The Fine Resolution of Tidal Harmonics

Abstract

The tides of deep seas are mainly due to the astronomical forces and these tides can be expressed mathematically by relating the laws of planetary motion with hydrodynamics. Such tides are simple and can be explained in terms of a small number of harmonic components which arise directly from astronomical origins or else indirectly through low order interaction between such terms. The terms developed by mutual interaction are few and are found in significant amplitudes only in the lower frequencies of the spectrum up to sixth-diurnal species. The effects of hydrographical conditions become significant in shallow water where the tide range is comparable with the depth. In the case of shallow coastal areas and estuaries, water in motion is subjected to forces, like bottom friction which change within the tidal cycle as a function of depth. Under these circumstances the rate of convergence of amplitudes of terms developed from high-order interaction becomes slow and the existence of more terms can be identified. These new terms are spread over the whole spectrum thus making it essential to scan it completely and in depth. The tidal characteristics of the Thames represent one such complex. Here the fact that the tide progresses for a long time in a shallow area before entering into the estuary, where it thus meets freshwater flow and a salinity gradient all result in severe distortion of the tide. In the Fine Resolution of Tidal Harmonics method (FRTH), nodal terms of the principal constituents are separated by analysing a data set from Southend of a length exceeding the lunar nodal period of 18.61 years. It is established that the nodal parameters ' f ' and u ' differ from those computed by using the equilibrium tide. This deviation appears to be a significant factor in the generation of humps ' in the residual spectrum discussed by Rossiter & Lennon. The analysis of a long span of data made it possible to resolve directly separable shallow water constituents whose speeds are as close as 0.0022 deg/hr to the speeds of astronomical terms and an attempt has been made to resolve those constituents which are not directly separable, with the help of the ' response function '. The existence of some new shallow water constituents has been confirmed, the most significant of these are in the semi-diurnal, third-diurnal and quarter-diurnal species. The relatively high level of background noise in the long period and diurnal species prohibits the separation of many small nodal terms and consequently their presence cannot be confirmed. No significant change was found in constituents of the sixth-diurnal and higher species. Redefinition of some shallow water * A 294 M. Amin constituents is required in order to facilitate their distinction from associated terms in the same narrow spectral band. However, due to practical problems this is not possible for every place. It has been found better to leave some indirectly separable constituents unresolved. The variance and spectrum of residuals show that predictions are considerably impr...

On perturbations of harmonic constants in the Thames Estuary

“…2 indicate that the harmonic method of analysis and prediction suffer from a systematic error introduced by the assumption that close terms in the spectrum, differing by one cycle during the period of the Moon's perigee or node and separable in 8.85 or 18.61 yr periods, have the same relationship both in the observed and the equilibrium tide. It was noted by Amin (1976) that their relationship in shallow water is different from the equilibrium tide; this research confirms those results. New terms are generated by tide-tide interaction, e.g.…”

Radiational tides at the southeastern coast of the Baltic Sea

“…HIGH RESOLUTION SPECTRA "High resolution tidal spectra" are normally understood as spectra with a frequency resolution sig nificantly better (smaller) than 1 cpy (cycle per year). Construction of such spectra makes it possible to reveal certain features of the formation of tidal oscilla tions, which are not seen in usual spectra and to inves tigate the fine structure of tidal oscillations [8]. The experience of the analysis done in [5] demonstrated that even in basins with weak tides, in particular, in the Baltic Sea, high resolution spectra appear to be a very effective means of tidal analysis, which makes it possi ble to distinguish and investigate a wide set of tidal harmonics.…”

On analysis and prediction of tides on the west coast of Great Britain

“…In comparing their performance, Cartwright & Rossiter (1 972) found that the Response Method was more efficient than the Extended Harmonic Method. Subsequently Amin (1976) investigated the Extended Harmonic Method through the fine resolution of tidal lines and suggested some modifications in definition, and selection, of some constituents. The difference in accuracy of tidal predictions from the two methods was not significant.…”