Paradigmatic case of long-term colocated wind–wave energy index trend in Canary Islands

Energy Conversion and Management 283 (2023) 116890 Available online 16 March 2023 0196-8904/© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman Paradigmatic case of long-term colocated wind–wave energy index trend in Canary Islands Alain Ulaziaa,∗, Jon Sáenzb,d, Aitor Saenz-Aguirrea, Gabriel Ibarra-Berasteguic,d, Sheila Carreno-Madinabeitiae aEnergy Engineering Department, University of the Basque Country (UPV/EHU), Engineering School of Gipuzkoa-Eibar, Spain bDepartment of Physics, University of the Basque Country (UPV/EHU), Sarriena Auzoa z/g, 48940 Leioa, Spain cEnergy Engineering Department, University of the Basque Country (UPV/EHU), Alda, Urkijo, 48013 Bilbao, Spain dPlentziako Itsas Estazioa, PIE (BEGIK), University of the Basque Country (UPV/EHU), Areatza Pasealekua, 48620 Plentzia, Spain eDepartment of Mathematics, University of the Basque Country (UPV/EHU), Paseo de la Universidad, 01006 Vitoria-Gasteiz, Spain ARTICLE INFO Keywords: Wave energy Wind energy Co-location index ERA5 Long-term energy trend Fluid mechanics ABSTRACT Previous studies based on remote sensing data and reanalysis have identified strong historical increments of wind speed in the area around the Canary Islands (Spain) without appreciating any increment of wave height. This decoupling of long-term trends for wind and wave data is not very common, and can be considered paradigmatic for an innovative study, with important implications for wind and wave hybrid or co-located energy production. In this study, wind and wave data from ERA5 reanalysis in the area around the Canary Islands have been used to compute a wind–wave energy co-location feasibility index between 1981– 2020 showing an increment of the index above +5%/decade. Furthermore, realistic wind and wave energy production has been calculated at an interesting hot-spot using a specific floating wind turbine co-located aside a oscillating buoy type wave energy converter. The corresponding capacity factor trend for wind energy (+0.8%/decade) and capture width ratio evolution for wave energy (−1.5%/decade) shows also the wind–wave decoupling, which constitutes a significant result for an original approach. 1. Introduction Renewable energy is showing a significant increase, almost doubling the share of energy from renewable sources in gross final energy consumption in the case of Europe [1]. However, 80% of current energy supply is still delivered by fossil fuels [2], and each country must include a decarbonization policy based on renewable energy sources to obtain a carbon-neutral society through further development of clean technologies and sustainable multi-period selection of locations [3]. For instance, Iberian Peninsula and Canary Islands constitute a paradigmatic case due to the their high wind and solar energy potential, showing very good previsions for their techno-economic assessment [4]. This will certainly contribute to meet the Spanish C02reduction objectives. This is an important issue since by 2030 Spain is committed to generate more than 74% of its electricity from renewable sources [5]. Among renewable energy sources, Ocean Renewable Energy (ORE) can offer a huge potential for electricity generation, mainly using the ∗Corresponding author. E-mail addresses: [email protected] (A. Ulazia), [email protected] (J. Sáenz), [email protected] (A. Saenz-Aguirre), [email protected] (G. Ibarra-Berastegui), [email protected] (S. Carreno-Madinabeitia). combination of wind and wave energy, as it was shown in specific geographical areas such as the Mediterranean [6] or the Chinese Sea [7], or within sustainable development objectives using renewable energy strategies in Europe [8]. In general terms, currently wave energy exhibits rather low Technology Readiness Level (TRL) values [9] and is not so technically developed as offshore wind technology. However, recent innovations have shown the potential of wave farms near the coast at providing a continuous apportion of energy into the grid [10]. In the case of a particular technology – Oscillating Water Column (OWC) – the TRL is currently at a value of 8 [11]. Recent studies on a fully operational wave farm [12], indicate that the energy generated by waves are predictable to a high extent in the short term, thus allowing the development of electricity management protocols to be applied in the overall energy market. An important challenge is the determination of how climate-driven changes in wave energy, will impact on the future electricity generated at a wave farm designed under current-day conditions. Similarly, future changes of https://doi.org/10.1016/j.enconman.2023.116890 Energy Conversion and Management 