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Modelling analysis of the sensitivity of shoreline change to a wave farm
ARTICLE IN PRESS
Ocean Engineering 34 (2007) 884–901 www.elsevier.com/locate/oceaneng
Modelling analysis of the sensitivity of shoreline change to a wave farm D.L. Millara,, H.C.M. Smitha, D.E. Reeveb a
Camborne School of Mines, University of Exeter in Cornwall, Tremough Campus, Penryn, Cornwall TR10 9EZ, UK b C-CODE, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK Received 14 August 2005; accepted 28 December 2005 Available online 24 July 2006
Abstract Change of shoreline wave climate caused by the installation of a wave farm is assessed using the SWAN wave model. The 30 MW-rated wave farm is called the ‘Wave Hub’ and will be located 20 km off the north coast of Cornwall, UK. Changes in significant wave height and mean wave period due to the presence of the Wave Hub are presented. The results suggest that the shoreline wave climate will be affected, although the magnitude of effects decreases linearly as wave energy transmitted increases. At probable wave energy transmission levels, the predicted change in shoreline wave climate is small. r 2006 Elsevier Ltd. All rights reserved. Keywords: Wave climate; Wave power; Shoreline environmental impact; Wave model; SWAN; Coastal engineering
1. Introduction 1.1. Wave Hub ‘Wave Hub’ is a sub-sea electrical grid connection point, proposed for installation on the seabed off the north coast of Cornwall on the UK’s southwest peninsula. If the project obtains all consents, it will be connected to the mainland electricity grid distribution and will provide a location for pre-commercial development of arrays of wave energy converters (WECs). The proposed location for Wave Hub is 20 km northwest of St Ives Bay (Fig. 1) where the water depth is 50–60 m (South West of England Regional Development Agency, 2005). Arrays of WECs will occupy the site over an area of 3000 m 1000 m. Although it is not yet known which devices will be initially deployed at the site, all potential WECs have the objective of converting the energy of the waves into electrical power. Removing energy from the waves at an offshore site will reduce the height and power of the waves as they propagate further towards the shoreline. The objective of the study presented herein is to estimate by how much the shoreline wave climate will be changed. Corresponding author. Fax: +44 1326 371859.
E-mail address: [email protected] (D.L. Millar). 0029-8018/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2005.12.014
The results of the study will be carried forward into assessments of impacts arising as a result of the development. A major concern is to allay any concerns of the surfing community. The study uses the latest version of the SWAN (Simulating WAves Near-shore) wave model, version 40.41 (Booij et al., 2004). 1.2. SWAN wave model SWAN is a third generation numerical wave model developed by Delft University of Technology to specifically model near-shore wave climate transformations (Booij et al., 1999). It simulates wave propagation, accounting for refraction due to variations in seabed and currents, shoaling, blocking and reflection due to opposing currents, and blockage, reflection or transmission due to obstacles. Wave energy can be dissipated in the model by activating processes such as whitecapping (Komen et al., 1984), bottom friction (Hasselmann et al., JONSWAP, 1973), depth-induced wave breaking (Battjes and Janssen, 1978) and wave–wave interaction (Eldeberky, 1996; Hasselmann et al., 1985). SWAN is based on the spectral action balance equation, q q q q q S Nþ cx N þ cy N þ cs N þ cy N ¼ . qt qx dy qs qy s
(1)
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Fig. 1. The area of study off the north coast of Cornwall, and the proposed Wave Hub location.
The action density N(s, y) equals the energy density E(s, y) divided by s, the frequency relative to any currents present. The rate of change of N in time is given by the first term of (1), with the second and third terms representing the spatial propagation of N in x- and y-space with velocity components cx and cy. The fourth term represents changes in the relative frequency due to variations in depth and currents, and the final term on the left-hand side is the directional propagation of N due to refraction. The term S(s, y) on the right-hand side is the source term of the equation, representing the generation and dissipation of energy density by the processes listed above. SWAN requires the input of a bathymetric grid and, optionally, input grids of current, wind, bottom friction and water level. Stationary or time-varying wave parameters must be established as input parameters at the model boundary. A range of wave parameters can be produced as outputs of the model and presented in a number of formats.
121300 W) and K2 (511000 N, 131240 W), and the Sevenstones lightship, shown in Fig. 2, are part of a worldwide network of data buoys recording hourly wave and meteorological conditions. SWAN requires a bathymetric input grid with sufficient spatial resolution to ensure that all relevant features of the seabed are properly resolved. For the near-shore region from the coastline to 5000 mE, a 50 m resolution grid was produced by interpolating data from three main sources:
BGS Sea Bed Sediment maps (Harrison, 1987) Shoreline Management Plan (Cornwall & Isles of Scilly Coastal Group, 1999) Admiralty Charts (Clarke, 2004)
West of 5000 mE, the bathymetric model was extended using the ETOP05 dataset, a digital elevation model with 5 min resolution (NSIDC, 2005). The datasets were combined to produce an input grid of bathymetric values covering the area shown in Fig. 2.
2. Modelling methodology 2.2. Modelling approach 2.1. Data sources Two sources of wave data were available for use in this study; output from the Wavewatch III global ‘nww3’ computer model (NOAA Wavewatch III, 2005), and realtime data from the NE Atlantic data buoys (NOAA, 2005). Wavewatch III is a third generation global spectral wave model, which provides estimates of wave parameters at 3hourly intervals. Data from the model was collected for 12 grid-points surrounding the southwest peninsula of England (Fig. 2). The NE Atlantic data buoys K1 (481420 N,
2.2.1. Boundary conditions The data buoys K1 and K2 are both located over 450 km west of the Cornish coastline; too far offshore to be used as input for the model. The non-uniform bathymetry of the region, characteristic of coastal areas, and the potential for wave directions spanning 0–3601 meant it was essential to have boundary conditions covering three sides of the input grid to fully enclose the Cornish peninsula. Boundary conditions were defined using data output from the following Wavewatch III grid points: WW2, WW3,
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150000
WW1
WW2
WW3
WW4
100000
50000 mN
WW5
Seven Stones
WW6
WW7
WW8
0
-50000 WW9 WW10
WW11
-100000 -100000
-50000
0
50000
100000
150000
WW12 200000
mE Fig. 2. Area covered by bathymetric grid, showing locations of Wavewatch III grid points and the Sevenstones lightship.
Table 1 Wave parameters for a reference sea state and corresponding values at Wavewatch III grid points Location
Reference wave State WW2 WW3 WW4 WW6 WW10 WW11 WW12
Significant wave height, Hs (m)
Mean wave period, Tm (s)
80
3.3
11.0
1.0
101 90 44 119 140 120 94
3.6 3.2 2.7 3.5 3.3 3.1 2.7
10.2 9.7 9.3 11.5 12.0 11.8 11.3
8.1 6.4 3.7 1.1 1.2 358.5 358.0
Water depth at gridpoint (m)
WW4, WW6, WW10, WW11 and WW12 (Fig. 2). Within SWAN, the boundary conditions can be set to vary continuously between each of a string of locations where the wave climate is defined precisely; in this case between locations WW2 and WW12 listed above. This interpolation between the points provided boundary conditions around three sides of the grid, with the fourth side containing the land mass. Wave data from the Sevenstones lightship, recorded simultaneously with the Wavewatch III predictions, has been used throughout this study to provide a near-shore ‘reference sea state’ for each set of boundary conditions. Table 1 gives an example of a set of reference sea state parameters and the corresponding parameters at each of the Wavewatch III grid points listed above. 2.2.2. Grid details A coarse computational grid with 5000 m resolution was created over the area defined by the seven Wavewatch
Wave direction (anti-clockwise from East), D (1)
points. A fine grid with 200 m resolution was defined as a nested grid within the coarse grid (Fig. 3). When defining grid resolutions, particularly for the fine grid model, a compromise had to be made between a high-resolution grid which would define as much seabed detail as possible, and the limitations imposed on the model by the available computational capacity. The 200 m grid chosen for this model means that seabed features below this size will not be resolved. The output of the coarse grid run defined boundary conditions for the fine grid model. For both the coarse and fine grid models, wind, current and localised bottom friction input grids were not generated. Wind and current were therefore assumed to be zero, and bottom friction constant over the grid. Both grid models were defined with 36 directional bins of 101, covering all possible wave directions. Fourteen frequency bins were defined, covering the full range of wave frequencies found in the Wavewatch III data. When
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150000
Coarse Grid 100000 Detail Grid
mN
50000
0
-50000
-100000 -100000
0
-50000
50000
100000
150000
200000
mE Fig. 3. Boundaries of the coarse and fine SWAN computational grids.
Directional distribution of wave energy
1.2
m=1, DSPR=37.5 m=2, DSPR=31.5
1.0
m=3, DSPR=27.6 m=5, DSPR=22.9
0.8
m=10, DSPR=17.1 m=50, DSPR=8.0
0.6
m=100, DSPR=5.7 m=800, DSPR=2.0
0.4 0.2 0.0 0
10
20
30
40
50
60
70
80
90
100
D-Dpeak / deg Fig. 4. Variation of directional distribution of incident wave energy with m and DSPR.
input into SWAN, the boundary conditions were defined as JONSWAP spectra (Hasselmann et al., JONSWAP, 1973), SWAN’s default spectral setting. When using nested grids in SWAN, the code interpolates spectral directions and frequencies in the respective direction and frequency grids. The directional distribution of incident wave energy is DðyÞ ¼ A cosm ðy ypeak Þ,
(2)
where ypeak is the peak spectral direction and m the power to which the cosine function is raised. Within SWAN, options exist to define the directional spread either by defining m or by defining the directional standard deviation, DSPR, of the cosm y function. In this study,
the default DSPR value of 301 was used. Fig. 4 shows how the directional energy distribution varies with m and DSPR. 2.2.3. Preliminary assessment of the coarse grid SWAN implementation against the WaveWatch III implementation As a preliminary test of the reliability of the coarse grid SWAN formulation (5000 m bathymetric grid resolution in easting and northing), SWAN output for the Sevenstones Lightship location was produced and compared with output for the same location interpolated directly from NOAA’s nww3 Wavewatch III model. This global implementation relies on a bathymetric grid with resolution 1.251 and 1.001 in longitude and latitude, respectively.
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of the nww3 implementation considered at the scale of the Cornwall peninsula. The conclusion of this assessment process was that the SWAN model produces realisations of sea states that are consistent with those of NOAA’s nww3 implementation, especially when the disparities in respective bathymetric and computational grid resolutions are considered.
