Determination of Harmonic Parameters with Temporal Variations: An Enhanced Harmonic Analysis Algorithm and Application to Internal Tidal Currents in the South China Sea

Abstract

As an effective tool to distinguish different tidal components, classical tidal current harmonic analysis has been widely used to obtain harmonic parameters of internal tidal currents. However, harmonic parameters cannot exactly reveal the motion of internal tides, as the irregular temporal variations for internal tides are significant in many regions of the world’s oceans. An enhanced harmonic analysis (EHA) algorithm based on the independent point scheme and cubic spline interpolation is presented in this paper to obtain harmonic parameters with temporal variations for different tidal constituents of internal tides. Moreover, this algorithm is applied to analyze 14 months of current data obtained from a mooring located on the continental shelf in the northeastern region of the South China Sea. The obvious irregular temporal variations for the four principal constituents—M2, K1, S2, and O1—of internal tides in this region are indicated. It is hoped that this algorithm might present a brand-new view for researchers to investigate the irregular temporal motions of internal tides.

Exploration of Tidal‐Fluvial Interaction in the Columbia River Estuary Using S_TIDE

“…Second, the harmonic parameters at IPs (red circles in Figure ) can be calculated through a specific algorithm (details are provided later). At last, harmonic parameters on the other points ( x 2 , x 4 , x 6 , x 8 ) can be interpolated between the IPs (Jin et al, ). is named independent points because values at other points are obtained by interpolating values at IPs or, in some sense, they depend on values at IPs (Guo et al, ).…”

“…The error estimation algorithm can be expressed in the following steps (Jin et al, ). First, the tidal part and subtidal part estimated by EHA are removed from the original observed time series to obtain the residual or noise.…”

“…Jin et al () borrowed from the work of Matte et al () and redefined the Rayleigh criterion of EHA for nonstationary internal tides. But we now think the redefined Rayleigh criterion is insufficient because it has no regard for the selection of IP number.…”

“…Based on the independent point (IP) scheme and cubic spline interpolation, Jin et al () developed the enhanced harmonic analysis (EHA) and applied this algorithm to internal tidal currents in the South China Sea to determine the harmonic parameters with temporal variations. But internal tides are very complicated and relevant observations are extremely limited, these all impede the EHA algorithm.…”

“…But internal tides are very complicated and relevant observations are extremely limited, these all impede the EHA algorithm. Thus, Jin et al () did not clarify how to select IP numbers for EHA and they also could not provide an explanation of the physical processes driving the temporal variations observed in the moored current data. In this paper, EHA is implemented in a MATLAB toolbox, S_TIDE, which is developed from the widely used T_TIDE.…”