283 (2023) 116890 2 A. Ulazia et al. List of Abbreviations C3S Copernicus Climate Change Service ECMWF European Centre for Medium-Range Weather Forecasts ERA5 5th reanalysis by ECMWF ERA-Interim 4th reanalysis by ECMWF FB Floating Body wave energy converter IFS Integrated Forecasting System LCOE Levelized Cost of Energy NCAR National Center for Atmospheric Research NCEP National Centers for Environmental Prediction NREL National Renewable Energy Laboratory ORE Ocean Renewable Energy OWC Oscillating Water Column TRL Technology Readiness Level WEC Wave Energy Converter WT Wind Turbine Nomenclature 𝐴𝐸𝑃 Annual Energy Production (kWh) 𝐵Frontal absorption width and diameter of the WEC 𝑐(0) Instantaneous Correlation 𝐶𝐿𝐹 Colocation Feasibility Index 𝐶𝐹 Capacity Factor 𝐶𝐼 Confidence Interval 𝐶𝑊 𝑅 Capture Width Ratio (m) 𝐷𝑏Diameter of the floating body 𝑔Acceleration of gravity (9.8 m/s2) 𝐻𝑠Significant wave height (m) 𝑀Molecular mass of dry air (28.9 kg/kmol) 𝑁Number of hours per year (8760 h) 𝑝Pressure (Pa) 𝑃(𝑈𝑖)Wind turbine power for wind speed 𝑈𝑖(kW) 𝑃𝑎𝑏𝑠 Absorbed Power of the WEC (kW) 𝑃𝑤𝑎𝑣𝑒 Theoretical Power of the wave front (kW) 𝑃𝑅Rated power of the wind turbine (kW) 𝑅Constant of ideal gases 𝑡Temperature (K) 𝑇𝑚Mean wave period (s) 𝑇𝑒Energy period of waves (s) 𝑈Wind speed (m/s) 𝑈𝑥Wind speed at 𝑥m height (m/s) 𝑊 𝐸𝐹 Wave Energy Flux (kW/m) 𝑊 𝑃 𝐷 Wind Power Density (W/m2) 𝑧0Sea roughness (m) 𝛼𝑖,𝑗 𝐶𝐿𝐹 index weight coefficients 𝜌Real air density (kg/m3) 𝜌0Standard air density (kg/m3) 𝜌𝑤sea water density (kg/m3) 𝜎Standard deviation 𝛥𝑇 Time resolution (1 h) sea level could also have an impact on the future electricity output some decades from now. Although uncertainties remain about these two issues, at least Oscillating Water Column (OWC) type converters – mainly due to their regulation mechanisms – seem to exhibit an excellent robustness and adaptability to wave climate changes [13]. Coming to the impact of sea-level rise on wave farms a recent study [14] suggests that it may be negligible. Therefore, predictability in the short term and robustness before long-term changes seem to be two major characteristics of wave energy. The combined exploitation of wind and wave energy is therefore drawing increasing attention in the recent scientific literature, showing strong synergies not only for energy production, but also for operation, maintenance, and protection of floating wind turbines and its structures against extreme events [15]. Although ocean extreme event analysis is an important aspect, it falls out of the scope of this study. Extreme event related index establishes a cut-off for the installation of offshore structures due to security issues. It is therefore a discrete indicator instead of a continuous one like a feasibility index related to the optimal combination of wind–wave. It is supposed that before a wind– wave feasibility study, or any other kind of wind and wave energy potential study, an extreme event assessment should verify whether an offshore installation is both, technologically and economically viable or not. Beyond these security and survival problems, this study is related to the optimal combination and hybridization of wind energy and wave energy. This combined approach [16] can play a key role at meeting the European objective for hydrogen production [17]. The present study emphasizes the importance of long-term wind [18] and wave energy trend analysis developed by the authors for Mutriku wave plant [13], Gulf of Biscay [19], Ireland [20] or Iceland [21], now, in a completely different environment. Now, instead of carrying out two independent analyses for wind and waves, this work constitutes a novel approach for the estimation of historical trends for the combined resource. To that purpose, a paradigmatic oceanic area such as the Canary Islands has been selected for this study, where the predominant wind (trade winds) and the swell (from the Atlantic Ocean) are aligned in opposite directions. All the seven islands of the Canary Archipelago show a great potential in OREs. El Hierro is referential in this sense, being a relevant case around the world for a totally independent electrical energy system based on wind energy with the wind-hydro project Gorona del Viento [22], and also with a high wave energy potential [23]. Other islands such as Tenerife and Gran Canaria also exhibit an important offshore wind and wave energy potential [24,25], and it can be concluded that this hybrid potential is generally strong for the seven islands. The study of historical wave energy and wind energy trends at the global scale have commonly shown a combined increment of both resources in the last decades, which has been hypothetically related to the effects of climatic change. This