Modelling Wave Energy for the North Coast of Spain

Maritime Engineering and Technology – Guedes Soares et al.© 2012 Taylor & Francis Group, London, ISBN 978-0-415-62146-5

Modelling wave energy for the north coast of Spain

A. Rute Bento, Paulo Martinho & C. Guedes SoaresCentre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico,Technical University of Lisbon, Portugal

ABSTRACT: Two state-of-the-art spectral models, WAVEWATCH III (Tolman 2009) and SWAN (Booij et al.1999), are used to create a wave prediction system with the aim to characterize wave energy conditions for theSpanish North Coast. Direct comparisons are made and statistical results are obtained to assess the reliability ofthe wave prediction system developed. The wave parameters considered for those comparisons are significantwave heights, mean and peak periods. Theoretical values of wave power are estimated and the spatial distributionof wave energy was evaluated considering a relevant scenario and some areas with greater energetic potential isidentified. Overall the wave prediction system gives reasonable results when compared with the buoy data and,therefore, the results obtained for wave power can be accepted as being near to the real potential for the northcoast of Spain.

1 INTRODUCTION

World energy consumption has been rising consid-erably and since traditional methods of energy con-sumption are contributing seriously to environmentalproblems there is an urgent need for non-pollutingpower generation.Wave energy is considered as a cleansource of energy, with low environmental impacts,in particular it is seen as a big source of energy notinvolving large CO2 emissions. However, difficultiesfacing wave power developments must be recognized,such as irregularities in wave amplitude, phase anddirection, which makes difficult for a device to obtainmaximum efficiency, and structural loading in theevent of extreme weather conditions. Nevertheless,the advantages of wave energy are clear; it combinescrucial economic, environmental, ethical and socialfactors (Clément et al. 2002).

Wave energy results from wind energy transfer tothe water at the free surface of the ocean and, afterbeing created, waves can travel long distances with lit-tle energy loss. Energy fluxes occurring in deep watersea waves can be very large and, though near the coast-line the average energy intensity of a wave decreases,reflection and refraction can still compensate that asthey lead to energy concentration spots (“hot spots”).

Situated at the end of the Atlantic fetch, the waveclimate at the western coast of Europe is known asbeing highly energetic. The long-term annual wavepower level increases from about 25 kW/m off thesouthernmost part of Europe’s Atlantic coastline upto 75 kW/m off Ireland and Scotland. The total waveenergy resource for Europe results in 320 GW (Clé-ment et al. 2002) (Fig. 1).

The potential of wave energy extraction can beacquired from analysis of wave conditions. Buoy data

Figure 1. Wave resource distribution.

can give a general idea of the wave conditions and itstendencies, but the time period of the measurementsis in general limited. Numerical models enable tobridge that time gap and to predict wave conditionsin various scenarios, that is why it is essential to usethem to characterize wave climate.

Several approaches have been made in order touse numerical models to evaluate wave conditions.A nearshore wave energy atlas has been developedfor Portugal (Pontes et al. 2005) based on a direc-tional wave spectrum hindcast for an 11-year period.A 44 year hindcast was also made for the wholeEuropean western coast in the context of HIPOCASproject (Hindcast Dynamic Processes of the Ocean andCoastal Areas of Europe) (Pilar et al. 2008). There, theWAM model was used, modified for two-way nesting,to provide results for processes of wave generationand deep water propagation. The output parameters

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were significant wave height, wave direction, meanand peak period, wind speed and direction, Hs for windsea, direction of wind sea, Tm for wind sea, Hs forswell, direction for swell and Tm for swell. In order toextend the study referred to the coastal environment,Rusu et al. (2008) used the SWAN (Booij et al. 1999)model to make a hindcast for the Iberian coast, withhigher quality than the one of Pontes et al. (2005) thatused a ray model. A regional meteorological modelwas also used in the coastal area and it was found thatthe skill of the model was improved with the finer gridwind fields (Rusu et al. 2008). After the HIPOCASproject (Pilar et al. 2008) and its extension to finitewater depth (Rusu et al. 2008) the effectiveness ofsuch complex wave prediction system was demon-strated by Rusu & Guedes Soares (2009). In that workthe spatial distribution patterns of the wave energy inthe Portuguese nearshore were also assessed.

