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There are a variety of requirements for future forecasts in relation to optimizing the production of wave energy. Daily forecasts are required to plan maintenance activities and allow power producers to accurately bid on wholesale energy markets, hourly forecasts are needed to warn of impending inclement conditions, possibly placing devices in survival mode, while wave-by-wave forecasts are required to optimize the real-time loading of the device so that maximum power is extracted from the waves over all sea conditions. In addition, related hindcasts over a long time scale may be performed to assess the power production capability of a specific wave site. This paper addresses the full spectrum of the aforementioned wave modeling activities, covering the variety of time scales and detailing modeling methods appropriate to the various time scales, and the causal inputs, where appropriate, which drive these models. Some models are based on a physical description of the system, including bathymetry, for example (e.g., in assessing power production capability), while others simply use measured data to form time series models (e.g., inwave-to-wave forecasting). The paper describes each of the wave forecasting problem domains, details appropriate model structures and how those models are parameterized, and also offers a number of case studies to illustrate each modeling methodology. © 2017 Alexis Mérigaud, Victor Ramos, Francesco Paparella, and John V. Ringwood.

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... • As to the duration of the forecast; Mérigaud et al. have classified ocean forecasting for wave energy production [7]: shortterm (in the order of seconds); medium-term (hourly and daily basis), useful for the wave energy market; and longterm (several years), used to evaluate the viability of a WEC project; • As to the purpose of the forecast, there are distinctions between the evolution with time of variables (e.g. wave elevation, or excitation force acting upon a particular WEC), and the evolution with time of statistical parameters of the variables (e.g. ...

... Performance enhancements could be achieved using short-term wave forecasting with basic equipment and minimal investment. Paparella et al. have published two studies on up-wave measurements to evaluate its relevance on short-term wave forecasting [7,15,16]. A finite impulse response (FIR) model was designed to study the up-wave measurements. ...

... According to Mérigaud et al., medium-term forecasts were useful for wave energy production for market participation [7]. Futhermore, basic sea state parameters were predicted: wave energy flux, significant wave height and wave period. ...

Abstract The high variability and unpredictability of renewable energy resources require optimization of the energy extraction, by operating at the best efficiency point, which can be achieved through optimal control strategies. In particular, wave forecasting models can be valuable for control strategies in wave energy converter devices. This work intends to exploit the short‐term wave forecasting potential on an oscillating water column equipped with the innovative biradial turbine. A Least Squares Support Vector Machine (LS‐SVM) algorithm was developed to predict the air chamber pressure and compare it to the real signal. Regressive linear algorithms were executed for reference. The experimental data was obtained at the Mutriku wave power plant in the Basque Country, Spain. Results have shown LS‐SVM prediction errors varying from 9% to 25%, for horizons ranging from 1 to 3 s in the future. There is no need for extensive training data sets for which computational effort is higher. However, best results were obtained for models with a relatively small number of LS‐SVM features. Regressive models have shown slightly better performance (8–22%) at a significantly lower computational cost. Ultimately, these research findings may play an essential role in model predictive control strategies for the wave power plant.

... • In the future, computationally efficient simulation tools will also be necessary for the realtime operation of WEC or WEC farms, including energy production forecasting for market participation, management of the WEC safe mode (to avoid structural damage, in case of dangerously high sea conditions), and predictive maintenance, as discussed in [5]. ...

... Four-wave interactions have been found essential to explain how the wave spectrum slowly evolves in time and space and, in particular, how the wave spectrum broadens to low frequencies which cannot be generated directly under the effect of wind [30]. As such, the computation of spectral energy transfers due to four-wave interactions is a challenging and crucial aspect of modern operational ocean weather forecasting models [5], referred to as 3 rd generation wave models. Note that, in numerical weather forecasting models, the other terms, namely wind forcing and wave dissipation, which govern the evolution of the wave spectrum in the energy balance equation, are also essentially non-linear phenomena. ...

... The scatter diagram must be evaluated based on sufficiently long historical data, at least 10 years according to IEC TS 62600-101 [54,55]. Such historical data may have been recorded at the site of interest (if a measurement device has been operating at the site for a sufficiently long time), or reconstructed from numerical ocean models [56], which is referred to as hindcast data [5]. An example of a scatter diagram is given in Fig. 2.3, which has been constructed from hourly wave spectra corresponding to the Belmullet wave dataset, although the record is far too short and incomplete to comply with the recommended 10 years. ...

Numerical simulation is essential, to assist in the development of wave energy technology. In particular, tasks such as power assessment, optimisation and structural design require a large number of numerical simulations to calculate the wave energy converter (WEC) outputs of interest, over a variety of wave conditions or physical parameters. Such challenges involve a sound understanding of the statistical properties of ocean waves, which constitute the forcing inputs to the wave energy device, and computationally efficient numerical techniques for the speedy calculation of WEC
outputs. This thesis studies the statistical characterisation, and numerical generation, of ocean waves, and proposes a novel technique for the numerical simulation of non-linear WEC models.
The theoretical foundations, the range of validity, and the importance of the statistical representation of ocean waves are first examined. Under relatively mild assumptions, ocean waves can be best described as a stationary Gaussian process, which is entirely characterised by its spectral density function (SDF). Various wave superposition techniques are discussed and rigorously compared, for the numerical generation of Gaussian wave elevation time series from a given SDF. In particular, the harmonic random amplitude (HRA) approach can simulate the target statistical properties with perfect realism. In contrast, the harmonic deterministic amplitude (HDA) approach is statistically inconsistent (because the generated time-series are non-Gaussian, and under-represent the short-term statistical variability of real ocean waves), but can be advantageous in the context of WEC simulations since, if it can be verified that HDA results are unbiased, the HDA method requires a smaller number of random realisations than the HRA method, to obtain accurate WEC power estimates.
When either HDA or HRA are used for the generation of wave inputs, the forcing terms of WEC mathematical models are periodic. Relying on a Fourier representation of the system inputs and variables, the harmonic balance (HB) method, which is a special case of spectral methods, is a suitable mathematical technique to numerically calculate the steady-state response of a non-linear system, under a periodic input. The applicability of the method to WEC simulation is demonstrated for those WEC models which are described by means of a non-linear integro-differential equation. In the proposed simulation framework, the WEC output, in a given sea state, is assessed by means of many, relatively short, simulations, each of which is efficiently solved using the HB method.
A range of four case studies is considered, comprising a flap-type WEC, a spherical heaving point-absorber, an array of four cylindrical heaving point-absorbers, and a pitching device. For each case, it is shown how the HB settings (simulation duration and cut-off frequency) can be calibrated. The accuracy of the HB method is assessed through a comparison with a second-order Runge-Kutta (RK2) time-domain integration scheme, with various time steps. RK2 results converge to the HB solution, as the RK2 time step tends to zero. Furthermore, in a Matlab implementation, the HB method is between one and three orders of magnitude faster than the RK2 method, depending on the RK2 time step, and on the method chosen for the calculation of the radiation memory terms in RK2 simulations. The HB formalism also provides an interesting framework, for studying the sensitivity of the WEC dynamics to system parameter variations, which can be utilised within a gradient-based parametric optimisation algorithm. An example of WEC gradient-based
parametric optimisation, carried out within the HB framework, is provided.

... Immediate horizon forecasts are necessary to improve the controller so that it can more efficiently capture power from the waves. [1] Despite the challenges associated with wave height forecasting for renewable wave energy applications, various algorithms have been developed to provide accurate forecasting for the next few minutes to the next few days. These algorithms can be clustered into four categories: physical models, statistical models, machine learning techniques, and hybrid approaches. ...