synchronized increment of both resources is well known based on reanalysis data or remote sensing data. Young et al. [26] used satellite data since the 80 s to the 90 s to compute global trends of wind speed and wave height, and this synchronized increment is general in the Atlantic Ocean with the exception of Macaronesian area and the Guinean Gulf. In other Atlantic regions like the Bay of Biscay in the last decades, the observations indicate a combination of positive trends for wave energy and a not clear pattern for wind speed [13]. All this makes Canary Islands an area of scientific interest for this type of studies. The special character of the Canarian marine climate within the interaction of wind and waves is also shown by the influence of trade winds on trans-hemispheric swell waves [27], or by singular ocean currents derived from a strong continental slope [28]. This fact makes the Canary Islands a paradigmatic case to study the historical evolution of wind and wave energy combination, which in this work, will be studied using reanalysis data and decadal trends of both resources. The focus will be to use a fine resolution analysis at previously identified hot spots based on a wind–wave co-location index [29] and the consequent optimal strategies of deployment of colocated wind–wave energy farms [16]. The discussion on the adoption of an analytical or a subjective index to measure the feasibility of the Energy Conversion and Management 283 (2023) 116890 3 A. Ulazia et al. Table 1 Comparison between the properties of ERA5 and the previous ECMWF’s reanalysis ERA-Interim. Properties ERA-Interim ERA5 Availability 1979 onwards 1950 onwards IFS model cycle 31r2 (2006) 41r2 (2016) Data assimilation 12-hour 4D-Var 12-hour 4D-Var ensemble Spatial resolution 79 km (TL255) 60 levels to 10 Pa 31 km (TL639) 137 levels to 1 Pa Ocean waves 1 degree 0.5 degree Output frequency 6-hourly for analyses 3-hourly for forecasts Hourly throughout (uncertainty 3-hourly) Output parameters Extensive Extended (e.g. 100 m wind) hybridization of both OREs is beyond this article due to its mathematical nature, but it opens a rich research line in analogy to other kind of indexes to measure techno-economic aspects such as energy poverty, as it is described in Section 4[30]. The reminder of the paper is structured as follows: after the introduction on the state of art of the hybridization of wave energy and wind energy, the specific ERA5 data used for this study will be explained (Section 2.1); then the methodology on the computation of decadal evolution in Section 2.2.2, and the description about the co-location feasibility index (CLF) in Section 2.2.3 will be shown. A specific section will be devoted to the method of computation on real energy production based on the power curve of specific turbine (Section 2.4.1) along with the power model of a specific wave energy device (Section 2.4.2); Section 3shows the decadal resource maps, the evolution of co-location index, and the evolution of real wave and wind energy production. The Discussion Section 4interprets qualitatively these results, and finally, Section 5concludes with a fundamental summary and outlooks for future developments. 2. Data and methods The following sections describes the data sources used for the study and the corresponding methods to develop the results. 2.1. Data The following sections describe the ERA5 reanalysis and the study area around Canary Islands, where the data sources are implemented. 2.1.1. ERA5 reanalysis Long-term variations of the wave and wind resource have been analysed employing ERA5 reanalysis data [31]. The European Centre for Medium-Range Weather Forecasts (ECMWF) processes all datasets using their Earth System model Integrated Forecasting System (IFS) and the results are distributed by the Copernicus Climate Change Service (C3S) and it already covers the period from 1950 to present [32]. This reanalysis combines huge amounts of historical observations from satellites, in-situ met-ocean data (onshore meteorological stations and offshore buoys), and snow data. The ERA5 reanalysis is the fifth major global reanalysis produced by the ECMWF (after ERA-Interim, see Table 1), and provides 1-hourly data at a spatial resolution of around 30 km all over the world for downloaded meteorological data: 1. For atmosphere and wind energy analysis these parameters are used: wind speed (𝑈), pressure (𝑝), and temperature (𝑡). 