Ocean Tides near Hawaii from Satellite Altimeter Data. Part II

Abstract

In Part I, the Chebyshev polynomial fitting (CPF) method has been proved to be effective to construct reliable cotidal charts for the eight major tidal constituents (M2, S2, K1, O1, N2, K2, P1, and Q1) near Hawaii and yields accurate results which are consistent with the Finite Element Solutions 2014 (FES2014), National Astronomical Observatory 99b (NAO.99b), and TPXO9 models. In this paper, the method is extended to estimate the harmonic constants of some minor tidal constituents. The mesoscale variation correction is applied to tidal elevations from satellite altimeters to eliminate the potential influence of background mesoscale ocean noise when estimating minor tidal constituents. This correction is necessary and makes the amplitude ratio between P1 and K1 constituents more consistent with the equilibrium tidal theory. Compared with the harmonic constants directly extracted from satellite altimeter data, FES2014 and NAO.99b yield mean root-mean-square (RMS) errors of 0.238 and 0.226 cm, respectively, while CPF method yields a mean RMS error of 0.210 cm, causing a 7-12% decrease in the RMS error. At the crossover points between ascending and descending tracks, the decrease of RMS errors becomes 15-18%. The accuracy of this method is also validated by comparing the estimated harmonic constants with those derived from tidal gauges and bottom pressure recorders. These results indicate that the CPF method is also effective for estimating harmonic constants of minor tidal constituents. More importantly, the CPF method can obtain the harmonic constants of minor tidal constituents directly from satellite altimeter data, instead of being inferred via admittance theory.

Two-Dimensional Numerical Simulation of Tide and Tidal Current of Eight Major Tidal Constituents in the Bohai, Yellow, and East China Seas

“…The crossover points are the intersection of ascending and descending satellite altimeter tracks. At the crossover points, the satellite observes twice in a single period, with more data than other observation points and a higher signal-to-noise ratio [17]. As a result, tidal constituents information obtained at crossover points are more reliable.…”

“…Fang et al [8] used 10 years of TOPEX/Poseidon (T/P) altimeter data to obtain empirical cotidal charts of the main diurnal, semidiurnal, and long-period constituents in BYES. Cotidal charts of various constituents near the Hawaiian were derived by fitting T/P altimeter data using Chebyshev polynomials fitting (CPF) [16][17][18]. The CPF method for processing altimeter data to obtain tidal harmonic constants has also been applied to the Bohai and Yellow Seas [19].…”

Fitting Cotidal Charts of Eight Major Tidal Components in the Bohai Sea, Yellow Sea Based on Chebyshev Polynomial Method

“…In this study, the harmonic constants calculated by the CPF are compared with the Finite Element Solutions 2014 (FES2014) model at a horizontal resolution of 1/16 [34,35]. Refer to the study of Xu, Wang, Wang, Lv and Chen [28] for more details on the NAO.99b, TPXO9 and FES2014 models, and refer to the study of Wang, Zhang, Xu, Wang and Lv [27] for more details on the EOT20 model. The harmonic constants of eight tidal gauges (Figure 1) were also compared with the harmonic constants of the CPF, TPXO9, FES2014, NAO.99b and EOT20 solutions.…”

“…In the present study, a new method based on CPF is proposed to calculate the full-field tidal harmonic constants in the shallow-water region of BYS, which provides a new direction for obtaining reliable harmonic constants in this region. The CPF was successfully applied in the area near Hawaii (the open ocean) and obtained precise cotidal charts of eight major constituents and minor tidal constituents [27,28]. This paper presents the application and results of the CPF method in the shallow-water region of BYS.…”

Equidistant Nodes Orthogonal Polynomial Fitting for Harmonic Constants of Long-Period Tides Based on Satellite Altimeter Data

“…This study employed a simple and effective method, the equidistant node orthogonal polynomial fitting (ENOPF) method, to obtain more accurate harmonic constants of the longperiod tidal constituents. The equidistant nodes orthogonal polynomial fitting method has been proven to be effective in the eight major tidal constituents and has been successfully used in Hawaii, the Bohai Sea, and the Yellow Sea area [34][35][36]. Fitting by orthogonal polynomials cannot only avoid the ill-condition caused by too many polynomials but also easily obtain the data used for fitting [37,38].…”