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Wave climate off the Swedish west coast
Renewable Energy 34 (2009) 1600–1606
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Wave climate off the Swedish west coast Rafael Waters*, Jens Engstro¨m, Jan Isberg, Mats Leijon ¨m Laboratory, Division for Electricity, Swedish Centre for Renewable Electric Energy Conversion, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden The Ångstro
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 February 2008 Accepted 11 November 2008 Available online 16 December 2008
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 data is a product of the WAM and SWAN wave models calibrated at one site by a wave measurement buoy. It is found that the average energy flux is approximately 5.2 kW/m in the offshore Skagerrak, 2.8 kW/m in the nearshore Skagerrak, and 2.4 kW/m in the Kattegat. One of the studied sites, i.e. site 9, is the location of a wave energy research site run by the Centre for Renewable Electric Energy Conversion at Uppsala University. This site has had a wave power plant installed since the spring of 2006, and another seven are planned to be installed during 2008. Wave energy as a renewable energy source was the driving interest that led to this study and the results are briefly discussed from this perspective. Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Wave climate Wave power Sea state Extreme waves Skagerrak Kattegat
1. Introduction Ocean wave energy has the potential to contribute large amounts of renewable energy to the world’s societies [1]. Today several technologies have been tested at large scale and in real sea conditions, 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 more detailed knowledge one has of the wave climate of a particular site, the easier it is for developers of wave energy systems to optimize the technology and make it competitive. The present study describes the specific wave climates at 13 locations off the west coast of Sweden, in the continuation of the North Sea called Skagerrak and Kattegat. It summarizes 8 years of wave data covering the years from 1997 to 2004. The investigated sites are spread out over varying depth and distance from land, from north to south in order to provide a comprehensive picture of the overall wave climate of the Swedish west coast. The wave climate of the sites are presented in terms of significant wave height, energy period, dominating wave directions, energy flux, annual energy distribution, the occurrence of extreme wave conditions, and statistical hundred-year waves. The model wave data has been calibrated with on-site measurements carried out by Uppsala 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
* Corresponding author. Tel.: þ46 18 471 5839; fax: þ46 18 471 5810. E-mail address: [email protected] (R. Waters). 0960-1481/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2008.11.016
perspective raises questions and visualizes aspects that are critical to wave power technology. It is well known that the wave climate off the west coast of Sweden is relatively calm in comparison to the coasts facing the oceans 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 of magnitude higher [5]. Moreover, the average total deepwater wave power resource along the Atlantic coasts of Europe amounts to about 290 GW [6]. Yet in spite of this it has been presumed that the available wave power resource of the Skagerrak can still be a viable source of renewable energy from a technical and economical perspective, mainly attributed to the high density of energy in ocean waves [7]. When the results of this paper are discussed from the perspective of a wave energy converter (WEC) the technology in mind is that described by Danielsson et al. [8] and Leijon et al. [9]. In brief 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 wave energy converters known to the authors. Although some recent studies have been carried out on the wave fields and wave energy resource of the Baltic sea, see e.g. [10–12], the documentation that can be found on the wave climate of Skagerrak and Kattegat is fragmented in time and sparse in spatial resolution. Documentation on the wave climate off the Swedish west coast saw most activity in the 1980s during the Swedish Wave Measuring Programme. The measurements were carried out by the Swedish Meteorological and Hydrological Institute (SMHI) using Wave rider buoys and Echo sounders [13,14]. Registrations of the wave climate along the west coast are limited to four locations and
R. Waters et al. / Renewable Energy 34 (2009) 1600–1606
concentrated on two areas: Trubaduren, Fladen, and La¨so¨ near Gothenburg; and Va¨dero¨arna further north. The measurements on these sites have not been carried out simultaneously, but rather each station has been running for a few years with some overlap. The longest time series are found at Trubaduren covering the years from 1978 to 2004 [15], though the available documentation only covers the period from 1 October 1978 to 28 February 1986 [14]. The information from Trubaduren is given only in the form of scatter diagrams. The measurement station Va¨dero¨arna is of special interest here since it can be compared to one of the measurement sites in this paper, i.e. site 4, see Fig. 2. During the time period from 1 April 1980 to 13 January 1981 the documented average significant wave height, Hs (sometimes given as Hm0 to show its origin in spectral analysis) at Va¨dero¨arna was 2.46 m, and the mean wave period was 5.42 s. The highest expected wave for a 100 year period at the same location was calculated to 18.3 m, however, as the author points out; the calculation is based on less than one year of measurements, which gives a rather low reliability [14]. As a rough estimate, the mean energy flux in the Skagerrak region of the Swedish west coast has been calculated to be about 6 kW/m [13]. In Jo¨nsson et al. [16] a hindcast model has been used to calculate the wave fields in the Baltic Sea and around Sweden. This hindcast study used data for one year (1999) and the results are compared to wave measurements made by the Swedish Meteorological and Hydrological Institute. A comprehensive report on the Swedish wave energy research up until 1987 can be found in Claesson [5].