2. However, in the case of wave data, the spatial resolution available is about 50 km, where these parameters are used: significant wave height (𝐻𝑠) and mean wave period (𝑇𝑚) or peak wave period (𝑇𝑝). Recent literature describes good evaluations of ERA5 against wind and wave observations, and not only for low roughness and turbulence areas of the ocean, but also for less predictable onshore locations in case of wind farms: •Versus wind farm data in the North of Europe [33]; •In the Iberian Peninsula versus offshore buoys anemometers [18]; •For Iberian and Canarian buoy wave data [34]; •For swell wave data [35]; •For global wave data versus altimeter measurements [36] ; •In China waters for wave data [37]. 2.1.2. Study area The climate of the Canary Island has long ago been identified as very interesting for wind energy due to the fact that the islands are located, especially during summer, under a strong influence of NorthEasterly trade winds associated to the Azores high pressure system. These summer trade winds are very regular and very frequently blow with speeds between 7 m/s and 11 m/s [38]. The Azores high represents during summer the surface response of the pressure field to the subsidence associated to the Hadley Circulation in the Atlantic sector, and some studies show that there is a positive trend in the area-averaged pressure of the Azores High [39], which makes the area interesting for a study like this one, which addresses the longterm behaviour of energy resources of the area. Furthermore, given its political membership to the European Union (Spain) in contrast to its geographical African origin in the form of volcanic islands, it constitutes a very interesting area for a isolated electrical grid based on renewable energies with few interconnections [40]. One-hourly data from 1981 to 2020 (40 years) have been downloaded in the Canary Islands for the present study, meaning that 350640 cases are analysed at each gridpoint in the analysed area, which covers longitudes in the interval [−19◦E, −13◦W] and latitudes in [27◦N, 30◦N], which is composed of 91 gridpoints in total for the geographical window that covers the seven Canary Islands: El Hierro, La Palma, La Gomera, Tenerife, Gran Canaria, Lanzarote and Fuerteventura. The steep bathymetry around the islands due to its volcanic origin is shown using shaded areas in Fig. 1, which reaches up to −5000 m depth in few kilometers [41]. In Section 3.2, a point of interest is selected for the behaviour of CLF at the South of Tenerife, where a zonal bathymetry transect (under the map) and meridional transect (on the left) are plotted as white lines through the point −17◦E and 27.5◦N. Both show that the sea deepens to thousands of meters in few kilometers from the coast and that the hot-spot depth is around −3500 m. 2.2. Methods The following sections derive the main parameters that interpret the results from the basic parameters of ERA5, describe the method of computation of these parameters’ trend per decade, and defines the CLF that determines the performance of wind–wave combination at a given location. 2.2.1. Derived magnitudes The Wave Energy Flux (𝑊 𝐸𝐹 ) is the usual indicator to characterize the energy transported by waves. It is stated in [kW/m], and is derived from the 𝐻𝑠and energy (mean) wave period (𝑇𝑒) [42,43] according to Eq. (1). 𝑊 𝐸𝐹 =𝜌𝑤𝑔2 64𝜋𝐻2 𝑠𝑇𝑒= 0.49𝐻2 𝑠𝑇𝑒(1) Energy Conversion and Management 283 (2023) 116890 4 A. Ulazia et al. Fig. 1. Map of the Canary Islands, with black labels showing the main islands (EH: El Hierro, LP: La Palma, LG: La Gomera, TE: Tenerife, GC: Gran Canaria, F: Fuerteventura and L: Lanzarote). The bathymetry around the islands is shown using shaded areas and the location of the buoys used in the study are shown by stars and labelled in red (TS: Tenerife Sur, SCT: Santa Cruz de Tenerife, GC: Gran Canaria, LPE: La Palma East). One meridional (zonal) transect through the point −17◦E and 27.5◦N is shown to the left (under) the map for reference and as white lines drawn in the map. It is to be taken into account that ERA5 denominates mean wave period to the energy period 𝑇𝑒[44] so the calculation of 𝑊 𝐸𝐹 is straightforward using (1) under the assumption of deep waters conditions. In the case of Canary Islands, this condition is met given its deep bathymetry as shown in Fig. 1. On the other hand, the magnitude that defines the kinetic power of the wind is the Wind Power Density (𝑊 𝑃 𝐷), and is given by Eq. (2): 𝑊 𝑃 𝐷 =1 2𝜌𝑈3(2) where 𝜌is the air density, calculated every hour from 𝑝and 𝑡, together with the molecular mass of the air 𝑀=28.9 kg/kmol, and the constant of the ideal gases 𝑅=8314 KJ/kgK. 𝜌=𝑝𝑀 𝑅𝑡 (3) After developing specific tools to reduce the huge computational effort involved [45,46], it is to be highlighted that the authors have shown in many previous studies the impact of air density changes in wind energy production. Instead of considering the standard value of 1.225 kg/m3as a constant in wind energy studies, authors have shown the impact of seasonal 𝜌variations as well as the small influence of humidity changes in the WPD at a given height and location annually [47] and seasonally [48]. 