*2.1. Data and Processing*

Shallow-water Acoustic Variability EXperiment 2015 (SAVEX15) was conducted on 14–28 May 2015, focusing on a relatively small area (water depth: ~100 m, area shown in Figure 1a,b) in the northern ECS [38–42]. During the experiment, two moorings (vertical line arrays [VLAs]) and underway conductivity–temperature–depth (UCTD) instruments were used to collect moored temperature (with no conductivity) time series at multiple depths and vertical profiles [43]. The two moorings (VLA1 and VLA2) deployed at water depths of 101 and 102 m, were horizontally separated by ~5.5 km; 25 temperature loggers and 5 Star-Oddi temperature–depth–tilt sensors were attached at nominal depths of 2–80 m with an interval of 1–5 m. The sampling time interval of the moored temperature sensors was 30 s.

Ieodo Ocean Research Station 2018 (IORS18) was conducted in the northern ECS in the vicinity of IORS (32◦7.40 N, 125◦10.90 E, constructed at a water depth of 41 m) on 28 August–1 September 2018 (Figure 1a,c). During the IORS18 experiment, UCTD was used to collect ship-based vertical profiles of temperature and salinity and the IORS-based time series of temperature and pressure data observed at nominal depths of 2, 5, 11, 16, 22, 32, and 37 m, with a typical sampling time interval of 60 s [44].

The depths of the moored temperature sensors attached to the VLAs were corrected using the tilt and pressure data recorded by five Star-Oddi temperature–depth–tilt sensors. After the removal of outliers, the moored temperature data were vertically interpolated using the Akima spline method [45] at 1 m intervals. The UCTD data were processed following the method described by Ullman and Herbert [46], except for the alignment process to correct the mismatch due to different time delays of the conductivity and temperature sensors. The raw temperature and conductivity measured by the UCTD were filtered with a cut-off period of four scans (0.25 s). The raw pressure measured using the UCTD was filtered with a cut-off period of 32 scans (2 s). The time delay between the conductivity and temperature sensors was corrected using lagged correlation. Then, spikes in the salinity data were removed by aligning the data of the temperature and conductivity sensors. After the alignment processing, the data were corrected for the effect of viscous heating and finally vertically averaged over 1 *dbar* bin.

To discuss the theoretical propagation speed of NLIWs in the northern ECS in the context of long-term and interannual variations, vertical profiles of temperature and salinity routinely observed every other month from 1990 to 2019, at two hydrographic stations of the National Institute of Fisheries Science (NIFS), Republic of Korea, were used in this study (red open circles in Figure 1a). To ensure the quality of the temperature and salinity data, vertical profiles containing unreasonable values (both global and local) were removed. Quality control procedures, such as the spike and gradient tests, were applied to extract reliable salinity and temperature profiles. Because the profiles are only available at standard depths (i.e., surface, 10, 20, 30, 50, 75, 100, 125, 150, 200, and 250 m), linear interpolation was conducted to determine data at 1 m vertical intervals [47].

Moderate resolution imaging spectroradiometer (MODIS) sensors onboard the National Aeronautics and Space Administration (NASA) satellites Terra and Aqua, provided true-color images from calibrated, corrected, and geo-located radiance (Level-1 B) data, with a spatial resolution of 250 m. As NLIWs induce the divergence and convergence of sea surface currents as they propagate, thereby modifying the sea surface roughness, they are visible in MODIS true-color images if they are in a sun-glint area [48]. In this study, two images obtained by MODIS Terra on 2 August 2015, and MODIS Aqua on 30 July 2018, were used to estimate the propagation direction of NLIWs from sea surface manifestations.