... These algorithms can be clustered into four categories: physical models, statistical models, machine learning techniques, and hybrid approaches. [2] There are three generations of phase-averaging wave models, which are based on energy-balance with source and sink terms [1]. First-generation models take into consideration only simplified wind fields and use these to calculate wave growth and spread in deep waters, but provide poor results in near-shore locations, while second-generation models take into consideration transient wind fields and nonlinear interactions. ...

... After the flap is struck by a wave, it pitches around the axis parallel to the wave crest and is then restored to its original position by the force of buoyancy. A current challenge that exists in the wave energy community is survivability during various sea conditions, including extreme sea states [1][2][3]. Currently, most OWSCs are designed to enter survival mode during these extreme conditions where they forego the opportunity to extract energy in attempts to preserve structural integrity [1]. While this compromise enhances OWSC survival, optimally energy could be collected in all sea states. ...

... A current challenge that exists in the wave energy community is survivability during various sea conditions, including extreme sea states [1][2][3]. Currently, most OWSCs are designed to enter survival mode during these extreme conditions where they forego the opportunity to extract energy in attempts to preserve structural integrity [1]. While this compromise enhances OWSC survival, optimally energy could be collected in all sea states. ...

Oscillating Wave Surge Converters (OWSCs) are designed to enter survival mode during extreme wave conditions where they forego the opportunity to extract energy to preserve structural integrity. While this is a good tradeoff, it is important that OWSC technology progresses to a point where energy is constantly extracted as long as waves are present. This work addresses the need for an OWSC that can extract wave energy in a wide range of sea conditions while minimizing structural overloading by regulating the fluid-structure interaction. The OWSC being studied here was conceptually designed and patented by researchers at NREL. It consists of a flap face that resembles household blinds, where the flaps can be opened or closed to accommodate the sea conditions. The performance of this variable geometry OWSC in various, shallow wave states was studied in two numerical modeling programs. Of particular interest were the flap’s hydrodynamic coefficients and potential power generation at a specific reference site. This configuration was predicted to mitigate wave forces by allowing some of the wave energy to pass through the device, thus preserving its structural integrity.

... It is essential to understand the wave resource for at least three reasons: (i) one needs to know what the average wave power is in the area where one wants to deploy WECs; (ii) one needs to know the waves in more detail if one wants to use control to optimize the efficiency of the WECs [65][66][67][68][69][70]; (iii) one wants to know when access to the WECs will be possible in case maintenance is needed [71,72]. Ocean waves are created by wind and then propagate freely in the ocean, forming swell. ...

... Short-term wave forecasting is still a largely open question, even if progress has been made recently [67,68]. One of the pressing questions is: How are free-surface evolutions best synthesized from wave spectra for power production assessment [69,70]? ...

The development of new wave energy converters has shed light on a number of unanswered questions in fluid mechanics, but has also identified a number of new issues of importance for their future deployment. The main concerns relevant to the practical use of wave energy converters are sustainability, survivability, and maintainability. Of course, it is also necessary to maximize the capture per unit area of the structure as well as to minimize the cost. In this review, we consider some of the questions related to the topics of sustainability, survivability, and maintenance access, with respect to sea conditions, for generic wave energy converters with an emphasis on the oscillating wave surge converter. New analytical models that have been developed are a topic of particular discussion. It is also shown how existing numerical models have been pushed to their limits to provide answers to open questions relating to the operation and characteristics of wave energy converters.

... Nonetheless, wave energy has a higher power density than solar, wind, and even ocean current [6,7]. Also, since ocean waves propagate with little attenuation, they can be detected several miles offshore, allowing for skilled forecasts many hours in advance [8,9]. ...

The deployment of offshore wind, wave, and ocean current technologies can be coordinated to provide maximum economic benefit. We develop a model formulation based on Mean-Variance portfolio theory to identify the optimal site locations for a given number of wind, wave, and ocean current turbines subject to constraints on their energy collection system and the maximum number of turbines per site location. A model relaxation is also developed to improve the computational efficiency of the optimization process, allowing the inclusion of more than 5000 candidate generation sites. The model is tested using renewable resource estimates from the coast of North Carolina, along the eastern US coast. Different combinations of technology-specific offshore technologies are compared in terms of their levelized cost of electricity and energy variability. The optimal portfolio results are then included in a capacity expansion model to derive economic targets that make the offshore portfolios cost-competitive with other generating technologies. Results of this work indicate that the integration of different offshore technologies can help to decrease the energy variability associated with marine energy resources. Furthermore, this research shows that substantial cost reductions are still necessary to realize the deployment of these technologies in the region investigated.

... Indeed, the conversion from wave energy to electricity can be affected by variations in the wave spectrum at the sub-daily to daily scales, affecting the efficiency of the power management system, which necessitates accurate high-resolution sea-state predictions up to a few days ahead (Widén et al., 2015). Wave forecasts are in fact crucial across all stages of WEC development, from the design and planning of the wave farm, to its commissioning, operation, maintenance and decommissioning (Mérigaud et al., 2017), and should be considered a permanent element of the industrial process. In addition, by being forced by atmospheric forecasts starting from a data-constrained initial condition, on the long run short-term operative wave forecasts also constitute an everexpanding dataset, capable of capturing the long-term trends of wave climate that impact WEC optimization and commercial development (Atan et al., 2016;Ulazia et al., 2020). ...

Ocean Energy is now emerging as a viable long-term form of renewable energy, which might contribute around 10% of EU power demand by 2050, if sufficient support is guaranteed along its road to full commercialization, allowing to further demonstrate the reliability, robustness and overall economic competitiveness of technologies. Although wave energy is still less developed than other marine renewables, its high density, great potential and minimal environmental impact have renewed the interest of developers, investors and governments globally, also in view of the increasing awareness of climate change and of the necessity to reduce carbon emissions. In parallel with technological development, the reliable characterization of wave climate and of the associated energy resource is crucial to the design of efficient Wave Energy Converters and to an effective site-technology matching, especially in low-energy seas. The preliminary scrutiny of suitable technologies and the identification of promising sites for their deployment often rely on wave climatological atlases, yet a more detailed characterization of the local resource is needed to account for high-frequency spatial and temporal variability that significantly impact power generation and the economic viability of WEC farms. We present a high-resolution assessment of the wave energy resource at specific locations in the Mediterranean Sea, based on a 7-years dataset derived from the operative wave forecast system that has been developed at ENEA and has been running since 2013. The selected areas correspond to the target regions of the Blue Deal project, where energy resource estimates were combined with technical and environmental considerations, so as to identify optimal sites for Blue Energy exploitation, from a Maritime Spatial Planning perspective. The available resource at selected sites is analysed together with site theoretical productivity for three state-of-the art WECs, showing interesting potential for future deployment.

... Wave energy has higher energy density and spreading potential when compared to other renewable energy sources. The environmental effects of wave energy have little, and therefore the amount of wave energy production is more predictable (Cornejo-Bueno et al., 2016;Castro et al., 2014;Kamranzad et al., 2017;Mérigaud et al., 2017). Studies on wave energy generation have accelerated in recent years due to the high power density of wave energy compared to other renewable energies. ...

