*2.3. Methodology*

First of all, the HYCOM reanalysis results were compared with in situ observations at mooring UIB6 for validation. A continuous wavelet transform was first performed to demonstrate the existence of NIWs. As tidal forcing was not considered in the HYCOM reanalysis results (GLBu0.08/expt\_19.1), the bandpass filtered NIWs rather than the raw currents were compared with those from in situ observations. To be consistent with previous studies [32,37], the fourth-order Butterworth filter was adopted and the cutoff *2.2. Data* 

where *ρ*0=1024 kg/m<sup>3</sup>

was calculated to explore their decay.

*J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 3 of 17

frequency of bandpass filtering was set to [0.58, 0.81] cpd corresponding to 0.80–1.13 times the local Coriolis frequency.

**Figure 1.**Bathymetry (shading, unit: m) of the northern SCS, track of typhoon Megi (colored lines) and position of mooring UIB6 (black plus). Six-hour positions of Megi's center are denoted by dots and the time at 00:00 from 19 to 24 October is labeled. Intensity of Megi is represented by various colors, as shown in the legend. TD, TS, STS, TY, STY and SuperTY are abbreviations of tropical depression (10.8–17.1 m/s), tropical storm (17.2–24.4 m/s), severe tropical storm (24.5–32.6 m/s), typhoon (32.7–41.4 m/s), severe typhoon (41.5–50.9 m/s) and super typhoon (>51.0 m/s), respectively. **Figure 1.** Bathymetry (shading, unit: m) of the northern SCS, track of typhoon Megi (colored lines) and position of mooring UIB6 (black plus). Six-hour positions of Megi's center are denoted by dots and the time at 00:00 from 19 to 24 October is labeled. Intensity of Megi is represented by various colors, as shown in the legend. TD, TS, STS, TY, STY and SuperTY are abbreviations of tropical depression (10.8–17.1 m/s), tropical storm (17.2–24.4 m/s), severe tropical storm (24.5–32.6 m/s), typhoon (32.7–41.4 m/s), severe typhoon (41.5–50.9 m/s) and super typhoon (>51.0 m/s), respectively.

After validation, the near-inertial kinetic energy density (NIKE) was calculated as:

$$\text{NIKE} = \frac{1}{2}\rho\_0 \left(u\_f^2 + v\_f^2\right) \tag{1}$$

November 2010 were used to analyze the ocean dynamical response to typhoon Megi. These data have a spatial resolution of 1/12.5° and a temporal interval of 3 h, which are available from www.hycom.org/data/glbu0pt08/expt-19pt1 (1 January 2021). The wind forcing used in the HYCOM is the 1-hourly National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR) wind data, which captured tywhere *ρ*<sup>0</sup> = 1024 kg/m<sup>3</sup> is the reference density, *u<sup>f</sup>* and *v<sup>f</sup>* are the zonal and meridional components of the bandpass filtered NIWs, respectively [32]. In this study, we also calculated the depth-integrated NIKE to investigate the horizontal distribution of Megi-induced NIWs. Based on the depth-integrated NIKE, the e-folding time of Megi-induced NIWs was calculated to explore their decay.

phoon Megi [37]. Additionally, note that the Navy Coupled Ocean Data Assimilation (NCODA) system was used for data assimilation when generating the reanalysis data. In addition, to validate the HYCOM reanalysis results, the bandpass filtered NIWs at mooring UIB6 (Figure 1) were used in this study, which are cited from [37]. *2.3. Methodology*  First of all, the HYCOM reanalysis results were compared with in situ observations To investigate the propagation of Megi-induced NIWs, we adopted the same method as [42,43] to separate the NIWs propagating in different directions. This method is based on Hilbert transform as well as filtering, Fourier transform and its inverse transform. For the time series of one-dimensional, two-dimensional and three-dimensional wave fields, this method can automatically identify waves propagating in two, four and eight directions, respectively. Refer to [42] for details of this method. In this study, we adopted this method to deal with the bandpass filtered NIWs along 118◦ E to explore the propagation of Megiinduced NIWs and their reflection at the continental slope of the northern SCS.

at mooring UIB6 for validation. A continuous wavelet transform was first performed to demonstrate the existence of NIWs. As tidal forcing was not considered in the HYCOM reanalysis results (GLBu0.08/expt\_19.1), the bandpass filtered NIWs rather than the raw Modal content is an important characteristic of internal waves [44–48]. Therefore, it was investigated for Megi-induced NIWs in this study. For the zonal and meridional components of NIWs,

$$\begin{cases} \boldsymbol{u}\_f(\boldsymbol{z},t) = \sum\_{\substack{n=0\\n\neq 0\\N\_{\rm in}}}^{N\_{\rm in}} \boldsymbol{u}\_{fn}(t) \cdot \boldsymbol{\Pi}\_n(\boldsymbol{z})\\ \boldsymbol{v}\_f(\boldsymbol{z},t) = \sum\_{n=0}^{N\_{\rm in}} \boldsymbol{v}\_{fn}(t) \cdot \boldsymbol{\Pi}\_n(\boldsymbol{z}) \end{cases} \tag{2}$$

