Modelling Wave Energy Resources for UK’s

Southwest Coast A. Rute Bento

#1, Paulo Martinho

#2, C. Guedes Soares

#3

# Centre for Marine Technology and Engineering

(CENTEC), Technical University of Lisbon,

Instituto Superior Técnico, 1049-001 Lisboa,

Portugal 1 rute.bento@mar.ist.utl.pt

2 paulo.martinho@mar.ist.utl.pt

3 guedess@mar.ist.utl.pt

Abstract - In the present study, a wave prediction system

based on two state-of-the-art spectral models, WAVEWATCH

III ™ and SWAN, was implemented in order to evaluate UK’s

wave conditions and to assess potential wave energy extraction.

The WWIII is used for wave generation and coupled with SWAN,

which is used for wave transformation in coastal areas. Wind

fields for model input were taken from NCEP’s Reanalysis 2,

with time steps of 6 hours. Wave parameters are obtained for

sites close to the coast and in particular for two tests sites: the

site off Cornwall (Wave Hub test site) and the site off the

Pembrokeshire Coast. Validation tests are carried out with buoy

data from the British Oceanographic Data Centre so that the

model's performance can be evaluated. The time period

considered is April and May, 1977.

Regarding the energetic assessment, a case study is

considered and an analysis is done for the energy transport per

unit of wave front and its theoretical values of wave power.

This work is developed in the framework of a European

project with intend to provide resource information to the

marine renewable energy sector.

Keywords— Renewable Energy, Wave Power, Spectral Models,

UK Nearshore, Wave Hub, Pembrokshire

I. INTRODUCTION

The wave energy is the most eye-catching form of ocean

energy, possibly because of its destructive effect. Wave energy

results from the winds as they blow across the oceans and

transfer energy to its surface. Once created, waves can travel

long distances with little energy loss. The power in a wave is

proportional to the square of the amplitude and to the period

of motion, so waves with periods around 7-10s and amplitudes

of 2m have energy fluxes commonly averaging between 40

and 70 kW per m width of oncoming wave. Nearer the

coastline the average energy decreases due to interaction with

the bottom, but this can be compensated by natural

phenomena such as refraction or reflection, leading to energy

concentrating areas known as “hot spots”. The long term

annual wave power level increases from about 25 kW/m off

the southernmost part of Europe’s Atlantic coastline (Canary

Islands) up to 75 kW/m off Ireland and Scotland. When

moving further north it decreases to 30 kW/m off the northern

part of the Norwegian coast (e.g. Fig. 1). Total wave energy

resource for Europe is estimated to be around 320 GW.

Fig.1 European Wave Energy Atlas, Average Theoretical Wave Power (kW)

Persistent efforts in R&D and the experience accumulated

during the past years have constantly improved the

performance of wave power techniques and have led today to

bringing wave energy closer to commercial exploitation than

ever before [1]. In the last years, most of the R&D activity in

wave energy has been taking place in Europe, largely due to

the financial support and coordination provided by the

European Commission and positive attitude adopted by some

European national governments. In general, the development

from concept to commercial stage has been found to be

difficult and slow. The wave energy absorption is a

theoretically difficult hydrodynamic process, in which

relatively complex diffraction and radiation wave phenomena

take place. This explains why a large part of the work on wave

energy published in the second half of the 1970s was on

theoretical hydrodynamics. The possibility of converting wave

energy into usable energy has also inspired numerous

inventors, more than on thousand patents has been registered

by 1980 and the number has been increasing since then [2].

978-1-61284-4577-0088-0/11/$26.00 ©2011 IEEE

Places where full-scale or intermediate sized wave energy

converters can be tested in real conditions at sea have been

specially developed during the past years. They consist of sea

areas exposed to waves and other processes, fitted with an

electrical connection to the grid, various environmental

sensors and other logistics such as sea bottom mooring and

supply vessels. These full-scale experimental facilities allow

for better understanding of the wave energy device’s response

and energy conversion and production. Among the dedicated

places are EMEC in Scotland, the “Wave Hub” off north

western coast of Cornwall and wave dragon test site off

Pembrokeshire, the SEM-REV under development in South

Brittany in France [3] and the Portuguese Pilot Zone in the

west coast of Portugal [4].