Background:
Various statistical methods are used for estimating sea state and wave characteristics using digital wave models. Several machine learning techniques help to develop the computational difficulties of these methods.
Materials and methods:
This study aims to estimate the wave power with Extreme Learning Machine (ELM), Regression, Restricted Boltzmann Machine (RBM), and RBM-ELM methods using nonlinear wave input parameters at different depths. Furthermore, the performance criteria are improved by applying the Relief feature selection algorithm to these methods. The input bias and input weights for the ELM have been determined using the RBM.
Results:
In the RBM-based presented method, the highest estimation values were obtained using Relief feature selection and without Relief as 96.96% and 94.02%, respectively. The highest accuracy rate based on ELM is 76.86% in the estimation of wave power without Relief. In the same way, the accuracy rate with Relief was calculated as 92.16%. These values were increased to 90.10% (without Relief) and 95.73% (with Relief) using the RBM-ELM method.
Conclusions:
This study demonstrates that the performance of the presented methods with Relief feature selection was improved.

... Though correlation is often the most valued performance metric, the RMSE, which carries the same unit as the measured variable, is even more important when considering, for example, the sensitivity of wave energy estimates to SWH (i.e., P ∝ H 2 s T p ). Here, minor increases or decreases in wave height (H 2 s ) had a disproportionate and extremely large impact on total energy estimates; thus, precise forecasts for wave energy conversion operations are of primary importance to the commercial viability of this emerging field [32][33][34]. An example is provided in Figure 8 where it can be observed that an observed significant wave height of 3 m (black line) with forecast errors of ±0.5 m for a given wave period (here ranging from 2-6 s), the maximum total wave energy predicted could then range anywhere from 18.75 kW/m for underestimations to overestimations of 36.75 kW/m, though the actual maximum value is 27 kW/m. ...

Wave forecasts, though integral to ocean engineering activities, are often conducted using
computationally expensive and time-consuming numerical models with accuracies that are blunted by numerical-model-inherent limitations. Additionally, artificial neural networks, though significantly computationally cheaper, faster, and effective, also experience difficulties with nonlinearities in the wave generation and evolution processes. To solve both problems, this study employs and couples empirical mode decomposition (EMD) and a long short-term memory (LSTM) network in a joint model for significant wave height forecasting, a method widely used in wind speed forecasting, but not yet for wave heights. Following a comparative analysis, the results demonstrate that EMD-LSTM significantly outperforms LSTM at every forecast horizon (3, 6, 12, 24, 48, and 72 h), considerably improving forecasting accuracy, especially for forecasts exceeding 24 h. Additionally, EMD-LSTM responds faster than LSTM to large waves. An error analysis comparing LSTM and EMD-LSTM demonstrates that LSTM errors are more systematic. This study also identifies that LSTM is not able to adequately predict high-frequency significant wave height intrinsic mode functions, which leaves room for further improvements.

... The random forest model had a high-precision forecasting ability because it could combine the information offered by atmospheric and sea state Sustainability 2020, 12, 698 5 of 20 variables successfully. Merigaud et al. [17] explored the full range of wave modeling activity, including various time scales, and introduced modeling methods of the time scales and the causality input driving the models. Some models were based on the physical description of the system, including sounding, while some models only used measured data to form time sequence models. ...

Forecasting China’s clean energy consumption has great significance for China in making sustainably economic development strategies. Because the main factors affecting China’s clean energy consumption are economic scale and population size, and there are three variables in total, this paper tries to simulate and forecast China’s clean energy consumption using the grey model GM (1, 3). However, the conventional grey GM (1, N) model has great simulation and forecasting errors, the main reason for which is the structural inconsistency between the grey differential equation for parameter estimation and the whitening equation for forecasting. In this case, this paper improves the conventional model and provides an improved model GM (1, N). The modeling results show that the improved grey model GM (1, N) built with the method proposed improves simulation and forecasting precision greatly compared with conventional models. To compare the model with other forecasting models, this paper builds a grey GM (1, 1) model, a regression model and a difference equation model. The comparison results show that the improved grey model GM (1, N) built with the method proposed shows simulation and forecasting precision superior to that of other models as a whole. In the final section, the paper forecasts China’s clean energy consumption from 2019 to 2025 using the improved grey model GM (1, N). The forecasting results show that, by 2025, China’s clean energy consumption shall reach the equivalent of 1.504976082 billion tons of standard coal. From 2019 to 2025, clean energy consumption shall increase by 11.32% annually on average, far above the economic growth rate, indicating China’s economic growth shall have a great demand for clean energy in the future. Studies have shown that China’s clean energy consumption shall increase rapidly with economic growth and population increase in the next few years.

Although wave energy prototypes have been proposed for more than 100 years, they have still not reached full commercialisation. The reasons for this are varied, but include the diversity of device operating principles, the variety of onshore/nearshore/offshore deployment possibilities, the diversity of the wave climate at various potential wave energy sites, and the consequent lack of convergence in technology and consensus. This distributed effort has, in turn, lead to a slow rate of progression up the learning curve, with a significant number of wave energy company liquidations and technical setbacks dampening investor confidence. Although a number of reviews on wave energy technology are already in the published literature, such a dynamic environment merits an up-to-date analysis and this review examines the wave energy landscape from a technological, research and commercial perspective. © 2021 The Authors. IET Renewable Power Generation published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology

Short-term forecasts of wave energy play a key role in the daily operation, maintenance planning, and electrical grid operation of power farms. In this study, we propose a short-term wave energy forecast scheme and use the North Indian Ocean (NIO) as a case study. Compared with the traditional forecast scheme, our proposed scheme considers more forecast elements. In addition to the traditional short-term forecast factors related to wave energy (wave power, significant wave height (SWH), wave period), our scheme emphasizes the forecast of a series of key factors that are closely related to the effectiveness of the energy output, capture efficiency, and conversion efficiency. These factors include the available rate, total storage, effective storage, cooccurrence of wave power-wave direction, co-occurrence of the SWH-wave period, and the wave energy at key points. In the regional nesting of numerical simulations of wave energy in the NIO, the selection of the southern boundary is found to have a significant impact on the simulation precision, especially during periods of strong swell processes of the South Indian Ocean (SIO) westerly. During tropical cyclone ‘VARDAH’ in the NIO, as compared with the simulation precision obtained with no expansion of the southern boundary (scheme-1), when the southern boundary is extended to the tropical SIO (scheme-2), the improvement in simulation precision is significant, with an obvious increase in the correlation coefficient and decrease in error. In addition, the improvement is much more significant when the southern boundary extends to the SIO westerly (scheme-3). In the case of strong swell processes generated by the SIO westerly, the improvement obtained by scheme-3 is even more significant.

With deepwater wave power generation being seriously considered as a viable option across the marine vicinity of India, seasonal disparity of mean power as well as short duration power variability are of interest in the context of site and technology selection. Past experience with an onshore wave power installation in the region has not been altogether encouraging, which justifies good concern on the two aspects.
This paper formulates closed form analytical expressions for short duration mean power generation and associated variability that may be conveniently employed for prior estimates of the two measures with reference to prospective installation sites and wave energy converter (WEC) technologies. The formulae evolved can serve as useful support at the stage of project planning and resource assessment, as well as for general viability analysis of marine power generation.
As part of the exercise, the concept of capture width function is introduced for feasible operating points of a WEC technology, inclusive of functional morphing and statistical morphing effects on output power. Illustrative examples cover eight deepwater grids spread across the marine neighborhood of India, and two candidate WEC technologies considered for operational viability.