The present work aims to evaluate a similar waveprediction system as the ones referred and analyzethe wave energy spatial distribution for the Northcoast of Spain. WAVEWATCH III (Tolman 2009) andSWAN (Booij et al. 1999) were the two state-of-the-artmodels implemented. Two parallel studies were doneby Bento et al. (2011a, b), within the same project,one for the Irish West Coast and another for UK’ssouthwest coast, known for having high average wavepower. A study of the wave conditions in coastal areaswas done for both places by coupling the wave modelsSWAN and WAVEWATCH III. Validation tests werecarried and results for wave power were obtained forspecific tests sites: Galway and Belmullet in Ireland’scase, Cornwall and Pembrokshire in UK’s case.

The north coast of Spain was the area consideredfor this study, from the NW corner of the IberianPeninsula to the SE Bay of Biscay. As a westernEuropean coastline, the north coast of Spain isexposed to powerful swells and it is also prominentin wave energy exploitation, with annual mean val-ues near to 40 kW/m in the section between Cape SanAdrián and Cape Ortegal, as can be seen in Figure 2.

Galicia has a very long coastline, approximately1659 km, and it is known to have great potential indeepwater energy. Two areas stand out in relation towave energy: the coast around Cape Estaca de Baresand the “Death Coast”, a name given after the manylives lost in shipwrecks caused by its energetic waves.Regarding wave power, its values in the Death Coastare in the order of 50 kW/m and annual wave energyexceeds 400 MWh/m (Iglesias & Carballo 2009). ForEstaca de Bares, buoys give a mean value of 40 kW/mand an annual mean around 360 MWh/m. Asturias,the region adjacent to Galicia which extends betweenRía de Ribadeo and Ría de la Tina Mayor (250 km),is battered by strong swells and its average wavepower exceeds 20 kW/m. In relation to annual waveenergy, it exceeds 200 MWh/m. The SE Bay of Biscay,like the other regions of the northern seaboard ofIberia, offers a noticeable potential for wave energyexploitation. The annual wave energy range between200–250 MWh/m in deep waters, but due to irregular

Figure 2. Annual Wave Energy for the North Coast of Spain.

bottom contours in this area hot spots emerge andthey are considered important areas for wave farmsites (Iglesias & Carballo 2010a, b, c).

2 DESCRIPTION OF THE WAVE HINDCASTSYSTEM

Third-generation spectral wave models are the currentstate-of-the-art for wave climate modeling and formthe essential structure of the majority of wave transfor-mation models including WAM, WWIII, SWAN andMike 21-SW. All are based on solving the spectralaction balance equation, which determines the evo-lution of the action density in space and time. Theaction density is defined as energy density divided bywave frequency and is used because, unlike energydensity, it is conserved in the presence of currents.The energy density is specified using the lineartwo dimensional wave spectrum, with wave energydistributed over frequency and propagation direction.

Here, E is the wave energy density, t is the time, xand y are the Cartesian coordinates, σ is the wavefrequency, θ is the direction of wave propagation, Cis the speed of wave energy propagation and S refersto the energy sources/sinks (Folley & Whittaker 2009)being expressed in Equation 2.

S in a combination of nonlinear interaction windwave (Snl), wind wave interaction (Sin) and a dissipa-tion term (Sds). For model initialization it should alsoconsider a linear input (Sln).

The wave hindcast system created uses the WWIIImodel for wave generation, covering approximatelythe entire North Atlantic basin (Fig. 3) while SWAN’sdomain covers Spain’s northern coastal environment(Fig. 4) and connects the large scale to the coastalsimulations.

WWIII has been developed at the Marine Modelingand Analysis Branch (MMAB) of the Environmen-tal Modeling Center (EMC) of the National Centers

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Figure 3. Implemented area for WAVEWATCH III.

