Modelling of the sea surface elevation based on a data analysis in the Greek seas

The theory of time series and especially of the autoregressive moving average (ARMA) models is used for modelling the sea surface elevation. Sea surface elevation is usually recorded by wave measuring devices, but rarely has it been analysed or analytically modelled. Except other traditional applications, forecasting of the wave characteristics in the short-term time scale is important for the optimization of the efficiency of the wave energy converters. The main objective of this work is, by using the Box-Jenkins methodology, the analytical description and forecasting of the sea-surface elevation process. A sample of 50825 records of sea surface elevation was collected by four different deep water locations at the Aegean and Ionian seas in Greece from 2000 to 2011. Analytical ARMA(p,q) models were fitted to a variety of potential parameter combinations, i.e. p, q = {0,1,2,3,4,5} for the examined time series in order to identify the most suitable ARMA model for this purpose. The diagnostic and suitability check, as well as the selection of the best model is carried out according to the Akaike and the Bayesian information criteria. The results obtained suggest that the ARMA(2,5) model is the optimum choice for the representation of the sea surface elevation. A further attempt has been made in order to highlight a possible relation between the best ARMA models and various spectral characteristics such as the significant height, the spectral peak period, the mean wave direction and the spectral bandwidth parameters of the corresponding sea-state. Finally, based on the best-fit ARMA model, a forecast of free surface elevation is carried out, confirming the model sufficiency by estimating the forecast errors.