A new method for parameterising omnidirectional wave spectra is presented. The method introduces additional parameters to the standard height and period parameters, which describe the level of unimodality / bimodality and the weighting between the swell and wind sea components of the spectrum. Data from 8 deep-water locations in the Atlantic, Pacific and Gulf of Mexico are used to demonstrate that the new shape parameters provide a consistent description of the shape of the spectra, independent of the wave climate. The new shape parameters provide a bounded parameter space of spectral shapes. This enables a designer of an offshore structure to select a discrete number of spectra from within a bounded range and be confident that they have covered all possibilities. The new spectral shape parameters are used to define a spectrum formed as the sum of two JONSWAP spectra, where the parameters of the spectrum are defined entirely in terms of the parameters of the measurements, without a need for partitioning and fitting. The agreement of the new spectrum with measurements is compared to existing models including Torsethaugen spectra and demonstrated to give significantly better results over both extreme and climatic conditions.

The shore mounted “Pico” OWC has a relief valve mounted in parallel to the turbine which connects the chamber to the atmosphere. The aperture of this valve is adjustable and can be used to regulate the pneumatic power exposed to the turbine. Here we develop an algorithm to actively control the relief valve aperture so that the peak pneumatic power of each wave cycle approaches but does not breach the turbine stall threshold, thus providing the maximum pneumatic power possible without the turbine stalling. The relief valve aperture is slow to adjust so the hydrodynamic and pneumatic behavior is foretasted to allow enough time to achieve the correct aperture before the wave reaches the chamber. The chamber hydrodynamics are foretasted using a neural network that considers hydrodynamic measurements made 60 meters up wave and other operational, environmental and preceding wave, parameters. Turbine stalls were identified approximately by the gradient in turbine vibration and the angular velocity dependent pneumatic power threshold for turbine stall is found empirically. The relationship between the foretasted chamber hydrodynamics, relief valve aperture and the resultant pneumatic behavior, is also found empirically and this is used to select the relief valve aperture that the control algorithm targets.

Short term forecasting is a vital interest to future implementations of a smart grid, particularly in the reliable integration of renewable energy resources. In this study we focus on multi-step prediction of high resolution wave power. Significant wave height data was first obtained from Belmullet Berth, Ireland and underwent several data preprocessing steps. These include a linear interpolation to fill irregular or missing data points, conversion to power using an interpolated power matrix of a Pelamis Device energy converter, and then exponential smoothing is applied. We utilized a nonlinear autoregressive recurrent neural network for 3, 6, 12 and 24 hour prediction. Our method showed highly accurate results when data has been smoothed, versus raw data, and when compared to previous studies.

Wave resource assessment and mapping for the deployment of wave energy converters is generally produced analyzing long term databases built running wave hindcast models. As a matter of fact, wave power time evolution shows a large variability and in some areas, a significant amount of this power is actually concentrated during short duration highly energetic events. During such storms, weather conditions can reach levels above the operability threshold of a wave energy converter. In such conditions, the wave energy device is set in a survivability mode, a configuration in which no power can be extracted and available resource should be considered blank for a proper assessment. Taking advantage of the availability of a new high resolution wave hindcast extending from the South of the North Sea to the Bay of Biscay a new wave resource assessment study is conducted, taking into account theoretical survivability thresholds. Wave energy flux regional maps accounting for survivability thresholds together with statistical studies conducted at regional and local scales including assessment of energetic events persistence and sensitivity to the survivability threshold provide some interesting insight on the weight of the stormy events in the evaluation of the actually extractable power.

Wave energy has great potential as a renewable source of electricity. Installed capacity is increasing, and developments in technology mean that wave energy is likely to play an important role in the future mix of electricity generation. Short-term forecasts of wave energy are required for the efficient operation of wave farms and power grids, as well as for energy trading. The intermittent nature of wave energy motivates the use of probabilistic forecasting. In this paper, we evaluate the accuracy of probabilistic forecasts of wave energy flux from a variety of methods, including unconditional and conditional kernel density estimation, univariate and bivariate autoregressive moving average generalised autoregressive conditional heteroskedasticity (ARMA-GARCH) models, and a regression-based method. The bivariate ARMA-GARCH models are implemented with different pairs of variables, such as (1) wave height and wave period, and (2) wave energy flux and wind speed. Our empirical analysis uses hourly data from the FINO1 research platform in the North Sea to evaluate density and point forecasts, up to 24 h ahead, for the wave energy flux. The empirical study indicates that a bivariate ARMA-GARCH model for wave height and wave period led to the greatest accuracy overall for wave energy flux density forecasting, but its usefulness for point forecasting decreases as the lead time increases. The model also performed well for wave power data that had been generated from wave height and wave period observations using a conversion matrix.

Balancing power is used to quickly restore the supply-demand balance in power systems. The need for this tends to be increased by the use of variable renewable energy sources (VRE) such as wind and solar power. This paper reviews three channels through which VRE and balancing systems interact: the impact of VRE forecast errors on balancing reserve requirements; the supply of balancing services by VRE generators; and the incentives to improve forecasting provided by imbalance charges. The paper reviews the literature, provides stylized facts from German market data, and suggests policy options. Surprisingly, while German wind and solar capacity has tripled since 2008, balancing reserves have been reduced by 15%, and costs by 50%.

The real-time control of wave energy converters (WECs) requires the prediction of the wave elevation at the location of the device in order to maximize the power extracted from the waves. One possibility is to predict the future wave elevation by combining its past history with the spatial information coming from a sensor which measures the free surface elevation up-wave of the WEC. As an application example, this paper focuses on the prediction of the wave elevation inside the chamber of the oscillating water column (OWC) for the Pico OWC plant in the Azores, and two different sensors for the measurement of the free surface elevation up-wave of the OWC were tested. The study showed that the use of the additional information coming from the up-wave sensor does not significantly improve the linear prediction of the chamber wave elevation given by a forecasting model based only on the past values of the chamber wave elevation.

It is widely acknowledged that real-time control of wave energy converters (WECs) can benefit from prediction of the excitation force. The prediction requirements (how far ahead into the future do we need to predict?) and the achievable predictions (how far ahead can we predict?) are quantified when unconstrained reactive control is implemented. The fundamental properties of the floating system that influence the length of the required forecasting horizon, as well as the achievable prediction, are characterized. The possibility of manipulating the control, based on prior knowledge of the wave spectral distribution, is also proposed for the reduction of the prediction requirements, such that they are within the range of predictability offered by simple stochastic predictors. The proposed methodology is validated on real wave data and heaving buoys with different geometries.

Sea-states are usually described by a single set of 5 parameters, no matter the actual number of wave systems they contain. We present an original numerical method to extract from directional spectra the significant systems constituting of a complex sea-state. An accurate descrip-tion of the energy distribution is then given by multiple sets of parameters. We use these results to assess the wave climatology in the Bay of Biscay and to estimate the power harnessable in this area by a particular Wave Energy Converter, the SEAREV. Results show that the fine description of sea-states yields a better assessment of the instantaneous device response. The discrepancy between the classical and multi-sets descriptions shows that the new one is preferable for the assessment of harnessable power and for device design.

