A novel method for internal wave monitoring based on expansion of the sound speed profile

For acoustic detection of internal waves, the core issue is to obtain the temporal and spatial distribution of the sound speed profile (SSP). In the inversion process, the SSP is usually expressed by a few parameters through expansion. However, information about internal waves may sometimes be hard to read directly from the inversion results. The aim of this paper is to characterize the internal waves directly though expansion coefficients. By deducing the dynamic equations of the internal waves, an orthogonal basis called the hydrodynamic normal modes (HNMs) can be extracted from a certain number of SSP samples. Unlike the existing widely used empirical orthogonal functions (EOFs), the HNMs have a more explicit physical meaning that is directly related to internal wave activity. The HNMs are then used to expand the SSP time series, and the expansion coefficients are derived. Eventually, information about internal waves can be read directly from the time derivative of the expansion coefficients of the first two modes. In this study, this method is applied to thermistor string profiles from the northern shelf of the South China Sea, where the SSP shows evident spatial and temporal variations due to internal waves. The results show that the SSP can be described approximately by the first two modes with adequate precision. The special oscillation structure of the time derivative of the expansion coefficients can be used to detect internal solitary waves. The expansion coefficients can also give information on internal solitary wave amplitude and width. According to theoretical and experimental analysis, it can be concluded that the internal waves monitoring method introduced in this paper is effective. The HNMs method is simple to apply and depends less on sample data than EOFs. It could be used as an efficient alternative to EOFs to expand the use of the SSP in highly variable areas, where internal waves are intensive.