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a more thorough description of the wave data generation see Barstow et al. [18]. During the spring of 2005 the Swedish Centre for Renewable Electric Energy Conversion of Uppsala University deployed a wave measurement buoy at site 9 [19]. Collected wave data from continuous measurements of that buoy were used to calibrate the data generated by the SWAN model in order to increase the accuracy of the modeled nearshore data. A qualitative view of the result of the calibration, in terms of significant wave height, energy period, and energy flux, is seen in Fig. 1. The result shows that the only significant difference between measured and simulated values is for the energy period at very small wave heights. This is due to the poor frequency response of the wave measurement buoy at low frequencies, as well as to difficulties in the simulations of very weak sea states. In other words, the uncertainties are greater in both measurements and simulations during weak sea states.
3. Extreme wave calculations Extreme wave calculations have been performed according to the recommendations of the International Association for Hydraulic Research [20]. Data sets have been chosen from all sites through the peaks over threshold method (POT), and the threshold level resulting in the best goodness of fit has been chosen throughout. The data has been fitted, by means of maximum likelihood, to the truncated three-parameter Weibull distribution:
2. Wave data
# Hs A C Hs0 A C FðHsÞ ¼ 1 exp þ B B
The wave data that this study has been based on was purchased from Fugro OCEANOR of Norway. The data consists of time series of relevant wave parameters representing every 6-h time period during the years 1997–2004. The data have been collected through the combined information from on-site wave-buoys, satellites, and a wave and wind model, WAM [17], run by the European Centre for Medium-range Weather Forecast. The information from the wavebuoys is used to calibrate the satellite altimeter data, and the satellite data is, in turn, used to calibrate the WAM model. Five of the studied points are located near shore at depths of approximately 15–30 m. At these locations, where the geography of sea floor and coastline will have a larger impact on the waves, the SWAN (Simulating Waves Nearshore) model has been used on the calibrated WAM data and a detailed description of bathymetry and coastline has been used. For
where F is the cumulative distribution function (CDF), Hs is significant wave height, Hs0 is the threshold significant wave height, A is the location parameter, B is the scale parameter, and C is the shape parameter. The truncated three-parameter Weibull distribution was chosen over the non-truncated case because, as shown by quantile–quantile plots, it proved more stable towards the highest waves where the regular three-parameter Weibull distribution in general overestimated the wave heights. The General extreme value distribution was also evaluated but suffered the same drawback as the regular three-parameter Weibull distribution. The Kolmogorov–Smirnov test was used to evaluate the goodness of fit between the data and the distribution. The resulting significance level is above 95% for all sites with the exception of site 3 for which the significance level is 87%.
"
(1)
Fig. 1. Comparison between the wave parameters simulated by the SWAN model and those measured by a wave measurement buoy located at site 9. Hs is significant wave height, TE is energy period, and J is energy flux.
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R. Waters et al. / Renewable Energy 34 (2009) 1600–1606
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 on incoming waves.
Table 1 Overview of the studied sites: Coordinates; water depth; mean energy flux with standard deviation, Jmean; maximum wave height from the 8 years of data, Hsmax; statistically derived 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 (m)
Jmean std.dev. (kW/m)
Jmax (kW/m)
Hsmax (m)
Hs(100) (m)
Hmax(100) (m)
1 2 3 4 5 6 7 8 9 10 11 12 13
58.83 N, 10.83 E 58.67 N, 10.92 E 58.70 N, 11.13 E 58.51 N, 10.93 E 58.33 N, 10.67 E 58.38 N, 11.00 E 58.40 N, 11.19 E 58.20 N, 11.08 E 58.20 N, 11.37 E 57.67 N, 11.33 E 57.71 N, 11.58 E 57.25 N, 11.75 E 56.87 N, 12.25 E
82 46 30 70 200 80 30 107 25 55 16 40 25
5.3 0.8 4.8 0.7 3.2 0.4 5.1 0.8 5.5 0.8 5.0 0.7 2.7 0.3 5.6 0.7 2.6 0.3 2.7 0.2 2.7 0.3 2.1 0.2 2.1 0.3
239.6 166.9 93.3 223.4 248.5 203.9 72.2 204.3 71.5 90.0 72.7 79.9 43.1
6.8 5.9 4.5 6.6 6.9 6.3 4.1 5.9 3.8 5.0 4.1 4.8 3.7
7.8 6.5 4.8 7.4 8.0 7.0 4.5 6.6 4.0 5.8 4.4 5.2 3.9
12.3 10.3 7.7 11.7 12.6 11.1 7.2 10.3 6.2 9.4 7.1 8.6 6.4
R. Waters et al. / Renewable Energy 34 (2009) 1600–1606
The return value Hs(R), where Hs is the significant wave height statistically reached on average once per return period R, is calculated according to:
FðHsðRÞÞ ¼ 1
s R
(2)
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In order to estimate the maximum height, Hmax(R), of a single wave in the wave record represented by the return value, it is assumed that the wave heights of any wave record will be Rayleigh distributed [21]. With this assumption the most probable value of Hmax(R) is calculated as:
rffiffiffiffiffiffiffiffiffiffiffiffi lnðNÞ 2
where s is the average time between the samples of the chosen data set, R is the return period, and F is the probability that is to be plugged into the CDF (Equation (1)). Equation (1) is then solved for Hs which is the wanted return value, Hs(R).