Large-scale commercial exploitation of wave energy is certain to require the deployment of wave energy converters (WECs) in arrays, creating ‘WEC farms’. An understanding of the hydrodynamic interactions in such arrays is essential for determining optimum layouts of WECs, as well as calculating the area of ocean that the farms will require. It is equally important to consider the potential impact of wave farms on the local and distal wave climates and coastal processes; a poor understanding of the resulting environmental impact may hamper progress, as it would make planning consents more difficult to obtain. It is therefore clear that an understanding the interactions between WECs within a farm is vital for the continued development of the wave energy industry.
To support WEC farm design, a range of different numerical models have been developed, with both wave phase-resolving and wave phase-averaging models now available. Phase-resolving methods are primarily based on potential flow models and include semi-analytical techniques, boundary element methods and methods involving the mild-slope equations. Phase-averaging methods are all based around spectral wave models, with supra-grid and sub-grid wave farm models available as alternative implementations.
The aims, underlying principles, strengths, weaknesses and obtained results of the main numerical methods currently used for modelling wave energy converter arrays are described in this paper, using a common framework. This allows a qualitative comparative analysis of the different methods to be performed at the end of the paper. This includes consideration of the conditions under which the models may be applied, the output of the models and the relationship between array size and computational effort. Guidance for developers is also presented on the most suitable numerical method to use for given aspects of WEC farm design. For instance, certain models are more suitable for studying near-field effects, whilst others are preferable for investigating far-field effects of the WEC farms. Furthermore, the analysis presented in this paper identifies areas in which the numerical modelling of WEC arrays is relatively weak and thus highlights those in which future developments are required.

Wavo spectra were measured along a profile extending 160 km into the North Sea westward from Sylt for a period of ten weeks in 1969. Currents, tides, air-sea temperature differences and turbulence in the atmospheric boundary layer were also measured. the goal of the experiment (described in Part 1) was to determine the structure of the source function governing the energy balance of the wave spectrum, with particular emphasis on wave growth under stationary offshore wind conditions (Part 2) and the attention of swell in water of finito depth (Part 3). The source functions of wave spectra generated by offshore winds exhibit a characteristic plus-minus signature associated with the shift of the sharp spectral peak towards lower frequencies. The two-lobed distribution of the source function can be explained quantitively by the nonlinear transfer due to resonant wave-wave interactions (second order Bragg scattering). The evolution of a pronounced peak and its shift towards lower frequencies can also be understood as a self-stabilizing feature of this process. The decay rates determined for incoming swell varied considerably, but energy attenuation factors of two along the length of the profile were typical. This is in order of magnitude agreement with expected damping rates due to bottom friction. However, the strong tidal modulation predicted by theory for the case of a quadratic bottom friction law was not observed. Adverse winds did not affect the decay rate. Computations also rule out wave-wave interactions or dissipation due to turbulence outside the bottom boundary layer as effective mechanisms of swell attenuation. We conclude that either the generally accepted friction law needs to be significantly modified or that some other mechanism, such as scattering by bottom irregularities, is the cause of the attenuation. The dispersion characteristics of thw swells indicated rather nearby origins, for which the classical DELTA-event model was generally inapplicable. A strong Doppler modulation by tidal currents was also observed. (A)

Control of wave energy converters requires knowl- edge of some seconds of the future behavior of certain physical quantities, in order to approach optimality. That is why short time prediction of the oncoming waves is a crucial problem in the field of wave energy, whose solu- tion could bring great benefits to the effectiveness of the devices and to their economical viability. This study is proposed as a preliminary approach to cope with this necessity, where wave forecasts are com- puted on the basis of past observations collected at the prediction site itself. Working on single point measure- ments allows the treatment of the wave elevation as a pure time series, so that a wide range of well established techniques from the stochastic time series modelling and forecasting field may be exploited. Among the proposed solutions there are some cyclical models, based on an ex- plicit representation of the a priori knowledge about the real process. It is then shown how a lot simpler and more effective solution can be obtained through classical AR models, which are shown to be able to implicitly repre- sent the cyclical behavior of real waves. As a compari- son with AR models some results obtained with neural networks are also provided.

Recently, the technology has been developed to make wave farms commercially viable. Since electricity is perishable, utilities will be interested in forecasting ocean wave energy. The horizons involved in short-term management of power grids range from as little as a few hours to as long as several days. In selecting a method, the forecaster has a choice between physics-based models and statistical techniques. A further idea is to combine both types of models. This paper analyzes the forecasting properties of a well-known physics-based model, the European Center for Medium-Range Weather Forecasts (ECMWF) Wave Model, and two statistical techniques, time-varying parameter regressions and neural networks. Thirteen data sets at locations in the Atlantic and Pacific Oceans and the Gulf of Mexico are tested. The quantities to be predicted are the significant wave height, the wave period, and the wave energy flux. In the initial tests, the ECMWF model and the statistical models are compared directly. The statistical models do better at short horizons, producing more accurate forecasts in the 1–5h range. The ECMWF model is superior at longer horizons. The convergence point, at which the two methods achieve comparable degrees of accuracy, is in the area of 6h. By implication, the physics-based model captures the underlying signals at lower frequencies, while the statistical models capture relationships over shorter intervals. Further tests are run in which the forecasts from the ECMWF model are used as inputs in regressions and neural networks. The combined models yield more accurate forecasts than either one individually.

The common methodology in dynamical regional climate downscaling employs a continuous integration of a limited-area model with a single initialization of the atmospheric fields and frequent updates of lateral boundary conditions based on general circulation model outputs or reanalysis data sets. This study suggests alternative methods that can be more skillful than the traditional one in obtaining high-resolution climate information. We use the Weather Research and Forecasting (WRF) model with a grid spacing at 36 km over the conterminous U.S. to dynamically downscale the 1-degree NCEP Global Final Analysis (FNL). We perform three types of experiments for the entire year of 2000: (1) continuous integrations with a single initialization as usually done, (2) consecutive integrations with frequent re-initializations, and (3) as (1) but with a 3-D nudging being applied. The simulations are evaluated in a high temporal scale (6-hourly) by comparison with the 32-km NCEP North American Regional Reanalysis (NARR). Compared to NARR, the downscaling simulation using the 3-D nudging shows the highest skill, and the continuous run produces the lowest skill. While the re-initialization runs give an intermediate skill, a run with a more frequent (e.g., weekly) re-initialization outperforms that with the less frequent re-initialization (e.g., monthly). Dynamical downscaling outperforms bi-linear interpolation, especially for meteorological fields near the surface over the mountainous regions. The 3-D nudging generates realistic regional-scale patterns that are not resolved by simply updating the lateral boundary conditions as done traditionally, therefore significantly improving the accuracy of generating regional climate information.

The energy transfer equation for well developed ocean waves, under the influence of wind, is considered, and the conditions for the existence of an equilibrium solutions in which wind input, wave-wave interaction and dissipation balance each other are studied. The paper is presented in three parts - a summary of what is known about the source terms in the energy transfer equation; the energy balance for the conventional Parson-Moskowitz spectrum as a candidate of a quasi equilibrium solution, and in the last section of the results of numerical experiments are presented. (from paper)

A description is given of a model developed for the prediction of the dissipation of energy in random waves breaking on a beach. The dissipation rate per breaking wave is estimated from that in a bore of corresponding height, while the probability of occurrence of breaking waves is estimated on the basis of a wave height distribution with an upper cut-off which in shallow water is determined mainly by the local depth. A comparison with measurements of wave height decay and set-up, on a plane beach and on a beach with a bar-trough profile, indicates that the model is capable of predicting qualitatively and quantitatively all the main features of the data.

In this paper we present a high resolution assessment of the wave energy resources in the Mediterranean. The energy resources are evaluated through of a numerical simulation performed on the entire Mediterranean basin for the period 2001-2010 using a third generation ocean wave model. The model results are extensively validated against most of the available wave buoy and satellite altimeter data. Starting from the model results a detailed analysis of wave energy availability in the Mediterranean Sea is carried out. The western Sardinia coast and the Sicily Channel are found to be among the most productive areas in the whole Mediterranean. Simulation results show the presence of significant spatial variations of wave power availability even on relatively small spatial scales along these two coastlines. For a number of selected locations in these two areas we present an in-depth investigation of the distribution of wave energy among wave heights, periods and directions. Seasonal and inter-annual variability of wave energy potential are also analyzed and discussed.

