The best wave energy resources are typically found far from land, especially in the far southern latitudes. However, these optimal locations often lie outside any single nation's exclusive economic zone (EEZ) and are located in deep ocean waters, though a few places stand out, namely Kerguelen Islands, the southern coast of Chile and the southern tip of New Zealand. The Kerguelen Islands are situated in a prime wave energy location, with a potential capacity factor exceeding 90% when using best of breed point-absorber wave energy converters (WECs). This could result in a levelised cost of electricity of 31.4 €/MWh by 2050. An earlier study showed that the Kerguelen Islands could support up to 7 GW of installable wave power capacity, utilising only 15% of the EEZ.

To evaluate the feasibility of establishing an energy hub on Kerguelen Islands, a scenario was developed using the EnergyPLAN modelling software. The scenario involves producing e-fuels and e-chemicals, which will be essential for sectors like marine and aviation transportation and chemicals as the world transitions to a defossilised economy. This analysis assumes that the islands could supply fuel for East Asia, particularly Japan, South Korea, and Taiwan. By 2050, the 7 GW wave power system could meet 3% of the demand for e-fuels and e-chemicals in these countries, producing 3.5 TWhth,LHV of e-kerosene, 2.6 TWhth,LHV of e-diesel, 19 TWhth,LHV of e-methanol, 2.5 TWhth,LHV of e-LNG, and 4.9 TWhth,LHV of e-ammonia. The cost projections for 2050 suggest that e-fuels and e-chemicals produced from Kerguelen Islands could be highly competitive, with projected costs of 95.0 €/MWh for e-kerosene and e-diesel, 78.7 €/MWh for e-methanol, 64.5 €/MWh for e-LNG, and 68.4 €/MWh for e-ammonia.

In addition to wave power, the system would incorporate 2 GWhcap of battery storage and 50 GWh of underground rock cavern hydrogen storage, further enhancing the energy hub's capacity and flexibility. These costs, assumed for 2050, are projected to be competitive compared to leading global sites, such as the Atacama Desert, which has excellent solar PV resources. For comparison, the Atacama Desert’s e-fuels production cost is estimated to range from 70-75 €/MWh, e-methanol is between 49-57 €/MWh and e-ammonia at 53 €/MWh.

However, the costs mentioned above do not include shipping costs. Shipping costs for ammonia for 10,000 km to East Asia could add up to 8 €/MWh, while shipping costs for methanol could add up to 4 €/MWh. For the Kerguelen Islands an attractive business model could be established to diversify the global e-fuels and e-chemicals production that may largely shift towards solar energy. This creates a promising opportunity for investment in a gigawatt-scale energy hub for e-fuels and e-chemicals on Kerguelen Islands, including the necessary infrastructure for shipping and workforce to maintain such a system.

Wave energy converter (WEC) arrays should be designed to ensure consistent and optimal power production over long operational periods. This requires an understanding of stochastic wave variability, interactive effects among devices and their mutual dependence. In this work, a computationally efficient surrogate modelling framework was developed using data-driven polynomial chaos expansion (PCE) to analyze the performance of WEC arrays under realistic sea state conditions spanning 30 years. For this purpose, using Latin hypercube sampling scheme on a joint probability distribution derived from the ECHOWAVE hindcast dataset, resulting $10^6$ combinations of significant wave height (Hs), wave period (Tp), and WEC radius (R) for two array configurations—interacting and non-interacting cases were evaluated. The surrogate model was set up to evaluate the performance of WEC arrays by means of global sensitivity analysis using Sobol indices. The results conclude that the interactive effects significantly alter the contribution of design parameters (like geometry and spatial configurations) to power output, emphasizing the inadequacy of single-device analysis for array optimization. The findings highlight the importance of tailored WEC design within arrays and offer a robust approach for long-term performance prediction and optimization of wave energy farms.

