Extracting tidal frequencies of the Persian Gulf and Oman Sea using multivariate least square harmonic estimation of sea level coastal height observations time series

Tidal observations have been widely used for a variety of applications. Realistic functional and stochastic models of tidal observation are then required. The functional model is complete if one knows the tide characteristics such as tidal frequencies (M2 and S2 for instance). The stochastic model is complete if we know noise characteristics of tidal observations. There is always a prediction error between the predicted values and the observed tide heights. This can be investigated when taking the noise characteristics of tidal time series observations. Functional model identification is however the subject of discussion in the present contribution. Tide data are frequently used for different applications such as safe navigation. Real tide gauge data can be expressed by their tidal constituents (frequencies) and a noise structure. Using tidal frequencies and tidal observations one can employ the functional model to predict tide. Therefore identifying tidal frequencies is an important issue for tidal analysis. So far, most of the available methods to determine tidal frequencies have been based on the theory, and sea level height observations have not seriously been used to extract tidal frequencies. The theory-based methods usually apply the ephemeris of Moon, Sun and other planets to extract tidal frequencies without the use of tidal observations. Following-up the study by Amiri-Simkooei et al. (2014), we further focus on extracting tidal frequencies using tidal observations. For this purpose, we apply the least squares harmonic estimation (LS-HE) to the multivariate tidal time series. As a generalization of the Fourier spectral analysis, LS-HE is neither limited to evenly spaced data nor to integer frequencies. We may also note that the main tidal constituents may change from one area to another area. In this contribution, we use the data sets of eight coastal tide gauge stations in Persian Gulf and Oman Sea between 1999 and 2010 with a sampling rate of 30 min using a multivariate analysis. In multivariate analysis, the frequencies contributed in tide structure are more obvious than in the univariate analysis. Such signals can thus simply be detected in the multivariate analysis. Using the above-mentioned data, 414 main tidal constituents have been extracted. Our extracted lists of frequencies (of the Persian Gulf and Oman Sea) are compared with the two lists of frequencies consisting of 50 and 121 frequencies by the study of Amiri-Simkooei et al. (2014), which was applied to UK tide gauge stations. In the present contribution, new frequencies that belong to the tide gauge stations of the Persian Gulf and Oman Sea have been identified. Finally, a six-month prediction is performed for all stations using the two lists of main frequencies obtained in the two studies. The prediction results of the two studies are then compared using the estimated root mean squared error (RMSE). The RMSE difference of our predicted data show a reduction ranging from 2 cm to 7 cm compared to that predicted using the frequency lists of Amiri-Simkooei et al. (2014). The estimated RMSE of tide prediction using the frequencies obtained in this study ranges from 9 to 16 cm.