The offshore wave energy potentials of the Italian seas has been studied by analyzing the wave measurements carried out by the Italian Wave Buoys Network. The annual and monthly average offshore wave power, varies between 1,6 kW/m and 9.05 kW/m. The Adriatic sea shows an average value around 2 kW/m, the smallest value around Italian coasts as expected. The Ionian, North and Middle Tyrrhenian seas are a bit more energetic reaching a value of about 3 kW/m whereas the South Tyrrhenian is characterized by a value of 4 kW/m. A completely different behavior is highlighted for the Alghero buoy (north-west Sardinia island) where the estimated power reaches the value up to 9 kW/m.

The control of wave energy converters can be significantly improved by taking into account the future incident wave elevation. For optimized energy yield it is, therefore, highly desirable to include wave prediction algorithms in the real-time control system. Recent research has shown that it is possible to predict up to one wave period with reasonable accuracy using rather simple autoregressive models, forecasting the wave elevation based on the past time series measured at the device itself. So far, the focus has been on the theoretical feasibility of short-term wave prediction. Comparably less publications deal with issues related to the real-time implementations of these prediction algorithms: causality, simplicity and robustness. In this study, adaptive filters are employed to estimate the future wave elevation. It is shown that they achieve about half a wave period with reasonable accuracy. Their real-time implementation is undemanding. Furthermore, their adaptability makes them robust to changing environmental conditions and only a minimum of supervisory control is required. The real-time feasibility is demonstrated by an example implementation on a programmable logic controller and measurement data from a wave rider buoy located in the North Sea.

A 14-year high resolution wave and wind hindcast was carried out for Ireland. The wind was dynamically downscaled from the ERA-Interim reanalysis to a 2.5 km horizontal resolution and 65 vertical levels, using the HARMONIE meso-scale model. The wave hindcast was derived using WAVEWATCH III on an unstructured grid with resolution ranging between 10 km offshore and 225 m in the nearshore, forced by the downscaled HARMONIE 10 m winds and ERA-Interim wave spectra. The wind and wave hindcasts were thoroughly validated against available buoy data, including wave buoys in nearshore locations and coastal synoptic stations. In addition, the significant wave heights and winds from the hindcasts were compared against all available altimeter data from the CERSAT database at Ifremer. The quality of both the wind and wave hindcasts was found to be good.The wave and wind energy resource in coastal areas was assessed, and discussed in terms of water depth, distance to shore, and seasonal and inter-annual variability. In addition, the current study investigates the nearshore wind and wave climate in conjunction with each other, and highlights two issues with relevance to the ocean renewable energy industry: (i) the complementarity between the wind and wave energy resource, and (ii) the accessibility for marine operations. Our study highlights sites around the Irish coast that might have been overlooked in terms of the potential for wind, wave or combined wind/wave energy installations.

The aim of this study is to establish a database for the hydrodynamic performance of Wave Energy Converters (WECs). The method relies on the collection and analysis of data available in the literature. The availability and presentation of these data vary greatly between sources. Thus, extrapolations have been made in order to derive an annual average for the capture width ratio (CWR) of the different technologies. These CWR are synthesized in a table alongside information regarding dimension, wave resource and operational principle of the technologies. It is observed that CWR is correlated to operational principle and dimension. Statistical methods are used to derive relationships between CWR and dimension for the different WEC operational principles.

In this paper, the performance of different ordinal and nominal multi-class classifiers is evaluated, in a problem of wave energy range prediction using meteorological variables from numerical models. This prediction could be used in problems of wave energy conversion in renewable and sustainable systems for energy supply. Specifically, the work is focused on ordinal classifiers, that have provided excellent performance in previous applications. The proposed techniques are novel with respect to alternative classification and regression techniques used up to date, the former not considering the order relation between classes in a multi-class problem and the latter needing, in general, more complex models. Another important novelty of the paper is to consider meteorological variables from numerical models as inputs of the classifiers, which has not been done before, to our knowledge, in this context. For this, a data matching is carried out between meteorological data, obtained from NCEP/NCAR Reanalysis Project in four points around the two buoys subjected to study (a buoy in the Gulf of Alaska and another one in the Southeast of United States), and the wave height or wave period collected by sensors in each buoy. Using this matching, the problem is tackled as an ordinal multi-class classification problem and the objective is to predict the range of height of the wave produced in each buoy and the range of energy flux generated. The classifiers to be compared and the model proposed are fully evaluated in both buoys. The results obtained are promising, showing an acceptable reconstruction by ordinal methods with respect to nominal ones in terms of wave height and energy flux.

This paper presents the analysis of the intra-annual power performance of different WECs (wave energy converters) at two locations of interest in the northern coastal region of Galicia (NW Spain). With this aim, the wave resource at the locations of interest is characterised by considering a procedure whose implementation on a coastal region produces the required wave spectral information for reconstructing the coastal resource in terms of monthly characterisation matrices with the adequate resolution for conducting accurate performance computations of WECs. Next, the monthly performance of different WECs at these locations is estimated through the combination of the characterisation matrices obtained and the efficiency of the technologies analysed. The results show that the analysis of the intra-annual performance of different technologies at different locations is a key aspect so as to define the most appropriate WEC-site combination for harnessing the wave energy resource in a coastal region. Finally, the information produced by implementing the methodology considered in this work allows the reconstruction of the wave resource at any coastal site (not only at the selected locations), in the form of monthly high resolution characterisation matrices, and thus, the monthly performance of any WEC-site combination can be computed.

The wave energy resource is usually characterized by a significant variability throughout the year. In estimating the power performance of a Wave Energy Converter (WEC) it is fundamental to take into account this variability; indeed, an estimate based on mean annual values may well result in a wrong decision making. In this work, a novel decision-aid tool, iWEDGE (intra-annual Wave Energy Diagram GEnerator) is developed and implemented to a coastal region of interest, the Death Coast (Spain), one of the regions in Europe with the largest wave resource. Following a comprehensive procedure, and based on deep water wave data and high-resolution numerical modelling, this tool provides the monthly high-resolution characterization matrices (or energy diagrams) for any location of interest. In other words, the information required for the accurate computation of the intra-annual performance of any WEC at any location within the region covered is made available. Finally, an application of iWEDGE to the site of a proposed wave farm is presented. The results obtained highlight the importance of the decision-aid tool herein provided for wave energy exploitation.

The selection of the appropriate wave energy converter (WEC) and site is the basis for the installation of a wave farm in a region. For this purpose, the estimation of the energy that any WEC would produce at any location of interest is fundamental. Despite all its importance, this information or the elements required for obtaining it are currently available only at specific coastal locations or areas of interest. This work develops a tool for computing the energy that any WEC would generate at any coastal location within the Rias Baixas Region (NW Spain). With this aim, a methodology which allows the consideration of almost all the total energy available is used to characterize the coastal resource with a high spatial resolution. Then, a matlab-based application called WEDGE (Wave Energy Diagram GEnerator) is implemented for easy access to the stored data and automatic reconstruction of the resource at any coastal site in terms of a high-resolution characterization matrix (or energy diagram). As a result, the information required for accurate energy production computation throughout the region is available whereby a combined WEC-site selection can be conducted. Finally, the tool is used to compute the energy production of a total of 23 WEC-site combinations in an area within this region where a wave farm has been recently proposed. The results will underline the importance of a combined WEC-site selection for proper decision-making regarding wave energy exploitation.