the local Coriolis frequency. After validation, the near-inertial kinetic energy density (NIKE) was calculated as: where *ufn* and *vfn* are the modal components of *u<sup>f</sup>* and *v<sup>f</sup>* with respect to mode *n* (*n* = 0, 1, . . . , *Nm*, *n* = 0 for the barotropic mode and *n* > 0 for baroclinic modes), and

the depth-integrated NIKE to investigate the horizontal distribution of Megi-induced NIWs. Based on the depth-integrated NIKE, the e-folding time of Megi-induced NIWs

$$\text{pre income anu } n > 0 \text{ or } \text{no occurrence moves,}\\ \text{a.u.}$$

$$\Pi\_n(z) = \rho\_0 c\_n^2 \frac{\mathbf{d} \Phi\_n(z)}{\mathbf{d}z} \tag{3}$$

are the normal modes corresponding to velocity, where Φ*n*(*z*) are the eigenfunctions of the eigenvalue problem for eigenspeed *cn*:

$$\frac{\mathbf{d}^2 \Phi\_n}{\mathbf{d}z^2} + \frac{N^2}{c\_n^2} \Phi\_n = 0 \tag{4}$$

subject to boundary conditions Φ*n*(0) = Φ*n*(−*H*) = 0, where *H* is the water depth and *N* is the buoyancy frequency [45].

Based on the temperature and salinity data of the HYCOM reanalysis results, the buoyancy frequency was calculated, and hence, normal modes Φ*<sup>n</sup>* and Π*n*. According to [47], the time-varying stratification has little influence on the modal decomposition result. Therefore, the time-averaged temperature and salinity were used to calculate the buoyancy frequency and normal modes Φ*<sup>n</sup>* and Π*n*. Figure 2 shows an example at 117.04◦ E, 18.48◦ N. In theory, *N<sup>m</sup>* should be infinite in modal decomposition. Whereas in practice, *N<sup>m</sup>* is usually set to be a certain value that is sufficient to capture the internal wave features. Generally, according to previous studies, 3, 5 and 10 are typical values used in modal decomposition [45–48]. Additionally, note that too large *N<sup>m</sup>* may cause overfitting [46]. In this study, we found that *N<sup>m</sup>* = 10 could well reproduce the NIKE and did not cause overfitting. Therefore, *N<sup>m</sup>* = 10 was adopted in the modal decomposition in this study. *J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 5 of 17

**Figure 2.** (**a**) Buoyancy frequency and normal modes (**b**) Φ and (**c**) Π of the first five baroclinic modes at 117.04°E, 18.48°N. **Figure 2.** (**a**) Buoyancy frequency and normal modes (**b**) Φ and (**c**) Π of the first five baroclinic modes at 117.04◦ E, 18.48◦ N. Note that the normal modes shown in (**b**,**c**) have been normalized.

## Note that the normal modes shown in (**b**,**c**) have been normalized. **3. Comparison with In Situ Observations**

**3. Comparison with In Situ Observations** Figure 3 displays the HYCOM zonal currents at mooring UIB6 as well as the continuous wavelet transformation of HYCOM zonal currents at 400 m depth at the mooring. It is clearly shown, that after the passage of typhoon Megi, oscillations appeared in the zonal currents. In Figure 3b, a peak exists near the local Coriolis frequency, suggesting that the Figure 3 displays the HYCOM zonal currents at mooring UIB6 as well as the continuous wavelet transformation of HYCOM zonal currents at 400 m depth at the mooring. It is clearly shown, that after the passage of typhoon Megi, oscillations appeared in the zonal currents. In Figure 3b, a peak exists near the local Coriolis frequency, suggesting that the oscillations in the zonal currents are Megi-induced NIWs.

oscillations in the zonal currents are Megi-induced NIWs. Figure 4 compares the NIWs extracted from in situ observations and the HYCOM reanalysis results at mooring UIB6. Although the temporal intervals of the HYCOM reanalysis results (3 h) and observations (1 h) are different, the NIWs extracted from the HYCOM reanalysis results show a good agreement with those from observations: Both NIWs were rapidly enhanced after the passage of typhoon Megi, suggesting that they were induced by typhoon Megi; both NIWs had upward-propagating phases, suggesting that their energy was downward-propagating, which is consistent with the general features of typhoon-induced NIWs [49–51]; both NIWs were quickly damped at mooring UIB6. This result preliminarily verifies the accuracy of the HYCOM reanalysis results. To quantitatively assess the HYCOM reanalysis results, Figure 5 shows the lowpass filtered current variance of NIWs (Var = *u* 2 *<sup>f</sup>* + *v* 2 *f* ; [37]) averaged between 50 and 420 m depth (the effective

Figure 4 compares the NIWs extracted from in situ observations and the HYCOM reanalysis results at mooring UIB6. Although the temporal intervals of the HYCOM reanalysis results (3 h) and observations (1 h) are different, the NIWs extracted from the HY-COM reanalysis results show a good agreement with those from observations: Both NIWs were rapidly enhanced after the passage of typhoon Megi, suggesting that they were induced by typhoon Megi; both NIWs had upward-propagating phases, suggesting that their energy was downward-propagating, which is consistent with the general features of typhoon-induced NIWs [49–51]; both NIWs were quickly damped at mooring UIB6. This

when Megi passed (00:00 on 22 October).

