Some Recent Investigations into the Harmonic Shallow Water Corrections Method of Tidal Predictions

To overcome the inadequacies of the harmonic method in the analysis and prediction of shallow water tidal regimes, Doodson (1957) devised a Harmonic Shallow Water Corrections (H.S.W.C.) method to improve the quality of predicted times and heights of tidal turning points. This method proved to be very powerful where the constituent M2 is relatively dominant in the tide. The theoretical background and technique of application as presented by Doodson is devised for hand calculations and for use on mechanical harmonic analogue machines which were geared for conventional constituents, not H.S.W.C. constituents. In this paper the method is reformulated using a spectral analysis technique, thus providing a clear explanation of the fundamental ideas involved. In the spectrum of a finite time series record sampled at regular intervals, all the energy at frequencies above the Nyquist frequency is aliased with frequencies below the Nyquist frequency. The aliasing phenomenon when applied to high and low waters, occurring at intervals of approximately half a lunar day, has the inherent advantage that numerous constituents combine together, even eliminating the need for separate identification. Caution must be exercised, however, due to the fact that the time interval of half a lunar day is an approximation only. Any selected constituents can be resolved by use of the least squares method. This technique will be free from previous limitations of a fixed length data (355 days) requirement, and it will also handle effectively discontinuous data. An intensive comparison of Extended Harmonic Method (E.H.M.), Improved Response Method (I.R.M.) and H.S.W.C. method, shows that all these methods are approaching their theoretical limits. Examination of residuals indicates that they are similar in accuracy, but for some typical requirements one method can compute predictions marginally better than the others