In this paper the assessment of the wave energy potential in nearshore coastal areas is investigated by means of artificial neural networks (ANNs). The performance of the ANNs is compared with in situ measurements and spectral numerical modelling (the conventional tool for wave energy assessment). For this purpose, 13 years of records of two buoys, one offshore and one inshore, with an hourly frequency are used to develop an ANN model for predicting the nearshore wave power. The best suited architecture was selected after assessing the performance of 480 ANN models involving twelve different architectures. The results predicted by the ANN model were compared with the measured data and those obtained by means of the SWAN (Simulating Waves Nearshore) spectral model. The quality in the predictions of the ANN model shows that this type of artificial intelligence models constitutes a powerful tool to forecast the wave energy potential at particular coastal site with great accuracy, and one that overcomes some of the disadvantages of the conventional tools for nearshore wave power prediction.

The estimation of energy production of a given WEC (wave energy converter) at a given coastal site is the basis for correct decision-making regarding wave energy exploitation in a coastal region. Nevertheless, the procedure followed by the conventional approach to characterize the wave energy resource does not provide the required information to obtain an accurate estimate. In this work, this information is provided for the region with the greatest resource in the Iberian Peninsula, the Death Coast (NW Spain). For this purpose, a geospatial database is produced by using a methodology which involves the consideration of virtually the totality of the resource together with the implementation of a high resolution spectral numerical model. In addition, a Matlab-based toolbox called WEDGE (Wave Energy Diagram GEnerator) is implemented to access the database and automatically generate high resolution energy diagrams (or characterization matrices) of the wave energy resource at any coastal location within this region. In this way, a precise computation of energy production of any WEC at any site of interest can now be performed. Finally, the functionality of the database is shown through a case study of a recently proposed wave farm.

Wave energy is of particular interest in the case of islands, and even more so if the electricity network of the island is isolated as in many Atlantic islands. The objective of this work is to analyse the impacts of wave exploitation on the nearshore wave climate of the island through a case study: the island of Tenerife (Spain), in the NE Atlantic, and a wave farm off its north coast. Two wave conditions, typical of winter and summer, and three values of the wave transmission coefficient of the Wave Energy Converters (WECs) are used. For each of these six cases, the neashore wave conditions in the lee of the farm are compared with the baseline scenario. The impact is characterized in terms of: wave height, power, energy period, directional spreading and energy dissipation due to bottom friction. We find that the impact is relevant, in particular in some of these cases, with the value of the wave transmission coefficient playing a significant role.

Real-time smooth reactive control and optimal damping of wave energy converters in irregular waves is difficult in part because the radiation impulse response function is real and causal, which constrains the frequency-dependent added mass and radiation damping according to the Kramers-Kronig relations. Optimal control for maximum energy conversion requires independent synthesis of the impulse response functions corresponding to these two quantities. Since both are non-causal, full cancellation of reactive forces and matching of radiation damping requires knowledge or estimation of device velocity into the future. To address this non-causality and the non-causality of the exciting force impulse response function, the use of up-wave surface elevation has been suggested in the literature for synthesis of the necessary control forces. The overall formulation here draws on draws on this approach and leads to smooth control that is near-optimal given the approximations involved in the time-shifting of the non-causal impulse response functions and the consequent up-wave distances at which wave surface elevation is required. A predominantly heaving submerged device comprised of three vertically stacked discs driving a hydraulic cylinder is studied. Absorbed power performance with the present near-optimal approach is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Simulation results are obtained for wave spectra at different significant wave heights and energy periods representing three locations along the U.S. coastline.

Successful application of active control could bring about significant improvements in the economics of wave energy conversion technology. This article presents an overview of several applications of active control in wave energy conversion. Early implementations of reactive and latching-type control are examined first. Next, the difficulties of real-time control are outlined, and some recent applications of time-domain control are reviewed. Active control providing an onboard reaction on deep-water floating devices is also discussed. Finally, control of secondary converters is reviewed briefly. The article concludes with some observations on possible future developments.

This paper is intended to fill a gap in the current literature comparing and contrasting the experience of a number of European countries, U.S. states, and Australia with regard to wind energy support policy and electricity market design. As wind penetrations increase, the nature of these arrangements becomes an increasingly important determinant of how effectively and efficiently this generation is integrated into the electricity industry. The jurisdictions considered in this paper exhibit a range of wind support policy measures from feed-in tariffs to green certificates, and electricity industry arrangements including vertically integrated utilities, bilateral trading with net pools, as well as gross wholesale pool markets. We consider the challenges that various countries and states have faced as wind generation expanded and how they have responded. Findings include the limitations of traditional feed-in tariffs at higher wind penetrations because they shield wind project developers and operators from the implications of their generation on wider electricity market operation. With regard to market design, wind forecasting and predispatch requirements are particularly important for forward markets, whereas the formal involvement of wind in scheduling and ancillary services (balancing and contingencies) is key for real-time markets.

Large-scale wave reanalysis databases (0.1°–1° spatial resolution) provide valuable information for wave climate research and ocean applications which require long-term time series (> 20 years) of hourly sea state parameters. However, coastal studies need a more detailed spatial resolution (50–500 m) including wave transformation processes in shallow waters. This specific problem, called downscaling, is usually solved applying a dynamical approach by means of numerical wave propagation models requiring a high computational time effort. Besides, the use of atmospheric reanalysis and wave generation and propagation numerical models introduce some uncertainties and errors that must be dealt with. In this work, we present a global framework to downscale wave reanalysis to coastal areas, taking into account the correction of open sea significant wave height (directional calibration) and drastically reducing the CPU time effort (about 1000 ×) by using a hybrid methodology which combines numerical models (dynamical downscaling) and mathematical tools (statistical downscaling). The spatial wave variability along the boundaries of the propagation domain and the simultaneous wind fields are taking into account in the numerical propagations to performance similarly to the dynamical downscaling approach. The principal component analysis is applied to the model forcings to reduce the data dimension simplifying the selection of a subset of numerical simulations and the definition of the wave transfer function which incorporates the dependency of the wave spatial variability and the non-uniform wind forcings. The methodology has been tested in a case study on the northern coast of Spain and validated using shallow water buoys, confirming a good reproduction of the hourly time series structure and the different statistical parameters.

Wave energy is an emerging and promising renewable energy technology. As the first pre-commercial and commercial prototypes are being tested at sea, there is a need for developers, governments and investors to be able to reliably estimate the energy production of devices as a function of the sea states they are to be deployed in. This estimation has traditionally relied on only two sea state parameters, the significant wave height and the energy period, but these do not account for frequency or directional spreading. The present paper investigates the suitability of further parameters to refine performance predictions. This is achieved through extensive wave tank testing of three types of wave energy converters (WECs) with different directionality properties. Statistical analyses of the measurements show the significant impact of frequency and directional spreading on the performance of WECs. Parametric models of the devices’ performance were devised for numerous sea state parameters. These results suggest that the traditional estimation method should be extended in order to include at least a parameter related to the spectral bandwith.

Wave energy will certainly have a significant role to play in the deployment of renewable energy generation capacities. As with wind and solar, probabilistic forecasts of wave power over horizons of a few hours to a few days are required for power system operation as well as trading in electricity markets. A methodology for the probabilistic forecasting of the wave energy flux is introduced, based on a log-Normal assumption for the shape of predictive densities. It uses meteorological forecasts (from the European Centre for Medium-range Weather Forecasts - ECMWF) and local wave measurements as input. The parameters of the models involved are adaptively and recursively estimated. The methodology is evaluated for 13 locations around North-America over a period of 15 months. The issued probabilistic forecasts substantially outperform the various benchmarks considered, with improvements between 6% and 70% in terms of Continuous Rank Probability Score (CRPS), depending upon the test case and the lead time. It is finally shown that the log-Normal assumption can be seen as acceptable, even though it may be refined in the future. (c) 2011 Elsevier Ltd. All rights reserved.