2.2.2. Decadal evolution The decadal evolution of 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷 density has been computed in percentage terms in both cases, by comparing the differences of the decadal averages of 𝑊 𝐸𝐹 (i.e., last decade 𝑊 𝐸𝐹4for 2011– 2020 minus first decade 𝑊 𝐸𝐹1for 1981–1990) with respect to the first decade: 100 𝑊 𝐸𝐹4−𝑊 𝐸𝐹1 𝑊 𝐸𝐹1 (4) The same can be done for the 3rth and 2nd decades, and for the 𝑊 𝑃 𝐷 trend (see Fig. 3). 2.2.3. Colocation index for wind and waves The 𝐶𝐿𝐹 for wind and wave energy defined by Astariz et al. is used in this study [29]. It depends on 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷, and on the instantaneous correlation (𝑐(0)) or the standard deviation of both magnitudes (𝜎𝑊 𝐸𝐹 and 𝜎𝑊 𝑃 𝐷). For the sake of brevity in this archival paper, the equation is not defined, but the general interpretation is simple, since it constitutes a score between 0 and 1, with 1 at the maximum co-location feasibility for the combination of wind and wave energy. According to Eq. (5), there are statistically weighted five terms in the equation for a given study area ranged between 0 and 1. 𝐶𝐿𝐹𝑖=𝛼𝑊 𝐸𝐹 𝑊 𝐸𝐹𝑖−𝑊 𝐸𝐹min 𝑊 𝐸𝐹max −𝑊 𝐸𝐹min (1)+ 𝛼𝑊 𝑃 𝐷 𝑊 𝑃 𝐷𝑖−𝑊 𝑃 𝐷min 𝑊 𝑃 𝐷max −𝑊 𝑃 𝐷min (2)+ 𝛼𝑐(0) 𝑐(0)max −𝑐(0)𝑖 𝑐(0)max −𝑐(0)min (3)+ 𝛼𝜎𝑊 𝐸𝐹 𝜎𝑊 𝐸𝐹 ,max −𝜎𝑊 𝐸𝐹 ,𝑖 𝜎𝑊 𝐸𝐹 ,max −𝜎𝑊 𝐸𝐹 ,min (4)+ 𝛼𝜎𝑊 𝑃 𝐷 𝜎𝑊 𝑃 𝐷,max −𝜎𝑊 𝑃 𝐷,𝑖 𝜎𝑊 𝑃 𝐷,max −𝜎𝑊 𝑃 𝐷,min (5) Energy Conversion and Management 283 (2023) 116890 5 A. Ulazia et al. Table 2 Main characteristics of the baseline NREL 5 MW wind turbine. Value Unit Rated power 5 MW Rotor diameter 123 m Hub height, diameter 90, 3 m Cut-in, rated, cut-out wind speed 3, 11.4, 25 m/s Cut-in, rated rotor speed 6.9, 12.1 rpm 1. The ratio between the difference of mean 𝑊 𝐸𝐹 with respect to the minimum 𝑊 𝐸𝐹 of the region and the difference between the maximum and minimum 𝑊 𝐸𝐹 . 2. The ratio between the difference of mean 𝑊 𝑃 𝐷 with respect to the minimum 𝑊 𝑃 𝐷 of the region and the difference between the maximum and minimum 𝑊 𝑃 𝐷. 3. The temporal correlation of 𝑊 𝑃 𝐷 and 𝑊 𝐸𝐹 at each gridpoint. 4. The ratio between the difference of the standard deviation of 𝑊 𝐸𝐹 with respect to the maximum standard deviation of the region and the difference between the maximum and minimum standard deviations. 5. The ratio between the difference of the standard deviation of 𝑊 𝑃 𝐷 with respect to the maximum standard deviation of the region and the difference between the maximum and minimum standard deviations. Obviously, the five terms should be between [0,1], and being 𝑖 substituted by 𝑊 𝐸𝐹 ,𝑊 𝑃 𝐷,𝑐(0),𝜎𝑊 𝐸𝐹 , or 𝜎𝑊 𝑃 𝐷, ∑ 𝑖 𝛼𝑖= 1 (6) In this way, according to the points 1 and 2 the average value of 𝑊 𝑃 𝐷 and 𝑊 𝐸𝐹 at the location should be as high as possible (near the maximum of the region) to improve 𝐶𝐿𝐹 . The same can be said for the correlation between 𝑊 𝑃 𝐷 and 𝑊 𝐸𝐹 . However, the points 4 and 5 establish that the standard deviations of 𝜎𝑊 𝐸𝐹 and 𝜎𝑊 𝑃 𝐷 should be as low as possible (low variability near the minimum of the region) in order to raise the value of 𝐶𝐿𝐹 . 2.3. Annual trends at a selected location The previous spatial method will be used to select a hotspot and interesting location due to 𝑊 𝑃 𝐷 and 𝑊 𝐸𝐹 variations. After this selection, a finer methodology is used at this location to find the annual variations of co-location feasibility and real energy production. The computation of the annual trends of 𝐶𝐿𝐹 and real productions using Capacity Factor (𝐶𝐹 ) and Capture Width Ratio (𝐶𝑊 𝑅) (see Sections 2.4.1 and 2.4.2) will be represented by linear regression and Theil–Sen method [49], which is a robust estimator which reduces the sensitivity of the trend to outliers by considering the medians instead of geometrical averages. 2.4. Real energy production The theoretical methods developed previously will be further developed introducing wind and wave data in power curves and power matrices of real wind turbines and Wave Energy Converters (WECs). This final approach can therefore offer strong commercial interpretations in the results. 2.4.1. Wind turbine The wind data at the identified hot-spot have been implemented on the power curve of the National Renewable Energy Laboratory (NREL) 5 MW wind turbine [50] for the computation of the Annual Energy Production (𝐴𝐸𝑃 ) and the 𝐶𝐹 .Table 2 describes the main characteristics of the turbine. However, previously, the wind speed at 10 m has to be raised to the wind speed at the hub height (90 m) by the log law [51]. The instantaneous one-hourly roughness (𝑧0) of the sea is obtained from wind speed at 10 m (𝑈10) and at 100 m (𝑈100) by Eq. (7). 