where N is the total number of zero-crossing waves in the wave record. The value of N has been found by calculating the number of
Fig. 3. Combined scatter and energy diagrams for sites 1 through 3. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
Fig. 4. Combined scatter and energy diagrams for sites 4 through 6. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
Hmax ðRÞ ¼ HsðRÞ
(3)
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R. Waters et al. / Renewable Energy 34 (2009) 1600–1606
peak periods, Tp, occurring during a half hour wave record. A method for estimating the peak period belonging to a return value, Hs(R), is given by Mathiesen et al. [20].
The location of the studied sites, together with information on water depth and wave climate parameters, is given in Table 1. Each
value of maximum energy flux and highest observed significant wave height is representative of a half-hour wave record. Eightyear mean energy flux is given together with standard deviation on an annual basis. Statistical hundred-year significant wave heights and hundred-year maximum single wave heights have been calculated as described in the previous section. Fig. 2 presents a map in two scales where the studied sites are marked together with wave roses. The wave roses are placed with their centers on the corresponding sites, and the roses
Fig. 5. Combined scatter and energy diagrams for sites 7 through 9. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
Fig. 6. Combined scatter and energy diagrams for sites 10 through 12. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
4. Results
R. Waters et al. / Renewable Energy 34 (2009) 1600–1606
Fig. 7. Combined scatter and energy diagram for site 13. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
themselves show the distributions in time of the direction on incoming waves. In Figs. 3–7 combined scatter and energy diagrams for the 13 sites can be found, all based on the 8 years of data. The numerical values represent the average annual occurrence of a combination of significant wave heights and energy periods, given in numbers of hours. The energy period has been divided into intervals of 1 s, while the significant wave height has been divided into intervals of one third of a meter. The colors in the figures show the average annual distribution of energy measured in kWh/(m*year), where numerical values are found in the color bar. For the annual energy a higher resolution was used with the energy period divided into 4 intervals per second, and the significant wave heights divided into 6 intervals per meter. Isolines have been calculated using the deep water energy flux approximation of Equation (4), and the same approximation has been used in calculating the energy weights of the scatter diagrams:
J ¼
r g2 T Hs2 64p E
(4)
1605
Fig. 8. Average monthly energy flux with standard deviation at site 5.
changes significantly when the waves move closer to land. The nearshore sites of Skagerrak, i.e. sites 3, 7 and 9, all exhibit an energy flux almost half of that found offshore. This is an expected result of the decreasing water depths towards these locations, which have the effect of damping the energy of the longer waves. Other contributing factors is that winds from the inland do not give rise to waves at nearshore locations, and refraction due to the bathymetry of the nearshore sites may have a small impact. In Kattegat the waves are smaller in average as well as in extremes. The average energy flux is approximately 2.4 kW/m with a higher flux towards the north. Regarding the statistical highest single wave appearing in a hundred years, the results of the present study indicate much smaller values then the 18.3 m, at site 4, previously noted by So¨derberg [14]. However, the data of that study only covered nine and a half months and, as noted in the introduction, the author himself thought that the reliability of the result was low. It is difficult to say more about the differing results here since the authors of the present paper do not know enough about the method used to calculate the extreme wave of that study. Fig. 8 shows the annual distribution of energy flux, at site 5, on a monthly basis with standard deviation. As expected, October
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 of gravity, TE is the energy period, and Hs is the significant wave height. For a thorough description of Equation (4) and the concepts of 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 of the studied sites. Following the scatter diagrams Site 5 has been chosen as a case study in order to give a more detailed illustration of the characteristics of the wave climate of the Swedish west coast. In Fig. 8 the average energy flux is presented on a monthly basis, with standard deviation showing variation over the eight studied years. In Fig. 9 the time-accumulated distribution of all 11,688 6-h values of energy flux is given. 5. Discussion As can be seen directly from the results, i.e. Table 1, the average energy flux of the studied offshore sites of Skagerrak is approximately 5.2 kW/m. Although this can be expected to vary somewhat had more points been included in the study it is close to the 6 kW/m previously noted by Mårtensson et al. [13]. The average energy flux
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 period of time.
