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Renewable Energy 34 (2009) 1600–1606

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Renewable Energy

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Wave climate off the Swedish west coast

Rafael Waters*, Jens Engstrom, Jan Isberg, Mats LeijonThe Ångstrom Laboratory, Division for Electricity, Swedish Centre for Renewable Electric Energy Conversion, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden

a r t i c l e i n f o

Article history:Received 28 February 2008Accepted 11 November 2008Available online 16 December 2008

Keywords:Wave climateWave powerSea stateExtreme wavesSkagerrakKattegat

* Corresponding author. Tel.: þ46 18 471 5839; faxE-mail address: rafael.waters@angstrom.uu.se (R.

0960-1481/$ – see front matter � 2008 Elsevier Ltd.doi:10.1016/j.renene.2008.11.016

a b s t r a c t

This paper presents and discusses the wave climate off the Swedish west coast. It is based on 8 years(1997–2004) of wave data from 13 sites, nearshore and offshore, in the Skagerrak and Kattegat. The datais a product of the WAM and SWAN wave models calibrated at one site by a wave measurement buoy. It isfound that the average energy flux is approximately 5.2 kW/m in the offshore Skagerrak, 2.8 kW/m in thenearshore Skagerrak, and 2.4 kW/m in the Kattegat. One of the studied sites, i.e. site 9, is the location ofa wave energy research site run by the Centre for Renewable Electric Energy Conversion at UppsalaUniversity. This site has had a wave power plant installed since the spring of 2006, and another seven areplanned to be installed during 2008. Wave energy as a renewable energy source was the driving interestthat led to this study and the results are briefly discussed from this perspective.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Ocean wave energy has the potential to contribute largeamounts of renewable energy to the world’s societies [1]. Todayseveral technologies have been tested at large scale and in real seaconditions, see e.g. [2–4], and some are nearing a commercial stage.In order for the wave energy converters (WECs) to be competitive,they have to be adapted to the local wave climate. The moredetailed knowledge one has of the wave climate of a particular site,the easier it is for developers of wave energy systems to optimizethe technology and make it competitive.

The present study describes the specific wave climates at 13locations off the west coast of Sweden, in the continuation of theNorth Sea called Skagerrak and Kattegat. It summarizes 8 years ofwave data covering the years from 1997 to 2004. The investigatedsites are spread out over varying depth and distance from land,from north to south in order to provide a comprehensive picture ofthe overall wave climate of the Swedish west coast. The waveclimate of the sites are presented in terms of significant waveheight, energy period, dominating wave directions, energy flux,annual energy distribution, the occurrence of extreme waveconditions, and statistical hundred-year waves. The model wavedata has been calibrated with on-site measurements carried out byUppsala University at one of the studied nearshore sites, i.e. site 9,see Fig. 2. The results are discussed from a wave power perspective,as this was the driving interest that led to this study and since this

: þ46 18 471 5810.Waters).

All rights reserved.

perspective raises questions and visualizes aspects that are criticalto wave power technology.

It is well known that the wave climate off the west coast ofSweden is relatively calm in comparison to the coasts facing theoceans of the world. The Norwegian coast, only 300 km to the west,has an average wave climate with an energy flux up to an order ofmagnitude higher [5]. Moreover, the average total deepwater wavepower resource along the Atlantic coasts of Europe amounts toabout 290 GW [6]. Yet in spite of this it has been presumed that theavailable wave power resource of the Skagerrak can still be a viablesource of renewable energy from a technical and economicalperspective, mainly attributed to the high density of energy inocean waves [7]. When the results of this paper are discussed fromthe perspective of a wave energy converter (WEC) the technology inmind is that described by Danielsson et al. [8] and Leijon et al. [9]. Inbrief the WEC consists of a linear generator of limited stroke length.The generator is located on the seabed and is connected, via a line,to a point absorber on the surface. The discussed points are,however, with few exceptions valid and important for all waveenergy converters known to the authors.