The comparison process was repeated over all reference sea states (as defined in Section 2.2.1), to form a dataset of disparities that can be examined statistically. The distribution of the disparities for significant wave height is presented in Fig. 5, where the disparity is expressed as the absolute difference between the results for the respective models over the result from the nww3 implementation. Fig. 5 demonstrates that over all reference sea states, approximately 80% of disparities have a magnitude of less than 20%. When a subset of reference sea states is formed by considering only those where waves propagate from western quadrants, approximately 90% of disparities have a magnitude of less than 20%. This subset is examined independently to remove instances where waves propagate from the direction of the land mass, which is not likely to be well represented by the very coarse resolution
2.2.4. Wave states Twelve-hourly Wavewatch III estimates of significant wave height, mean wave period and wave direction were obtained for the period 2nd December 2002–9th November 2003. Gaps in the data led to the elimination of a number of days’ data, giving a final set of 529 distinct wave states, of which Table 1 represents one such wave state. The reference sea states for the set, shown in the scatter diagram
Percentage of data points
60 50 40 30 All Data Waves from West
20 10 0 0
10
20 30 40 50 60 70 80 90 Percentage difference in Hs between model output and recorded data
100
Fig. 5. Distribution of disparities in significant wave height produced from SWAN and NOAA’s nww3 global implementation at Sevenstones lightship.
Significant Wave Height / m 0.0- 0.5
0.5-1.0
1.0-1.5
1.5-2.0
2.0- 2.5
2.5-3.0
3.0-3.5
3.5-4 .0
4.0- 4.5
4.5-5.0
5.0 -5.5
5.5-6 .0
6.0-6.5
6.5-7.0
7.0- 7.5
7.5-8.0
8.0- 8.5
8.5-9.0
> 9.0
3.5-4.0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4.0-4.5
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
4.5-5.0
0
15
16
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5.0-5.5
1
16
37
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5.5-6.0
1
17
41
29
14
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6.0-6.5
4
34
54
30
35
9
0
0
0
0
0
0
0
0
0
0
0
0
0
6.5-7.0
1
33
41
52
58
25
2
0
0
0
0
0
0
0
0
0
0
0
0
7.0-7.5
6
25
20
34
51
52
9
2
0
0
0
0
0
0
0
0
0
0
0
7.5-8.0
11
16
27
46
34
22
25
4
2
0
0
0
0
0
0
0
0
0
0
0.1
8.0-8.5
10
11
55
55
46
14
12
12
4
4
0
0
0
0
0
0
0
0
0
Mean
8.5-9.0
0
7
27
37
44
14
10
17
6
1
0
0
0
0
0
0
0
0
0
0.09 0.08 0.07
Wave
9.0-9.5
0
7
5
25
24
19
22
10
14
5
3
0
0
0
0
0
0
0
0
Period
9.5-10.0
0
1
2
18
11
12
18
9
9
10
3
5
0
0
0
0
0
0
0
/s
10.0-10.5
0
4
2
10
19
17
9
16
17
13
5
4
1
2
0
0
0
0
0
10.5-11.0
0
3
1
11
9
26
9
13
7
7
3
5
3
0
0
0
0
0
0
11.0-11.5
0
1
0
6
9
3
11
12
5
7
3
1
1
0
0
0
0
0
0
11.5-12.0
0
0
0
5
12
2
4
14
4
3
0
2
0
1
0
0
0
0
0
12.0-12.5
0
1
0
0
0
0
2
2
5
0
18
1
1
0
1
0
0
0
0
12.5-13.0
0
2
0
0
0
0
1
2
1
6
4
1
3
1
2
0
0
0
0
13.0-13.5
0
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
13.5-14.0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
14.0-14.5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
14.5-15.0
0
0
0
0
0
0
1
0
4
1
1
0
0
0
0
0
2
0
0
15.0-15.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
15.5-16.0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
>16.0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.01
0.06 0.05 0.04
0.03
0.02
Fig. 6. Scatter diagram showing the set of 529 distinct wave states for the reference sea state over all directions, overlaid with wave steepness contours.
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in Fig. 6 and overlaid with wave steepness contours, cover a range of wave heights (0.3–8.4 m), periods (4.5–15.1 s) and directions (0–359.91). 2.2.5. Model physics The wave dissipating forces of whitecapping, bottom friction and triad wave–wave interaction were set to their SWAN default values because no additional data was available to suggest otherwise. However the nonlinear quadruplet interactions were deactivated because it is not recommended to use quadruplets in combination with zero wind conditions. In addition, the default settings for diffraction were used. Arrays of WECs deployed at the Wave Hub site were represented as a 4 km partially transmitting obstacle, aligned approximately parallel to the incoming wave crests at the wave hub site. As it is not known exactly how much wave energy will be absorbed by the WECs, model runs were completed for each set of boundary conditions with energy transmission by the obstacle set at 0%, 40%, 70% and 90%. These energy transmission percentages were set for specific reasons:
0%—Represents complete absorption of all incoming wave energy at the obstacle—an unachievable scenario. It is expected that this would produce the largest possible shoreline effect. 70%—Represents an array of densely spaced, highefficiency WECs. This would be an optimistic target for a wave farm developer to achieve. 90%—Represents lower efficiency, widely spaced WECs, a more realistic scenario at the Wave Hub site. 40%—Included in the study to enable the establishment of trends, although it is extremely improbable that this could be attained in reality.
When waves approach such an obstacle in SWAN, the only change to the wave spectrum is a reduction of localised wave height along the length of the obstacle, and
889
it is assumed that the frequencies are unchanged (Booij et al., 2004). This is illustrated through plots of the JONSWAP wave spectra for the sea state produced by the boundary conditions listed in Table 1 immediately before and after an obstacle for an incoming wave (Fig. 7). The energy density for each frequency has reduced by 75%. In order to model a partially transmitting obstacle SWAN requires definition of a transmission coefficient defined as the ratio of the transmitted significant wave height over the incident significant wave height. In order to more readily introduce the idea of energy transmitted or absorbed by an array of wave energy converters, in the following, when ‘wave energy transmission’, ‘energy transmission’ or simply ‘transmission’ is referred to, this means the wave energy passing through the obstacle as a proportion of that incident upon it. The parameter required by SWAN, the ratio of wave heights, is the square root of the energy transmission as described in this section. 2.2.6. Model output The model was set to output two sets of results:
Significant wave height, mean period, wave direction and energy transport at 500 m intervals across the whole domain of the fine grid. Significant wave height, mean period and wave direction at points of approximately 500 m spacing and 10 m water depth along the coastline (Fig. 8).
A computer programme was written to drive the creation of three SWAN files for each set of boundary conditions and transmission percentage; a coarse grid model to provide boundary conditions for the fine model, a fine grid model with no Wave Hub obstacle, and a fine grid model with a partially transmitting obstacle at the Wave Hub site. The program was designed to run each model and process the results.
Spectral Energy Density / m2/s
16 Before Obstacle
14 12 10 8 6
After Obstacle
4 2 0 0
0.05
0.1
0.15 0.2 Frequency / Hz
0.25
0.3
0.35
Fig. 7. Comparison of wave energy density spectrum before and after passing through partially transmitting obstacle with a transmission coefficient of 0.5.
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90000 Harlyn Bay 80000
Newquay
mN
70000 St Agnes Head 60000
Godrevy Pt 50000 Pendeen 40000
30000 120000
130000
140000
150000
160000
170000
180000
190000
mE Fig. 8. Locations of shoreline model output points.
3. Results 3.1. Results over computational grid Results were initially examined by calculating the change due to the Wave Hub in each wave climate parameter at each point on the grid. The changes in significant wave height DHs, mean period DTm, and wave energy transport DEt were calculated using DH s ¼ H s H 0s , DT m ¼ T m T 0m , DE t ¼ E t E 0t ,
ð3Þ
where Hs, Tm and Et represent output values at specific locations on the grid from the model run with no Wave Hub, and H0 s, T0 m and E0 t the corresponding values from the run with the Wave Hub. These calculations were performed for each set of boundary conditions and over every grid point, for each energy transmission. Data from the Sevenstones lightship, obtained for the same times and dates as the Wavewatch III data, were used to indicate reference sea states corresponding to a completely defined set of boundary conditions, as described in Section 2.2.1. An example of results obtained for a reference state of H s ¼ 3:3 m, T m ¼ 11 s and D ¼ 11, corresponding to the boundary conditions listed in Table 1, is shown in Fig. 9: a contour plot of DHs for 0% wave energy transmission.
The results indicate that both wave height and energy transport are similarly affected by the Wave Hub. The largest differences can be seen in the region immediately behind the Wave Hub site, with refraction due to bathymetric change and diffraction due to the obstacle diminishing the effect as the waves propagate shoreward. For most reference sea states, an appreciable stretch of coastline is affected. As expected, increasing the amount of wave energy transmitted through the Wave Hub site diminishes these effects. The mean period decreases slightly (a result of its nature as an integrated parameter) in the area directly behind the Wave Hub, but increases at the edges of this area, with the effect spreading along almost the whole coastline studied.
3.2. Analysis of results at the shoreline 3.2.1. Overview of results To gain detailed understanding of the shoreline wave climate, results were sampled at locations of approximately 10 m water depth and 500 m spacing (Fig. 8). Differences in significant wave height and mean period due to the Wave Hub were calculated at each shoreline location as described in the previous section. All wave directions are referenced in Cartesian co-ordinates, with the direction in degrees defining the direction of wave propagation measured anticlockwise from the positive x-axis of the system (East). As before, data from the Sevenstones lightship is used to
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90000
80000
70000 mN
0.1m
60000 0.6m 0.4m 0.3m 50000
0.2m
0.1m 40000
30000 120000
130000
140000
150000
160000
170000
180000
190000
mE Fig. 9. Changes in significant wave height, DHs, due to the Wave Hub for 0% energy transmission. (Reference state: H s ¼ 3:3 m, T m ¼ 11 s and D ¼ 11).
provide a reference sea state that maps to a set of boundary conditions at WW2–WW12. Figs. 10(a–c) give examples of the results obtained for the changes in significant wave height along the shoreline for different reference sea states, and demonstrate how these vary with incoming wave direction. The x-axis of each chart gives the x co-ordinate of each measurement location in OSGB36 National Grid Eastings, and the y-axis measures the change in significant wave height introduced by the Wave Hub. For demonstration purposes, these results are for 0% transmission because this produces the largest effect. Waves from the west (Fig. 10(a)) produce the largest changes in Hs in the central section of coastline, with the effects diminishing towards the eastern and western extremes, confirming the picture provided by Fig. 9. When waves approach from the southwest (Fig. 10(b)), the effects are seen along the eastern section of the coastline, with no effect on the western section. Waves from the northwest (Fig. 10(c)) produce greatest effects in the central and western section, and have negligible effect in the eastern section. The variation in DHs at the shoreline with varying energy transmission at the Wave Hub is demonstrated in Fig. 11(a) for the reference sea state used in Fig. 10(a). Fig. 11(b) presents the same results, but normalised using DH s H s H 0s ¼ 100% Hs Hs
(4)
for each shoreline location to show the percentage change in significant wave height. Although the data points in both plots are discrete values as before, they have been connected to enable easier identification of data for each transmission percentage. As can be seen from Figs. 11(a and b), both DHs and DHs/Hs reduce as wave energy transmission increases. At 0% transmission, the maximum DHs is 0.22 m for the reference sea state presented, corresponding to 9.7% of Hs without the Wave Hub. At 90% transmission however, these figures have reduced to a maximum DHs of 0.02 m, a 0.9% change. From the full set of shoreline height and period differences obtained, three further sets of results are presented: 1. Results at each location are averaged over all reference sea states to assess the most affected sections of coastline. 2. Results for every reference state are averaged over all shoreline locations to evaluate which sea states produce the greatest effect. 3. Results at specific beaches are presented to assess the impact on popular surfing locations.