Different numerical modeling methods have been developed and applied to evaluate a variety of performance indicators of wave energy converters (WECs), including the power performance, structural loads, levelized cost of energy, etc. Based on the modeling fidelity, the commonly used numerical modeling approaches can be classified as linear modeling, weakly nonlinear modeling and fully nonlinear modeling approaches. Each method differs in accuracy and computational efficiency, making them suitable for different stages of WEC design. However, the selection of modeling approach could significantly impact evaluation outcomes. For instance, simplified linear models may underestimate structural loads or overestimate energy production in some operational conditions, potentially leading to less cost-effective designs. Given the widespread utilization of these models, it is essential to understand the uncertainties brought by them in performance evaluations. This work is dedicated to benchmarking different linear-potential-flow-based numerical models for evaluating the systematic performance of WECs. Three representative numerical modeling approaches are considered in this work, including linear frequency-domain modeling, statistically linearized spectral-domain modeling and Cummins equation-based nonlinear time-domain modeling. A generic point absorber WEC is considered as the research reference in this work, and different sea sites are taken into account. The numerical models are utilized to predict critical performance indicators, including power performance, the annual energy production, the capacity factor, the levelized cost of energy and the PTO fatigue loads. By comparing the results, this work identifies the uncertainties associated with different modeling approaches in evaluating WEC performance.

To date the use of the JONSWAP parametric spectrum is still widely accepted in many engineering applications, including the wave energy sector. Nevertheless, in the last 15 years many studies have progressively shown the necessity to implement more detailed and realistic spectral information in order to reduce the errors (or differences) introduced when the JONSWAP spectrum fails to describe more complex sea states. In the present study, the changes in produced power estimations, related to different spectral representations, are analysed. All power production estimates are obtained through 30 years simulations of point-absorber Wave Energy Converter (WEC) arrays, using the HAMS-MREL Boundary Element Method (BEM) solver. To assess the effects of the wave energy distribution on power production, 3 different spectral forcing are considered. Two based on the JONSWAP spectrum, and 1 using spectra time series from the ECHOWAVE hindcast specially developed for wave energy applications. For comparison purposes, the hindcast spectra is used as reference, since it can accurately represent the sea states evolution in time including the occurrence of multimodal conditions, which are not considered by the JONSWAP formulation. Additionally, 3 locations with different wave climates are analysed within European coastal waters. Recent results, focused on the response of a single (point-absorber) WEC, show that the differences in the mean yearly production can be > 12% when compared to reference hindcast data. The generalised analysis presented here, including the hydrodynamic interactions between multiple WECs within an array, is an important step forward in the understanding and quantification of the uncertainties present in power production assessments.

Wave energy as a renewable resource has been shown to have immense potential. Up to date research has predominately focused on sector focused approaches, with devices being explored in small applications, or solely on their own merit. However, when discussing the integration to energy systems with high share of renewable energies, large levels of electrical interconnectivity and grid balancing infrastructure, the role of wave energy is often “lost”. This work further refines the approach of integrating wave energy in the European and UK energy system, highlighting potential future pathways to improve wave energy considerations.

This study assesses the input source of climate data for evaluation of wave energy production and economics. The comparison of ERA5 and a high-fidelity wave dataset across all Europe, the ECHOWAVE database, show a clear benefit for wave energy. When ERA5 is utilised to assess the potential of wave energy, the usefulness and integration of wave energy is not reflected in the system. This works shows that a proper representation of wave energy in terms of climate, power production methodologies and economic considerations.

HAMS-MREL is a recently developed open-source BIEM solver, which allows for the solution of the diffraction and radiation problem for multiple floating rigid structures, taking into account their interaction. This has shown to highly accurate when compared with semi-analytical solutions/commercial solver WAMIT, within a computationally efficient framework that is parallelized. The solver is currently capable of providing the hydrodynamic coefficients (added mass and radiation damping) and exciting forces for all 6 rigid body modes per body. With this research, the solver has been extended significantly to include the following features for the multiple body interaction problem 1) Removal of irregular frequencies, 2) Global symmetry, 3) Wave fields and 4) Generalized modes. This study contributes further to the open-source domain with the development of highly accurate numerical tools for the accelerated deployment of offshore renewables.

