K. Kardakaris, Stochastic investigation and simulation of wind waves for energy production: Applications for utilization, Diploma thesis, 148 pages, Department of Water Resources and Environmental Engineering – National Technical University of Athens, Athens, July 2020.
In the last three decades, scientific interest has been focused on the use of the oceans for energy production, especially through wind wave exploitation, examining both the phenomenon and the technologies that can be applied. Waves are the main factor in the design of coastal and offshore projects, have probabilistic structure and follow specific probabilistic distribution laws; thus, requiring the use of combined stochasticdeterministic rather than pure deterministic models for their study. The present thesis aims to model the phenomenon, using stochastic methods, to explain its behavior and the possibility of its forecast. For the needs of the analysis, oceanographic data are examined from 24 floating buoys, scattered, both in the North and Southern Hemisphere of the Earth, which record the significant wave height and the average wave period. Initially, the periodicity that governs the phenomenon is studied and it turns out that it is mainly single (seasonal), in contrast to the generative cause of wind waves (wind), which has double (diurnal and seasonal). Therefore, a deterministic periodic model is constructed, that describes the monthly average values and the monthly values of standard deviation of each variable, while for the asymmetry a constant value is obtained. At the same time, the statistical characteristics of the variables are calculated by fitting known marginal distributions. The three-parameter PBF (Pareto-Burr-Feller or also known as Singh-Maddala) is optimally fitted and therefore the monthly and average parameters are calculated, while the largest part of the analysis, for supervisory reasons, is applied to the station with the most available data. In order to study the purely stochastic part of the phenomenon, it is necessary to perform the process of homogenization, with which any kind of periodicity from the marginal structure is removed, before the production of the synthetic timeseries (stochastic synthesis). Then, it is necessary to study the dependence structure of the phenomenon, through the Hurst-Kolmogorov (HK) dynamics. At this stage, we use the climacogram, a stochastic tool for estimating long-term persistence, fitting three possible stochastic schemes to the stations’ mean climacogram, taking into consideration the bias effect, resulting to the Generalized Hurst-Kolmogorov model (GHK) as the optimal solution. The stochastic synthesis of the GHK model is chosen to be performed with the Symmetric Moving Average scheme. The parameters obtained from the GHK model, together with the first four statistical moments calculated through the parameters from 4 | Σ ε λ ί δ α the fitted PBF distribution, are the input data of the SMA_GHK model, which performs the production of the synthetic timeseries of each variable. However, the output timeseries do not contain the periodicity that was previously removed from the marginal structure. Thus, the process of reverse homogenization is performed, with the help now of the periodic model that was constructed earlier, so as to complete the production of the synthetic timeseries and to fully define the proposed model. Finally, the necessary checks are made, in order to confirm the preservation, both of the probabilistic behavior and of the dependence structure (stochastic behavior) and correlation. The last step is to calculate the energy potential through the significant wave height and average wave period of both synthetic and observed timeseries, in order to estimate the strength of the model and the reliability of its application, for short-term or long-term forecast, having either long or short timeseries. These conclusions are derived with the help of two applications, one for an offshore station SE of Australia (large number of available data) and one for a point in the Aegean Sea, north of Astypalaia, where the available data are few and have emerged after simulation.