On tidal analyses with measurement errors

This work presents an approach to estimate measurement errors in tidal analysis. Independent methods deductive and inductive were used. The results showed good agreement. Theoretically deduced results were compared with computer assisted proofs. Both cases showed that measurement errors cannot be ignored but must be considered before deciding to accept or reject the determined tidal constituents. A real sea-level record from Cananéia, Brazil, assumed as an error free series (EFS) was used, from which synthetic series were obtained by the addition of statistically distributed known errors. Fourier analysis was applied to the series, taken as following a mixed model, and the results were compared. It was possible to show that measurement errors in amplitudes, due to the recording device, may add ±√2σ to each tidal constituent, where σis the measurement error’ s standard deviation, which degrades the determination of the tidal constituent amplitudes. All tidal constituents smaller than that value must be rejected. Errors due to clock mechanisms generate spectral spreading of energy, by aliasing to high frequencies and by dispersion in both spectral directions. A method based on Fourier Interpolation was adequate to recover the original series spoiled by acceleration or deceleration of the tide gauge’ s clock. Added timing errors distributed in a jittered sampling manner were reckoned to minimize aliasing, improving the analysis of amplitudes, but not of the phases.