1. Introduction

The exploitation of ocean renewable energy is currently recognized as an potential alternative to the reduction of fossil fuels resources consumption. One of the main advantage is the high power density of the wave resource in coastal waters, thus providing a great number of potential locations for energy exploitation^[1]. Over the last decades, a wide range of technologies were therefore tested and deployed in real sea conditions to convert wave energy into electricity, the great part of these applications being dedicated to the European shelf seas. The exploitation of the wave resource may especially be valuable for marine regions with high energy costs such as island territories by complementing other forms of renewable resources (such as solar, wind and tidal stream energies) and leading to lower energy infrastructure costs and reduced energy storage requirements^[2]. However, the development of the wave energy sector requires to guarantee the capital investment and the economical return of next-generation projects. And these objectives involve refined assessments of available resource and expected generated power. We conducted here an up-to-date review of the basic preliminary investigations of a wave energy project that may pave the way for refined design and advanced testing of full-scale devices. This review encompasses different approaches and techniques applied to available observations (in situ and satellite), hindcast and reanalysis archives, and refined simulations specifically dedicated to wave power assessments. Further details are available in the review entitled “Wave Energy Assessment for Exploitation” and published in open access in the Special Issue of the Journal of Marine Science and Engineering dedicated to “Numerical Assessments of Tidal Stream and Wave Energy in Coastal Shelf Seas”: https://www.mdpi.com/2077-1312/8/9/705^[3]

2. Wave Energy Characterization

2.1. Wave Power Computation

Wave resource assessments aim primary at characterizing the available wave energy flux (also denominated the wave power density or wave energy potential per unit crest, in W m^-1), defined as the integral of the wave energy spectrum

\( P=\rho g \int_0^{2\pi} \int_0^\infty c_g(\sigma) E(\sigma,\theta) d\sigma d\theta \)

Table 1. Estimations of the calibration coefficient \( \alpha \) between the peak period \( T_p \) and the energy period \( T_e \) (\( T_e=\alpha T_p \))^[3].

2.2. Wave Energy Metrics

3. Exploitation of Available Data

Different data may be exploited to characterize the wave energy in the marine environment. This includes (i) observations from in situ wave buoys, (ii) remote sensing measurements from satellite altimeters, and (iii) hindcast and reanalysis archives primary implemented to characterize the wave climate over the past decades.

Observations are, most the time, not available in locations retained for wave energy exploitation. However, the exploitation of these data may provide valuable information to characterize the available resource. In situ observations were thus exploited in a number of resource assessments, especially off the coast of U.S.A covered by a high density of NDBC wave buoys (National Data Buoy Center – National Oceanic and Atmospheric Administration – NOAA)^[17][18]. But the exploitation of in situ observations was also particularly useful to refine the estimation of the calibration coefficient between the energy period and default statistical periods (such as \( T_p \) or the mean wave period \( T_m \)), thus improving assessment of offshore available wave power density with the deep-water formulation^[9].

Satellite observations are characterized by important spatial and temporal limitations for assessing the available wave energy resource. Nevertheless, these measurements were able to image through clouds and provide day-and-night data, thus resulting in a long-term and extensive monitoring of the sea state. Satellite observations constitute therefore a promising alternative to local in situ wave buoys or time-consuming complex numerical modelling. The exploitation of multi-satellite altimeters provided thus cartographies of areas with the highest energy, but also a preliminary assessment of the temporal variability of the wave resource at seasonal and monthly time scales^[19][20]. However, these exploitations for wave energy resource assessment require (i) to derive the wave period with a series of inversion models and (ii) further assumptions about the relationship between the energy period and statistical wave periods.

Hindcast Databases and Reanalysis Archives may provide valuable information in the reconnaissance stage of a wave energy project saving time in the implementation, computation and validation of numerical simulations. These databases were thus exploited to (i) investigate the temporal variability of the wave energy resource, and (ii) exhibit the long-term evolutions by identifying decadal changes in wave power density^{[21][22][23].} Considering the offshore applications of these databases, the available wave energy resource was estimated by relying on the deep-water formulation and adopting a constant calibration coefficient between the energy period and the peak or mean periods. Most of hindcast databases rely furthermore on oceanic wave models with limitations for the resolution of wave coastal processes. These numerical simulations were also conducted with coarse spatial resolutions, insufficient to capture coastlines topography and water depths variability in nearshore waters, as well as to approach processes at refined spatial scales. Hindcast data tend therefore to be less reliable in the coastal area primary targeted for WEC implementation.

4. Numerical Simulations

Numerical wave models may offer a wide range of spectral information, reducing the uncertainties in resource assessments associated with the exploitation of the deep-water formulation and/or databases with reduced spatial and temporal resolutions, and a coarse definition of physical processes impacting wave propagation. Simulations specifically dedicated to wave power assessments may be classified into (i) basic modelling implemented for preliminary evaluation of the power density from the distribution of energy spectrum over frequencies and directions, and (ii) more complex approaches integrating wave-current interactions or energy extraction.

Wave energy simulations are conducted with phase-averaged spectral wave models that resolve the evolution of the wave energy density by taking into account the processes of generation, dissipation and nonlinear wave-wave interactions. These numerical investigations may be classified with respect to the spatial scales covered, thus considering (i) continental shelf scale applications, (ii) regional assessments along the coastline of a marine country, and (iii) local study on a targeted wave farm. Complementing resource assessments based on the exploitation of hindcast databases and reanalysis archives, shelf-scale investigations cover several decades by adopting, most of the time, coarse spatial resolutions between 1/10 and 1/5 °. In spite of increased spatial resolutions – between 0.01 and 0.05 °, regional scale investigations may also cover several decades. But these refined simulations integrate shallow-water processes (such as bottom friction and depth-induced refraction) and rely on the spectral formulation to compute the wave power density, thus providing a refined assessment of the available resource in comparison with shelf-scale applications. Coastal investigations require, however, spatial resolutions of few hundreds of meter reached with embedded simulations or unstructured computational grids, and this restricts the period of time covered. Nevertheless, simulations succeed in simulating a minimum period of 10 years following IEC technical specifications, thus characterizing the temporal evolution of the wave energy over the area targeted for energy exploitation^[24].

More complex numerical resource assessments may be adopted to reduce uncertainties associated with the modelling setup, the method retained to compute wave power or the physical processes considered. Particular attention may therefore be dedicated to wave and current interactions. Indeed, in locations with strong wave and tide regimes, tidal currents may impact wave propagation through a series of mechanisms including flattening/steepening, refraction, blocking or breaking. And these effects may result in important variations of the wave energy flux over 60 %^[25]. Current-induced refraction appears as one of the major mechanisms leading to these modulations of the wave energy in coastal shelf seas. However, numerical simulations require (i) refined spatial resolutions to approach the spatial variations of tidal current magnitudes and directions, and (ii) advanced coupling between the wave and tidal circulation models. For these reasons, resource assessments with tidal effects are restricted to short simulation periods. Refined simulations may also consider WEC effects (especially energy extraction) on the available resource and the generated power. However, state-of-the-art phase averaged models are not adapted to approach the complex interactions between operating devices and hydrodynamics, and these effects are, most of the time, disregarded estimating the generated power from the combination of wave scatter diagrams and WEC power matrices^[26].