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R. Waters et al. / Renewable Energy 34 (2009) 1600–1606
through March, the winter half of the year, shows a markedly higher average energy flux that is up to several times higher than during the calm summer months. The intermittent nature of ocean waves is a problematic area for ocean wave energy capture, especially the extreme power differences experienced in storms compared to average power levels which can have a harmful effect on the survivability of the WECs. During the studied 8 years there have been a few occurrences of extreme 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 times the overall average. However, only 7 days out of the studied 8 years exhibit levels of energy flux exceeding 100 kW/m. However, among these the most powerful flux reaches a half-hour average of 250 kW/m, a full 45 times higher than the overall average. In all, the energy flux reaches higher than 13.5 kW/m only during 10% of the time, and close to 50% of the total energy is found in sea states with a significant wave height between 1 and 3 m and an energy period between 4 and 7 s. When designing a wave energy converter for a certain site, as for the ones described here there are many parameters to consider. The design choices may vary a great deal depending on where one chooses to focus, and any decision will be a compromise. The extreme levels of energy flux discussed above are a reality in the oceans that all designers of wave energy converters must consider, and with great respect. Although most likely published only in regular media rather than in scientific journals, the harsh conditions of the oceans and the extreme power of ocean waves have wrecked many attempts to wave energy conversion. The WECs must be designed to survive in these conditions. However, since a wave energy converter cannot be designed to have an installed power corresponding to the 100-year wave some compromise is needed in order for the WEC to be of realistic proportions from an economical perspective. One alternative would be to design the WEC after the average energy flux, but the results presented in this paper clearly show that this is a bad choice. In the case of site 5 as much as 79% of the annual energy is found in wave climates with a higher energy flux than the average 5.5 kW/m. Perhaps the best alternative for a design basis are the combined scatter and energy diagrams, see Figs. 3–7, as these contain the most information. In the diagrams it is clearly visible where the energy is located and hence for which energy flux, wave height and period the WEC could be designed for. 6. Conclusion The wave climate off the west coast of Sweden has been presented based on 8 years of wave data from 13 studied sites in the Skagerrak and Kattegat. The mean energy flux was found to be approximately 5.2 kW/m in offshore Skagerrak, 2.8 kW/m in nearshore Skagerrak, and 2.4 kW/m in the Kattegat, though values up to 55 times the average flux have been recorded on the site located most offshore. Statistical hundred-year waves have been estimated to 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 in the Kattegat. Discussions on wave energy converters conclude that the design sea state should be chosen with awareness of what fraction 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, Draka Cable AB, the Go¨ran Gustavsson Research Foundation, Vargo¨ns Research Foundation, Falkenberg Energy AB and the Wallenius Foundation. Hanna Paradis of Seabased Industries AB, and Thomas Go¨tschl of Uppsala University are acknowledged for their help with maps over Skagerrak and Kattegat. Stephen Barstow of Fugro Oceanor is thanked for discussions on wave data and extreme wave analysis.
References [1] Duckers LJ. Wave energy: crests and troughs. Renewable Energy 1994;5:1444–52. [2] Boake CB, Whittaker TJT, Folley M. Overview and initial operational experience of the LIMPET wave energy plant. Proceedings of the 12th International Offshore and Polar Engineering Conference 2002:586–94. [3] Kofoed JP, Frigaard P, Friis-Madsen E, Sørensen HC. Prototype testing of the wave energy converter wave dragon. Renewable Energy 2006;31:181–9. [4] Waters R, Stålberg M, Danielsson O, Svensson O, Gustafsson S, Stro¨mstedt E, et al. Experimental results from sea trials of an offshore wave energy system. Applied Physics Letters 2007:90. 034105. [5] Claesson L. Energi från havets vågor. Efn-report No. 21, Energiforskningsna¨mnden, Stockholm, Sweden; 1987. [6] Pontes MT. Assessing the European wave energy resource. Journal of Offshore Mechanics and Arctic Engineering 1998;120:226–31. [7] Leijon M, Bernhoff H, Berg M, Ågren O. Economical considerations of renewable electric energy production - especially development of wave energy. Renewable Energy 2003;28:1201–9. [8] Danielsson O, Eriksson M, Leijon M. Study of a longitudinal flux permanent magnet linear generator for wave energy converters. International Journal of Energy Research 2006;30:1130–45. [9] Leijon M, Danielsson O, Eriksson M, Thorburn K, Bernhoff H, Isberg J, et al. An electrical approach to wave energy conversion. Renewable Energy 2006;31: 1309–19. [10] Bernhoff H, Sjo¨stedt E, Leijon M. Wave energy resources in sheltered sea areas: A case study of the Baltic Sea. Renewable Energy 2006;31:2164–70. [11] Henfridsson U, Neimane V, Strand K, Kapper R, Bernhoff H, Danielsson O, et al. Wave energy potential in the Baltic Sea and the Danish part of the North Sea, with reflections on the Skagerrak. Renewable Energy 2007;32:2069–84. [12] Broman B, Hammarklint