Although some recent studies have been carried out on the wavefields and wave energy resource of the Baltic sea, see e.g. [10–12],the documentation that can be found on the wave climate of Ska-gerrak and Kattegat is fragmented in time and sparse in spatialresolution. Documentation on the wave climate off the Swedishwest coast saw most activity in the 1980s during the Swedish WaveMeasuring Programme. The measurements were carried out by theSwedish Meteorological and Hydrological Institute (SMHI) usingWave rider buoys and Echo sounders [13,14]. Registrations of thewave climate along the west coast are limited to four locations and

R. Waters et al. / Renewable Energy 34 (2009) 1600–1606 1601

concentrated on two areas: Trubaduren, Fladen, and Laso nearGothenburg; and Vaderoarna further north. The measurements onthese sites have not been carried out simultaneously, but rathereach station has been running for a few years with some overlap.The longest time series are found at Trubaduren covering the yearsfrom 1978 to 2004 [15], though the available documentation onlycovers the period from 1 October 1978 to 28 February 1986 [14].The information from Trubaduren is given only in the form ofscatter diagrams. The measurement station Vaderoarna is of specialinterest here since it can be compared to one of the measurementsites in this paper, i.e. site 4, see Fig. 2. During the time period from1 April 1980 to 13 January 1981 the documented average significantwave height, Hs (sometimes given as Hm0 to show its origin inspectral analysis) at Vaderoarna was 2.46 m, and the mean waveperiod was 5.42 s. The highest expected wave for a 100 year periodat the same location was calculated to 18.3 m, however, as theauthor points out; the calculation is based on less than one year ofmeasurements, which gives a rather low reliability [14]. As a roughestimate, the mean energy flux in the Skagerrak region of theSwedish west coast has been calculated to be about 6 kW/m [13]. InJonsson et al. [16] a hindcast model has been used to calculate thewave fields in the Baltic Sea and around Sweden. This hindcaststudy used data for one year (1999) and the results are compared towave measurements made by the Swedish Meteorological andHydrological Institute. A comprehensive report on the Swedishwave energy research up until 1987 can be found in Claesson [5].

2. Wave data

The wave data that this study has been based on was purchasedfrom Fugro OCEANOR of Norway. The data consists of time series ofrelevant wave parameters representing every 6-h time period duringthe years 1997–2004. The data have been collected through thecombined information from on-site wave-buoys, satellites, anda wave and wind model, WAM [17], run by the European Centre forMedium-range Weather Forecast. The information from the wave-buoys is used to calibrate the satellite altimeter data, and the satellitedata is, in turn, used to calibrate the WAM model. Five of the studiedpoints are located near shore at depths of approximately 15–30 m. Atthese locations, where the geography of sea floor and coastline willhave a larger impact on the waves, the SWAN (Simulating WavesNearshore) model has been used on the calibrated WAM data anda detailed description of bathymetry and coastline has been used. For

Fig. 1. Comparison between the wave parameters simulated by the SWAN model and those mis energy period, and J is energy flux.

a more thorough description of the wave data generation see Barstowet al. [18]. During the spring of 2005 the Swedish Centre for Renew-able Electric Energy Conversion of Uppsala University deployeda wave measurement buoy at site 9 [19]. Collected wave data fromcontinuous measurements of that buoy were used to calibrate thedata generated by the SWAN model in order to increase the accuracyof the modeled nearshore data. A qualitative view of the result of thecalibration, in terms of significant wave height, energy period, andenergy flux, is seen in Fig. 1. The result shows that the only significantdifference between measured and simulated values is for the energyperiod at very small wave heights. This is due to the poor frequencyresponse of the wave measurement buoy at low frequencies, as wellas to difficulties in the simulations of very weak sea states. In otherwords, the uncertainties are greater in both measurements andsimulations during weak sea states.

3. Extreme wave calculations

Extreme wave calculations have been performed according tothe recommendations of the International Association forHydraulic Research [20]. Data sets have been chosen from all sitesthrough the peaks over threshold method (POT), and the thresholdlevel resulting in the best goodness of fit has been chosenthroughout. The data has been fitted, by means of maximum like-lihood, to the truncated three-parameter Weibull distribution:

