A modified tidal harmonic analysis model for short-term water level observations

Abstract

Tidal constants of major semi-diurnal and diurnal constituents are essential for understanding tidal features and long-term tidal prediction. Widely-used classical harmonic analysis (CHA) model requires at least half-year hourly sea level records to resolve eight major semi-diurnal and diurnal constituents based on the Rayleigh criterion. When the analyzed records are short (typically shorter than one month), most previous studies adopt tidal inference method to infer more constituents in the CHA model. The performance of tidal inference method depends on the accuracy of given inference relationships. In this paper, we propose a modified harmonic analysis model on the basis of the credo of smoothness (i.e. MHACS) which indicates inherent natural links between major astronomical diurnal and semi-diurnal constituents. In the CHA, tidal constituents are independent of each other and estimated individually. However, in the MHACS, major constituents are connected via smooth functions of frequency (linear or quadratic functions) indicated by the credo of smoothness. MHACS aims to determine such smooth functions via least squares and then calculate all major tides simultaneously. A series of ideal and practical experiments are conducted to examine the effectiveness of MHACS. It is found that MHACS can derive relatively accurate tidal constants of eight major tides from short-term hourly tide gauge records and satellite altimeter observations. As a general and understandable method, MHACS is easy to realize and can be widely used to analyze diverse tidal signals in the global ocean except diurnal resonant regions where semi-diurnal tidal admittances may be distorted by nonlinear interactions. Furthermore, it should be noted that widely-used tidal inference method can be considered as a special case of MHACS when tidal admittances are assumed as constant functions of frequency.