The proper design of wave energy converters (WECs) is crucial for ensuring robustness in harsh wave climates without incurring the additional expense of unnecessary overdesign. The power take-off (PTO) mechanism, serving as a vital link between the moving body and the electric generator, is a key component in the design load analysis of WECs. However, the setting of PTO system parameters significantly impacts the dynamic behavior of the entire WEC system, leading to alterations in estimated loads. This work is dedicated to studying the influence of PTO control strategies on the identification of extreme loads of a heaving point absorber WEC. A nonlinear time-domain model is established to estimate the dynamic responses and loads of the WEC. Both PTO loads and end-stop loads under extreme conditions are examined, considering the wave climate of a realistic sea site. The results suggest that the PTO setting strategies significantly impact the extreme load exerted on both the PTO system and the end-stop system. Varying the PTO damping within a certain range could lead to a difference of 57% and 63% in short-term extreme loads for the PTO system and the end-stop system, respectively. Furthermore, the impacts of the PTO control strategy appear to be specific to each WEC component. The PTO parameters selected for reducing the extreme PTO loads might increase the extreme end-stop loads. A holistic examination is therefore recommended for estimating the extreme loads of WECs.

To accelerate the energy transition, offshore renewable energy is increasingly moving toward array deployment. This shift demands accurate, reliable analysis of hydrodynamics and array interactions at low computational cost. Frequency-domain tools, especially those based on the Boundary Integral Equation Method (BIEM), have thus become widely adopted in the renewables community. Hydrodynamic Analysis of Marine Structures-Marine Renewable Energies Lab (HAMS-MREL) is a recently developed open-source multi-body BIEM solver that computes diffraction and radiation problems, yielding hydrodynamic coefficients and excitation forces on structures. The solver has been validated across a range of geometries using experiments, semi-analytical solutions, and cross-model comparisons, demonstrating high accuracy. This study extends HAMS-MREL with several new features—including wave field calculations (free-surface elevation and pressure), global symmetry, irregular frequency suppression, and generalized (dry) modes—all of which have been validated for accuracy and computational efficiency. OpenMP parallelization has been integrated into each feature, delivering significant computational speed-ups ranging from 13.5 to 47.2.

In order to reduce the Levelized Cost Of Energy (LCOE) of Wave Energy Converters (WECs) and make them competitive with conventional energy sources, they would need to be deployed in large numbers as farms similar to Offshore Wind. Given their significant capacity, Offshore wind turbines are often placed at large distances apart, to reduce destructive wake effects, while maintaining a high energy density per unit area. However, WECs within a farm, are much smaller with much lower capacities and stronger inter device interactions due to the presence of a highly dense fluid. Therefore, larger number of WECs can be deployed in closer proximity to produce comparable energy density per unit area. As we move towards hybrid systems with floating solar, wind and wave energy amongst others, efficiency in deployment within an area becomes key. Conventional wave farm concepts that have been extensively studied such as 1) wave farms of different types of WECs (Point Absorber, Attenuator, Flap etc) also referred to as homogeneous arrays (same device in multiple numbers) and 2) wave farms with different sizes and drafts of one type of WEC also referred to as heterogeneous arrays. To date, studies have focused on multiple devices with similar geometries interacting through the same degrees of freedom. With this research, the authors explore mixed wave energy farms, which are wave farms utilizing different types of wave energy converters in the same farm. With the focus on the hydrodynamics and power produced by wave energy converters, this research provides for the first time insights into the interaction of devices, with varying geometries and degrees of freedom, thus entering an entirely new domain of wave farm research.

This study examines the potential contribution of marine renewable generators in Greece, in order to achieve a 100% renewable energy system by 2050. Using PyPSA-Eur, a cost-optimization model of the European energy system, possible energy transition pathways are explored, across five-year intervals from 2030 to 2050. For each five-year target, a new cost assumption dataset is used, one that follows estimated cost reduction learning rates. This version of the model is called PyPSA-Eur-MREL, and is modified to include marine power generators, i.e. floating wind, wave, tidal and floating solar, but also high fidelity climate data, in the scale of 5.5 km ² for wind and 4 km ² for wave resources. Three different approaches were employed in this investigation: greenfield, generator constrained, and a high-load scenario inspired by Greece's National Energy and Climate Plan (NECP). The analysis focused on generator capacity and performance, the levels of utilization and availability of each energy carrier and the land-use impact of onshore and offshore generators. While the first two scenarios exhibit similar overall system capacities, they differ in land-use requirements, with the constrained case installing more bottom-fixed wind turbines (1.2 GW), thereby reducing land occupation. The high-load scenario introduces floating wind turbines (4.5 GW), however, the scale of onshore installations remains substantial, covering nearly one-third of Greece's total land area.

