*3.2. IORS18*

On 30 August 2018 during the IORS18, the existence of NLIWs was confirmed from the isotherm displacements observed by a series of vertical profiling UCTD measurements, particularly at 11:11 UTC (vertical red dashed line in Figure 7b), and the time-depth pattern of temperature measurements at the IORS, at 10:32 UTC (vertical grey dashed line in

*3.2. IORS18*

*3.2. IORS18*

Figure 7a). The NLIWs observed at IORS were 2370 s earlier than those observed at the UCTD (Figure 8a). The 18 ◦C isotherm displacements observed from the UCTD and IORS were comparable, ranging from 23 to 31 m (Figure 8a). The NLIWs (the leading NLIW among a set observed by the UCTD) had an amplitude (*η*0) of 6.8 and 7.0 *m* derived from the IORS and UCTD observations, respectively (Figures 7 and 8a). The densities at the upper and lower layers (*ρ*<sup>1</sup> and *<sup>ρ</sup>*2) were 1018.18 and 1024.99 kg·m−<sup>3</sup> , and thicknesses of the upper and lower layers (*h*<sup>1</sup> and *h*2) were 24.0 and 28.0 m, respectively (Figure 8b and Table 1). pattern of temperature measurements at the IORS, at 10:32 UTC (vertical grey dashed line in Figure 7a). The NLIWs observed at IORS were 2370 s earlier than those observed at the UCTD (Figure 8a). The 18 °C isotherm displacements observed from the UCTD and IORS were comparable, ranging from 23 to 31 m (Figure 8a). The NLIWs (the leading NLIW among a set observed by the UCTD) had an amplitude () of 6.8 and 7.0 de‐ rived from the IORS and UCTD observations, respectively (Figures 7 and 8a). The densi‐ ties at the upper and lower layers (ଵ and ଶ) were 1018.18 and 1024.99 kg ∙ mିଷ, and thicknesses of the upper and lower layers (ℎଵ and ℎଶ) were 24.0 and 28.0 m, respectively (Figure 8b and Table 1). pattern of temperature measurements at the IORS, at 10:32 UTC (vertical grey dashed line in Figure 7a). The NLIWs observed at IORS were 2370 s earlier than those observed at the UCTD (Figure 8a). The 18 °C isotherm displacements observed from the UCTD and IORS were comparable, ranging from 23 to 31 m (Figure 8a). The NLIWs (the leading NLIW among a set observed by the UCTD) had an amplitude () of 6.8 and 7.0 de‐ rived from the IORS and UCTD observations, respectively (Figures 7 and 8a). The densi‐ ties at the upper and lower layers (ଵ and ଶ) were 1018.18 and 1024.99 kg ∙ mିଷ, and thicknesses of the upper and lower layers (ℎଵ and ℎଶ) were 24.0 and 28.0 m, respectively (Figure 8b and Table 1).

On 30 August 2018 during the IORS18, the existence of NLIWs was confirmed from the isotherm displacements observed by a series of vertical profiling UCTD measure‐ ments, particularly at 11:11 UTC (verticalred dashed line in Figure 7b), and the time‐depth

On 30 August 2018 during the IORS18, the existence of NLIWs was confirmed from the isotherm displacements observed by a series of vertical profiling UCTD measure‐ ments, particularly at 11:11 UTC (verticalred dashed line in Figure 7b), and the time‐depth

*J. Mar. Sci. Eng.* **2021**, *9*, 1089 10 of 16

*J. Mar. Sci. Eng.* **2021**, *9*, 1089 10 of 16

**Figure 7.** Time‐depth pattern of water temperature observed at the (**a**) IORS and (**b**) UCTD during IORS18. The contour interval is 2 °C. The 18 °C isotherm is denoted by a thick black line. Time of NLIW observations at the IORS and UCTD are denoted by vertical grey and red dashed lines, re‐ spectively. Depths of thermistors attached to the IORS are denoted by black squares on the left axes. **Figure 7.** Time-depth pattern of water temperature observed at the (**a**) IORS and (**b**) UCTD during IORS18. The contour interval is 2 ◦C. The 18 ◦C isotherm is denoted by a thick black line. Time of NLIW observations at the IORS and UCTD are denoted by vertical grey and red dashed lines, respectively. Depths of thermistors attached to the IORS are denoted by black squares on the left axes. **Figure 7.** Time‐depth pattern of water temperature observed at the (**a**) IORS and (**b**) UCTD during IORS18. The contour interval is 2 °C. The 18 °C isotherm is denoted by a thick black line. Time of NLIW observations at the IORS and UCTD are denoted by vertical grey and red dashed lines, re‐ spectively. Depths of thermistors attached to the IORS are denoted by black squares on the left axes.

