Applied Ocean Research 69 (2017) 76–86 Contents lists available at ScienceDirect Applied Ocean Research journal homepage: www.elsevier.com/locate/apor Modelling of the sea surface elevation based on a data analysis in the Greek seas Nikos T. Martzikos a,∗ , Takvor H. Soukissian b a Laboratory of Harbour Works, School of Civil Engineering, National Technical University of Athens, 5, Heroon Polytechniou Str., 157-80, Zografos, Greece b Hellenic Centre for Marine Research, Institute of Oceanography, 46.7 km Athens-Sounion Ave, 19013 Anavyssos, Greece a r t i c l e i n f o Article history: Received 22 May 2017 Received in revised form 22 October 2017 Accepted 23 October 2017 Keywords: Stochastic processes Sea surface elevation Time series forecasting ARMA model Wave energy a b s t r a c t 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. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction The assessment and modelling of prevailing wave conditions in a sea area is of interest for ship design, harbour activities, and operational service of platforms. Wave energy applications and the optimal efficiency of the wave energy converters are also directly related to the forecasting of sea surface elevation (sse). Wave cli- mate and sea state parameters such as the significant wave height, the spectral peak period and the mean wave direction are of great importance in marine structural design and ocean engineering. Therefore, several studies have analysed and modelled time series of relevant wave parameters at different locations. The majority of them focuses on wave spectral characteristics and in particular on the significant wave height. However, time series of sse has rarely been analysed. ∗ Corresponding author. E-mail address: nmartzikos@central.ntua.gr (N.T. Martzikos). The sea surface elevation, denoted as  (t ), at a fixed position of the free surface, is represented as a stationary, ergodic and Gaussian stochastic process of the following form: (t ; ˇ) = ∞  i=1 A i cos[2f i t + ϕ i (ˇ)], (1) where A i is, at each frequency, Rayleigh distributed and denotes the amplitude, ϕ i ( ˇ ) is the phase, which is modelled as a random variable uniformly distributed in [0, 2], f i is the frequency of small amplitude components of (1), i.e. f i = 1/T i , where T i is wave period, and i = 1, 2, . . .; ˇ is a choice variable. See also [1] and [2]. Each particular record  (t ) of the free sse is considered as one of the infinite possible realizations that could occur in the same place and under the same experimental conditions. Since the stochastic process which is represented by relation (1) is ergodic, the statis- tical analysis of the stochastic process is practically feasible from only one realization of it. A realization of (t ; ˇ) is a set of records  (t ) at every time instant t. In practice, this realization consists a discrete-time time series, i.e.  (t i ) =  (t 1 ) ,  (t 2 ) , . . .,  (t n ). https://doi.org/10.1016/j.apor.2017.10.008 0141-1187/© 2017 Elsevier Ltd. All rights reserved.