FðHsÞ ¼ 1� exp

"��

Hs� AB

�C

þ�

Hs0 � AB

�C#

(1)

where F is the cumulative distribution function (CDF), Hs issignificant wave height, Hs0 is the threshold significant waveheight, A is the location parameter, B is the scale parameter, and C isthe shape parameter. The truncated three-parameter Weibulldistribution was chosen over the non-truncated case because, asshown by quantile–quantile plots, it proved more stable towardsthe highest waves where the regular three-parameter Weibulldistribution in general overestimated the wave heights. TheGeneral extreme value distribution was also evaluated but sufferedthe same drawback as the regular three-parameter Weibull distri-bution. The Kolmogorov–Smirnov test was used to evaluate thegoodness of fit between the data and the distribution. The resultingsignificance level is above 95% for all sites with the exception of site3 for which the significance level is 87%.

easured by a wave measurement buoy located at site 9. Hs is significant wave height, TE

Fig. 2. Map presenting the location of the studied sites. The wave roses are placed with their center on the studied sites and show the distribution in time of the direction onincoming waves.

Table 1Overview of the studied sites: Coordinates; water depth; mean energy flux with standard deviation, Jmean; maximum wave height from the 8 years of data, Hsmax; statisticallyderived significant wave height appearing on average once per 100 years, Hs(100); and the highest single wave statistically appearing on average once per 100 years, Hmax(100).

Site no. Coordinates Depth Jmean � std.dev. Jmax Hsmax Hs(100) Hmax(100)(m) (kW/m) (kW/m) (m) (m) (m)

1 58.83�N, 10.83�E 82 5.3 � 0.8 239.6 6.8 7.8 12.32 58.67�N, 10.92�E 46 4.8 � 0.7 166.9 5.9 6.5 10.33 58.70�N, 11.13�E 30 3.2 � 0.4 93.3 4.5 4.8 7.74 58.51�N, 10.93�E 70 5.1 � 0.8 223.4 6.6 7.4 11.75 58.33�N, 10.67�E 200 5.5 � 0.8 248.5 6.9 8.0 12.66 58.38�N, 11.00�E 80 5.0 � 0.7 203.9 6.3 7.0 11.17 58.40�N, 11.19�E 30 2.7 � 0.3 72.2 4.1 4.5 7.28 58.20�N, 11.08�E 107 5.6 � 0.7 204.3 5.9 6.6 10.39 58.20�N, 11.37�E 25 2.6 � 0.3 71.5 3.8 4.0 6.210 57.67�N, 11.33�E 55 2.7 � 0.2 90.0 5.0 5.8 9.411 57.71�N, 11.58�E 16 2.7 � 0.3 72.7 4.1 4.4 7.112 57.25�N, 11.75�E 40 2.1 � 0.2 79.9 4.8 5.2 8.613 56.87�N, 12.25�E 25 2.1 � 0.3 43.1 3.7 3.9 6.4

R. Waters et al. / Renewable Energy 34 (2009) 1600–16061602

R. Waters et al. / Renewable Energy 34 (2009) 1600–1606 1603

The return value Hs(R), where Hs is the significant wave heightstatistically reached on average once per return period R, is calcu-lated according to:

FðHsðRÞÞ ¼ 1� sR

(2)

where s is the average time between the samples of the chosen dataset, R is the return period, and F is the probability that is to beplugged into the CDF (Equation (1)). Equation (1) is then solved forHs which is the wanted return value, Hs(R).

Fig. 3. Combined scatter and energy diagrams for sites 1 through 3. Colors showannual energy transport per meter of wave front (kWh/(m*year)). Numbers giveaverage occurrence in hours per year. Isolines present the energy flux in accordancewith Equation (1). Results are based on an 8-year average.

In order to estimate the maximum height, Hmax(R), of a singlewave in the wave record represented by the return value, it isassumed that the wave heights of any wave record will be Rayleighdistributed [21]. With this assumption the most probable value ofHmax(R) is calculated as:

HmaxðRÞ ¼ HsðRÞffiffiffiffiffiffiffiffiffiffiffiffilnðNÞ

2

r(3)

where N is the total number of zero-crossing waves in the waverecord. The value of N has been found by calculating the number of

Fig. 4. Combined scatter and energy diagrams for sites 4 through 6. Colors showannual energy transport per meter of wave front (kWh/(m*year)). Numbers giveaverage occurrence in hours per year. Isolines present the energy flux in accordancewith Equation (1). Results are based on an 8-year average.