3.2.2. Results averaged over all reference states The differences in significant wave height due to the Wave Hub were averaged at each location over all 529
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0.40 St Agnes Head
Godrevy Pt
Pendeen
Newquay
Harlyn Bay
Change in Hs /m
0.30
0.20
0.10
0.00 135000 West (a)
145000
155000
165000 x / mE
175000
185000 East
0.40
Change in Hs /m
Pendeen
St Agnes Head
Godrevy Pt
0.30
Newquay
Harlyn Bay
0.20
0.10
0.00 135000 (b)
145000
155000
W
165000
175000
185000 E
x / mE
0.40 Pendeen
Godrevy Pt
St Agnes Head
Newquay
Harlyn Bay
Change in Hs / m
0.30
0.20
0.10
0.00 (c)
135000 W
145000
155000
165000 x / mE
175000
185000 E
Fig. 10. (a) DHs along the coastline for reference sea state H s ¼ 3:3 m, T m ¼ 11 s, D ¼ 11 (0% transmission of wave energy at the Wave Hub site), (b) DHs along the coastline for reference sea state H s ¼ 4:7 m, T m ¼ 10:6 s, D ¼ 64:91 (0% transmission of wave energy at the Wave Hub site), (c) DHs along the coastline for reference sea state H s ¼ 4:2 m, T m ¼ 8:4 s, D ¼ 314:91 (0% transmission of wave energy at the Wave Hub site).
reference states for each transmission percentage. The maximum differences at each location over all reference states were also found, and the averages and maxima
plotted against the x-co-ordinates of their locations (Figs. 12(a–c)) for 0%, 70% and 90% transmissions (the unachievable worst-case scenario results, and the two more
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0.25 0%
Change in Hs /m
0.20
40% 70%
0.15
90%
0.10
0.05
0.00 135000 (a)
145000
155000
165000
175000
185000
x / mE
W
E
12 0%
% Change in Hs
10 8
40% 70% 90%
6 4 2
(b)
0 135000 W
145000
155000
165000 x / mE
175000
185000 E
Fig. 11. (a) DHs along the coastline for reference sea state H s ¼ 3:3 m, T m ¼ 11 s, D ¼ 11, and varying wave energy transmission percentages at the Wave Hub site, (b) DHs/Hs along the coastline for reference sea state H s ¼ 3:3 m, T m ¼ 11 s, D ¼ 11, and varying wave energy transmission percentages at the Wave Hub site.
realistic scenarios). Percentage changes in significant wave height at each location were calculated for each boundary condition (Eq. (4)), and averages and maxima of these were also plotted (Figs. 13(a–c)). The differences in absolute wave height (Figs. 12(a–c)) indicate that the central section of coastline is most affected, with average differences in wave height of around 10 cm over the full set of sea states modelled for the 0% transmission scenario, reducing to 3 cm for 70% transmission and 1 cm for 90%. At eastern and western extremes, the averages are significantly lower. The three peaks in the average height differences at approximately 158 000, 176 000 and 184 000 mE all occur at locations where a stretch of west facing coast culminates in a headland at the northern end (in these three cases Godrevy Point, Penhale Point and Trevose Head). Comparing the absolute height differences with the percentage height differences (Figs. 13(a–c)), a similar pattern is obtained, with average changes in DHs/Hs in the central section of coastline decreasing from around 5% at 0% transmission to 0.5% at
90% transmission. The large maxima at the western end in both plots contrasts with the low average values at these points, suggesting that the effect of the Wave Hub on the wave climate due to a small number of reference wave states is substantial, while overall there is minimal impact in this area because of the low frequency of waves from a northerly direction. 3.2.3. Results averaged over all locations Averaging the results for each reference state over all coastline locations produced an alternative set of results, enabling an assessment of the impact of specific reference sea states. Plotting the maximum and average DHs for each set of reference states against the corresponding reference wave direction at Sevenstones lightship indicates the range of wave directions for which the Wave Hub will have maximum effect on the shoreline wave climate (Figs. 14(a–c)). Average wave height differences for wave directions between 901 and 2401 are less than 1 cm, even at 0% transmission, which is to be expected because these
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0.45
Change in Hs / m
0.40
Maximum Average
0% Transmission
0.35 0.30 0.25 0.20 0.15 0.10 0.05
0.00 135000 W (a)
145000
155000
165000 x /mE
0.14
Change in Hs / m
0.12
175000
185000 E
70% Transmission Maximum Average
0.10 0.08 0.06 0.04 0.02
0.00 135000 W (b)
145000
155000
165000 x /mE
175000
185000 E
0.05
Change in Hs / m
0.04
90% Transmission
Maximum Average
0.03 0.02 0.01
0.00 135000 W (c)
145000
155000
165000 x /mE
175000
185000 E
Fig. 12. (a–c) Maximum and average DHs for 0%, 70% and 90% wave energy transmission at the Wave Hub site for each shoreline location, over all reference states.
waves would be propagating away from the shoreline. Some significant maximum values are recorded within this range however, because the directions are those of the reference sea state at Sevenstones which, although a good approximation, is not necessarily the same as at the model boundaries. As expected, the larger values of DHs due to the presence of the Wave Hub occur when waves approach from westerly directions between approximately 3301 and 301. In the absolute worst-case scenario, the largest DHs is 0.41 m
(0% transmission). For a wave farm with highly efficient WECs (70% transmission, 30% absorption), the largest DHs is 0.13 m. For a wave farm with devices of lower efficiency or wider spacing (90% transmission, 10% absorption), the largest DHs is 0.04 m. Table 2 shows the maximum absolute and percentage differences in DHs and DTm caused by the differing transmission percentages at the Wave Hub site. The significant wave height or mean period predicted at the location of the maximum value with no Wave Hub
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25
% Change in Hs
0% Transmission
Maximum Average
20 15 10 5
(a)
0 135000 W
145000
8
165000 x /mE
Maximum Average
7 % Change in Hs
155000
175000
185000 E
70% Transmission
6 5 4 3 2 1
0 135000 W (b)
145000
155000
165000 x /mE
175000
185000 E
2.5
% Change in Hs
90% Transmission
Maximum Average
2.0 1.5 1.0 0.5 0.0 135000 W (c)
145000
155000
165000 x /mE
175000
185000 E
Figs. 13. (a–c) Maximum and average DHs/Hs for 0%, 70% and 90% wave energy transmission at the Wave Hub site for each shoreline location, over all reference states.
structure in place is also given, along with the reference sea state parameters at Sevenstones lightship. The corresponding average values are given in Table 3. Plotting these maxima and averages against the transmission percentage (Figs. 15(a–d)) identifies coherent behaviour across different model runs. The trends indicated suggest that the Wave Hub impact is linear (all trend lines have R2 values in excess of 0.98), although it remains to be investigated whether or not such a conclusion applies outside the domain of computer
modelling. It should be noted that the maximum percentage height differences result from a situation where a very small original wave height undergoes a substantial percentage change due to the Wave Hub even though the absolute height difference is minimal.
3.2.4. Results at specific beaches Results over all boundary conditions and transmission percentages are presented in greater detail in Table 4 for
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Waves from West 0.45 0.40
Waves from West
Maximum Average
0.35 Change in Hs / m
Waves from East
0% Transmission
0.30 0.25 0.20 0.15 0.10 0.05 0.00 0
30
60
90
(a)
120 150 180 210 240 Reference Direction / degrees
270
300
330
360
0.14 Maximum Average
Change in Hs / m
0.12
70% Transmission
0.10 0.08 0.06 0.04 0.02 0.00 0
30
60
90
(b)
120 150 180 210 240 Reference Direction / degrees
270
300
330
360
0.045 Maximum Average
0.040 Change in Hs / m
0.035
90% Transmission
0.030 0.025 0.020 0.015 0.010 0.005 0.000 0
(c)
30
60
90
120 150 180 210 240 Reference Direction / degrees
270
300
330
360
Figs. 14. (a–c) Maximum and average DHs for 0%, 70% and 90% wave energy transmission at the Wave Hub site, for each reference direction, over all locations.
the beaches shown in Fig. 16, specifically chosen because of their popularity as surfing locations. Table 4 shows the maximum and average DHs and DHs/Hs over all reference states and for each transmission percentage at each beach location. The larger effects appear to occur south of Fistral, closer to the Wave Hub site. The effects due to the Wave Hub decrease at each location with increasing wave energy transmission at the Wave Hub site. At 90% transmission, no site has a maximum DHs of more than 3 cm, and average differences are all 1 cm or less.
