Harmonic tidal analysis methods on time and frequency domains: similarities and differences for the Gulf of Trieste,Italy, and Paranaguá Bay, Brazil

Two years of sea level data obtained at Trieste, Italy, and Paranaguá, Brazil, were used to compare the performances of two tidal analysis methodologies, one in the time domain (HMB) and other in the frequency domain (HMF). For each station, the first year was analyzed to estimate the tidal constituents while the second year was used to compare observations against forecasted sea levels. With respect to tidal dynamics, results from both methods showed that the semi-diurnal atmospheric tide S2_p is disturbing the sea constituent S2 as well as other frequencies, particularly in the diurnal species in the subtropical case of Paranaguá. These results are in agreement with theoretical development and numerical simulations available in the literature. On the methodological side, both methods showed equivalent performances although HMF is more user-friendly and offers better and more comprehensive results. The main reason seems to be linked to the deepen exploitation of astronomical and physical aspects of the tidal constituents generation and discrimination, considering that HMF can estimate more than 170 while HMB estimates around 110. Also, HMF showed better results for shallow water and long term components. However, the residuals showed that a significant amount of oscillating energy is left behind by both methods, suggesting that other deterministic signals not present in the astronomic tidal frequencies of sea water have to be considered. It is concluded that a better stochastic model for tidal analysis and forecast needs to be formulated in order to better represent the physics of sea level: while tidal forecast with the usual methods seems to work well in many practical cases, the high dependence of numerical models on initial and boundary conditions suggests that sea level harmonic constituents estimation has to be improved.