**5. Concluding Remarks**

We present a novel method to estimate the propagation speed and direction of NLIWs using widely collected underway and moored observations, and the results of applying the method to two cases of NLIWs observed in May 2015 (SAVEX15) and August 2018 (IORS18). Two-layered KdV theory and satellite images were used to discuss the results of the proposed method. The propagation direction of NLIWs was estimated with respect to a moving ship using the Doppler shift relationship (1. *Doppler shift* method) and independently using the time lag between the NLIWs observed at two different locations (2. *time lag* method). Then, the propagation speed and direction were optimized to minimize the difference in propagation directions derived from the two methods by iterating the propagation speed in the range of ±30% at a resolution of 0.01 m·s −1 . The results derived from the proposed method are robust, as the range of iterative propagation speeds is comparable to the interannual variation of theoretical propagation speeds estimated using historical hydrographic data, yielding an error of less than 15% for the propagation direction. Because in situ observations of NLIWs are still challenging to collect and propagation speed and direction cannot be directly measured from subsurface instruments, our proposed method for estimating the propagation speed and direction of NLIWs using common underway and moored measurements is of practical importance, particularly over a broad shelf, such as the northern ECS, where the multi-directional propagation of multi-mode NLIWs from multiple sources is often observed.

**Author Contributions:** Conceptualization, S.-W.L. and S.-H.N.; methodology, S.-W.L. and S.-H.N.; validation, S.-W.L. and S.-H.N.; formal analysis, S.-W.L.; investigation, S.-W.L. and S.-H.N.; data curation, S.-W.L.; writing—original draft preparation, S.-W.L.; writing—review and editing, S.-W.L. and S.-H.N.; visualization, S.-W.L.; supervision, S.-H.N.; project administration, S.-H.N. Both authors have read and agreed to the published version of the manuscript.

**Funding:** SAVEX15 was funded by the US ONR (N00014-13-1-0510), KIOST (PE99531), and KRISO (PES1940). This work was funded by the Ministry of Oceans and Fisheries, Republic of Korea through the "Establishment of the Ocean Research Station in the Jurisdiction Zone and Convergence Research" and "Deep Water Circulation and Material Cycling in the East Sea (20160040)".

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data supporting this manuscript are available from the corresponding author upon reasonable request. SAVEX15 data are available from Lee et al. [43], IORS18 data are available at the Korea Institute of Ocean Science and Technology (KIOST; https: //kors.kiost.ac.kr/en/; accessed on 5 October 2021), historical CTD data are available at NIFS (http://www.nifs.go.kr/kodc/eng/index.kodc; accessed on 5 October 2021), and MODIS satellite images are available at NASA (http://worldview.earthdata.nasa.gov; accessed on 5 October 2021).

**Acknowledgments:** We would like to thank Heechun Song, Sea-Moon Kim, and Byoung-Nam Kim, all individuals who participated in the SAVEX15 experiment, and Jae-Seol Shim, Jin-Young Jeong, Yong Sun Kim, In-Ki Min, Kwang-Young Jeong, and Da-Eun Yeo who participated in IORS18 experiments and provided technical support for the IORS.

**Conflicts of Interest:** The authors declare no conflict of interest.