Wave energy holds substantial promise as a renewable resource, but its commercial deployment remains limited. Research primarily focuses on individual wave energy converter (WEC) devices, while the interactions within WEC arrays have received less attention. Optimizing these interactions is essential for maximizing energy capture and minimizing operational costs. However, due to the variability of wave conditions, it is unlikely that a single WEC configuration will be effective across all scenarios. Therefore, to optimize performance, a large number of simulations are required, which is computationally expensive with traditional high-fidelity numerical methods. This paper addresses this challenge by utilizing a surrogate model based on polynomial chaos expansion (PCE), which efficiently captures the behavior of a WEC array over a 30-year probabilistic based on a high-fidelity wave dataset. The surrogate model is compared to a frequency domain model, demonstrating a high efficiency. The surrogate model is used to simulate the performance of an array of five point absorber WECs under varying wave conditions. The study highlights the following requirements for optimal array performance: the spatial configuration of WECs must consistently produce optimal power throughout the operational period and must adapt to the high variability of wave parameters. The results reveal that the fixed array configuration under study, produces power that is inconsistent over varying sea conditions, showing suboptimal energy production under most wave conditions, and higher power output only under less probable wave scenarios. These findings provide insights into the physical interactions influencing WEC array performance and can inform future design methodologies for wave energy farms. The proposed surrogate modeling framework offers a highly efficient tool for conducting large-scale probabilistic analyses of WEC arrays, significantly reducing computational effort while enabling more accurate performance predictions.

Harnessing wave energy from the oceans using wave energy converters (WECs) offers a huge opportunity to diversify Europe’s future renewable energy system. Although the energy conversion of this pre-commercial technology is not directly linked to greenhouse gas emissions, environmental sustainability over the full life cycle needs to be ensured for a future-proof large-scale application of WECs. Therefore, we present a cradle-to-grave full life cycle assessment (LCA) study for a generic point absorber WEC based on a fully transparent and adaptable life cycle inventory. Within the study we assess the environmental impacts of a single point absorber device, the influence of different hull materials, hotspots in the impacts of WEC components, and variations induced by different deployment locations. For a WEC deployed in the North Sea, we found a global warming impact of 300-325gCO2eq./kWh with periphery and 52-77gCO2eq./kWh without periphery, depending on the hull material. Using an alternative fibre-reinforced concrete material for the hull can reduce the impact across all categories by between 10% (marine eutrophication) and 78% (human toxicity, carcinogenic). In addition to the WEC itself we found that the electrical cable and vessel operations, particularly for maintenance, are significant contributors. These two elements will also be relevant to other marine renewables such as offshore wind and floating solar. Overall, this study shows potential for improving environmental impacts from WECs and identifies possible levers to achieve such a reduction.

This article investigates the methodology and applicability of the statistical linearization (SL) method to incorporating multi-variate non-differentiable nonlinearities, with a focus on floating renewable energy devices. The SL method serves as a highly competitive approach for analyzing floating renewable energy structures, such as wave energy converters (WECs) and floating wind energy turbines, because it inherently combines adequate accuracy and high computational efficiency. The origin of high accuracy comes from its incorporation of nonlinear effects through statistically linearized representations. Yet, the statistically linearized solutions have only been derived and verified for a limited number of nonlinearities of floating renewable energy devices, mostly simply-formed and differentiable in their mathematical expressions. However, floating renewable energy devices usually exhibit a complex dynamic mechanism, in which the relevant nonlinear effects could appear to be highly complex for linearization process to describe. These nonlinear effects could make a significant impact on the system dynamics, exemplified by external machinery force saturation and nonlinear hydrostatics of floaters with a non-uniform geometry. To push forward the boundary of the SL method, it is crucial to demonstrate how it applies to nonlinearities of different features. In this paper, the existing SL method is extended to address the nonlinear effects expressed as multi-variate non-differentiable functions. Several case studies are carried out to exemplify the application of the extended SL approach to the concerned nonlinearities in floating renewable energy devices. The accuracy and computational efficiency of the extended SL approach are evaluated by verifying against the corresponding nonlinear time-domain (TD) and linear frequency-domain (FD) models. Despite the complexity of the given nonlinearities, the relative errors of the SL approach are no more than 6 % while its computational time is comparable to the FD model, being thousands of times faster than the TD model. Comparatively, the FD model leads to a relative error of over 70% in some cases.

