2.2.5. Estimation of Propagation Direction Using Satellite Images

The propagation directions from the MODIS images (Figure 3) were estimated from the horizontal curvature of the leading fronts from the sea surface manifestations [28]. The propagation direction was calculated by the direction of the center of the straight line connecting the endpoints of the manifestations to the center of the arc for the manifestations. For example, a manifestation of NLIW is shown in the blue box in Figure 3a,c. The orange curvature line from both endpoints (Points A and B) is the leading front of the NLIW. Point C is the center of line AB. Point D is the center of the arc AB. In this case, the angle between

the vectors from C to D, measured counter-clockwise from the east, is the propagation direction. *J. Mar. Sci. Eng.* **2021**, *9*, 1089 7 of 16

**Figure 3.** (**a**,**b**) Two satellite images where (**c**,**d**) surface manifestations of NLIWs (orange lines) are confirmed, from MODIS Terra at 02:50 UTC on 02 August 2015, and MODIS Aqua at 04:44 UTC on 30 July 2018. The blue box is the example of the propagation direction calculation. The SAVEX15 and IORS are marked by a red box and yellow star, respectively. **Figure 3.** (**a**,**b**) Two satellite images where (**c**,**d**) surface manifestations of NLIWs (orange lines) are confirmed, from MODIS Terra at 02:50 UTC on 02 August 2015, and MODIS Aqua at 04:44 UTC on 30 July 2018. The blue box is the example of the propagation direction calculation. The SAVEX15 and IORS are marked by a red box and yellow star, respectively.

#### **3. Applications 3. Applications**

*3.1. SAVEX15 3.1. SAVEX15*

On 23 May 2015 during the SAVEX15, the existence of NLIWs was confirmed from a series of UCTD profiling measurements, for example, at 15:56 UTC (vertical red dashed line in Figure 4b), and the time‐depth pattern of temperature variations observed at the northern mooring VLA1 at 15:02 UTC (vertical grey dashed line in Figure 4a). The NLIW was observed at VLA1 3239 s earlier than that observed in the UCTD measurements (Fig‐ ures 4 and 5a). The 13 °C isotherm displacements, derived from the UCTD and VLA1 observations, commonly range from 27 to 35 m (Figure 5a). The NLIW has an amplitude () of 6.1 and 5.9 m estimated from UCTD and VLA1 observations, respectively (Figures 4 and 5a). The two‐layered theoretical parameters of the NLIWs are listed in Table 1, along with the estimated parameters, where the upper and lower layer densities (ଵ and ଶ) are 1023.35 and 1025.17 kg ∙ mିଷ, respectively, and the upper and lower layer thicknesses (ℎଵ and ℎଶ) are 34.8 and 65.2 m, respectively (Figure 5b and Table 1). On 23 May 2015 during the SAVEX15, the existence of NLIWs was confirmed from a series of UCTD profiling measurements, for example, at 15:56 UTC (vertical red dashed line in Figure 4b), and the time-depth pattern of temperature variations observed at the northern mooring VLA1 at 15:02 UTC (vertical grey dashed line in Figure 4a). The NLIW was observed at VLA1 3239 s earlier than that observed in the UCTD measurements (Figures 4 and 5a). The 13 ◦C isotherm displacements, derived from the UCTD and VLA1 observations, commonly range from 27 to 35 m (Figure 5a). The NLIW has an amplitude (*η*0) of 6.1 and 5.9 m estimated from UCTD and VLA1 observations, respectively (Figures 4 and 5a). The two-layered theoretical parameters of the NLIWs are listed in Table 1, along with the estimated parameters, where the upper and lower layer densities (*ρ*<sup>1</sup> and *<sup>ρ</sup>*2) are 1023.35 and 1025.17 kg·m−<sup>3</sup> , respectively, and the upper and lower layer thicknesses (*h*<sup>1</sup> and *h*2) are 34.8 and 65.2 m, respectively (Figure 5b and Table 1).

**Table 1.** Nonlinear internal wave parameters for the two cases observed, with calculated and estimated values. **Table 1.** Nonlinear internal wave parameters for the two cases observed, with calculated and estimated values.


௦ ሺsecሻ Time lag between two different observations 3239 2370 ௦ ሺmሻ Distance between two different observations 2233 3045 ௦ ሺm ∙ sିଵሻ Speed between two different observations 0.69 1.29


**Figure 4.** Time‐depth pattern of water temperature observed from (**a**) northern mooring (VLA1) and (**b**) UCTD during the SAVEX15. The contour interval is 0.5 °C. The 13 °C isotherm is denoted by a thick black line. The times of NLIW observations at the VLA1 and UCTD are denoted by vertical grey and red dashed lines, respectively. Depths of thermistors attached to the VLA1 are denoted by black squares on the left axes. **Figure 4.** Time-depth pattern of water temperature observed from (**a**) northern mooring (VLA1) and (**b**) UCTD during the SAVEX15. The contour interval is 0.5 ◦C. The 13 ◦C isotherm is denoted by a thick black line. The times of NLIW observations at the VLA1 and UCTD are denoted by vertical grey and red dashed lines, respectively. Depths of thermistors attached to the VLA1 are denoted by black squares on the left axes.