𝑈100 𝑈10 =log(100∕𝑧0) log(10∕𝑧0)⇒𝑧0=𝑒 log(10)(2𝑈10−𝑈100) 𝑈10−𝑈100 (7) After that, wind speed at the hub height is obtained using the log law in Eq. (8). 𝑈90 =𝑈10 log(90∕𝑧0) log(10∕𝑧0)(8) Furthermore, the normalization of the wind speed is given by the cubic root of the ratio between air densities, being 𝜌0the standard air density, and 𝜌the real air density [48] (see Eq. (9)). 𝑈90𝑛=(𝜌 𝜌0)1 3 𝑈90 (9) Finally, the annual production 𝐴𝐸𝑃 (kWh) is given by Eq. (10), where N=8760 is the hours per year, 𝑃(𝑈𝑖)is the power produced in kW by the turbine for each wind-speed 𝑈𝑖of the time series, and 𝛥𝑇 = 1ℎ, the time resolution of the time series. 𝐴𝐸𝑃 = 𝑁 ∑ 𝑖=1 𝑃(𝑈𝑖)𝛥𝑇 (10) 𝐴𝐸𝑃 is divided by the ideal production at rated power 𝑃𝑅= 5000 kW to obtain 𝐶𝐹 according to the Equation 𝐶𝐹 =𝐴𝐸𝑃 𝑃𝑅⋅365.25 ⋅24 (11) This parameter 𝐶𝐹 is selected as an adimensional ratio in order to normalize the real production of the wind turbine and compare it with other ratio (𝐶𝑊 𝑅) that expresses an similar concept of the selected WEC, see Section 2.4.2. 2.4.2. Point absorber wave energy converter A WEC model of floating body type of developed by Oigarden and Olsen was used in deep water condition [52,53], having the absorbed wave power 𝑃𝑎𝑏𝑠 in kW as a function of 𝐻𝑠and 𝑇𝑝: 𝑃𝑎𝑏𝑠 = 4.5𝐷2.4 𝑏𝐻1.7 𝑠𝑇−0.9 𝑝(12) . where 𝐷𝑏denotes the diameter of the floating body. 𝐷𝑏= 2 m is adopted in the first approximation by the inventors [52], and in the 40 years evolution presented in Section 3.3.3. This WEC was designed to be partially filled with water, changing the water volume within, thus adapting the natural frequency of the device to the incident wave period. Therefore, 𝐶𝑊 𝑅 can be obtained considering 𝑃𝑎𝑏𝑠 as the really absorbed power, and 𝑃𝑤𝑎𝑣𝑒 the theoretical wave power given by 𝑊 𝐸𝐹 along the transversal longitude of the wave for 𝐷𝑏(frontal width of the device 𝐵=𝐷𝑏). 𝐶𝑊 𝑅 =𝑃𝑎𝑏𝑠 𝑃𝑤𝑎𝑣𝑒 =𝑃𝑎𝑏𝑠 𝑊 𝐸𝐹 ⋅𝐵(13) This parameter, 𝐶𝑊 𝑅, is selected as an adimensional ratio in order to normalize the real production of the WEC device and compare it with wind turbine’s 𝐶𝐹 , which is also a ratio. 3. Results The Table 3 summarizes all the main results and the confidence intervals at 95% confidence level for 𝐶𝐿𝐹 ,𝐶𝐹 ,𝐶𝑊 𝑅, and the real power production of the wind turbine and the WEC. In the next sections, the origin and visual representations of these final values are shown with a brief interpretation of these previous results. Energy Conversion and Management 283 (2023) 116890 6 A. Ulazia et al. Fig. 2. Absolute average value in the 1980–1989 initial decade of 𝑊 𝐸𝐹 (left in kW/m) and 𝑊 𝑃 𝐷 (right in W/m2). 3.1. Resource maps of decadal differences Fig. 2 shows the average 𝑊 𝐸𝐹 (left) and 𝑊 𝑃 𝐷 (right) from 1980 to 1989, the first referential decade with respect to which the relative variations of the following decades will be computed. For the following interpretation of the final results it should be noted the strong reduction of wind energy potential in the Southwest of Tenerife (around 200 W/m2at 10 m height), under the protection of Northeastern trade winds (around 500 W/m2in the North with peaks of 900 W/m2 between islands), an effect that is also considerable for 𝑊 𝐸𝐹 , but in a weaker way (from 15 kW/m to 10 kW/m). These spatial distributions are very similar to values found in previous literature for wave energy assessment and offshore wind energy assessment [25,54]. The decadal differences in percent for 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷 (Fig. 3) show a relevant increase, which reach up to 15% and 18% between the main islands of Tenerife and Gran Canaria for the last decade during the 2010s. In the case of 𝑊 𝑃 𝐷, there is even a decrease near the coast of Africa that reaches -5%, but the general trend is clearly incremental during the decades. However, the increment difference between 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷 (Fig. 4) is the relevant question here, in order to analyse the decadal variation of the feasibility of wind and wave energy combination. This study shows a huge difference of 18% between both historical trends at a gridpoint in the south of Tenerife and La Palma (longitude = −17◦E, latitude = 27.5◦N), due to the high increase of 𝑊 𝐸𝐹 and the reduction of 𝑊 𝑃 𝐷 from the decade of 1980s to the last decade of 2010s. This location also corresponds to the highly protected area from trade winds according to energy potential maps of Fig. 2. 3.2. Evolution of the co-location index at a relevant location The identified hotspot at the mentioned gridpoint (−17◦E, 27.5◦N) will be used for the study of the annual evolution of 𝐶𝐿𝐹 during the 40 years of analysis. Thus, the five terms of the 𝐶𝐿𝐹 equation have been computed for each year from 1980 to 2019 with around 350400 cases analysed, and statistical weight of each term has been subjective keeping the values of the original work of Astariz et al. [29], and weighting above all the index for the values of wave energy and wind energy, lower for the correlation, and giving a low specific weight to the variability for the two standard deviations (see Expression (14)). 