T, Rannat K, Soomere T, Valdmann A. Trends and extremes of wave fields in the north-eastern part of the Baltic Proper. Oceanologia 2006;48:165–84. [13] Mårtensson M, Bergdahl L. On the wave climate of the southern Baltic. Report Series A:15, Department of Hydraulics. Sweden: Chalmers University of Technology; 1987. [14] So¨derberg P. The Swedish coastal wave climate. SSPA Research Report No. 104. Gothenburg, Sweden: SSPA; 1987. [15] Lindow H. Swedish Meteorological and Hydrological Institute, personal communication; 2007. [16] Jo¨nsson A, Broman B, Rahm L. Variations in the Baltic Sea wave fields. Ocean Engineering 2002;30:107–26. [17] The WAMDI Group. The WAM Modelda third generation wave prediction model. Journal of Physical Oceanography 1988;18:1775–810. [18] Barstow SF, Mørk G, Lønseth L, Mathisen JP, Schjølberg P. The role of satellite wave data in the WORLDWAVES project. Proceedingsof the 5th International Symposium on Ocean Wave Measurement and Analysis. Madrid, Spain; 2005. [19] Gustafsson S, Svensson O, Sundberg J, Bernhoff H, Leijon M, Danielsson O, et al. Experiments at Islandsberg on the west coast of Sweden in preparation of the construction of a pilot wave power plant. Proceedings of the 6th European Wave and Tidal Energy Conference. Glasgow, UK; 2005. [20] Mathiesen M, Goda Y, Hawkes PJ, Mansard E, Martı´n MJ, Peltier E, et al. Recommended practice for extreme wave analysis. Journal of Hydraulic Research 1994;32:803–14. [21] Muir L, El-Shaarawi AH. On the calculation of extreme wave heights: a review. Ocean Engineering 1986;13:93–118. [22] Cruz J. Ocean Wave Energy. Berlin Heidelberg: Springer; 2008.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Wave climate off the Swedish west coast Rafael Waters*, Jens Engstro¨m, Jan Isberg, Mats Leijon ¨m Laboratory, Division for Electricity, Swedish Centre for Renewable Electric Energy Conversion, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden The Ångstro
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 February 2008 Accepted 11 November 2008 Available online 16 December 2008
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 data is a product of the WAM and SWAN wave models calibrated at one site by a wave measurement buoy. It is found that the average energy flux is approximately 5.2 kW/m in the offshore Skagerrak, 2.8 kW/m in the nearshore Skagerrak, and 2.4 kW/m in the Kattegat. One of the studied sites, i.e. site 9, is the location of a wave energy research site run by the Centre for Renewable Electric Energy Conversion at Uppsala University. This site has had a wave power plant installed since the spring of 2006, and another seven are planned to be installed during 2008. Wave energy as a renewable energy source was the driving interest that led to this study and the results are briefly discussed from this perspective. Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Wave climate Wave power Sea state Extreme waves Skagerrak Kattegat
1. Introduction Ocean wave energy has the potential to contribute large amounts of renewable energy to the world’s societies [1]. Today several technologies have been tested at large scale and in real sea conditions, 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 more detailed knowledge one has of the wave climate of a particular site, the easier it is for developers of wave energy systems to optimize the technology and make it competitive. The present study describes the specific wave climates at 13 locations off the west coast of Sweden, in the continuation of the North Sea called Skagerrak and Kattegat. It summarizes 8 years of wave data covering the years from 1997 to 2004. The investigated sites are spread out over varying depth and distance from land, from north to south in order to provide a comprehensive picture of the overall wave climate of the Swedish west coast. The wave climate of the sites are presented in terms of significant wave height, energy period, dominating wave directions, energy flux, annual energy distribution, the occurrence of extreme wave conditions, and statistical hundred-year waves. The model wave data has been calibrated with on-site measurements carried out by Uppsala 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
* Corresponding author. Tel.: þ46 18 471 5839; fax: þ46 18 471 5810. E-mail address: [email protected] (R. Waters). 0960-1481/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2008.11.016
perspective raises questions and visualizes aspects that are critical to wave power technology. It is well known that the wave climate off the west coast of Sweden is relatively calm in comparison to the coasts facing the oceans 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 of magnitude higher [5]. Moreover, the average total deepwater wave power resource along the Atlantic coasts of Europe amounts to about 290 GW [6]. Yet in spite of this it has been presumed that the available wave power resource of the Skagerrak can still be a viable source of renewable energy from a technical and economical perspective, mainly attributed to the high density of energy in ocean waves [7]. When the results of this paper are discussed from the perspective of a wave energy converter (WEC) the technology in mind is that described by Danielsson et al. [8] and Leijon et al. [9]. In brief 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 wave energy converters known to the authors. Although some recent studies have been carried out on the wave fields and wave energy resource of the Baltic sea, see e.g. [10–12], the documentation that can be found on the wave climate of Skagerrak and Kattegat is fragmented in time and sparse in spatial resolution. Documentation on the wave climate off the Swedish west coast saw most activity in the 1980s during the Swedish Wave Measuring Programme. The measurements were carried out by the Swedish Meteorological and Hydrological Institute (SMHI) using Wave rider buoys and Echo sounders [13,14]. Registrations of the wave climate along the west coast are limited to four locations and