This study presents a first long term (30 years) assessment to quantify the effects of both, the wave spectrum representation, and occurrences of multi-modal sea states, on power production estimations from a point-absorber Wave Energy Converter (WEC). Analysis in 3 different offshore locations (Portugal, Ireland and The Netherlands) is included to ensure robustness of results. In general, traditional methods based on the use of the JONSWAP spectrum, with an adequate gamma shape value, can lead to mean overestimation in yearly power production >12% when compared to reference hindcast spectral data. This can be partially reduced when capping is applied to power production, but still can be close to 10%. An alternative method is proposed to modulate the JONSWAP spectrum at each time step which helps to reduce differences, but leads to slight yearly underestimations (−2.5 to −5% in average). Although in all analyzed sites the occurrences of multi-modal spectra is >30%, contribution to errors due to misrepresentation of these sea states are estimated to be of about 2.5%. These findings provide valuable insights on the uncertainties introduced in power production estimations, related to wave conditions characterization, that can have important economic impact when planning for large scale deployments.

As the necessity for the decarbonisation of the global electricity market increases, a range of renewable energy technologies will be implemented, one of which is wave energy. A key step in this process is the thorough quantification of both the power resource at locations of interest, and the impacts of these devices on the natural environment. The present work streamlines these 2 processes into one methodology by investigating the long-term impacts of an array of 20 WECs on the nearshore Dutch wave climate, while also calculating the potential power resource at the site considering intra-array wake effects. Simulations of 10 year duration were conducted in the baseline scenario (no farm present) and with 2 array configurations, using the spectral wave model SWAN on an unstructured mesh. It was demonstrated that the power production of the farm during this period, when wake effects are considered, is calculated to be up to 1.8% less than traditional methods. The presence of the farm is shown to reduce significant wave height and wave power in its lee, with the effects being largely attenuated at the coast. It was shown that the magnitude of the change is dependent on both the period and height of the waves at the farm, and notably the magnitude of the reduction does not increase consistently with the wave height, contradicting the sentiment that wave farms are effective protection mechanisms against damaging high-energy conditions. Furthermore, the present work suggests that changes to the nearshore breaker index may impact longshore currents that are essential for nutrient and sediment transport, the effect of which on the ecosystem is not yet well quantified.

The Energy Transition requires meticulous planning, taking into consideration economic, technical, social, and resource constraints. In Europe ambitious targets have been set for system electrification, however, integrating the potential of marine renewables have not been thoroughly investigated. This study extends the framework of PyPSA-Eur into PyPSA-Eur-MREL that for the first time incorporates all marine renewables, using high resolution datasets, that uncover the potential of marine renewables. Marine renewables are modelled in terms of power estimations, deployment strategies and revised packing density, and expected benefits for 2030, and 2050 across all European Countries are quantified. Higher spatio-temporal data have an immediate impact in estimates, and reduction of energy storage by 73%. Wind energy has a reduced installation capacity by 50%, but the higher fidelity of resource matches production to demand and reduces curtailments up to 60%. System costs with high resolution data are 40% reduced to 160 billion € for a 2030 100% renewable reliant system. The benefits of having more marine renewables are not limited to cost and more efficient demand matching, reduced energy storage, but it also with the area required to decarbonise the system. The results are encouraging and outline the importance and further need for marine renewable energies.

The deployment of marine renewables (MRE) is important for transitioning to a low-carbon energy system. However, their performance is highly dependent on the deployment location, making the selection of feasible sites critical for large-scale implementation. To contribute meaningfully to Europe’s renewable energy strategy and support a carbon-neutral energy system by 2050, the environmental performance of MREs must be taken into account in site selection, beyond the typical economic and technical aspects. Therefore, this study presents a geospatial analysis of the climate change mitigation potential of two wave energy converters, floating offshore photovoltaics, and floating wind turbines in northern European coastal waters. By combining a detailed life cycle assessment model of the four MREs with spatial data, the distribution of their life cycle global warming impact and carbon payback periods is assessed across multiple regions. The results show significantly varying impact levels of the different MREs, with carbon-neutral deployment not guaranteed at every location. Wave energy converters only partially reach carbon neutrality, while floating photovoltaics fail to do so across the entire study area. Floating wind turbines can be considered carbon-neutral nearly across their entire theoretical application area. The findings highlight the importance of taking into account site-specific environmental performance of MREs in order to ensure a positive contribution to climate change mitigation. By providing spatially explicit maps of MREs’ global warming impacts and carbon payback periods, this study enables as the first of its kind the inclusion of climate change mitigation considerations in the site selection process for MREs.