4. Discussion 4.1. Is there an effect? The results demonstrate that the installation of WECs at the Wave Hub site will have an impact on the wave climate off the north coast of Cornwall. The proposed Wave Hub location, coupled with the predominant wave climate from westerly and southwesterly directions, means that taking energy from the waves at the Wave Hub site will particularly affect the stretch of coastline studied. The
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Table 2 Maximum values of DHs and DTm over all locations for differing wave energy transmission percentages at the Wave Hub site Transmission %
Max DHs (m)
Max DHs/Hs (%)
Max DTm (s)
Max DTm/Tm (%)
0 (Absolute worst case scenario)
0.41 H s ¼ 4:14 m H sðrefÞ ¼ 6:1 m T mðrefÞ ¼ 11:4 s DðrefÞ ¼ 20:51
21.7 H s ¼ 0:13 m H sðrefÞ ¼ 1:5 m T mðrefÞ ¼ 6:3 s DðrefÞ ¼ 36:01
2.78 T m ¼ 9:21 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 14:7 s DðrefÞ ¼ 15:91
30.2 T m ¼ 9:21 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 14:7 s DðrefÞ ¼ 15:91
40 (Very unlikely scenario)
0.24 H s ¼ 4:14 m H sðrefÞ ¼ 6:1 m T mðrefÞ ¼ 11:4 s DðrefÞ ¼ 20:51
13.3 H s ¼ 0:13 m H sðrefÞ ¼ 1:5 m T mðrefÞ ¼ 6:3 s DðrefÞ ¼ 36:01
1.67 T m ¼ 9:21 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 14:7 s DðrefÞ ¼ 15:91
17.9 T m ¼ 9:21 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 14:7 s DðrefÞ ¼ 15:91
70 (Efficient, closely spaced WECs)
0.13 H s ¼ 2:42 m H sðrefÞ ¼ 4:7 m T mðrefÞ ¼ 12:7 s DðrefÞ ¼ 0:71
6.7 H s ¼ 0:13 m H sðrefÞ ¼ 1:5 m T mðrefÞ ¼ 6:3 s DðrefÞ ¼ 36:01
0.55 T m ¼ 10:89 s H sðrefÞ ¼ 4:7 m T mðrefÞ ¼ 12:7 s DðrefÞ ¼ 0:71
5.1 T m ¼ 9:86 s H sðrefÞ ¼ 4:7 m T mðrefÞ ¼ 12:7 s DðrefÞ ¼ 0:71
90 (Less efficient, widely spaced WECs)
0.04 H s ¼ 4:14 m H sðrefÞ ¼ 6:1 m T mðrefÞ ¼ 11:4 s DðrefÞ ¼ 20:51
2.3 H s ¼ 0:13 m H sðrefÞ ¼ 1:5 m T mðrefÞ ¼ 6:3 s DðrefÞ ¼ 36:01
0.37 T m ¼ 9:41 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 10:2 s DðrefÞ ¼ 81:21
4.0 T m ¼ 9:41 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 10:2 s DðrefÞ ¼ 81:21
Table 3 Average values of DHs and DTm over all locations for varying wave energy transmission percentages at the Wave Hub site Transmission %
Av DHs (m)
Av DHs/Hs (%)
Av DTm (s)
Av DTm/Tm (%)
0 40 70 90
0.06 0.04 0.02 0.01
3.04 1.85 0.91 0.31
0.01 0.01 0.00 0.00
0.12 0.08 0.04 0.01
most affected area appears to be the section of coast between Godrevy Point and Towan Head. There will be an impact on the coastline when waves approach from directions below approximately 901 and above approximately 2401. The area of coastline affected will vary with the direction the waves approach from. 4.2. How significant is the effect? When considering these results, it should be remembered that although the full range of energy transmissions at the Wave Hub site has been considered, these would not all be achievable in reality. At present, only the developers of WECs know the exact energy absorption and transmission of their devices. Additionally, it is not yet known which WECs will be deployed at the Wave Hub site, in what configuration and with what spacing. This makes it impossible to do more than estimate the actual transmission of wave energy at the site. Consequently this study has considered the full range of possible transmission percentages. Although no array of WECs will ever absorb all, or
even most, incoming wave energy i.e. transmit 0% or 40%, these results allow a full spectrum of scenarios to be presented, and the trends obtained can be used to produce estimates of the effects when a good approximation of wave power absorption is known. The potential differences in wave period are so small as to be negligible. The maximum potential height differences at various surfing beaches are all below 10 cm for 70% transmission, and will be smaller as the energy transmission increases further, as is likely. In addition, these maximum values will only occur with a small number of sea states over the course of the year. In reality, it appears that most beaches would not see more than 1 or 2 cm difference in wave height on average. The motivation for this work was partly to determine whether the effects of the WaveHub will be measurable practically. The results suggest that any signal could easily be swamped by natural wave climate variability year-toyear. It also appears unlikely that the effects of the Wave Hub will be felt by shoreline sea users. 4.3. Use of results The work presented herein can be used by developers of WECs to assess how their own devices would affect the wave climate if installed at the Wave Hub site. Using Fig. 15(a), it can be seen that an array of devices transmitting, for example, 86% of incident wave energy would produce a maximum difference in significant wave height at the shoreline of approximately 6 cm, and an average difference of around 1 cm. However the maximum height difference will only occur if sufficiently large waves
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898 0.45 0.40
Change in Hs / m
y = -0.0041x + 0.4085
Maximum:
0.35
R2 = 0.9993
0.30 Average:
y = -0.0006x + 0.0585
0.25
R2 = 1
0.20 0.15 0.10 0.05 0.00
(a) -0.05
0
20
40
60
80
100
Transmission %
40 35 Maximum: y = -0.3606x + 35.256 R2 = 0.9964
% Change in Hs
30 25
Average:
y = -0.0304x + 3.0471 R2 = 0.9999
20 15 10 5 0
(b)
-5
0
20
40
60 Transmission %
80
100
Change in Tm / s
3.0 2.5
Maximum:
2.0
Average:
y = -0.0258x + 2.7773 R2 = 0.9802 y = 0.0001x -0.014 R2 = 0.9974
1.5 1.0 0.5 0.0 0
20
40
60
80
100
Transmission %
(c) -0.5 35 30
Maximum:
R2 = 0.9873
25 % Change in Tm
y = -0.2841x + 30.045
Average:
20
y = 0.0013x -0.1267 R2 = 0.9974
15 10 5 0 0
(d)
-5
20
40 60 Transmission %
80
100
Fig. 15. (a) Maximum DHs against wave energy transmission percentage, (b) Maximum DHs/Hs against wave energy transmission percentage, (c) Maximum DTm against wave energy transmission percentage, (d) Maximum DTm/Tm against wave energy transmission percentage.
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Table 4 Maximum and average DHs and DHs/Hs at popular surfing locations Location
Parameter
0%
40%
70%
90%
Gwithian
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.23 11.72 0.05 3.44
0.13 6.87 0.03 2.11
0.06 3.29 0.02 1.06
0.02 1.08 0.01 0.36
Porthtowan
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.23 9.18 0.07 4.68
0.15 5.52 0.04 2.85
0.09 3.16 0.02 1.41
0.02 0.97 0.01 0.47
Perranporth
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.33 17.26 0.09 6.57
0.20 10.21 0.05 3.99
0.09 4.93 0.03 1.96
0.03 1.63 0.01 0.65
Fistral
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.18 11.19 0.05 3.96
0.11 6.58 0.03 2.37
0.05 3.17 0.01 1.15
0.02 1.06 0.00 0.38
Newquay Bay
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.07 7.25 0.01 1.19
0.04 4.30 0.01 0.73
0.04 2.35 0.00 0.36
0.01 0.88 0.00 0.12
Watergate Bay
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.18 8.34 0.02 1.90
0.09 4.94 0.01 1.15
0.04 2.4 0.01 0.57
0.01 0.79 0.00 0.19
Constantine Bay
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.09 9.65 0.02 1.72
0.06 6.20 0.01 1.05
0.03 3.28 0.01 0.53
0.01 1.15 0.00 0.18
Harlyn Bay
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.07 11.72 0.01 1.55
0.05 8.08 0.01 0.95
0.04 4.63 0.00 0.49
0.01 1.67 0.00 0.17
approach the coastline from a westerly direction, and will only be felt at a small number of sites, close to Perranporth. At other sites, and for other wave directions, height differences will be substantially smaller. The Wave Dragon is an offshore overtopping device that elevates waves into a reservoir above sea level from which the water passes back to the sea via low head Kaplan hydro turbines (Kofoed et al., 2004). Device performance is published for a 7 MW-rated Wave Dragon operating in seas with a mean wave power density of 36 kW/m, a good approximation for the wave climate at the Wave Hub site. A Wave Dragon installed in this wave climate would have a width of 300 m and produce 20 GWh/y of power (Wave Dragon, 2005). On the assumption of a 300 m spacing between Wave Dragon units, seven units could be spaced in a 3900 m array, the approximate length of array modelled in this study. Seven units would generate a total of 140 GWh/y of electrical power when the total annual wave energy incident upon this 3900 m long array totals 1230 GWh/y.
Therefore the wave power converted to electricity is approximately 11% of the total (ignoring losses in turbine and generator that will be relatively small), corresponding to a transmission percentage through the array of 89%. Although it is not known whether Wave Dragon will be one of the WECs deployed at the Wave Hub site, this calculation indicates that wave energy transmission percentages closer to 90% are more realistic than those at 70%. 5. Conclusions This study has shown that while the proposed Wave Hub development will potentially affect the wave climate off the north coast of Cornwall, it is likely that these effects will be small. It has been demonstrated how these effects vary with location and wave direction. More specifically:
Changes in significant wave height due to the Wave Hub decrease linearly at the shoreline with increasing wave energy transmission through the Wave Hub site.
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Harlyn Bay Constantine Bay
Watergate Bay Towan Head Fistral
Newquay Bay
Perranporth
Porthtowan Godrevy Point Gwithian
Fig. 16. Locations of bays where changes in wave climate are presented in greater detail.
A realistic scenario for a wave farm developer of 90% wave energy transmission produces an average change in significant wave height at the shoreline of 1 cm or less over the 11 months of sea states modelled. The maximum change in shoreline significant wave height for 90% transmission is 4 cm, but this will be an infrequent event as it depends on shoreline location and specific offshore wave conditions. The most affected stretch of coastline is between Godrevy Point and Towan Head, with results diminishing beyond these points. Waves approaching the shoreline from directions between 3301 and 301 will produce the largest effects, while wave directions between 901 and 2401 will produce negligible effects.
There is little cause for concern that effects introduced by the Wave Hub will be felt by shoreline users of the sea. Acknowledgements The second author is funded by the CSM Trust. The authors are also grateful to Surfers Against Sewage, Regen SW and OceanProspect Ltd for useful comments on the draft manuscript.
References Battjes, J.A., Janssen, J.P.F.M., 1978. Energy loss and set-up due to breaking of random waves. Proceedings of the 19th International Conference on Coastal Engineering, ASCE, 569–587. Booij, N., Ris, R.C., Holthuijsen, L.H., 1999. A third-generation wave model for coastal regions, Part I, model description and validation. Journal of Geophysical Research 104 (C4), 7649–7666. Booij, N., Haagsma, I.J.G., Holthuijsen, L.H., Kieftenburg, A.T.M.M., Ris, R.C., van der Westhuysen, A.J., Zijlema, M., 2004. SWAN Cycle III version 40.41 User Manual [online]. Available from: http:// fluidmechanics.tudelft.nl/swan/default.htm [Accessed 7 April 2005]. Clarke, J.P., 2004. SC 5603 Falmouth to Padstow, fourth ed. Hydrographic Office, Taunton, UK. Cornwall & Scilly Isles Coastal Group, 1999. Land’s End to Hartland Point Shoreline Management Plan, vol. 1–3. Halcrow Group Ltd. Eldeberky, Y., 1996. Nonlinear transformation of wave spectra in the nearshore zone. Ph.D. Thesis, Department of Civil Engineering, Delft University of Technology, The Netherlands. Harrison, D.J., 1987. Lands End Sea Bed Sediments and Quatenary Geology, 1:250,000. Ordinance Survey on behalf of British Geological Survey, Southampton. Hasselmann, K., Barnett, T.P., Bouws, E., Carlson, H., Cartwright, D.E., Enke, K., Ewing, J.A., Gienapp, H., Hasselmann, D.E., Kruseman, P., Meerburg, A., Muller, P., Olbers, D.J., Richter, K., Sell, W., Walden, H., 1973. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Dtsch Hydrogr Z. Suppl. 12, A8. Hasselmann, S., Hasselmann, K., Allender, J.H., Barnett, T.P., 1985. Computations and parameterizations of the nonlinear energy transfer
ARTICLE IN PRESS D.L. Millar et al. / Ocean Engineering 34 (2007) 884–901 in a gravity wave spectrum. Hamburger Geophys. Einzelschr., Serie A. 52, 8. Kofoed, J.P., Frigaard, P., Friis-Madsen, E., Sorensen, H.C., 2004. Prototype testing of the wave energy converter Wave Dragon [online]. Available from: http://www.wavedragon.net/library/conference_ articles_etc/Wave%20Dragon%20ME_02%20paper1.pdf [Accessed 6 July 2005]. Komen, G.J., Hasselmann, S., Hasselmann, K., 1984. On the existence of a fully developed wind-sea spectrum. Journal of Physical Oceanography 18, 1020–1034. NOAA, 2005. National Data Buoy Center [online]. Available from: http:// www.ndbc.noaa.gov [Accessed 7 April 2005].