**Figure 8.** Information related to NLIWs observed at the IORS and UCTD during IORS18. (**a**) Time‐ series of the depth of the 18 °C isotherm observed at the IORS (red) and UCTD (blue), and (**b**) vertical profiles of density obtained from the UCTD measurements (grey) at 11:02–11:59 UTC on 30 August 2018. In (**b**), the average profile is marked in blue, and minimum and maximum densities at the **Figure 8.** Information related to NLIWs observed at the IORS and UCTD during IORS18. (**a**) Time‐ series of the depth of the 18 °C isotherm observed at the IORS (red) and UCTD (blue), and (**b**) vertical profiles of density obtained from the UCTD measurements (grey) at 11:02–11:59 UTC on 30 August 2018. In (**b**), the average profile is marked in blue, and minimum and maximum densities at the **Figure 8.** Information related to NLIWs observed at the IORS and UCTD during IORS18. (**a**) Timeseries of the depth of the 18 ◦C isotherm observed at the IORS (red) and UCTD (blue), and (**b**) vertical profiles of density obtained from the UCTD measurements (grey) at 11:02–11:59 UTC on 30 August 2018. In (**b**), the average profile is marked in blue, and minimum and maximum densities at the upper and lower layers (corresponding to *ρ*<sup>1</sup> and *ρ*2), respectively, are shown with red dashed lines.

When the ship moved at a speed of 1.38 m·s <sup>−</sup><sup>1</sup> and a direction of 334◦ (southeastward), the apparent propagation direction *φds* of NLIWs had the angular difference *θds* of ±126◦ with the ship course *φsh* (Figure 9a), derived from the *Doppler shift* method using Equation (15), resulting in *φds* = 208◦ (southwestward) or *φds* = 100◦ (northward). From the distance (*Dobs* = 3045 m) between the two measurement locations (IORS and ship) and

lines.

the time lag of the NLIW arrivals (*Tobs* = 2370 s), the observed propagation direction of NLIW *<sup>φ</sup>tl* was estimated to have an angular difference *<sup>θ</sup>tl* = ±45◦ with *φobs* (Figure 9b), derived from the *time lag* method using Equation (17), resulting in *φtl* = 198◦ (southwestward) or *φtl* = 288◦ (southeastward). Thus, more consistent propagation directions of *φds* = 208◦ and *φtl* = 198◦ were selected to optimize the propagation speed and direction. By minimizing |]*φtl* − *φds*|, optimal propagation speed (*ciw*) of 1.06 m·s <sup>−</sup><sup>1</sup> was derived from the iterative calculations, yielding *φds* = 205◦ and *φtl* = 205◦ with |*φtl* − *φds*| = 0 ◦ , and the resulting propagation direction (*φiw*) of 205◦ was obtained. and ship) and the time lag of the NLIW arrivals (௦ = 2370 s), the observed propagation direction of NLIW ௧ was estimated to have an angular difference ௧ ൌ േ45° with ௦ (Figure 9b), derived from the *time lag* method using Equation (17), resulting in ௧ ൌ 198° (southwestward) or ௧ ൌ 288° (southeastward). Thus, more consistent propaga‐ tion directions of ௗ௦ ൌ 208° and ௧ ൌ 198° were selected to optimize the propagation speed and direction. By minimizing |௧ െ ௗ௦|, optimal propagation speed (௪) of 1.06 m ∙ sିଵ was derived from the iterative calculations, yielding ௗ௦ ൌ 205° and ௧ ൌ 205° with |௧ െ ௗ௦| ൌ 0°, and the resulting propagation direction (௪) of 205° was obtained.

upper and lower layers (corresponding to ଵ and ଶ), respectively, are shown with red dashed

