A note on interpreting tidal harmonic constants

Abstract

The amplitudes and phase lags of tides or tidal currents, which are collectively known as tidal harmonic constants (THCs), cannot be interpolated linearly and separately. Mistreatment for the interpolations could occur, and indeed, it is seen even in the literature. This note clarifies this topic by providing correct formulas to interpret THCs. One has to perform a nonlinear and coupled interpolation of THCs to have equivalence to the liner interpolation in the time domain. Similarly, tidal current ellipse parameters (ep-parameters) cannot be interpolated linearly and separately. To interpolate ep-parameters, this note recommends that one should first convert them to amplitude and phase lag parameters (ap-parameters) and then use the nonlinear and coupled interpolants proposed herein to interpolate the ap-parameters, followed by converting the results back to ep-parameters. Examples are provided to illustrate the problems and MATLAB functions are provided in Appendix as interpolating tools.