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NOAA Wavewatch III, 2005. NOAA/NCEP Operational Wave Models [online]. Available from: http://polar.ncep.noaa.gov/waves [Accessed 7 April 2005]. NSIDC, 2005. ETOP05 Elevation Data for Areas Greater than 50 degrees North [online]. Available from: http://nsidc.org/data/arcss016.html [Accessed 7 April 2005]. South West of England Regional Development Agency, 2005. Wave Hub Technical Feasibility Study. Halcrow Group Ltd. Wave Dragon, 2005. Short presentation and fact sheet about Wave Dragon [online]. Available from: http://www.wavedragon.net/library/ general_material/wd-folder_11-02_150dpi_rgb.pdf [Accessed 20 June 2005].
Ocean Engineering 34 (2007) 884–901 www.elsevier.com/locate/oceaneng
Modelling analysis of the sensitivity of shoreline change to a wave farm D.L. Millara,, H.C.M. Smitha, D.E. Reeveb a
Camborne School of Mines, University of Exeter in Cornwall, Tremough Campus, Penryn, Cornwall TR10 9EZ, UK b C-CODE, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK Received 14 August 2005; accepted 28 December 2005 Available online 24 July 2006
Abstract Change of shoreline wave climate caused by the installation of a wave farm is assessed using the SWAN wave model. The 30 MW-rated wave farm is called the ‘Wave Hub’ and will be located 20 km off the north coast of Cornwall, UK. Changes in significant wave height and mean wave period due to the presence of the Wave Hub are presented. The results suggest that the shoreline wave climate will be affected, although the magnitude of effects decreases linearly as wave energy transmitted increases. At probable wave energy transmission levels, the predicted change in shoreline wave climate is small. r 2006 Elsevier Ltd. All rights reserved. Keywords: Wave climate; Wave power; Shoreline environmental impact; Wave model; SWAN; Coastal engineering
1. Introduction 1.1. Wave Hub ‘Wave Hub’ is a sub-sea electrical grid connection point, proposed for installation on the seabed off the north coast of Cornwall on the UK’s southwest peninsula. If the project obtains all consents, it will be connected to the mainland electricity grid distribution and will provide a location for pre-commercial development of arrays of wave energy converters (WECs). The proposed location for Wave Hub is 20 km northwest of St Ives Bay (Fig. 1) where the water depth is 50–60 m (South West of England Regional Development Agency, 2005). Arrays of WECs will occupy the site over an area of 3000 m 1000 m. Although it is not yet known which devices will be initially deployed at the site, all potential WECs have the objective of converting the energy of the waves into electrical power. Removing energy from the waves at an offshore site will reduce the height and power of the waves as they propagate further towards the shoreline. The objective of the study presented herein is to estimate by how much the shoreline wave climate will be changed. Corresponding author. Fax: +44 1326 371859.
E-mail address: [email protected] (D.L. Millar). 0029-8018/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2005.12.014
The results of the study will be carried forward into assessments of impacts arising as a result of the development. A major concern is to allay any concerns of the surfing community. The study uses the latest version of the SWAN (Simulating WAves Near-shore) wave model, version 40.41 (Booij et al., 2004). 1.2. SWAN wave model SWAN is a third generation numerical wave model developed by Delft University of Technology to specifically model near-shore wave climate transformations (Booij et al., 1999). It simulates wave propagation, accounting for refraction due to variations in seabed and currents, shoaling, blocking and reflection due to opposing currents, and blockage, reflection or transmission due to obstacles. Wave energy can be dissipated in the model by activating processes such as whitecapping (Komen et al., 1984), bottom friction (Hasselmann et al., JONSWAP, 1973), depth-induced wave breaking (Battjes and Janssen, 1978) and wave–wave interaction (Eldeberky, 1996; Hasselmann et al., 1985). SWAN is based on the spectral action balance equation, q q q q q S Nþ cx N þ cy N þ cs N þ cy N ¼ . qt qx dy qs qy s
(1)
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Fig. 1. The area of study off the north coast of Cornwall, and the proposed Wave Hub location.
The action density N(s, y) equals the energy density E(s, y) divided by s, the frequency relative to any currents present. The rate of change of N in time is given by the first term of (1), with the second and third terms representing the spatial propagation of N in x- and y-space with velocity components cx and cy. The fourth term represents changes in the relative frequency due to variations in depth and currents, and the final term on the left-hand side is the directional propagation of N due to refraction. The term S(s, y) on the right-hand side is the source term of the equation, representing the generation and dissipation of energy density by the processes listed above. SWAN requires the input of a bathymetric grid and, optionally, input grids of current, wind, bottom friction and water level. Stationary or time-varying wave parameters must be established as input parameters at the model boundary. A range of wave parameters can be produced as outputs of the model and presented in a number of formats.
121300 W) and K2 (511000 N, 131240 W), and the Sevenstones lightship, shown in Fig. 2, are part of a worldwide network of data buoys recording hourly wave and meteorological conditions. SWAN requires a bathymetric input grid with sufficient spatial resolution to ensure that all relevant features of the seabed are properly resolved. For the near-shore region from the coastline to 5000 mE, a 50 m resolution grid was produced by interpolating data from three main sources:
BGS Sea Bed Sediment maps (Harrison, 1987) Shoreline Management Plan (Cornwall & Isles of Scilly Coastal Group, 1999) Admiralty Charts (Clarke, 2004)
West of 5000 mE, the bathymetric model was extended using the ETOP05 dataset, a digital elevation model with 5 min resolution (NSIDC, 2005). The datasets were combined to produce an input grid of bathymetric values covering the area shown in Fig. 2.
2. Modelling methodology 2.2. Modelling approach 2.1. Data sources Two sources of wave data were available for use in this study; output from the Wavewatch III global ‘nww3’ computer model (NOAA Wavewatch III, 2005), and realtime data from the NE Atlantic data buoys (NOAA, 2005). Wavewatch III is a third generation global spectral wave model, which provides estimates of wave parameters at 3hourly intervals. Data from the model was collected for 12 grid-points surrounding the southwest peninsula of England (Fig. 2). The NE Atlantic data buoys K1 (481420 N,
2.2.1. Boundary conditions The data buoys K1 and K2 are both located over 450 km west of the Cornish coastline; too far offshore to be used as input for the model. The non-uniform bathymetry of the region, characteristic of coastal areas, and the potential for wave directions spanning 0–3601 meant it was essential to have boundary conditions covering three sides of the input grid to fully enclose the Cornish peninsula. Boundary conditions were defined using data output from the following Wavewatch III grid points: WW2, WW3,
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150000
WW1
WW2
WW3
WW4
100000
50000 mN
WW5
Seven Stones
WW6
WW7
WW8
0
-50000 WW9 WW10
WW11
-100000 -100000
-50000
0
50000
100000
150000
WW12 200000
mE Fig. 2. Area covered by bathymetric grid, showing locations of Wavewatch III grid points and the Sevenstones lightship.
Table 1 Wave parameters for a reference sea state and corresponding values at Wavewatch III grid points Location
Reference wave State WW2 WW3 WW4 WW6 WW10 WW11 WW12
Significant wave height, Hs (m)
Mean wave period, Tm (s)
80
3.3
11.0
1.0
101 90 44 119 140 120 94
3.6 3.2 2.7 3.5 3.3 3.1 2.7
10.2 9.7 9.3 11.5 12.0 11.8 11.3
8.1 6.4 3.7 1.1 1.2 358.5 358.0
Water depth at gridpoint (m)
WW4, WW6, WW10, WW11 and WW12 (Fig. 2). Within SWAN, the boundary conditions can be set to vary continuously between each of a string of locations where the wave climate is defined precisely; in this case between locations WW2 and WW12 listed above. This interpolation between the points provided boundary conditions around three sides of the grid, with the fourth side containing the land mass. Wave data from the Sevenstones lightship, recorded simultaneously with the Wavewatch III predictions, has been used throughout this study to provide a near-shore ‘reference sea state’ for each set of boundary conditions. Table 1 gives an example of a set of reference sea state parameters and the corresponding parameters at each of the Wavewatch III grid points listed above. 2.2.2. Grid details A coarse computational grid with 5000 m resolution was created over the area defined by the seven Wavewatch
Wave direction (anti-clockwise from East), D (1)
points. A fine grid with 200 m resolution was defined as a nested grid within the coarse grid (Fig. 3). When defining grid resolutions, particularly for the fine grid model, a compromise had to be made between a high-resolution grid which would define as much seabed detail as possible, and the limitations imposed on the model by the available computational capacity. The 200 m grid chosen for this model means that seabed features below this size will not be resolved. The output of the coarse grid run defined boundary conditions for the fine grid model. For both the coarse and fine grid models, wind, current and localised bottom friction input grids were not generated. Wind and current were therefore assumed to be zero, and bottom friction constant over the grid. Both grid models were defined with 36 directional bins of 101, covering all possible wave directions. Fourteen frequency bins were defined, covering the full range of wave frequencies found in the Wavewatch III data. When
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887
150000
Coarse Grid 100000 Detail Grid
mN
50000
0
-50000
-100000 -100000
0
-50000
50000
100000
150000
200000
mE Fig. 3. Boundaries of the coarse and fine SWAN computational grids.