**Figure 5.** (**a**) Time‐series of 13 °C isotherm depth observed at the VLA1 (red) and UCTD (blue), and (**b**) vertical profiles of density obtained from the UCTD measurements (grey) at 15:10–16:14 UTC on 23 May 2015. In (**b**), the average profile is marked in blue, and minimum and maximum densities at the upper and lower layers (corresponding to ଵ and ଶ), respectively, are shown with red dashed lines. **Figure 5.** (**a**) Time-series of 13 ◦C isotherm depth observed at the VLA1 (red) and UCTD (blue), and (**b**) vertical profiles of density obtained from the UCTD measurements (grey) at 15:10–16:14 UTC on 23 May 2015. 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. **Figure 5.** (**a**) Time‐series of 13 °C isotherm depth observed at the VLA1 (red) and UCTD (blue), and (**b**) vertical profiles of density obtained from the UCTD measurements (grey) at 15:10–16:14 UTC on 23 May 2015. In (**b**), the average profile is marked in blue, and minimum and maximum densities at the upper and lower layers (corresponding to ଵ and ଶ), respectively, are shown with red dashed lines.

When the ship moved at a speed of 0.47 m ∙ sିଵ and a direction of 148° (northwest‐ ward), the apparent propagation direction ௗ௦ of NILWs had an angular difference ௗ௦ of േ60° with ship course ௦ (Figure 6a), derived from the *Doppler shift* method using Equation (15), resulting in ௗ௦ ൌ 208° (southwestward) or ௗ௦ ൌ 88° (northward). From the distance (௦ = 2233 m) between the two measurement locations (VLA1 and ship) and the time lag of the NLIW arrivals (௦ = 3239 s), the observed propagation direction of NILWs ௧ was estimated to have an angular difference ௧ of േ19° with ௦ (Figure 6b), derived from the *time lag* method using Equation (17), resulting in ௧ ൌ 211° (southwestward) or ௧ ൌ 249° (slightly more southwestward). Thus, more con‐ sistent propagation directions of ௗ௦ ൌ 208° and ௧ ൌ 211° were selected to optimize the propagation speed and direction. By minimizing |௧ െ ௗ௦|, the optimal propagation speed (௪) of 0.64 m ∙ sିଵ was derived from the iterative calculations, yielding ௗ௦ ൌ 208° and ௧ ൌ 211° with |௧ െ ௗ௦| ൌ 3°, and the resultant propagation direction (௪) of 210° (southwestward). When the ship moved at a speed of 0.47 m·s <sup>−</sup><sup>1</sup> and a direction of 148◦ (northwestward), the apparent propagation direction *φds* of NILWs had an angular difference *θds* of ±60◦ with ship course *φsh* (Figure 6a), derived from the *Doppler shift* method using Equation (15), resulting in ]*φds* = 208◦ (southwestward) or *φds* = 88◦ (northward). From the distance (*Dobs* = 2233 m) between the two measurement locations (VLA1 and ship) and the time lag of the NLIW arrivals (*Tobs* = 3239 s), the observed propagation direction of NILWs *φtl* was estimated to have an angular difference *θtl* of ±19◦ with *φobs* (Figure 6b), derived from the *time lag* method using Equation (17), resulting in *φtl* = 211◦ (southwestward) or *φtl* = 249◦ (slightly more southwestward). Thus, more consistent propagation directions of *φds* = 208◦ and *φtl* = 211◦ were selected to optimize the propagation speed and direction. By minimizing |*φtl* − *φds*|, the optimal propagation speed (*ciw*) of 0.64 m·s <sup>−</sup><sup>1</sup> was derived from the iterative calculations, yielding *φds* = 208◦ and *φtl* = 211◦ with |*φtl* − *φds*| = 3 ◦ , and the resultant propagation direction (*φiw*) of 210◦ (southwestward). When the ship moved at a speed of 0.47 m ∙ sିଵ and a direction of 148° (northwest‐ ward), the apparent propagation direction ௗ௦ of NILWs had an angular difference ௗ௦ of േ60° with ship course ௦ (Figure 6a), derived from the *Doppler shift* method using Equation (15), resulting in ௗ௦ ൌ 208° (southwestward) or ௗ௦ ൌ 88° (northward). From the distance (௦ = 2233 m) between the two measurement locations (VLA1 and ship) and the time lag of the NLIW arrivals (௦ = 3239 s), the observed propagation direction of NILWs ௧ was estimated to have an angular difference ௧ of േ19° with ௦ (Figure 6b), derived from the *time lag* method using Equation (17), resulting in ௧ ൌ 211° (southwestward) or ௧ ൌ 249° (slightly more southwestward). Thus, more con‐ sistent propagation directions of ௗ௦ ൌ 208° and ௧ ൌ 211° were selected to optimize the propagation speed and direction. By minimizing |௧ െ ௗ௦|, the optimal propagation speed (௪) of 0.64 m ∙ sିଵ was derived from the iterative calculations, yielding ௗ௦ ൌ 208° and ௧ ൌ 211° with |௧ െ ௗ௦| ൌ 3°, and the resultant propagation direction (௪) of 210° (southwestward).

**Figure 6.** Propagation direction of NLIW observed during the SAVEX15, estimated from (**a**) *Doppler shift* method and (**b**) *time lag* method. The ௦, ௦, ௗ௦, and ௧ are labelled in the plots. Date and times of the corresponding events are noted in the right bottom corner. **Figure 6.** Propagation direction of NLIW observed during the SAVEX15, estimated from (**a**) *Doppler shift* method and (**b**) *time lag* method. The ௦, ௦, ௗ௦, and ௧ are labelled in the plots. Date and times of the corresponding events are noted in the right bottom corner. **Figure 6.** Propagation direction of NLIW observed during the SAVEX15, estimated from (**a**) *Doppler shift* method and (**b**) *time lag* method. The *φsh*,*φobs*, *θds*, and *θtl* are labelled in the plots. Date and times of the corresponding events are noted in the right bottom corner.
