Least Squares Analysis of Noise-Free Tides Using Energy Conservation and Relative Concentration of Periods Criteria

In this article, a new approach to tidal harmonic analysis is introduced. This approach incorporates more constituents in the least squares method for a fixed duration of noise-free tidal record and results in a more accurate tidal prediction. Moreover, it is demonstrated that 135 days of hourly data, which is significantly less than 369 days data in the Rayleigh criterion, is sufficient for the analysis of 68 main tidal constituents with excellent accuracy. Simultaneous variations of tidal constituents amplitudes are studied while the accuracy of the Rayleigh criterion is evaluated. It is observed that a more reliable criterion for inclusion or omission of tidal constituents in the least squares analysis instead of the Rayleigh criterion may be strived for, since the latter solely estimates the mutual effects of two neighboring constituents while neglecting the collective and combined effects of all constituents. Hence, an energy criterion as well as an allowable error value were introduced in the quest for better accuracy. Using this concept and considering the combined effects of all pertinent constituents, a novel approach is developed enabling the proper selection of tidal constituents for the least squares method of tidal analysis. According to this new approach, the underlying constituents are selected considering the time-span of the tidal time-series record, the tidal potential amplitude coefficients of the constituents, a concentration coefficient and the standard deviation of all constituents periods.