Directional distribution of wave energy
1.2
m=1, DSPR=37.5 m=2, DSPR=31.5
1.0
m=3, DSPR=27.6 m=5, DSPR=22.9
0.8
m=10, DSPR=17.1 m=50, DSPR=8.0
0.6
m=100, DSPR=5.7 m=800, DSPR=2.0
0.4 0.2 0.0 0
10
20
30
40
50
60
70
80
90
100
D-Dpeak / deg Fig. 4. Variation of directional distribution of incident wave energy with m and DSPR.
input into SWAN, the boundary conditions were defined as JONSWAP spectra (Hasselmann et al., JONSWAP, 1973), SWAN’s default spectral setting. When using nested grids in SWAN, the code interpolates spectral directions and frequencies in the respective direction and frequency grids. The directional distribution of incident wave energy is DðyÞ ¼ A cosm ðy ypeak Þ,
(2)
where ypeak is the peak spectral direction and m the power to which the cosine function is raised. Within SWAN, options exist to define the directional spread either by defining m or by defining the directional standard deviation, DSPR, of the cosm y function. In this study,
the default DSPR value of 301 was used. Fig. 4 shows how the directional energy distribution varies with m and DSPR. 2.2.3. Preliminary assessment of the coarse grid SWAN implementation against the WaveWatch III implementation As a preliminary test of the reliability of the coarse grid SWAN formulation (5000 m bathymetric grid resolution in easting and northing), SWAN output for the Sevenstones Lightship location was produced and compared with output for the same location interpolated directly from NOAA’s nww3 Wavewatch III model. This global implementation relies on a bathymetric grid with resolution 1.251 and 1.001 in longitude and latitude, respectively.
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of the nww3 implementation considered at the scale of the Cornwall peninsula. The conclusion of this assessment process was that the SWAN model produces realisations of sea states that are consistent with those of NOAA’s nww3 implementation, especially when the disparities in respective bathymetric and computational grid resolutions are considered.
The comparison process was repeated over all reference sea states (as defined in Section 2.2.1), to form a dataset of disparities that can be examined statistically. The distribution of the disparities for significant wave height is presented in Fig. 5, where the disparity is expressed as the absolute difference between the results for the respective models over the result from the nww3 implementation. Fig. 5 demonstrates that over all reference sea states, approximately 80% of disparities have a magnitude of less than 20%. When a subset of reference sea states is formed by considering only those where waves propagate from western quadrants, approximately 90% of disparities have a magnitude of less than 20%. This subset is examined independently to remove instances where waves propagate from the direction of the land mass, which is not likely to be well represented by the very coarse resolution
2.2.4. Wave states Twelve-hourly Wavewatch III estimates of significant wave height, mean wave period and wave direction were obtained for the period 2nd December 2002–9th November 2003. Gaps in the data led to the elimination of a number of days’ data, giving a final set of 529 distinct wave states, of which Table 1 represents one such wave state. The reference sea states for the set, shown in the scatter diagram
Percentage of data points
60 50 40 30 All Data Waves from West
20 10 0 0
10
20 30 40 50 60 70 80 90 Percentage difference in Hs between model output and recorded data
100
Fig. 5. Distribution of disparities in significant wave height produced from SWAN and NOAA’s nww3 global implementation at Sevenstones lightship.
Significant Wave Height / m 0.0- 0.5
0.5-1.0
1.0-1.5
1.5-2.0
2.0- 2.5
2.5-3.0
3.0-3.5
3.5-4 .0
4.0- 4.5
4.5-5.0
5.0 -5.5
5.5-6 .0
6.0-6.5
6.5-7.0
7.0- 7.5
7.5-8.0
8.0- 8.5
8.5-9.0
> 9.0
3.5-4.0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4.0-4.5
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
4.5-5.0
0
15
16
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5.0-5.5
1
16
37
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5.5-6.0
1
17
41
29
14
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6.0-6.5
4
34
54
30
35
9
0
0
0
0
0
0
0
0
0
0
0
0
0
6.5-7.0
1
33
41
52
58
25
2
0
0
0
0
0
0
0
0
0
0
0
0
7.0-7.5
6
25
20
34
51
52
9
2
0
0
0
0
0
0
0
0
0
0
0
7.5-8.0
11
16
27
46
34
22
25
4
2
0
0
0
0
0
0
0
0
0
0
0.1
8.0-8.5
10
11
55
55
46
14
12
12
4
4
0
0
0
0
0
0
0
0
0
Mean
8.5-9.0
0
7
27
37
44
14
10
17
6
1
0
0
0
0
0
0
0
0
0
0.09 0.08 0.07
Wave
9.0-9.5
0
7
5
25
24
19
22
10
14
5
3
0
0
0
0
0
0
0
0
Period
9.5-10.0
0
1
2
18
11
12
18
9
9
10
3
5
0
0
0
0
0
0
0
/s
10.0-10.5
0
4
2
10
19
17
9
16
17
13
5
4
1
2
0
0
0
0
0
10.5-11.0
0
3
1
11
9
26
9
13
7
7
3
5
3
0
0
0
0
0
0
11.0-11.5
0
1
0
6
9
3
11
12
5
7
3
1
1
0
0
0
0
0
0
11.5-12.0
0
0
0
5
12
2
4
14
4
3
0
2
0
1
0
0
0
0
0
12.0-12.5
0
1
0
0
0
0
2
2
5
0
18
1
1
0
1
0
0
0
0
12.5-13.0
0
2
0
0
0
0
1
2
1
6
4
1
3
1
2
0
0
0
0
13.0-13.5
0
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
13.5-14.0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
14.0-14.5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
14.5-15.0
0
0
0
0
0
0
1
0
4
1
1
0
0
0
0
0
2
0
0
15.0-15.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
15.5-16.0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
>16.0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.01
0.06 0.05 0.04
0.03
0.02
Fig. 6. Scatter diagram showing the set of 529 distinct wave states for the reference sea state over all directions, overlaid with wave steepness contours.
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in Fig. 6 and overlaid with wave steepness contours, cover a range of wave heights (0.3–8.4 m), periods (4.5–15.1 s) and directions (0–359.91). 2.2.5. Model physics The wave dissipating forces of whitecapping, bottom friction and triad wave–wave interaction were set to their SWAN default values because no additional data was available to suggest otherwise. However the nonlinear quadruplet interactions were deactivated because it is not recommended to use quadruplets in combination with zero wind conditions. In addition, the default settings for diffraction were used. Arrays of WECs deployed at the Wave Hub site were represented as a 4 km partially transmitting obstacle, aligned approximately parallel to the incoming wave crests at the wave hub site. As it is not known exactly how much wave energy will be absorbed by the WECs, model runs were completed for each set of boundary conditions with energy transmission by the obstacle set at 0%, 40%, 70% and 90%. These energy transmission percentages were set for specific reasons:
0%—Represents complete absorption of all incoming wave energy at the obstacle—an unachievable scenario. It is expected that this would produce the largest possible shoreline effect. 70%—Represents an array of densely spaced, highefficiency WECs. This would be an optimistic target for a wave farm developer to achieve. 90%—Represents lower efficiency, widely spaced WECs, a more realistic scenario at the Wave Hub site. 40%—Included in the study to enable the establishment of trends, although it is extremely improbable that this could be attained in reality.
When waves approach such an obstacle in SWAN, the only change to the wave spectrum is a reduction of localised wave height along the length of the obstacle, and
889
it is assumed that the frequencies are unchanged (Booij et al., 2004). This is illustrated through plots of the JONSWAP wave spectra for the sea state produced by the boundary conditions listed in Table 1 immediately before and after an obstacle for an incoming wave (Fig. 7). The energy density for each frequency has reduced by 75%. In order to model a partially transmitting obstacle SWAN requires definition of a transmission coefficient defined as the ratio of the transmitted significant wave height over the incident significant wave height. In order to more readily introduce the idea of energy transmitted or absorbed by an array of wave energy converters, in the following, when ‘wave energy transmission’, ‘energy transmission’ or simply ‘transmission’ is referred to, this means the wave energy passing through the obstacle as a proportion of that incident upon it. The parameter required by SWAN, the ratio of wave heights, is the square root of the energy transmission as described in this section. 2.2.6. Model output The model was set to output two sets of results:
Significant wave height, mean period, wave direction and energy transport at 500 m intervals across the whole domain of the fine grid. Significant wave height, mean period and wave direction at points of approximately 500 m spacing and 10 m water depth along the coastline (Fig. 8).
A computer programme was written to drive the creation of three SWAN files for each set of boundary conditions and transmission percentage; a coarse grid model to provide boundary conditions for the fine model, a fine grid model with no Wave Hub obstacle, and a fine grid model with a partially transmitting obstacle at the Wave Hub site. The program was designed to run each model and process the results.
Spectral Energy Density / m2/s
16 Before Obstacle
14 12 10 8 6
After Obstacle
4 2 0 0
0.05
0.1
0.15 0.2 Frequency / Hz
0.25
0.3
0.35
Fig. 7. Comparison of wave energy density spectrum before and after passing through partially transmitting obstacle with a transmission coefficient of 0.5.
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90000 Harlyn Bay 80000
Newquay
mN
70000 St Agnes Head 60000
Godrevy Pt 50000 Pendeen 40000
30000 120000
130000
140000
150000
160000
170000
180000
190000
mE Fig. 8. Locations of shoreline model output points.
3. Results 3.1. Results over computational grid Results were initially examined by calculating the change due to the Wave Hub in each wave climate parameter at each point on the grid. The changes in significant wave height DHs, mean period DTm, and wave energy transport DEt were calculated using DH s ¼ H s H 0s , DT m ¼ T m T 0m , DE t ¼ E t E 0t ,
ð3Þ
where Hs, Tm and Et represent output values at specific locations on the grid from the model run with no Wave Hub, and H0 s, T0 m and E0 t the corresponding values from the run with the Wave Hub. These calculations were performed for each set of boundary conditions and over every grid point, for each energy transmission. Data from the Sevenstones lightship, obtained for the same times and dates as the Wavewatch III data, were used to indicate reference sea states corresponding to a completely defined set of boundary conditions, as described in Section 2.2.1. An example of results obtained for a reference state of H s ¼ 3:3 m, T m ¼ 11 s and D ¼ 11, corresponding to the boundary conditions listed in Table 1, is shown in Fig. 9: a contour plot of DHs for 0% wave energy transmission.
The results indicate that both wave height and energy transport are similarly affected by the Wave Hub. The largest differences can be seen in the region immediately behind the Wave Hub site, with refraction due to bathymetric change and diffraction due to the obstacle diminishing the effect as the waves propagate shoreward. For most reference sea states, an appreciable stretch of coastline is affected. As expected, increasing the amount of wave energy transmitted through the Wave Hub site diminishes these effects. The mean period decreases slightly (a result of its nature as an integrated parameter) in the area directly behind the Wave Hub, but increases at the edges of this area, with the effect spreading along almost the whole coastline studied.