Figure 4. Bathymetry of the north coast of Spain.

Table 1. Computational grids for the wave hindcast system.

Limits

Bathymetries Latitude Longitude Resolution

North Atlantic (15◦N–72◦N) (66◦W–7◦E) 1◦ × 1◦Spain (41◦N–45◦N) (11◦W–1◦W) 0.05◦ × 0.1◦

for Environmental Prediction (NCEP) and tends to bemore efficient at global scales, while SWAN, whichwas developed at Delft University of Technology,offers advantages at smaller scales and for shallowwater processes. Both are widely used spectral wavemodels that have been validated in a various situ-ations. Recent improvements in SWAN allow it tobe used effectively for sub oceanic scales. Therefore,the wave prediction system implemented considersa large SWAN domain that covers the entire coastalenvironment.

Two NOAA datasets are used as inputs for WWIII.The bathymetry came from GEODAS database andthe wind fields are taken from NCEP’s Reanalysis2, with time steps of 6 hours (4 × daily data). Theresults are generated with a time step of 3 hours.Afterwards, WWIII data are used as boundary con-ditions for SWAN. For the SWAN runs, the windfields considered are the same as in WWIII, but thebathymetries were taken from GEBCO’s database.Computational grids can be seen in Table 1.

Figure 5. Illustration of the buoy locations.

Table 2. Coordinates and depth of the buoys considered.

Coordinates

Latitude Longitude Depth

Buoy 1 42.12◦N 9.43◦W 600 mBuoy 2 43.40◦N 9.21◦W 386 mBuoy 3 43.74◦N 6.17◦W 450 mBuoy 4 43.64◦N 3.05◦W 600 m

Figure 6. Hs time series of Buoy 1 vs SWAN results.

3 VALIDATION TESTS IN THE TIME DOMAIN

Measurements from four wave buoys owned byPuertos Del Estado were used. Their location is shownin Figure 5 and specified in Table 2.

For the simulations, comparisons in the timedomain are carried out against the in situ measure-ments. For these validations, the time period consid-ered is from October 1st to November 13th, 2010,although some data from this time period may not beincluded due to buoy failure. The time resolution ofthe simulations was of 1 h.

Time series for Significant Wave Height (Hs) areshown in Figures 6–9. Figures 10–13 show the timeseries for MeanWave Period (Tm) while Figures 14–17illustrates the Peak Period. Each compare buoy resultswith SWAN’s output.

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It can be observed that, for the Hs time series,simulation results by SWAN show the same behavioras the buoy data, although SWAN performed betterfor buoys 1, 2 and 3, than for buoy 4. In terms of

Figure 10. Tm time series of Buoy 1 vs SWAN results.



Mean Period (Tm) SWAN clearly underestimates realdata and for the Peak Period (Tp) simulations translatebetter the buoy behavior, even though it still has thetendency to underestimate.

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Figure 14. Tp time series of Buoy 1 vs SWAN results.


For the analyses of the significant wave height,scatter plots are also presented in the Figures 18–21.The scatter plots for buoys 1, 2 and 3 show amore homogeneous distribution of results around the



Figure 18. Hs scatter plot for buoy 1.

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observation line than the for buoy 4, where the resultsare mostly bellow the observation line. Nevertheless,this corroborates what was previously noted in the Hstime series.

To better understand the performance of the model,a statistical evaluation was made. The computedstatistics were the average values of measurements(Bm) and simulations (Sm), the bias, root mean squareerror (RMSE), scatter index (SI) and Pearson’s Cor-relation Coefficient (r) and can be expressed by themathematical expressions:

Here Xi represent the measured values, Yi the simu-lated values and n the number of observations. Theresults are shown in Table 3, 4 and 5.