Numerical modelling plays a pivotal role in the design and optimization of wave energy converters. Spectral-domain (SD) modelling has recently received significant research interest as a newly emerging numerical tool. SD modelling is commonly characterized as an extension of frequency-domain (FD) modelling but can incorporate nonlinearities. Thereby, it combines high computational efficiency and adequate accuracy. Previous studies have demonstrated the applicability of SD modelling to a variety of nonlinear hydrostatic/hydrodynamic effects, including viscous drag force, nonlinear hydrostatic force, nonlinear mooring force, etc. However, there also exist influential nonlinear effects in the power generation phase in wave energy conversion. For instance, previous studies have demonstrated that the current limit of the electrical generator could impact the PTO force and the dynamics of the whole system. Therefore, it is necessary to further develop the SD modelling to cover the entire wave-to-wire process in WECs.

In this paper, a SD model is derived to simulate the wave-to-wire process of a point absorber WEC. A mechanical PTO system coupled with a rotary permanent-magnet generator is considered for the WEC. Representative nonlinear effects of the wave-to-wire process are incorporated, including viscous drag force, nonlinear PTO force, and the current limit of the generator. A nonlinear time-domain (TD) wave-to-wire model is established correspondingly to serve as the accuracy reference because it is inherently associated with higher modelling fidelity. The dynamic response and the power performance of the proposed SD model are verified against those of the nonlinear TD wave-to-wire model. Additionally, the computational efficiency of the proposed SD model and the TD model is identified and compared.

The increasing global demand for wind power underscores the importance of understanding and characterizing extreme ramp events, which are significant fluctuations in wind power generation over short periods that pose challenges for grid integration. This study focuses on modeling frontal low-level jets (FLLJs) and associated extreme ramp-down events, particularly their impact on wind power production at Belgium offshore wind farms. Using the Weather Research and Forecasting (WRF) model, we analyzed five cases of extreme wind power ramp-down events, including in-depth analysis of two cases and generalization of three additional cases. We assessed the sensitivity of various model configurations, including initial and boundary condition (IC/BC) datasets (ERA5 and CERRA), the activation of Fitch wind farm parameterization (WFP), planetary boundary layer (PBL) schemes, and single- versus nested-domain configuration. Our findings indicate that CERRA IC/BCs provide a superior representation of atmospheric flow compared to ERA5, resulting in more accurate predictions of ramp timing, intensity, and FLLJ characteristics. The WFP significantly impacts wind power output by modeling turbine interactions and wake effects, leading to slightly lower wind speeds. The scale-aware Shin and Hong PBL scheme yielded a stronger FLLJ core at higher altitudes with a more pronounced jet nose, although wind speeds below 200 m were lower compared to the Mellor–Yamada–Nakanishi–Niino 2.5 scheme. Single-domain configuration proved more effective in simulating wind power ramps but had higher core heights and higher wind speeds below 200 m, resulting in a diffused jet profile. Our analysis highlights that reliable simulation of extreme ramps associated with FLLJs using a single-domain configuration could reduce computational costs. Further, the FLLJs and associated extreme ramps can be predicted 1 d in advance, offering substantial benefits for operational efficiency in wind energy management.

Understanding the effects of arrays of Wave Energy Converters (WEC) on the wave fields is still an ongoing effort. Many publications have proposed different approaches to incorporate WEC farms in wave models to assess sea state changes in the near and far field. In the present study, a practical iterative method is proposed to incorporate the spectral response of a WEC obtained from the HAMS-MREL Boundary Element Model (BEM) in the SWAN spectral wave model. This allows to change the transmission and reflection properties of the WEC, represented in the model as an obstacle, at each time step. Since the response of a WEC simulated in the BEM model is defined in the frequency domain, it is possible to relate the absorbed power, at each discrete frequency, to the transmission coefficient applied at each frequency used to discretize the wave spectrum in SWAN. In this case, the method is applied to a single point-absorber type device since its response is independent of the waves’ directions. Validation of the method is done comparing the omnidirectional spectrum obtained downwave of the WEC in SWAN, with the spectrum reconstructed using the regular wave fields information (for each frequency) obtained in HAMS-MREL.