Megi's track, Megi-induced NIWs damped quickly with the e-folding time generally smaller than one week; whereas away from Megi's track, the e-folding time was longer. It is clearly shown that to the west of Luzon Island and the Luzon Strait, two remarkable zones exist where the e-folding time was longer than 20 days. [31,32,34,37]. To investigate the damping of Megi-induced NIWs, Figure 10a illustrates the e-folding time of depth-integrated NIKE. It is interesting to find that the e-folding time of Megi-induced NIWs was site-dependent and varied from several days to approximate a month. Along Megi's track, Megi-induced NIWs damped quickly with the e-folding time generally smaller than one week; whereas away from Megi's track, the e-folding time was longer. It is clearly shown that to the west of Luzon Island and the Luzon Strait, two remarkable zones exist where the e-folding time was longer than 20 days.

**Figure 10.** (**a**) The e-folding time (shading, unit: days) of depth-integrated NIKE. The orange curve denotes the track of typhoon Megi. (**b**) Lowpass filtered depth-integrated NIKE at points A (blue solid; 117.04°E, 18.48°N) and B (orange dashed; 119.52°E, 18.48°N) which are marked by black crosses in (**a**). The filled and open circles (squares) locate the maximum and e-folding values of depth-integrated NIKE at point A and B, respectively. **Figure 10.** (**a**) The e-folding time (shading, unit: days) of depth-integrated NIKE. The orange curve denotes the track of typhoon Megi. (**b**) Lowpass filtered depth-integrated NIKE at points A (blue solid; 117.04◦ E, 18.48◦ N) and B (orange dashed; 119.52◦ E, 18.48◦ N) which are marked by black crosses in (**a**). The filled and open circles (squares) locate the maximum and e-folding values of depth-integrated NIKE at point A and B, respectively.

To study the difference of e-folding time along and far away from Megi's track, Figure 10b displays the time series of lowpass filtered depth-integrated NIKE at points A (117.04°E, 18.48°N) and B (119.52°E, 18.48°N) as two examples. At point A which is nearly on Megi's track, the NIKE was quickly strengthened as the response to typhoon Megi, reached the peak value (26.5 kJ/m<sup>2</sup> ) on 23 October, and quickly damped thereafter. On 26 October, the NIKE reached the e-folding of its peak value. Therefore, the e-folding time To study the difference of e-folding time along and far away from Megi's track, Figure 10b displays the time series of lowpass filtered depth-integrated NIKE at points A (117.04◦ E, 18.48◦ N) and B (119.52◦ E, 18.48◦ N) as two examples. At point A which is nearly on Megi's track, the NIKE was quickly strengthened as the response to typhoon Megi, reached the peak value (26.5 kJ/m<sup>2</sup> ) on 23 October, and quickly damped thereafter.

here was 3.1 days. Moreover, the strengthening and damping processes of Megi-induced

ferent. First, because point B is far away from Megi's track, the peak value of NIKE was

evolution here is different from that at point A: Accompanied with the passage of typhoon Megi, the NIKE increased and reached the peak value on 21 October; then the NIKE damped; however, before the NIKE damped to the e-folding of its peak value, it was strengthened again and then exhibited some fluctuations until 7 November. On 14 November, the NIKE at point B reached the e-folding of its peak value. In this case, the e-

To explore the possible cause of different damping features of NIKE at points A and B, Figure 11 illustrates the depth-integrated NIKE along the 18.48°N section. As point A is nearly on Megi's track, the NIKE near point A was the strongest along this section. With time going on, the NIKE at point A gradually propagated westward, which is consistent with the result shown in Figure 6. The NIKE at point A damped quickly with significant NIKE existing from 20 to 26 October. As for point B, because it is far away from Megi's track, Megi-induced NIKE here was not significant and only lasted from 19 to 24 October.

, which is much smaller than that at point A. Second, the pattern of NIKE

folding time at point B was 24.0 days.

only 6.0 kJ/m<sup>2</sup>

positions of points A and B.

tions at its own frequency.

On 26 October, the NIKE reached the e-folding of its peak value. Therefore, the e-folding time here was 3.1 days. Moreover, the strengthening and damping processes of Megiinduced NIKE at point A were nearly symmetric. However, the situation at point B was much different. First, because point B is far away from Megi's track, the peak value of NIKE was only 6.0 kJ/m<sup>2</sup> , which is much smaller than that at point A. Second, the pattern of NIKE evolution here is different from that at point A: Accompanied with the passage of typhoon Megi, the NIKE increased and reached the peak value on 21 October; then the NIKE damped; however, before the NIKE damped to the e-folding of its peak value, it was strengthened again and then exhibited some fluctuations until 7 November. On 14 November, the NIKE at point B reached the e-folding of its peak value. In this case, the e-folding time at point B was 24.0 days.

