*Article* **Estimation of Propagation Speed and Direction of Nonlinear Internal Waves from Underway and Moored Measurements**

**Seung-Woo Lee <sup>1</sup> and Sunghyun Nam 1,2,\***


**Abstract:** Propagation speed and direction of nonlinear internal waves (NLIWs) are important parameters for understanding the generation and propagation of waves, and ultimately clarifying regional ocean circulation. However, these parameters cannot be directly measured from in-situ instruments, but can only be estimated from post-processing in situ data. Herein, we present two methods and an optimal approach to estimate the propagation speed and direction of waves using underway and moored observations. The *Doppler shift* method estimates these parameters from apparent observations concerning a moving ship using the Doppler shift induced by the changing relative distance of the NLIWs from the moving ship. The *time lag* method estimates the parameters using the distance between two locations of the NLIW observed at different times and the time lag. To optimize the speed and direction of NLIWs, the difference in the propagation direction independently estimated by the two methods needs to be minimized concerning the optimal propagation speed to yield the optimal propagation direction. The methods were applied to two cases observed in the northern East China Sea in May 2015 and August 2018. This study has practical significance for better estimating the propagation speed and direction of NILWs particularly over a broad continental shelf.

**Keywords:** nonlinear internal wave; propagating speed; propagating direction; underway observation; moored observation; East China Sea
