# Modeling instantaneous water level changes of Caspian Sea using satellite altimetry observations

Authors

1 Associate Professor, Department of Surveying and Geomatics Engineering, University College of Engineering, University of Tehran, Iran

2 M.Sc. student of Geodesy (Hydrography) , Department of Surveying and Geomatics Engineering, University College of Engineering, University of Tehran

3 M.Sc., Department of Surveying and Geomatics Engineering, University College of Engineering, University of Tehran, Iran

Abstract

Sea level changes are of particular significance because of their influence on the industries such as fishery, shipping, marine transport, harbor design, and power constructions in marine and coastal regions. Considering the possible irreparable environmental and economic damages, studying the sea level changes with time is necessary.
Several methods, including experimental methods and numerical models, have been developed to predict the sea wave behavior. Time series analysis is one of the approaches for detecting sea level variations and short-term and long-term prediction. For this purpose, different methods have been proposed including ARMA, MA and AR time series models.
With the advent of satellite altimetry in 1973, it was made possible to monitor the sea level with high accuracy (Anzenhofer et al. 1999). Altimetry satellites collect height information from different points on the Earth along the determined orbits. The main mission of these satellites is to measure the sea level at different times and locations.
In this study, data from the altimetry satellite Jason-2 from 2008 to 2012 is analyzed using different time series processes.
The time series for the instantaneous water level is influenced by seasonal, periodical and stochastic variations due to environmental factors.
Fourier analysis is a convenient and efficient mathematical tool for modeling the behavior of a periodic phenomenon.
Having the water level and the measurement time, a time series of the variations is derived. The water level model is considered as a linear combination of trigonometric functions as below:

The above equation is called the Fourier series for the sequence  in which  and  are the Fourier coefficients. If  and  are determined for each given frequency, the numerical value of the periodic phenomena can be computed at each  epoch.
Frequency estimation is one of the most important steps in modeling. For this purpose Fourier spectral analysis method was used to find the time series’ frequency, and least square method relying on the concept of time series stationary to achieve more accurate frequency. The results show that after removal of main frequencies of two steps with a period greater than 19 days and greater than 4 hours, data were completely stationary and were prepared for the modeling using time series.
The main purpose of this study is to choose the best model for the prediction of the sea level in the region under study based on the prediction error criteria. The trend for water level variations from 2008 to 2012, the improvement in relative accuracy of estimation, and the water level prediction in the long-term interval are also investigated.
To investigate the performance of the different models in estimation of the time series values in the long-term interval, absolute mean error, root mean square error, Akaike information criterion (AIC), Bayesian information criterion (BIC) and Schwarz Bayesian criterion (SBC) are used. The results show that the AR(6) time series model is more efficient than MA(q) and ARMA(p,q) models, predicting the variations with lower errors. The statistical analysis of the instantaneous water level shows that the absolute mean error is 3.8 mm, and the root mean square error is 1.43 cm/day.

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Main Subjects

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