To explore the possible cause of different damping features of NIKE at points A and B, Figure 11 illustrates the depth-integrated NIKE along the 18.48◦ N section. As point A is nearly on Megi's track, the NIKE near point A was the strongest along this section. With time going on, the NIKE at point A gradually propagated westward, which is consistent with the result shown in Figure 6. The NIKE at point A damped quickly with significant NIKE existing from 20 to 26 October. As for point B, because it is far away from Megi's track, Megi-induced NIKE here was not significant and only lasted from 19 to 24 October. Thereafter, the NIWs initially generated at 118.8◦ E propagated eastward to point B and lasted to 1 November, which caused the fluctuations of NIKE at point B (Figure 9c). Similar results can be found at other points with long e-folding time. Based on these results, it can be concluded that the local long damping time of NIKE is related to the NIWs propagating from other sites. *J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 12 of 17 Thereafter, the NIWs initially generated at 118.8°E propagated eastward to point B and lasted to 1 November, which caused the fluctuations of NIKE at point B (Figure 9c). Similar results can be found at other points with long e-folding time. Based on these results, it can be concluded that the local long damping time of NIKE is related to the NIWs propagating from other sites.

**Figure 11.** Depth-integrated NIKE (shading, unit: kJ/m<sup>2</sup> ) as a function of time along 18.48°N. Black dashed lines indicate **Figure 11.** Depth-integrated NIKE (shading, unit: kJ/m<sup>2</sup> ) as a function of time along 18.48◦ N. Black dashed lines indicate positions of points A and B.

#### **5. Modal Content 5. Modal Content**

Finally, attention is paid to the modal content of Megi-induced NIWs. We also choose the results at points A and B as examples, for which the modal NIKE is shown in Figure 12. Note that in the modal decomposition in this study, a total of 11 (one barotropic and Finally, attention is paid to the modal content of Megi-induced NIWs. We also choose the results at points A and B as examples, for which the modal NIKE is shown in Figure 12. Note that in the modal decomposition in this study, a total of 11 (one barotropic and the first ten baroclinic) modes were taken into consideration.

the first ten baroclinic) modes were taken into consideration. It is clearly shown that Megi-induced NIWs at point A were dominated by mode-2 which accounted for 45% of the total NIKE. Following mode-2 were mode-3 and mode-1, which occupied 21% and 10% of the total NIKE, respectively. The sum of the first three baroclinic modes accounted for 76% of the total NIKE. The proportions of the other modes in the total NIKE were smaller than 10% and generally exhibited a decreasing trend with the increase in mode number. Moreover, the NIKE of the dominant modes, especially mode-2 and mode-3, synchronously varied with the total NIKE.

It is clearly shown that Megi-induced NIWs at point A were dominated by mode-2 which accounted for 45% of the total NIKE. Following mode-2 were mode-3 and mode-1, which occupied 21% and 10% of the total NIKE, respectively. The sum of the first three baroclinic modes accounted for 76% of the total NIKE. The proportions of the other modes

**Figure 12.** Modal NIKE at points (**a**) A (117.04°E, 18.48°N) and (**b**) B (119.52°E, 18.48°N). The values in the brackets indicate the proportions of modal NIKE in the total NIKE. Note that the modal NIKE has been lowpass filtered to remove oscilla-

the first ten baroclinic) modes were taken into consideration.

**Figure 12.** Modal NIKE at points (**a**) A (117.04°E, 18.48°N) and (**b**) B (119.52°E, 18.48°N). The values in the brackets indicate the proportions of modal NIKE in the total NIKE. Note that the modal NIKE has been lowpass filtered to remove oscillations at its own frequency. **Figure 12.** Modal NIKE at points (**a**) A (117.04◦ E, 18.48◦ N) and (**b**) B (119.52◦ E, 18.48◦ N). The values in the brackets indicate the proportions of modal NIKE in the total NIKE. Note that the modal NIKE has been lowpass filtered to remove oscillations at its own frequency.

Thereafter, the NIWs initially generated at 118.8°E propagated eastward to point B and lasted to 1 November, which caused the fluctuations of NIKE at point B (Figure 9c). Similar results can be found at other points with long e-folding time. Based on these results, it can be concluded that the local long damping time of NIKE is related to the NIWs prop-

) as a function of time along 18.48°N. Black dashed lines indicate

Finally, attention is paid to the modal content of Megi-induced NIWs. We also choose the results at points A and B as examples, for which the modal NIKE is shown in Figure 12. Note that in the modal decomposition in this study, a total of 11 (one barotropic and

agating from other sites.

**Figure 11.** Depth-integrated NIKE (shading, unit: kJ/m<sup>2</sup>

**5. Modal Content**

positions of points A and B.

It is clearly shown that Megi-induced NIWs at point A were dominated by mode-2 which accounted for 45% of the total NIKE. Following mode-2 were mode-3 and mode-1, which occupied 21% and 10% of the total NIKE, respectively. The sum of the first three baroclinic modes accounted for 76% of the total NIKE. The proportions of the other modes The modal content at point B exhibited a different pattern from that at point A. During 16 to 24 October, the locally generated NIWs were dominated by mode-2, mode-3 and mode-1, which was consistent with that at point A; the evolution of mode-2 and mode-3 generally agreed with that of the total NIKE. However, after 24 October, the NIKE of mode-4, mode-5 and mode-6 started to enhance and gradually became dominant. During 5 to 15 November, mode-7 became the most significant mode. On average, mode-2 was the strongest and accounted for 26% of the total NIKE at point B; the contributions of mode-3 to mode-7 were comparable, for which the proportions of modal NIKE in the total NIKE were all greater than 10%.