R. Waters et al. / Renewable Energy 34 (2009) 1600–1606
concentrated on two areas: Trubaduren, Fladen, and La¨so¨ near Gothenburg; and Va¨dero¨arna further north. The measurements on these sites have not been carried out simultaneously, but rather each station has been running for a few years with some overlap. The longest time series are found at Trubaduren covering the years from 1978 to 2004 [15], though the available documentation only covers the period from 1 October 1978 to 28 February 1986 [14]. The information from Trubaduren is given only in the form of scatter diagrams. The measurement station Va¨dero¨arna is of special interest here since it can be compared to one of the measurement sites in this paper, i.e. site 4, see Fig. 2. During the time period from 1 April 1980 to 13 January 1981 the documented average significant wave height, Hs (sometimes given as Hm0 to show its origin in spectral analysis) at Va¨dero¨arna was 2.46 m, and the mean wave period was 5.42 s. The highest expected wave for a 100 year period at the same location was calculated to 18.3 m, however, as the author points out; the calculation is based on less than one year of measurements, which gives a rather low reliability [14]. As a rough estimate, the mean energy flux in the Skagerrak region of the Swedish west coast has been calculated to be about 6 kW/m [13]. In Jo¨nsson et al. [16] a hindcast model has been used to calculate the wave fields in the Baltic Sea and around Sweden. This hindcast study used data for one year (1999) and the results are compared to wave measurements made by the Swedish Meteorological and Hydrological Institute. A comprehensive report on the Swedish wave energy research up until 1987 can be found in Claesson [5].
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a more thorough description of the wave data generation see Barstow et al. [18]. During the spring of 2005 the Swedish Centre for Renewable Electric Energy Conversion of Uppsala University deployed a wave measurement buoy at site 9 [19]. Collected wave data from continuous measurements of that buoy were used to calibrate the data generated by the SWAN model in order to increase the accuracy of the modeled nearshore data. A qualitative view of the result of the calibration, in terms of significant wave height, energy period, and energy flux, is seen in Fig. 1. The result shows that the only significant difference between measured and simulated values is for the energy period at very small wave heights. This is due to the poor frequency response of the wave measurement buoy at low frequencies, as well as to difficulties in the simulations of very weak sea states. In other words, the uncertainties are greater in both measurements and simulations during weak sea states.
3. Extreme wave calculations Extreme wave calculations have been performed according to the recommendations of the International Association for Hydraulic Research [20]. Data sets have been chosen from all sites through the peaks over threshold method (POT), and the threshold level resulting in the best goodness of fit has been chosen throughout. The data has been fitted, by means of maximum likelihood, to the truncated three-parameter Weibull distribution:
2. Wave data
# Hs A C Hs0 A C FðHsÞ ¼ 1 exp þ B B
The wave data that this study has been based on was purchased from Fugro OCEANOR of Norway. The data consists of time series of relevant wave parameters representing every 6-h time period during the years 1997–2004. The data have been collected through the combined information from on-site wave-buoys, satellites, and a wave and wind model, WAM [17], run by the European Centre for Medium-range Weather Forecast. The information from the wavebuoys is used to calibrate the satellite altimeter data, and the satellite data is, in turn, used to calibrate the WAM model. Five of the studied points are located near shore at depths of approximately 15–30 m. At these locations, where the geography of sea floor and coastline will have a larger impact on the waves, the SWAN (Simulating Waves Nearshore) model has been used on the calibrated WAM data and a detailed description of bathymetry and coastline has been used. For
where F is the cumulative distribution function (CDF), Hs is significant wave height, Hs0 is the threshold significant wave height, A is the location parameter, B is the scale parameter, and C is the shape parameter. The truncated three-parameter Weibull distribution was chosen over the non-truncated case because, as shown by quantile–quantile plots, it proved more stable towards the highest waves where the regular three-parameter Weibull distribution in general overestimated the wave heights. The General extreme value distribution was also evaluated but suffered the same drawback as the regular three-parameter Weibull distribution. The Kolmogorov–Smirnov test was used to evaluate the goodness of fit between the data and the distribution. The resulting significance level is above 95% for all sites with the exception of site 3 for which the significance level is 87%.