𝛼𝑊 𝐸𝐹 = 0.35; 𝛼𝑊 𝑃 𝐷 = 0.35; 𝛼𝑐(0) = 0.2; 𝛼𝜎𝑊 𝐸𝐹 = 0.05; 𝛼𝜎𝑊 𝑃 𝐷 = 0.05; (14) This election according to [29], establishes the same index weight for 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷, not only for their absolute values (𝛼𝑊 𝐸𝐹 and 𝛼𝑊 𝑃 𝐷), but also for their variability within the standard deviation of the signals (𝛼𝜎𝑊 𝐸𝐹 and 𝛼𝜎𝑊 𝑃 𝐷 ). Fig. 5 shows a clear increment of 𝐶𝐿𝐹 along the 40 years from 0.44 to 0.51, showing also the confidence interval of the trend at a 95% confidence level using Theil–Sen method [49]. Although the value of 𝑊 𝑃 𝐷 remains almost constant at this point, this positive evolution is due to the strong increment of 𝑊 𝐸𝐹 at this point, which has a high statistical weight (0.35). The low variations of the correlation and standard deviations does not affect the final product of 𝐶𝐿𝐹 . 3.3. Real energy production The evaluation of the annual real production considering the power curve of the NREL 5 MW wind turbine for the computation of 𝐶𝐹 (see Section 2.4.1), and the floating device model’s annual average 𝐶𝑊 𝑅 (see Section 2.4.2), show approximately a similar behaviour: positive in the case of the wind turbine (Fig. 7), and negative in the case of the WEC (Fig. 8). The selected gridpoint using the described 𝐶𝐿𝐹 method shows therefore a long-term wind–wave energy compensation also for realistic electrical energy production. For that, previous to the energy production estimations, the first following Section 3.3.1 analyzes the instantaneous wind and wave power in kW considering the entire time series of four decades 1-hourly. 3.3.1. Power production by decades Firstly, Fig. 6 shows the decade boxplots of each device, the floating body (a) and the wind turbine (b), according to their instantaneous production in kW at each moment of the time series (40 years, 1 hourly). Although there is a relevant increment of power production for waves, it is no clear the trend of wind power production. This instantaneous power will be the base for the computation of 𝐶𝐹 and 𝐶𝑊 𝑅 in the following sections. 3.3.2. Evolution of the annual capacity factor of the wind turbine The selected gridpoint does not show a good 𝐶𝐹 , since the best offshore locations’ 𝐶𝐹 reach 0.40–0.50, but it is above a reasonable limit approximating 0.30 [55]. However, the 40-year trend is positive, showing a relevant increment at a 95% confidence level described by the shaded area (See Table 3). The linear fitting method or the Theil– Sen method [49] show a similar slope value and confidence interval, with a rise of 𝐶𝐹 around 0.02 starting from 0.27 in 40 year period. Table 3 in Section 4shows the exact values of the confidence interval. 3.3.3. Evolution of the annual average capture width ratio of the floating device The selected gridpoint shows a reasonable 𝐶𝑊 𝑅 for a floating device around 0.40–0.50 [56]. The 40-year trend is again relevant at a 95% confidence level, but there is a reduction of the value (See Table 3). The negative slope computed by the linear method or the Theil–Sen method [49] are similar, showing an absolute reduction of 𝐶𝑊 𝑅 around 0.02 starting from 0.45. Energy Conversion and Management 283 (2023) 116890 7 A. Ulazia et al. Fig. 3. Decadal differences with respect to 1980s initial decade in percent (by rows) for 𝑊 𝑃 𝐷 (left column) and 𝑊 𝐸𝐹 (right column). 4. Discussion A statistical summarizing of the previous graphical results shows the significance of the obtained confidence intervals and trends. Table 3 resumes the confidence intervals (CI 95%) calculated by means of the Theil–Sen method for the trend analysis of 𝐶𝐿𝐹 ,𝐶𝐹 and 𝐶𝑊 𝑅 per decade (by columns). Wind turbine’s (WT) and floating body’s (FB) power (kW) is also shown in the final rows. The last column shows the slope in percent per decade according to the central value. Although the positive trend of WT’s 𝐶𝐹 is not statistically significant, the numeric values of the inverse trends of wave energy and wind energy are coherent with the previous graphical representations, and the final result in percent per decade show very relevant variations mainly for the negative slope of 𝐶𝑊 𝑅 and the positive value of 𝐶𝐿𝐹 that reaches the 5%. This is a very important value, since a projection of this trend along a century would increment the co-location index from 0.4–0.5 to 0.7–0.8. It should be noted also the strong increment in percent of FB’s power due to the increment of 𝑊 𝐸𝐹 , which is offset in the calculation of 𝐶𝑊 𝑅 due to the