When the ship moved at a speed of 1.38 m ∙ sିଵ and a direction of 334° (southeast‐ ward), the apparent propagation direction ௗ௦ of NLIWs had the angular difference ௗ௦ of േ126° with the ship course ௦ (Figure 9a), derived from the *Doppler shift* method using Equation (15), resulting in ௗ௦ ൌ 208° (southwestward) or ௗ௦ ൌ 100° (north‐ ward). From the distance (௦ = 3045 m) between the two measurement locations (IORS

*J. Mar. Sci. Eng.* **2021**, *9*, 1089 11 of 16

**Figure 9.** Propagation direction of NLIW observed during IORS18, estimated from (**a**) *Doppler shift* method and (**b**) *time lag* method. The ௦, ௦, ௗ௦, and ௧ are labeled in the plots. Dates and times of the corresponding events are noted in the right bottom corner. **Figure 9.** Propagation direction of NLIW observed during IORS18, estimated from (**a**) *Doppler shift* method and (**b**) *time lag* method. The *φsh*, *φobs*, *θds*, and *θtl* are labeled in the plots. Dates and times of the corresponding events are noted in the right bottom corner.

#### **4. Discussion 4. Discussion**

Herein, we discussed whether the propagation speeds of NLIWs estimated using the proposed method are reasonable based on the KdV theory and previous observations. Interannual variations of the theoretical propagation speed (ௗ.௪, NIFS‐SAVEX15) in May from 1994 to 2019 derived from the NIFS historical hydrographic data near the SAVEX15 area range from 0.36 to 0.71 m ∙ sିଵ, with a temporal mean and standard devi‐ ation of 0.50 and 0.09 m ∙ sିଵ, respectively (red line in Figure 10a). A long‐term decreasing trend was observed in May ௗ.௪ (NIFS‐SAVEX15) at a rate of −0.004 m ∙ sିଵ ∙ yrିଵ (red dotted line in Figure 10a), primarily because of the decreasing density stratification, that is, increasing ଵ and decreasing ଶ with no significant change in ℎଵ and ℎଶ in May (red lines in Figure 10b,c). The propagation speed for May 2015 estimated using the pro‐ posed method ( ௪ ) was consistent with the theoretical propagation speed ( ௗ.௪ ; SAVEX15) derived from the hydrographic data obtained during SAVEX15 and that (NIFS‐ SAVEX15) derived from the nearby NIFS data, with minor (<0.05 m ∙ sିଵ) differences (closed square, open square, and open circle in Figure 10a). Similarly, interannual variations in the theoretical propagation speed (ௗ.௪, NIFS‐ Herein, we discussed whether the propagation speeds of NLIWs estimated using the proposed method are reasonable based on the KdV theory and previous observations. Interannual variations of the theoretical propagation speed (*cKdV*.*iw*, NIFS-SAVEX15) in May from 1994 to 2019 derived from the NIFS historical hydrographic data near the SAVEX15 area range from 0.36 to 0.71 m·s −1 , with a temporal mean and standard deviation of 0.50 and 0.09 m·s −1 , respectively (red line in Figure 10a). A long-term decreasing trend was observed in May *cKdV*.*iw* (NIFS-SAVEX15) at a rate of −0.004 m·s −1 ·yr−<sup>1</sup> (red dotted line in Figure 10a), primarily because of the decreasing density stratification, that is, increasing *ρ*<sup>1</sup> and decreasing *ρ*<sup>2</sup> with no significant change in *h*<sup>1</sup> and *h*<sup>2</sup> in May (red lines in Figure 10b,c). The propagation speed for May 2015 estimated using the proposed method (*ciw*) was consistent with the theoretical propagation speed (*cKdV*.*iw*; SAVEX15) derived from the hydrographic data obtained during SAVEX15 and that (NIFS-SAVEX15) derived from the nearby NIFS data, with minor (<0.05 m·s −1 ) differences (closed square, open square, and open circle in Figure 10a).

IORS18) in August from 1994 to 2019 derived from the NIFS historical hydrographic data

in Figure 10) [33].