R. Waters et al. / Renewable Energy 34 (2009) 1600–16061604

peak periods, Tp, occurring during a half hour wave record. Amethod for estimating the peak period belonging to a return value,Hs(R), is given by Mathiesen et al. [20].

4. Results

The location of the studied sites, together with information onwater depth and wave climate parameters, is given in Table 1. Each

Fig. 5. Combined scatter and energy diagrams for sites 7 through 9. Colors showannual energy transport per meter of wave front (kWh/(m*year)). Numbers giveaverage occurrence in hours per year. Isolines present the energy flux in accordancewith Equation (1). Results are based on an 8-year average.

value of maximum energy flux and highest observed significantwave height is representative of a half-hour wave record. Eight-year mean energy flux is given together with standard deviation onan annual basis. Statistical hundred-year significant wave heightsand hundred-year maximum single wave heights have beencalculated as described in the previous section.

Fig. 2 presents a map in two scales where the studied sitesare marked together with wave roses. The wave roses are placedwith their centers on the corresponding sites, and the roses

Fig. 6. Combined scatter and energy diagrams for sites 10 through 12. Colors showannual energy transport per meter of wave front (kWh/(m*year)). Numbers giveaverage occurrence in hours per year. Isolines present the energy flux in accordancewith Equation (1). Results are based on an 8-year average.

Fig. 7. Combined scatter and energy diagram for site 13. Colors show annual energytransport per meter of wave front (kWh/(m*year)). Numbers give average occurrencein hours per year. Isolines present the energy flux in accordance with Equation (1).Results are based on an 8-year average.

Fig. 8. Average monthly energy flux with standard deviation at site 5.

Fig. 9. Cumulative frequency of occurrence of sea states as a function of time at site 5.Each of the total 11,688 data points is represented by a circle referring to a 6-h periodof time.

R. Waters et al. / Renewable Energy 34 (2009) 1600–1606 1605

themselves show the distributions in time of the direction onincoming waves.

In Figs. 3–7 combined scatter and energy diagrams for the 13sites can be found, all based on the 8 years of data. The numericalvalues represent the average annual occurrence of a combination ofsignificant wave heights and energy periods, given in numbers ofhours. The energy period has been divided into intervals of 1 s,while the significant wave height has been divided into intervals ofone third of a meter. The colors in the figures show the averageannual distribution of energy measured in kWh/(m*year), wherenumerical values are found in the color bar. For the annual energya higher resolution was used with the energy period divided into 4intervals per second, and the significant wave heights divided into6 intervals per meter. Isolines have been calculated using the deepwater energy flux approximation of Equation (4), and the sameapproximation has been used in calculating the energy weights ofthe scatter diagrams:

J ¼ r g2

64pTEHs2 (4)

where J is energy flux in watts per meter of crest length,r ¼ 1025 kg/m3 is the density of sea water, g is the acceleration ofgravity, TE is the energy period, and Hs is the significant waveheight. For a thorough description of Equation (4) and the conceptsof energy period and significant wave height see Cruz [22]. In Figs.3–7 the period has been limited to 12 s to ease the comparison ofthe studied sites.

Following the scatter diagrams Site 5 has been chosen as a casestudy in order to give a more detailed illustration of the charac-teristics of the wave climate of the Swedish west coast. In Fig. 8 theaverage energy flux is presented on a monthly basis, with standarddeviation showing variation over the eight studied years. In Fig. 9the time-accumulated distribution of all 11,688 6-h values ofenergy flux is given.

5. Discussion

As can be seen directly from the results, i.e. Table 1, the averageenergy flux of the studied offshore sites of Skagerrak is approxi-mately 5.2 kW/m. Although this can be expected to vary somewhathad more points been included in the study it is close to the 6 kW/mpreviously noted by Mårtensson et al. [13]. The average energy flux

changes significantly when the waves move closer to land. Thenearshore sites of Skagerrak, i.e. sites 3, 7 and 9, all exhibit an energyflux almost half of that found offshore. This is an expected result ofthe decreasing water depths towards these locations, which havethe effect of damping the energy of the longer waves. Othercontributing factors is that winds from the inland do not give rise towaves at nearshore locations, and refraction due to the bathymetryof the nearshore sites may have a small impact. In Kattegat thewaves are smaller in average as well as in extremes. The averageenergy flux is approximately 2.4 kW/m with a higher flux towardsthe north.