In general, for Hs, the 3rd buoy has the bestresults and the 4th buoy has the worst results. Forthe first two buoys the statistical results for Hs aregood; it can be observed that the bias values are below0.1 m, and all correlation coefficients are above 0.8.For mean and peak periods the results were not asgood as for Hs, as expected. Nevertheless, buoy 4 hasthe best results for both mean and peak periods. Thedifferences between measured periods and simulatedperiods may be a result of the different processes usedin obtaining the values. For SWAN they result fromspectral analysis and for the buoys they result from adirect analysis of the data.

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Table 3. Statistical results for Hs.

Significant Wave Height

Bm Sm Bias RMSE SI r

Buoy 1 (n = 21) 2.513 2.564 −0.050 0.626 0.249 0.899Buoy 2 (n = 211) 2.738 2.660 0.079 0.647 0.236 0.875Buoy 3 (n = 206) 1.944 1.778 0.166 0.430 0.221 0.902Buoy 4 (n = 207) 1.909 1.257 0.652 0.948 0.496 0.813

Table 4. Statistical results for Tm.

Mean Period


Buoy 1 (n = 21) 7.002 3.850 3.152 3.323 0.475 0.714Buoy 2 (n = 211) 6.830 3.907 2.923 3.076 0.450 0.772Buoy 3 (n = 206) 6.910 3.328 3.582 3.792 0.549 0.840Buoy 4 (n = 207) 6.487 4.930 1.558 1.975 0.304 0.809

Table 5. Statistical results for Tp.

Mean Period


Buoy 1 (n = 21) 11.431 8.929 2.502 3.555 0.311 0.514Buoy 2 (n = 211) 10.945 8.727 2.218 3.126 0.286 0.668Buoy 3 (n = 206) 11.120 8.805 2.315 3.672 0.330 0.548Buoy 4 (n = 207) 10.929 10.071 0.858 2.598 0.238 0.630

4 WAVE ENERGY ASSESSEMENT

With the SWAN model, it is possible to calculateenergy transport per unit of wave front (W/m). It iscomputed considering the following formula:

Here x, y are the problem coordinate system and cx,cy are the propagation velocities of wave energy in thegeographical space.

Wave power can afterwards be calculated using theformula:

Afterwards the wave power is normalized dividingeach value by the maximum wave power computedfor that scenario.

An evaluation of significant wave height’s spa-tial distribution (Fig. 22) and its wave power result

Figure 22. Hs spatial distribution. In the background sig-nificant wave height scalar fields and in foreground wavevectors.

(Fig. 23) is made for wave energy assessment. Onecase study is considered. It corresponds to 2010/11/09,at 6 h, where one of the highest values of Hs isencountered.

Evaluating theoretical results for wave energy, itcan be observed that, in general, the northwesterncoast registers higher values of wave energy. It is alsovisible that half of the North Spanish coast is underthe shadow effect caused by Bay of Biscay’s northern

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Figure 23. Computed Normalized Wave power (W/m). Inbackground wave power scalar fields and in foregroundenergy transport vectors.

area. The section between Cape San Adrián and CapeOrtegal registers the highest values for wave power,while Santander registers the lowest values for wavepower.

5 CONCLUSIONS

WWIII and SWAN, both state-of-the-art spectralmodels, are used to create a wave prediction sys-tem to evaluate wave conditions for Spain’s Northerncoast. Having in mind that the important wave param-eters for wave energy analysis are the significant waveheight and the wave period, the ability of the model tosimulate wave energy is tested. To have a percep-tion of the accuracy of the numerical wave model,a validation analysis of the computed results againstbuoy measurements is made and theoretical valuesfor the energy transport components are obtained.

Taken as a whole, the results are good whencomparing significant wave height with buoy data.For mean and peak period the results are not as goodas was expected. They have the same time evolu-tion but have an almost constant bias. The results forwave power depend mainly on significant wave heightand thus they should be fairly accurate.

ACKNOWLEDGEMENTS

This work has been performed within the projectMAREN – Marine Renewable Energy, Energy Extrac-tion and Hydro-environmental Sustainability, which ispartially funded by the Atlantic Area Programme.

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Modelling Wave Energy for the North Coast of Spain