This study presents a methodology to obtain the power performance of a two-body heave converter. First, the methodology relies on a time domain model which represents the motion of the two bodies throughout the time. This time model was built substituting the entire equation system with a state-space system, thereby avoiding the convolution integral of the radiation force. This technique is demonstrated to be a reliable and very efficient method in terms of speed. Then, based on this model the instantaneous power of the device can be obtained. The performance of the device is shown through the power production matrix and the 60 year series power production statistics. This long series is obtained by means of using the MaxDiss selection technique in order to compute only the power of the most representative sea states and the Radial Basis Function (RBF) interpolation technique which interpolates in order to obtain the complete power series.

A full discrete spectral model for propagation generation and dissipation of wind waves for arbitrary depth, current and wind fields is presented (WAVEWATCH). This model incorporates all relevant wave-current interaction mechanisms including changes of absolute frequencies due to unsteadiness of depth and currents. The model furthermore explicitly accounts for growth and decay of wave energy and for nonlinear resonant wave-wave interactions. The numerical schemes for propagation are basically second-order accurate. Effect of refraction and frequency shifts (due to unsteadiness of depth and current) are calculated on a fixed grid, also using second-order schemes. This paper focuses on the governing equations and the numerical algorithms. Furthermore some results for academic and realistic cases are presented to illustrate some features and merits of the model.

Measurements of fetch-limited wave spectra from various sources indicate an approximate invariance of the normalized spectral shape with fetch. It has been suggested from investigations of the spectral energy balance that this can be explained by the shape-stabilizing influence of nonlinear resonant wave-wave interactions, which are also responsible for the migration of the spectral peak to lower frequencies. Analyses of a series of further data sets obtained under non-uniform, non-stationary wind conditions show that the invariance of the spectral shape is not restricted to uniform-wind, fetch-limited situations, but applies generally for a growing wind sea. The observed shape invariance is exploited in a wave prediction model by projecting the full transport equation for the two-dimensional spectral continuum onto two variables characterizing the energy and frequency scales of the spectrum. Inspection of the resultant equations reveals further simplifications, enabling the system to be reduced to a single prediction equation for one scale variable, the peak frequency. This is feasible because of the rapid adjustment of the spectrum to a quasi-equilibrium level in which the atmospheric input is balanced by the nonlinear transfer of energy out of the central region of the spectrum to higher and lower frequencies. The balance occurs sufficiently rapidly to be treated as a local response process, thereby providing a relation between the energy level of the spectrum (characterized, for example, by Phillip' constant α), the peak frequency fm, and the local wind speed U (the latter two occurring only in the non-dimensional combination ν=Ufm/g).
The directional distribution of the wave spectrum is also established locally and can be regarded as a given function of the non-dimensional frequency f/fm and ν. For the remaining independent scale parameter, the peak frequency, the dominant source term in the transport equation is determined by the nonlinear energy transfer, which can be computed rigorously. To lowest order, the one-parameter wave model is independent of the relative contributions of the atmospheric input and dissipation in the central region of the spectrum. However, because of lack of (consistent) direct measurements of the atmospheric input or dissipation, the quasi-equilibrium relation inferred between α and ν must be calibrated empirically, for example, by comparison with fetch-limited data. Within the scatter of the data, all data acts analyzed (with two exceptions, where the data were considered questionable) were reasonably consistent with a common α–ν relation. The residual scatter of the data is thought to be associated largely with small (sub-grid) scale inhomogeneities of the wind field and may represent a natural limitation of the accuracy achievable with deterministic wave models. A complete wave model would need to combine the proposed parametric model for growing wind seas with a swell propagation model.

Deterministic sea-wave prediction (DSWP) models are appearing in the literature designed for quiescent interval prediction in marine applications dominated by large swell seas. The approach has focused upon spectral methods which are straightforward and intuitively attractive. However, such methods have the disadvantage that while the sea is aperiodic in nature, the standard discrete spectral processing techniques force an absolutely periodic structure onto the resulting sea surface prediction models. As it is the shape of the sea surface that is important in such applications, particularly near the end of the domain which is important, the standard windowing techniques used in signal processing work to reduce leakage artifacts cannot be employed. This has necessitated the use of end matching methods that can be both inconvenient and may reduce the fraction of the time for which legitimate predictions are available. As a result, an investigation has been undertaken of the use of finite impulse response prediction filters to provide the necessary dispersive phase shifting required in DSWP systems. The present work examines the theoretical basis for such filters and explores their properties together with their application to both long and short crested swell seas. It is shown that wide band forms of such filters are only convergent in the sense of distributions having both infinite duration impulse responses and asymptotically divergent first derivatives. However, appropriate band limitation can produce useful finite impulse responses allowing implementation via standard discrete convolution methods. It is demonstrated that despite the prediction filters having a non-causal impulse response such filters can be used in practice due to a combination of the asymmetric nature of the impulse response and the fundamental nature of the prediction process. The findings are confirmed against actual sea-wave data.

The aim of this study is to estimate the mean annual power absorption of a selection of eight Wave Energy Converters (WECs) with different working principles. Based on these estimates a set of power performance measures that can be related to costs are derived. These are the absorbed energy per characteristic mass [kWh/kg], per characteristic surface area [MWh/m(2)], and per root mean square of Power Take Off (PTO) force [kWh/N]. The methodology relies on numerical modelling. For each device, a numerical Wave-to-Wire (W2W) model is built based on the equations of motion. Physical effects are modelled according to the state-of-the-art within hydrodynamic modelling practise. Then, the W2W models are used to calculate the power matrices of each device and the mean annual power absorption at five different representative wave sites along the European Coast, at which the mean level of wave power resource ranges between 15 and 88 kW per metre of wave front. Uncertainties are discussed and estimated for each device. Computed power matrices and results for the mean annual power absorption are assembled in a summary sheet per device. Comparisons of the selected devices show that, despite very different working principles and dimensions, power performance measures vary much less than the mean annual power absorption. With the chosen units, these measures are all shown to be of the order of 1.

The Portuguese wave-power resource is estimated using 3 years of data from the U.K. Meteorological Office's wind-wave model, in addition to available wave buoy measurements for northern Portugal. The large-scale resource assessment includes basic statistics and the variability. The annual power averages 30–40 MW/km for the northern coasts, the main power being incident from directions between North and West. The variability is studied by means of power-duration curves and scatter tables. The present paper also includes a brief description of the preliminary survey of the Azores and Madeira archipelagos and of the mainland southwestern coast.

This volume examines the interaction between ocean waves and oscillating
systems. With a focus on linear analysis of low-amplitude waves, the
text is designed to convey a thorough understanding of wave
interactions. Topics include the background mathematics of oscillations,
gravity waves on water, the dynamics of wave-body interactions, and the
absorption of wave energy by oscillating bodies. While the focus is on
linear theory, the practical application of energy storage and transport
is interwoven throughout. Each chapter ends with problems. A solutions
manual is available for instructors.

The model proposed by Phillips (1957) for the generation of water waves by the random fluctluations of normal pressure already present in a turbulent wind is generalized to include energy transfer associated with the interaction between surface wave and mean air flow (Miles 1957). It is found that this energy transfer may increase by an order of magnitude the surface displacements produced by a given distribution of pressure fluctuations in the principal stage of development.