*J. Mar. Sci. Eng.* **2021**, *9*, 1089 12 of 16

near the IORS ranged from 0.42 to 0.86 m ∙ sିଵ, with a temporal mean and standard devi‐ ation of 0.66 and 0.10 m ∙ sିଵ, respectively (blue line in Figure 10a). However, the long‐ term trend in August ௗ.௪ (NIFS‐IORS18) was positive (at a rate of 0.003 m ∙ sିଵ ∙ yrିଵ; blue dotted line in Figure 10a) because of the increasing density stratification between the layers, that is, decreasing ଵ and increasing ଶ with no significant change in ℎଵ and ℎଶ in August (blue lines in Figure 10b,c). In contrast to May 2015, the propagation speed for August 2018 estimated using the proposed method (௪) was not consistent with the the‐ oretical propagation speed (ௗ.௪; IORS18) derived from the hydrographic data obtained during IORS18 and that (NIFS‐IORS18) derived from the nearby NIFS data, yielding sig‐ nificant (>0.25 m ∙ sିଵ) differences (closed square, open square, and open circle in Figure 10a). The difference in density stratification between the NIFS and IORS18 data cannot explain the difference in ௪ from the theoretical propagation speeds of ௗ.௪ (IORS18) and ௗ.௪ (NIFS‐IORS18), implying the limitation of theoretical estimation. A similar difference in the observed propagation speed from the theoretical propagation speed in the area near the IORS was reported from the observations in August 2005 (blue diamond

**Figure 10.** (**a**) Time series of propagation speed estimated from the method proposed in this study (colored squares; red for SAVEX15 and blue for IORS18) and KdV theory (open squares, open circles, and colored lines). KdV theory was ap‐ plied using the NIFS historical hydrographic data for May (red line and open circle) and August (blue line and open circle), and hydrographic data obtained during SAVEX15 and IORS18 (open squares). The propagation speed of NLIWs observed in the northern ECS in August 2005 [33] is denoted by a blue diamond. Time series of (**b**) thickness (ℎଵ and ℎଶ) and (**c**) density (ଵ and ଶ) of the upper (solid lines) and lower (dashed lines) layers derived from the NIFS historical hydro‐ graphic data for May (red) and August (blue), and hydrographic data obtained during SAVEX15 and IORS18 (open squares and circles for upper and lower layers, respectively). Long‐term trends of (**a**) propagation speed, (**b**) layer thick‐ ness, and (**c**) layer density from 1994 to 2019 are remarked with dotted lines. To determine whether the propagation directions of NLIWs estimated using the pro‐ **Figure 10.** (**a**) Time series of propagation speed estimated from the method proposed in this study (colored squares; red for SAVEX15 and blue for IORS18) and KdV theory (open squares, open circles, and colored lines). KdV theory was applied using the NIFS historical hydrographic data for May (red line and open circle) and August (blue line and open circle), and hydrographic data obtained during SAVEX15 and IORS18 (open squares). The propagation speed of NLIWs observed in the northern ECS in August 2005 [33] is denoted by a blue diamond. Time series of (**b**) thickness (*h*<sup>1</sup> and *h*2) and (**c**) density (*ρ*<sup>1</sup> and *ρ*2) of the upper (solid lines) and lower (dashed lines) layers derived from the NIFS historical hydrographic data for May (red) and August (blue), and hydrographic data obtained during SAVEX15 and IORS18 (open squares and circles for upper and lower layers, respectively). Long-term trends of (**a**) propagation speed, (**b**) layer thickness, and (**c**) layer density from 1994 to 2019 are remarked with dotted lines.