3.2. Analysis of results at the shoreline 3.2.1. Overview of results To gain detailed understanding of the shoreline wave climate, results were sampled at locations of approximately 10 m water depth and 500 m spacing (Fig. 8). Differences in significant wave height and mean period due to the Wave Hub were calculated at each shoreline location as described in the previous section. All wave directions are referenced in Cartesian co-ordinates, with the direction in degrees defining the direction of wave propagation measured anticlockwise from the positive x-axis of the system (East). As before, data from the Sevenstones lightship is used to
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90000
80000
70000 mN
0.1m
60000 0.6m 0.4m 0.3m 50000
0.2m
0.1m 40000
30000 120000
130000
140000
150000
160000
170000
180000
190000
mE Fig. 9. Changes in significant wave height, DHs, due to the Wave Hub for 0% energy transmission. (Reference state: H s ¼ 3:3 m, T m ¼ 11 s and D ¼ 11).
provide a reference sea state that maps to a set of boundary conditions at WW2–WW12. Figs. 10(a–c) give examples of the results obtained for the changes in significant wave height along the shoreline for different reference sea states, and demonstrate how these vary with incoming wave direction. The x-axis of each chart gives the x co-ordinate of each measurement location in OSGB36 National Grid Eastings, and the y-axis measures the change in significant wave height introduced by the Wave Hub. For demonstration purposes, these results are for 0% transmission because this produces the largest effect. Waves from the west (Fig. 10(a)) produce the largest changes in Hs in the central section of coastline, with the effects diminishing towards the eastern and western extremes, confirming the picture provided by Fig. 9. When waves approach from the southwest (Fig. 10(b)), the effects are seen along the eastern section of the coastline, with no effect on the western section. Waves from the northwest (Fig. 10(c)) produce greatest effects in the central and western section, and have negligible effect in the eastern section. The variation in DHs at the shoreline with varying energy transmission at the Wave Hub is demonstrated in Fig. 11(a) for the reference sea state used in Fig. 10(a). Fig. 11(b) presents the same results, but normalised using DH s H s H 0s ¼ 100% Hs Hs
(4)
for each shoreline location to show the percentage change in significant wave height. Although the data points in both plots are discrete values as before, they have been connected to enable easier identification of data for each transmission percentage. As can be seen from Figs. 11(a and b), both DHs and DHs/Hs reduce as wave energy transmission increases. At 0% transmission, the maximum DHs is 0.22 m for the reference sea state presented, corresponding to 9.7% of Hs without the Wave Hub. At 90% transmission however, these figures have reduced to a maximum DHs of 0.02 m, a 0.9% change. From the full set of shoreline height and period differences obtained, three further sets of results are presented: 1. Results at each location are averaged over all reference sea states to assess the most affected sections of coastline. 2. Results for every reference state are averaged over all shoreline locations to evaluate which sea states produce the greatest effect. 3. Results at specific beaches are presented to assess the impact on popular surfing locations.
3.2.2. Results averaged over all reference states The differences in significant wave height due to the Wave Hub were averaged at each location over all 529
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0.40 St Agnes Head
Godrevy Pt
Pendeen
Newquay
Harlyn Bay
Change in Hs /m
0.30
0.20
0.10
0.00 135000 West (a)
145000
155000
165000 x / mE
175000
185000 East
0.40
Change in Hs /m
Pendeen
St Agnes Head
Godrevy Pt
0.30
Newquay
Harlyn Bay
0.20
0.10
0.00 135000 (b)
145000
155000
W
165000
175000
185000 E
x / mE
0.40 Pendeen
Godrevy Pt
St Agnes Head
Newquay
Harlyn Bay
Change in Hs / m
0.30
0.20
0.10
0.00 (c)
135000 W
145000
155000
165000 x / mE
175000
185000 E
Fig. 10. (a) DHs along the coastline for reference sea state H s ¼ 3:3 m, T m ¼ 11 s, D ¼ 11 (0% transmission of wave energy at the Wave Hub site), (b) DHs along the coastline for reference sea state H s ¼ 4:7 m, T m ¼ 10:6 s, D ¼ 64:91 (0% transmission of wave energy at the Wave Hub site), (c) DHs along the coastline for reference sea state H s ¼ 4:2 m, T m ¼ 8:4 s, D ¼ 314:91 (0% transmission of wave energy at the Wave Hub site).
reference states for each transmission percentage. The maximum differences at each location over all reference states were also found, and the averages and maxima
plotted against the x-co-ordinates of their locations (Figs. 12(a–c)) for 0%, 70% and 90% transmissions (the unachievable worst-case scenario results, and the two more
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0.25 0%
Change in Hs /m
0.20
40% 70%
0.15
90%
0.10
0.05
0.00 135000 (a)
145000
155000
165000
175000
185000
x / mE
W
E
12 0%
% Change in Hs
10 8
40% 70% 90%
6 4 2
(b)
0 135000 W
145000
155000
165000 x / mE
175000
185000 E
Fig. 11. (a) DHs along the coastline for reference sea state H s ¼ 3:3 m, T m ¼ 11 s, D ¼ 11, and varying wave energy transmission percentages at the Wave Hub site, (b) DHs/Hs along the coastline for reference sea state H s ¼ 3:3 m, T m ¼ 11 s, D ¼ 11, and varying wave energy transmission percentages at the Wave Hub site.
realistic scenarios). Percentage changes in significant wave height at each location were calculated for each boundary condition (Eq. (4)), and averages and maxima of these were also plotted (Figs. 13(a–c)). The differences in absolute wave height (Figs. 12(a–c)) indicate that the central section of coastline is most affected, with average differences in wave height of around 10 cm over the full set of sea states modelled for the 0% transmission scenario, reducing to 3 cm for 70% transmission and 1 cm for 90%. At eastern and western extremes, the averages are significantly lower. The three peaks in the average height differences at approximately 158 000, 176 000 and 184 000 mE all occur at locations where a stretch of west facing coast culminates in a headland at the northern end (in these three cases Godrevy Point, Penhale Point and Trevose Head). Comparing the absolute height differences with the percentage height differences (Figs. 13(a–c)), a similar pattern is obtained, with average changes in DHs/Hs in the central section of coastline decreasing from around 5% at 0% transmission to 0.5% at
90% transmission. The large maxima at the western end in both plots contrasts with the low average values at these points, suggesting that the effect of the Wave Hub on the wave climate due to a small number of reference wave states is substantial, while overall there is minimal impact in this area because of the low frequency of waves from a northerly direction. 3.2.3. Results averaged over all locations Averaging the results for each reference state over all coastline locations produced an alternative set of results, enabling an assessment of the impact of specific reference sea states. Plotting the maximum and average DHs for each set of reference states against the corresponding reference wave direction at Sevenstones lightship indicates the range of wave directions for which the Wave Hub will have maximum effect on the shoreline wave climate (Figs. 14(a–c)). Average wave height differences for wave directions between 901 and 2401 are less than 1 cm, even at 0% transmission, which is to be expected because these
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0.45
Change in Hs / m
0.40
Maximum Average
0% Transmission
0.35 0.30 0.25 0.20 0.15 0.10 0.05
0.00 135000 W (a)
145000
155000
165000 x /mE
0.14
Change in Hs / m
0.12
175000
185000 E
70% Transmission Maximum Average
0.10 0.08 0.06 0.04 0.02
0.00 135000 W (b)
145000
155000
165000 x /mE
175000
185000 E
0.05
Change in Hs / m
0.04
90% Transmission
Maximum Average
0.03 0.02 0.01
0.00 135000 W (c)
145000
155000
165000 x /mE
175000
185000 E
Fig. 12. (a–c) Maximum and average DHs for 0%, 70% and 90% wave energy transmission at the Wave Hub site for each shoreline location, over all reference states.
waves would be propagating away from the shoreline. Some significant maximum values are recorded within this range however, because the directions are those of the reference sea state at Sevenstones which, although a good approximation, is not necessarily the same as at the model boundaries. As expected, the larger values of DHs due to the presence of the Wave Hub occur when waves approach from westerly directions between approximately 3301 and 301. In the absolute worst-case scenario, the largest DHs is 0.41 m
(0% transmission). For a wave farm with highly efficient WECs (70% transmission, 30% absorption), the largest DHs is 0.13 m. For a wave farm with devices of lower efficiency or wider spacing (90% transmission, 10% absorption), the largest DHs is 0.04 m. Table 2 shows the maximum absolute and percentage differences in DHs and DTm caused by the differing transmission percentages at the Wave Hub site. The significant wave height or mean period predicted at the location of the maximum value with no Wave Hub
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25
% Change in Hs
0% Transmission
Maximum Average
20 15 10 5
(a)
0 135000 W
145000
8
165000 x /mE
Maximum Average
7 % Change in Hs
155000
175000
185000 E
70% Transmission
6 5 4 3 2 1
0 135000 W (b)
145000
155000
165000 x /mE
175000
185000 E
2.5
% Change in Hs
90% Transmission
Maximum Average
2.0 1.5 1.0 0.5 0.0 135000 W (c)
145000
155000
165000 x /mE
175000
185000 E
Figs. 13. (a–c) Maximum and average DHs/Hs for 0%, 70% and 90% wave energy transmission at the Wave Hub site for each shoreline location, over all reference states.
structure in place is also given, along with the reference sea state parameters at Sevenstones lightship. The corresponding average values are given in Table 3. Plotting these maxima and averages against the transmission percentage (Figs. 15(a–d)) identifies coherent behaviour across different model runs. The trends indicated suggest that the Wave Hub impact is linear (all trend lines have R2 values in excess of 0.98), although it remains to be investigated whether or not such a conclusion applies outside the domain of computer
modelling. It should be noted that the maximum percentage height differences result from a situation where a very small original wave height undergoes a substantial percentage change due to the Wave Hub even though the absolute height difference is minimal.
3.2.4. Results at specific beaches Results over all boundary conditions and transmission percentages are presented in greater detail in Table 4 for
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Waves from West 0.45 0.40
Waves from West
Maximum Average
0.35 Change in Hs / m
Waves from East
0% Transmission
0.30 0.25 0.20 0.15 0.10 0.05 0.00 0
30
60
90
(a)
120 150 180 210 240 Reference Direction / degrees
270
300
330
360
0.14 Maximum Average
Change in Hs / m
0.12
70% Transmission
0.10 0.08 0.06 0.04 0.02 0.00 0
30
60
90
(b)
120 150 180 210 240 Reference Direction / degrees
270
300
330
360
0.045 Maximum Average
0.040 Change in Hs / m
0.035
90% Transmission
0.030 0.025 0.020 0.015 0.010 0.005 0.000 0
(c)
30
60
90
120 150 180 210 240 Reference Direction / degrees
270
300
330
360
Figs. 14. (a–c) Maximum and average DHs for 0%, 70% and 90% wave energy transmission at the Wave Hub site, for each reference direction, over all locations.
the beaches shown in Fig. 16, specifically chosen because of their popularity as surfing locations. Table 4 shows the maximum and average DHs and DHs/Hs over all reference states and for each transmission percentage at each beach location. The larger effects appear to occur south of Fistral, closer to the Wave Hub site. The effects due to the Wave Hub decrease at each location with increasing wave energy transmission at the Wave Hub site. At 90% transmission, no site has a maximum DHs of more than 3 cm, and average differences are all 1 cm or less.