"
(1)
Fig. 1. Comparison between the wave parameters simulated by the SWAN model and those measured by a wave measurement buoy located at site 9. Hs is significant wave height, TE is energy period, and J is energy flux.
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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 on incoming waves.
Table 1 Overview of the studied sites: Coordinates; water depth; mean energy flux with standard deviation, Jmean; maximum wave height from the 8 years of data, Hsmax; statistically derived 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 (m)
Jmean std.dev. (kW/m)
Jmax (kW/m)
Hsmax (m)
Hs(100) (m)
Hmax(100) (m)
1 2 3 4 5 6 7 8 9 10 11 12 13
58.83 N, 10.83 E 58.67 N, 10.92 E 58.70 N, 11.13 E 58.51 N, 10.93 E 58.33 N, 10.67 E 58.38 N, 11.00 E 58.40 N, 11.19 E 58.20 N, 11.08 E 58.20 N, 11.37 E 57.67 N, 11.33 E 57.71 N, 11.58 E 57.25 N, 11.75 E 56.87 N, 12.25 E
82 46 30 70 200 80 30 107 25 55 16 40 25
5.3 0.8 4.8 0.7 3.2 0.4 5.1 0.8 5.5 0.8 5.0 0.7 2.7 0.3 5.6 0.7 2.6 0.3 2.7 0.2 2.7 0.3 2.1 0.2 2.1 0.3
239.6 166.9 93.3 223.4 248.5 203.9 72.2 204.3 71.5 90.0 72.7 79.9 43.1
6.8 5.9 4.5 6.6 6.9 6.3 4.1 5.9 3.8 5.0 4.1 4.8 3.7
7.8 6.5 4.8 7.4 8.0 7.0 4.5 6.6 4.0 5.8 4.4 5.2 3.9
12.3 10.3 7.7 11.7 12.6 11.1 7.2 10.3 6.2 9.4 7.1 8.6 6.4
R. Waters et al. / Renewable Energy 34 (2009) 1600–1606
The return value Hs(R), where Hs is the significant wave height statistically reached on average once per return period R, is calculated according to:
FðHsðRÞÞ ¼ 1
s R
(2)
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In order to estimate the maximum height, Hmax(R), of a single wave in the wave record represented by the return value, it is assumed that the wave heights of any wave record will be Rayleigh distributed [21]. With this assumption the most probable value of Hmax(R) is calculated as:
rffiffiffiffiffiffiffiffiffiffiffiffi lnðNÞ 2
where s is the average time between the samples of the chosen data set, R is the return period, and F is the probability that is to be plugged into the CDF (Equation (1)). Equation (1) is then solved for Hs which is the wanted return value, Hs(R).
where N is the total number of zero-crossing waves in the wave record. The value of N has been found by calculating the number of
Fig. 3. Combined scatter and energy diagrams for sites 1 through 3. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
Fig. 4. Combined scatter and energy diagrams for sites 4 through 6. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
Hmax ðRÞ ¼ HsðRÞ
(3)
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peak periods, Tp, occurring during a half hour wave record. A method for estimating the peak period belonging to a return value, Hs(R), is given by Mathiesen et al. [20].
The location of the studied sites, together with information on water depth and wave climate parameters, is given in Table 1. Each
value of maximum energy flux and highest observed significant wave height is representative of a half-hour wave record. Eightyear mean energy flux is given together with standard deviation on an annual basis. Statistical hundred-year significant wave heights and hundred-year maximum single wave heights have been calculated as described in the previous section. Fig. 2 presents a map in two scales where the studied sites are marked together with wave roses. The wave roses are placed with their centers on the corresponding sites, and the roses
Fig. 5. Combined scatter and energy diagrams for sites 7 through 9. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
Fig. 6. Combined scatter and energy diagrams for sites 10 through 12. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
4. Results
R. Waters et al. / Renewable Energy 34 (2009) 1600–1606
Fig. 7. Combined scatter and energy diagram for site 13. Colors show annual energy transport per meter of wave front (kWh/(m*year)). Numbers give average occurrence in hours per year. Isolines present the energy flux in accordance with Equation (1). Results are based on an 8-year average.
themselves show the distributions in time of the direction on incoming waves. In Figs. 3–7 combined scatter and energy diagrams for the 13 sites can be found, all based on the 8 years of data. The numerical values represent the average annual occurrence of a combination of significant wave heights and energy periods, given in numbers of hours. The energy period has been divided into intervals of 1 s, while the significant wave height has been divided into intervals of one third of a meter. The colors in the figures show the average annual distribution of energy measured in kWh/(m*year), where numerical values are found in the color bar. For the annual energy a higher resolution was used with the energy period divided into 4 intervals per second, and the significant wave heights divided into 6 intervals per meter. Isolines have been calculated using the deep water energy flux approximation of Equation (4), and the same approximation has been used in calculating the energy weights of the scatter diagrams:
J ¼
r g2 T Hs2 64p E
(4)
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Fig. 8. Average monthly energy flux with standard deviation at site 5.