Regarding the statistical highest single wave appearing ina hundred years, the results of the present study indicate muchsmaller values then the 18.3 m, at site 4, previously noted bySoderberg [14]. However, the data of that study only covered nineand a half months and, as noted in the introduction, the authorhimself thought that the reliability of the result was low. It isdifficult to say more about the differing results here since theauthors of the present paper do not know enough about themethod used to calculate the extreme wave of that study.

Fig. 8 shows the annual distribution of energy flux, at site 5, ona monthly basis with standard deviation. As expected, October

R. Waters et al. / Renewable Energy 34 (2009) 1600–16061606

through March, the winter half of the year, shows a markedlyhigher average energy flux that is up to several times higher thanduring the calm summer months.

The intermittent nature of ocean waves is a problematic area forocean wave energy capture, especially the extreme power differ-ences experienced in storms compared to average power levelswhich can have a harmful effect on the survivability of the WECs.During the studied 8 years there have been a few occurrences ofextreme levels of energy flux, see Fig. 9. 1.1% of the time, or 33 days,have seen average levels of energy flux over 55 kW/m, i.e. ten timesthe overall average. However, only 7 days out of the studied 8 yearsexhibit levels of energy flux exceeding 100 kW/m. However, amongthese the most powerful flux reaches a half-hour average of250 kW/m, a full 45 times higher than the overall average. In all, theenergy flux reaches higher than 13.5 kW/m only during 10% of thetime, and close to 50% of the total energy is found in sea states witha significant wave height between 1 and 3 m and an energy periodbetween 4 and 7 s.

When designing a wave energy converter for a certain site, as forthe ones described here there are many parameters to consider. Thedesign choices may varya great deal depending onwhere one choosesto focus, and any decision will be a compromise. The extreme levels ofenergy flux discussed above are a reality in the oceans that alldesigners of wave energy converters must consider, and with greatrespect. Although most likely published only in regular media ratherthan in scientific journals, the harsh conditions of the oceans andthe extreme power of ocean waves have wrecked many attempts towave energy conversion. The WECs must be designed to survive inthese conditions. However, since a wave energy converter cannot bedesigned to have an installed power corresponding to the 100-yearwave some compromise is needed in order for the WEC to be ofrealistic proportions from an economical perspective. One alternativewould be to design the WEC after the average energy flux, but theresults presented in this paper clearly show that this is a bad choice. Inthe case of site 5 as much as 79% of the annual energy is found in waveclimates with a higher energy flux than the average 5.5 kW/m.Perhaps the best alternative for a design basis are the combinedscatter and energy diagrams, see Figs. 3–7, as these contain the mostinformation. In the diagrams it is clearly visible where the energy islocated and hence for which energy flux, wave height and period theWEC could be designed for.

6. Conclusion

The wave climate off the west coast of Sweden has been pre-sented based on 8 years of wave data from 13 studied sites in theSkagerrak and Kattegat. The mean energy flux was found to beapproximately 5.2 kW/m in offshore Skagerrak, 2.8 kW/m in near-shore Skagerrak, and 2.4 kW/m in the Kattegat, though values up to55 times the average flux have been recorded on the site locatedmost offshore. Statistical hundred-year waves have been estimatedto range from approximately 10.3 to 12.6 m in offshore Skagerrak,from 6.2 to 7.7 m in nearshore Skagerrak, and from 6.4 to 9.4 m inthe Kattegat. Discussions on wave energy converters conclude thatthe design sea state should be chosen with awareness of whatfraction of available energy is to be converted by the WEC.

Acknowledgements

This project was supported by the Swedish Energy Agency,Vattenfall AB, the Gothenburg Energy Research Foundation, DrakaCable AB, the Goran Gustavsson Research Foundation, VargonsResearch Foundation, Falkenberg Energy AB and the WalleniusFoundation. Hanna Paradis of Seabased Industries AB, and ThomasGotschl of Uppsala University are acknowledged for their help withmaps over Skagerrak and Kattegat. Stephen Barstow of FugroOceanor is thanked for discussions on wave data and extreme waveanalysis.

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