**Figure 3.** (**a**) HYCOM zonal currents at UIB6 (shading, unit: m/s) as a function of time and depth. (**b**) Continuous wavelet transform (shading, unit: m/s) of HYCOM zonal currents at 400 m depth at UIB6 as a function of time and frequency. The horizontal black solid line indicates the local inertial frequency. In (**a**,**b**), the vertical black dashed lines denote the time

measuring range at UIB6; [37]) for both observations and HYCOM reanalysis results. As seen, both the HYCOM and observed current variance shows the development and decaying of Megi-induced NIWs at UIB6. The correlation coefficient between the HYCOM and observed current variance is 0.97 with a *p*-value much smaller than 0.01, suggesting good consistency between them. Additionally, note that the peak value of the HYCOM current variance is greater than that of the observed current variance. This is reasonable because tidal forcing was not considered in the HYCOM reanalysis results (GLBu0.08/expt\_19.1); hence, nonlinear interaction between NIWs and internal tides cannot occur. As the nonlinear interaction between internal waves can transfer a significant amount of energy [52], the ignored tidal forcing in the HYCOM reanalysis results (GLBu0.08/expt\_19.1) finally leads to an overestimation of the energy and current variance of NIWs. Although the HYCOM reanalysis results overestimate the intensity of NIWs, it may only have a limited influence on the distribution, decaying and modal content of NIWs, which are the main focus of this study. **Figure 2.** (**a**) Buoyancy frequency and normal modes (**b**) Φ and (**c**) Π of the first five baroclinic modes at 117.04°E, 18.48°N. Note that the normal modes shown in (**b**,**c**) have been normalized. **3. Comparison with In Situ Observations** Figure 3 displays the HYCOM zonal currents at mooring UIB6 as well as the continuous wavelet transformation of HYCOM zonal currents at 400 m depth at the mooring. It is clearly shown, that after the passage of typhoon Megi, oscillations appeared in the zonal currents. In Figure 3b, a peak exists near the local Coriolis frequency, suggesting that the oscillations in the zonal currents are Megi-induced NIWs. *J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 6 of 17

*J. Mar. Sci. Eng.* **2021**, *9*, x FOR PEER REVIEW 5 of 17

**Figure 3.** (**a**) HYCOM zonal currents at UIB6 (shading, unit: m/s) as a function of time and depth. (**b**) Continuous wavelet transform (shading, unit: m/s) of HYCOM zonal currents at 400 m depth at UIB6 as a function of time and frequency. The horizontal black solid line indicates the local inertial frequency. In (**a**,**b**), the vertical black dashed lines denote the time when Megi passed (00:00 on 22 October). **Figure 3.** (**a**) HYCOM zonal currents at UIB6 (shading, unit: m/s) as a function of time and depth. (**b**) Continuous wavelet transform (shading, unit: m/s) of HYCOM zonal currents at 400 m depth at UIB6 as a function of time and frequency. The horizontal black solid line indicates the local inertial frequency. In (**a**,**b**), the vertical black dashed lines denote the time when Megi passed (00:00 on 22 October). amount of energy [52], the ignored tidal forcing in the HYCOM reanalysis results (GLBu0.08/expt\_19.1) finally leads to an overestimation of the energy and current variance of NIWs. Although the HYCOM reanalysis results overestimate the intensity of NIWs, it may only have a limited influence on the distribution, decaying and modal content of NIWs, which are the main focus of this study.

Figure 4 compares the NIWs extracted from in situ observations and the HYCOM

**Figure 4.** Comparison of (**a**,**c**) zonal and (**b**,**d**) meridional currents of NIWs (shading, unit: m/s) between (**a**,**b**) observations and (**c**,**d**) HYCOM reanalysis results at UIB6.The vertical black dashed line in each subfigure denotes the time when Megi passed (00:00 on 22 October). **Figure 4.** Comparison of (**a**,**c**) zonal and (**b**,**d**) meridional currents of NIWs (shading, unit: m/s) between (**a**,**b**) observations and (**c**,**d**) HYCOM reanalysis results at UIB6.The vertical black dashed line in each subfigure denotes the time when Megi passed (00:00 on 22 October).

**Figure 5.** Comparison of lowpass filtered depth-averaged current variance of NIWs between observations (blue solid) and HYCOM reanalysis results (orange dashed) at UIB6. The vertical black dashed line indicates the time when Megi passed (00:00 on 22 October). **Figure 5.** Comparison of lowpass filtered depth-averaged current variance of NIWs between observations (blue solid) and HYCOM reanalysis results (orange dashed) at UIB6. The vertical black dashed line indicates the time when Megi passed (00:00 on 22 October).