4. Discussion 4.1. Is there an effect? The results demonstrate that the installation of WECs at the Wave Hub site will have an impact on the wave climate off the north coast of Cornwall. The proposed Wave Hub location, coupled with the predominant wave climate from westerly and southwesterly directions, means that taking energy from the waves at the Wave Hub site will particularly affect the stretch of coastline studied. The
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Table 2 Maximum values of DHs and DTm over all locations for differing wave energy transmission percentages at the Wave Hub site Transmission %
Max DHs (m)
Max DHs/Hs (%)
Max DTm (s)
Max DTm/Tm (%)
0 (Absolute worst case scenario)
0.41 H s ¼ 4:14 m H sðrefÞ ¼ 6:1 m T mðrefÞ ¼ 11:4 s DðrefÞ ¼ 20:51
21.7 H s ¼ 0:13 m H sðrefÞ ¼ 1:5 m T mðrefÞ ¼ 6:3 s DðrefÞ ¼ 36:01
2.78 T m ¼ 9:21 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 14:7 s DðrefÞ ¼ 15:91
30.2 T m ¼ 9:21 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 14:7 s DðrefÞ ¼ 15:91
40 (Very unlikely scenario)
0.24 H s ¼ 4:14 m H sðrefÞ ¼ 6:1 m T mðrefÞ ¼ 11:4 s DðrefÞ ¼ 20:51
13.3 H s ¼ 0:13 m H sðrefÞ ¼ 1:5 m T mðrefÞ ¼ 6:3 s DðrefÞ ¼ 36:01
1.67 T m ¼ 9:21 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 14:7 s DðrefÞ ¼ 15:91
17.9 T m ¼ 9:21 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 14:7 s DðrefÞ ¼ 15:91
70 (Efficient, closely spaced WECs)
0.13 H s ¼ 2:42 m H sðrefÞ ¼ 4:7 m T mðrefÞ ¼ 12:7 s DðrefÞ ¼ 0:71
6.7 H s ¼ 0:13 m H sðrefÞ ¼ 1:5 m T mðrefÞ ¼ 6:3 s DðrefÞ ¼ 36:01
0.55 T m ¼ 10:89 s H sðrefÞ ¼ 4:7 m T mðrefÞ ¼ 12:7 s DðrefÞ ¼ 0:71
5.1 T m ¼ 9:86 s H sðrefÞ ¼ 4:7 m T mðrefÞ ¼ 12:7 s DðrefÞ ¼ 0:71
90 (Less efficient, widely spaced WECs)
0.04 H s ¼ 4:14 m H sðrefÞ ¼ 6:1 m T mðrefÞ ¼ 11:4 s DðrefÞ ¼ 20:51
2.3 H s ¼ 0:13 m H sðrefÞ ¼ 1:5 m T mðrefÞ ¼ 6:3 s DðrefÞ ¼ 36:01
0.37 T m ¼ 9:41 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 10:2 s DðrefÞ ¼ 81:21
4.0 T m ¼ 9:41 s H sðrefÞ ¼ 4:3 m T mðrefÞ ¼ 10:2 s DðrefÞ ¼ 81:21
Table 3 Average values of DHs and DTm over all locations for varying wave energy transmission percentages at the Wave Hub site Transmission %
Av DHs (m)
Av DHs/Hs (%)
Av DTm (s)
Av DTm/Tm (%)
0 40 70 90
0.06 0.04 0.02 0.01
3.04 1.85 0.91 0.31
0.01 0.01 0.00 0.00
0.12 0.08 0.04 0.01
most affected area appears to be the section of coast between Godrevy Point and Towan Head. There will be an impact on the coastline when waves approach from directions below approximately 901 and above approximately 2401. The area of coastline affected will vary with the direction the waves approach from. 4.2. How significant is the effect? When considering these results, it should be remembered that although the full range of energy transmissions at the Wave Hub site has been considered, these would not all be achievable in reality. At present, only the developers of WECs know the exact energy absorption and transmission of their devices. Additionally, it is not yet known which WECs will be deployed at the Wave Hub site, in what configuration and with what spacing. This makes it impossible to do more than estimate the actual transmission of wave energy at the site. Consequently this study has considered the full range of possible transmission percentages. Although no array of WECs will ever absorb all, or
even most, incoming wave energy i.e. transmit 0% or 40%, these results allow a full spectrum of scenarios to be presented, and the trends obtained can be used to produce estimates of the effects when a good approximation of wave power absorption is known. The potential differences in wave period are so small as to be negligible. The maximum potential height differences at various surfing beaches are all below 10 cm for 70% transmission, and will be smaller as the energy transmission increases further, as is likely. In addition, these maximum values will only occur with a small number of sea states over the course of the year. In reality, it appears that most beaches would not see more than 1 or 2 cm difference in wave height on average. The motivation for this work was partly to determine whether the effects of the WaveHub will be measurable practically. The results suggest that any signal could easily be swamped by natural wave climate variability year-toyear. It also appears unlikely that the effects of the Wave Hub will be felt by shoreline sea users. 4.3. Use of results The work presented herein can be used by developers of WECs to assess how their own devices would affect the wave climate if installed at the Wave Hub site. Using Fig. 15(a), it can be seen that an array of devices transmitting, for example, 86% of incident wave energy would produce a maximum difference in significant wave height at the shoreline of approximately 6 cm, and an average difference of around 1 cm. However the maximum height difference will only occur if sufficiently large waves
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898 0.45 0.40
Change in Hs / m
y = -0.0041x + 0.4085
Maximum:
0.35
R2 = 0.9993
0.30 Average:
y = -0.0006x + 0.0585
0.25
R2 = 1
0.20 0.15 0.10 0.05 0.00
(a) -0.05
0
20
40
60
80
100
Transmission %
40 35 Maximum: y = -0.3606x + 35.256 R2 = 0.9964
% Change in Hs
30 25
Average:
y = -0.0304x + 3.0471 R2 = 0.9999
20 15 10 5 0
(b)
-5
0
20
40
60 Transmission %
80
100
Change in Tm / s
3.0 2.5
Maximum:
2.0
Average:
y = -0.0258x + 2.7773 R2 = 0.9802 y = 0.0001x -0.014 R2 = 0.9974
1.5 1.0 0.5 0.0 0
20
40
60
80
100
Transmission %
(c) -0.5 35 30
Maximum:
R2 = 0.9873
25 % Change in Tm
y = -0.2841x + 30.045
Average:
20
y = 0.0013x -0.1267 R2 = 0.9974
15 10 5 0 0
(d)
-5
20
40 60 Transmission %
80
100
Fig. 15. (a) Maximum DHs against wave energy transmission percentage, (b) Maximum DHs/Hs against wave energy transmission percentage, (c) Maximum DTm against wave energy transmission percentage, (d) Maximum DTm/Tm against wave energy transmission percentage.
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Table 4 Maximum and average DHs and DHs/Hs at popular surfing locations Location
Parameter
0%
40%
70%
90%
Gwithian
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.23 11.72 0.05 3.44
0.13 6.87 0.03 2.11
0.06 3.29 0.02 1.06
0.02 1.08 0.01 0.36
Porthtowan
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.23 9.18 0.07 4.68
0.15 5.52 0.04 2.85
0.09 3.16 0.02 1.41
0.02 0.97 0.01 0.47
Perranporth
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.33 17.26 0.09 6.57
0.20 10.21 0.05 3.99
0.09 4.93 0.03 1.96
0.03 1.63 0.01 0.65
Fistral
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.18 11.19 0.05 3.96
0.11 6.58 0.03 2.37
0.05 3.17 0.01 1.15
0.02 1.06 0.00 0.38
Newquay Bay
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.07 7.25 0.01 1.19
0.04 4.30 0.01 0.73
0.04 2.35 0.00 0.36
0.01 0.88 0.00 0.12
Watergate Bay
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.18 8.34 0.02 1.90
0.09 4.94 0.01 1.15
0.04 2.4 0.01 0.57
0.01 0.79 0.00 0.19
Constantine Bay
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.09 9.65 0.02 1.72
0.06 6.20 0.01 1.05
0.03 3.28 0.01 0.53
0.01 1.15 0.00 0.18
Harlyn Bay
Max DHs (m) Max DHs/Hs (%) Av DHs (m) Av DHs/Hs (%)
0.07 11.72 0.01 1.55
0.05 8.08 0.01 0.95
0.04 4.63 0.00 0.49
0.01 1.67 0.00 0.17
approach the coastline from a westerly direction, and will only be felt at a small number of sites, close to Perranporth. At other sites, and for other wave directions, height differences will be substantially smaller. The Wave Dragon is an offshore overtopping device that elevates waves into a reservoir above sea level from which the water passes back to the sea via low head Kaplan hydro turbines (Kofoed et al., 2004). Device performance is published for a 7 MW-rated Wave Dragon operating in seas with a mean wave power density of 36 kW/m, a good approximation for the wave climate at the Wave Hub site. A Wave Dragon installed in this wave climate would have a width of 300 m and produce 20 GWh/y of power (Wave Dragon, 2005). On the assumption of a 300 m spacing between Wave Dragon units, seven units could be spaced in a 3900 m array, the approximate length of array modelled in this study. Seven units would generate a total of 140 GWh/y of electrical power when the total annual wave energy incident upon this 3900 m long array totals 1230 GWh/y.
Therefore the wave power converted to electricity is approximately 11% of the total (ignoring losses in turbine and generator that will be relatively small), corresponding to a transmission percentage through the array of 89%. Although it is not known whether Wave Dragon will be one of the WECs deployed at the Wave Hub site, this calculation indicates that wave energy transmission percentages closer to 90% are more realistic than those at 70%. 5. Conclusions This study has shown that while the proposed Wave Hub development will potentially affect the wave climate off the north coast of Cornwall, it is likely that these effects will be small. It has been demonstrated how these effects vary with location and wave direction. More specifically:
Changes in significant wave height due to the Wave Hub decrease linearly at the shoreline with increasing wave energy transmission through the Wave Hub site.
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Harlyn Bay Constantine Bay
Watergate Bay Towan Head Fistral
Newquay Bay
Perranporth
Porthtowan Godrevy Point Gwithian
Fig. 16. Locations of bays where changes in wave climate are presented in greater detail.
A realistic scenario for a wave farm developer of 90% wave energy transmission produces an average change in significant wave height at the shoreline of 1 cm or less over the 11 months of sea states modelled. The maximum change in shoreline significant wave height for 90% transmission is 4 cm, but this will be an infrequent event as it depends on shoreline location and specific offshore wave conditions. The most affected stretch of coastline is between Godrevy Point and Towan Head, with results diminishing beyond these points. Waves approaching the shoreline from directions between 3301 and 301 will produce the largest effects, while wave directions between 901 and 2401 will produce negligible effects.
There is little cause for concern that effects introduced by the Wave Hub will be felt by shoreline users of the sea. Acknowledgements The second author is funded by the CSM Trust. The authors are also grateful to Surfers Against Sewage, Regen SW and OceanProspect Ltd for useful comments on the draft manuscript.
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