changes significantly when the waves move closer to land. The nearshore sites of Skagerrak, i.e. sites 3, 7 and 9, all exhibit an energy flux almost half of that found offshore. This is an expected result of the decreasing water depths towards these locations, which have the effect of damping the energy of the longer waves. Other contributing factors is that winds from the inland do not give rise to waves at nearshore locations, and refraction due to the bathymetry of the nearshore sites may have a small impact. In Kattegat the waves are smaller in average as well as in extremes. The average energy flux is approximately 2.4 kW/m with a higher flux towards the north. Regarding the statistical highest single wave appearing in a hundred years, the results of the present study indicate much smaller values then the 18.3 m, at site 4, previously noted by So¨derberg [14]. However, the data of that study only covered nine and a half months and, as noted in the introduction, the author himself thought that the reliability of the result was low. It is difficult to say more about the differing results here since the authors of the present paper do not know enough about the method used to calculate the extreme wave of that study. Fig. 8 shows the annual distribution of energy flux, at site 5, on a monthly basis with standard deviation. As expected, October
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 of gravity, TE is the energy period, and Hs is the significant wave height. For a thorough description of Equation (4) and the concepts of 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 of the studied sites. Following the scatter diagrams Site 5 has been chosen as a case study in order to give a more detailed illustration of the characteristics of the wave climate of the Swedish west coast. In Fig. 8 the average energy flux is presented on a monthly basis, with standard deviation showing variation over the eight studied years. In Fig. 9 the time-accumulated distribution of all 11,688 6-h values of energy flux is given. 5. Discussion As can be seen directly from the results, i.e. Table 1, the average energy flux of the studied offshore sites of Skagerrak is approximately 5.2 kW/m. Although this can be expected to vary somewhat had more points been included in the study it is close to the 6 kW/m previously noted by Mårtensson et al. [13]. The average energy flux
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 period of time.
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through March, the winter half of the year, shows a markedly higher average energy flux that is up to several times higher than during the calm summer months. The intermittent nature of ocean waves is a problematic area for ocean wave energy capture, especially the extreme power differences experienced in storms compared to average power levels which can have a harmful effect on the survivability of the WECs. During the studied 8 years there have been a few occurrences of extreme 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 times the overall average. However, only 7 days out of the studied 8 years exhibit levels of energy flux exceeding 100 kW/m. However, among these the most powerful flux reaches a half-hour average of 250 kW/m, a full 45 times higher than the overall average. In all, the energy flux reaches higher than 13.5 kW/m only during 10% of the time, and close to 50% of the total energy is found in sea states with a significant wave height between 1 and 3 m and an energy period between 4 and 7 s. When designing a wave energy converter for a certain site, as for the ones described here there are many parameters to consider. The design choices may vary a great deal depending on where one chooses to focus, and any decision will be a compromise. The extreme levels of energy flux discussed above are a reality in the oceans that all designers of wave energy converters must consider, and with great respect. Although most likely published only in regular media rather than in scientific journals, the harsh conditions of the oceans and the extreme power of ocean waves have wrecked many attempts to wave energy conversion. The WECs must be designed to survive in these conditions. However, since a wave energy converter cannot be designed to have an installed power corresponding to the 100-year wave some compromise is needed in order for the WEC to be of realistic proportions from an economical perspective. One alternative would be to design the WEC after the average energy flux, but the results presented in this paper clearly show that this is a bad choice. In the case of site 5 as much as 79% of the annual energy is found in wave climates with a higher energy flux than the average 5.5 kW/m. Perhaps the best alternative for a design basis are the combined scatter and energy diagrams, see Figs. 3–7, as these contain the most information. In the diagrams it is clearly visible where the energy is located and hence for which energy flux, wave height and period the WEC could be designed for. 6. Conclusion The wave climate off the west coast of Sweden has been presented based on 8 years of wave data from 13 studied sites in the Skagerrak and Kattegat. The mean energy flux was found to be approximately 5.2 kW/m in offshore Skagerrak, 2.8 kW/m in nearshore Skagerrak, and 2.4 kW/m in the Kattegat, though values up to 55 times the average flux have been recorded on the site located most offshore. Statistical hundred-year waves have been estimated to 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 in the Kattegat. Discussions on wave energy converters conclude that the design sea state should be chosen with awareness of what fraction 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, Draka Cable AB, the Go¨ran Gustavsson Research Foundation, Vargo¨ns Research Foundation, Falkenberg Energy AB and the Wallenius Foundation. Hanna Paradis of Seabased Industries AB, and Thomas Go¨tschl of Uppsala University are acknowledged for their help with maps over Skagerrak and Kattegat. Stephen Barstow of Fugro Oceanor is thanked for discussions on wave data and extreme wave analysis.
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