An approach to the spectral analysis of the Jason-2 satellite altimetry observations based on stationary time series Case study: spectral analysis of instantaneous sea level of the Caspian Sea

With the advent of the satellite altimetry in 1973, new scientific applications become possible in oceanography, marine sciences and Earth-related studies, and it was made possible to monitor the sea level with high accuracy and tidal modeling in a global scale. Advances in the sensors technology and different satellite altimetry missions in the recent years led to a great evolution in geodesy and the gravity field modeling studies. The oceanic tide is a periodic phenomenon of rise and fallen of the sea level that has emerged from the combination of waves with different periods. It is governed by the gravitational action of the solar system bodies essentially the moon and the sun, it translates by a transport of water masses. Tide phenomenon is of particular significance among researchers in different scientific societies such as Geodesy, Geophysics, and Oceanography. Since tide is one of the most effective factors on instantaneous sea level fluctuations, it is necessary to know the status of tidal in all offshore projects. So, we can have wider and more optimal exploitation of marine resources with known of the main components of the tide, and finally, the tide phenomenon and sea levels could be predicted with the exact knowledge of the tidal frequencies. Several methods, including Least squares method, Fourier analysis, and statistical methods, have been developed to determine the tidal frequencies. Fourier analysis is a convenient and efficient mathematical tool for modeling the behavior of a periodic phenomenon. In this study, main constituent frequencies of time-series and finally, tidal frequencies in Caspian Sea are determined using the Fourier analysis method relying on the concept of stationary time-series. In this way, first, for a closer look at the data and better visibility of other fluctuations in time-series, the trend component is removed from the data using the Fourier seriese. Next, the frequencies that make up the time-series were identified by the Fourier analysis and least squares method, and as mentioned, the concept of stationary time-series is used to find the main components of the tide in this study. Data from the altimetry satellite Jason-2 from 2008 to early 2014 is analyzed to form the instantaneous sea level time-series in 7 points in Caspian Sea that indicates large instantaneous sea level fluctuations. For time-series, the suitable model for tide modeling can be determined by the following equ ation: where is amplitude, is frequency, is related phase, and is the number of frequencies contained in the model. A discrete set of frequencies can be achieved by in a time-series with equidistant data, where is the time of the first observation and is related to the last. Nyquist Frequency is calculated as. So, the above equation can be written as: So, the amplitudes related to each frequency can be calculated using a least squares adjustment and much more effective frequencies contained in the signal can be identified based on these amplitudes. This analysis uses the concept of Aliased Frequency to calculate the main tidal components in 7 points in Caspian Sea, including: SSA، SA، S2، M2، MF، MM، S4 and M6 component. Finally, spectral analysis is used to study the effect of Volga River on the Caspian Sea level changes.