posed method are physically reasonable, we compared the ௪ values with those derived from satellite images and previous observations. The ௪ values estimated during the two experiments (SAVEX15 and IORS18) using the proposed method were consistent with those derived from MODIS images. Despite the fact that the surface manifestations of NLIWs observed in the two MODIS images were distant (56–123 km from the SAVEX15 area and 42–190 km from the IORS) from the locations of NLIWs observed during the two experiments, south‐westward‐propagating NLIWs (propagation direction of 186–209°) were consistently found in the two images (Figure 3). Previous observations Similarly, interannual variations in the theoretical propagation speed (*cKdV*.*iw*, NIFS-IORS18) in August from 1994 to 2019 derived from the NIFS historical hydrographic data near the IORS ranged from 0.42 to 0.86 m·s −1 , with a temporal mean and standard deviation of 0.66 and 0.10 m·s −1 , respectively (blue line in Figure 10a). However, the long-term trend in August *cKdV*.*iw* (NIFS-IORS18) was positive (at a rate of 0.003 m·s −1 ·yr−<sup>1</sup> ; blue dotted line in Figure 10a) because of the increasing density stratification between the layers, that is, decreasing *ρ*<sup>1</sup> and increasing *ρ*<sup>2</sup> with no significant change in *h*<sup>1</sup> and *h*<sup>2</sup> in August (blue lines in Figure 10b,c). In contrast to May 2015, the propagation speed for August 2018 estimated using the proposed method (*ciw*) was not consistent with the theoretical propagation speed (*cKdV*.*iw*; IORS18) derived from the hydrographic data obtained during IORS18 and that (NIFS-IORS18) derived from the nearby NIFS data, yielding significant (>0.25 m·s −1 ) differences (closed square, open square, and open circle in Figure 10a). The difference in density stratification between the NIFS and IORS18 data cannot explain the difference in *ciw* from the theoretical propagation speeds of *cKdV*.*iw* (IORS18) and *cKdV*.*iw* (NIFS-IORS18), implying the limitation of theoretical estimation. A similar difference in the observed propagation speed from the theoretical propagation speed in the area near the IORS was reported from the observations in August 2005 (blue diamond in Figure 10) [33].

To determine whether the propagation directions of NLIWs estimated using the proposed method are physically reasonable, we compared the *φiw* values with those derived from satellite images and previous observations. The *φiw* values estimated during the two experiments (SAVEX15 and IORS18) using the proposed method were consistent with those derived from MODIS images. Despite the fact that the surface manifestations of NLIWs observed in the two MODIS images were distant (56–123 km from the SAVEX15 area and 42–190 km from the IORS) from the locations of NLIWs observed during the two experiments, south-westward-propagating NLIWs (propagation direction of 186–209◦ ) were consistently found in the two images (Figure 3). Previous observations based on satellite SAR and optical images taken between 1993 and 2004 [35] and SAR images taken between 2014 and 2015 [36] in the northern ECS also support the south-westwardpropagating NILWs (propagation direction ranging from 212◦ to 245◦ ), which may be dominant among the various NLIWs propagating in multiple directions from multiple sources in the northern ECS (Figure 1a).

The two-layered classical (ordinary) KdV theory used in this study has clear limitations. The classical KdV theory is very simplified and assumes weak non-linearity and weak dispersiveness. In fact, NLIWs observed in many areas have been better explained by the eKdV theory than by the KdV theory. However, propagation speeds, in cases of SAVEX15 and IORS18, derived based on the eKdV theory (*ceKdV*.*iw*) including the cubic non-linearity are not significantly different from those based on the KdV theory (*cKdV*.*iw*), yielding the difference less than 0.02 m·s <sup>−</sup><sup>1</sup> due to relatively small *η*<sup>0</sup> (Table 1). Furthermore, as in the case of NLIWs in the South China Sea, finite-depth theory may be theoretically more appropriate than shallow-water theory where the KdV and eKdV theories are based on [53]. The theoretical propagation speeds in the forms of Equations (6) and (9) are limited to the case of no background pedestal condition that could not be considered in this study and might affect the speed significantly. The rigid lid assumption of the KdV and eKdV theories at the top boundary is not fully realistic, although reasonable in many cases, because the resonant interaction between the surface and internal waves supports the possible need for the presence of a free surface at the top boundary to yield more realistic theoretical estimates [54]. In addition, the results presented in this study are limited to only mode-1 NLIWs by applying the two-layered system, yet the vertical profiles of mean density observed during the two experiments (Figures 5b and 8b) support normal mode decompositions (J. Klinck's Matlab program dynmodes.m, available online at http://github.com/sea-mat/dynmodes; accessed on 5 October 2021) for the first three modes corresponding to 49%, 18%, and 14% for SAVEX15 and 50%, 21%, and 13% for IORS18, respectively. Multi-mode NLIWs beyond the mode-1 NLIWs in the region, not investigated in this study, yet explaining about half of NLIWs, need to be examined in the future.