increase of the divisor in Eq. (13). These strong trends are not strange, because previous literature on global historical trends of wind speed and wave height shows a Energy Conversion and Management 283 (2023) 116890 8 A. Ulazia et al. Fig. 4. Increment difference in four decades (2011–2010 minus 1980–1989) between 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷. Fig. 5. CLF trend at the identified hotspot. Table 3 This table summarizes the main results of this article, showing the numerical values of the trends per decade with their confidence intervals. In columns, confidence intervals (CI 95%) of the Theil–Sen method for the inferior, central and superior value (per decade). In rows, the Co-location Feasibility index, Capacity Factor, capture width ratio, and the Wind turbine and floating body power in kW. The last column shows the decadal increment in percent based on the central value. CI 95% Inferior Central Superior %/10y CLF 0.01 0.020 0.025 +5.6 CF 0.000 0.0017 0.0040 +0.8 CWR −0.010 −0.007 −0.005 −1.5 WT (kW) −2.3 21.7 26.6 +1.6 FB (kW) 0.13 0.16 0.27 +17 synchronized general increment in the Atlantic Ocean with the exception of the North-West African coast, Guinea Gulf, and Canary Islands [26,57]. This fact has been also corroborated by this study showing not only the decoupling of 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷, but also the corresponding decoupling of wind energy and wave energy production by a selected wind turbine and WEC according to 𝐶𝐹 and 𝐶𝑊 𝑅 (see Figs. 7 and 8). High resolution Global Wind Atlas [58] also validates the 𝐶𝐹 values identified at the hot-spot (−17◦E, 27.5◦N), under the protection of trade winds, with values around 0.30. This global atlas offers wind resource mapping at 250 m horizontal grid spacing, and 𝐶𝐹 resource mapping at 10, 50, 100, 150 and 200 m above ground/sea level. Since the extension of the ERA5 grid reaches the 0.5◦resolution, the Global Wind Atlas shows that these data correspond to the area at the South of La Gomera, where 𝐶𝐹 reduces significantly near the coast even below 0.20. The adoption of subjective specific weighs for the 𝛼parameters in Expression (14) and Eq. (5) can be improved in the future using analytic mathematical methodology for index generation, as it is used in other kind of energy index generation such in the case of energy poverty in a multidimensional approach [59]. The incorporation of analytical criteria to axiomatically determine the 𝛼parameters can be very interesting in future research, introducing, for instance, Levelized Cost of Energy (LCOE) values of offshore wind energy and wave energy to select a ratio between 𝛼𝑊 𝐸𝐹 and 𝛼𝑊 𝑃 𝐷. This fact would be important in the construction of a new analytical index given the lower LCOE of offshore wind energy up to 160 e/MWh [60] compared to wave energy’s LCOE, which is between 370–1200 e/MWh [61]. According to these preliminary data, 𝛼𝑊 𝑃 𝐷 and 𝛼𝑊 𝐸𝐹 can be different in a future research that would modify the original adoption of Astariz et al. [62], but this approach would therefore constitute a new and deeper axiomatic in analytical hierarchy process described by mathematicians in applications to index generation [63]. Anyway, this new approach would need to open a future research line between mathematics and techno-economic wave energy engineering, introducing also the statistics about survivability risk and extreme oceanic events as a previous step of the mathematical modelling of the improved index. It is not possible currently to attribute the detected trends to climate change induced by increased concentration of greenhouse gases. Local analyses located north of the Canary Islands using National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) data show that Northern Hemisphere models of variability such as the North Atlantic Oscillation or decadal signals in the ocean such as the Atlantic Multicedal Oscillation [64] affect the area. On the other hand, even though some papers identify a widening (poleward shift) of the Hadley Cell during the last decades [65], there are still some doubts regarding the seasonal or regional characteristics of the expansion of the tropics [66]. Besides that, the relevant literature has Energy Conversion and Management 283 (2023) 116890 9 A. Ulazia et al. Fig. 6. Power production in kW of the 5 MW wind turbine and the floating body WEC showing the boxplots corresponding to each decade. Each box shows the first and the third quartile in the up and down limits, and the median is represented by the line at the middle. Fig. 7. Capacity Factor trend at the identified hotspot of the selected wind turbine. Fig. 8. Capture Width Ratio trend at the identified hotspot of the selected Wave Energy Converter.