Wave energy is abundant and the amount of energy varies

from site-to-site and from day-to-day, depending on the

location and weather conditions. A general idea about the

existing wave energy conditions offshore or nearshore can be

given using real data, but there are some restrictions due to the

fact that the time period of measurements may be limited, so

the interest is to use numerical models which are able to

predict the wave characteristics in various locations for

whatever period of time. Therefore, characterization of the

wave climate is a basic prerequisite for the strategic planning

of wave energy utilization and for the design of wave energy

devices. This evaluation has been done before for other

purposes, namely navigation, and harbor, coastal and offshore

engineering. A 44-year wave hindcast for the North East

Atlantic European coast has been performed by Pilar et al. [5],

within the HIPOCAS project [6]. The hindcast wave model

used was WAM modified for two-way nesting. The output

parameters were significant wave height, wave direction,

mean and peak period, wind speed and direction, Hs for wind

sea, direction of wind sea, Tm for wind sea, Hs for swell,

direction for swell and Tm for swell. In order to complement

this study, another developed by Rusu et al. [7] was

preformed, which couples WAM for deep water conditions

and SWAN [8] for nearshore results. A regional

meteorological model was also used in the coastal area and it

was found that the skill of the model was improved with the

finer grid wind fields [9]. Afterwards, a study has been carried

out regarding wave energy assessment in relation with wave

conditions. This system coupling WAM and SWAN was used

and validated by Rusu and Guedes Soares [10], with the aim

of demonstrating the effectiveness of using a wave prediction

system for assessing the spatial distribution patterns of the

wave energy in the Portuguese nearshore.

In comparison with the referred studies, in this work the

WAVEWATCH III [11] model has been coupled with the

SWAN model, as an alternative for WAM. The goal is to do a

similar study as the one done for the HIPOCAS project [6] but

also with nearshore wave energy data as output.

The area chosen for this study is the Southwest part of

UK. UK has one of the highest wave power levels in Europe,

as the large fetch of wind blows across the ocean from

America. Studying the wave climate at key areas around the

UK, the accessible resource in deep water was estimated to be

600-700 TWh/year and that for the nearshore at 100 – 140

TWh/year. Several “hot spots” were identified along the

coastline, where wave energy was concentrated [3]. Its

potential wave power is illustrated in Figure 2.

Fig.2 Southwest UK Theoretical Wave Power (kW/m)

Two test sites will be analyzed: the site off Cornwall

(Wave Hub test site) and the site off the Pembrokeshire Coast.

The Wave Hub Project plans to develop a 20 MW grid

connected infrastructure for the demonstration of small arrays

of pre-commercial wave devices, some 10 miles off the

northern coast of Cornwall (e.g. Fig 3). Along with the wave

resource, a significant driver for the project was the spare grid

capacity currently available within the SW transmission

system along with a ready made and direct link into the grid

provided by a sub station at the coastal town of Hayle [12].

Fig.3 The area proposed for the Wave Hub location, off the north coast of

Cornwall.

In the waters around Wales, almost the entire

commercially exploitable wave energy resource lies off the

Pembrokeshire, therefore, a deployment of a Wave Dragon

has been proposed (e.g. Fig.4). The project is for a 4-7MW

demonstrator and a larger wave array is planned for

deployment in several years time [13, 14].

Fig.4 The location proposed for the Wave Dragon deployment, off the

Pembrokeshire coast.

II. DESCRIPTION OF THE WAVE HINDCAST SYSTEM

WAVEWATCH III ™ [11,15] and SWAN [8] are a full-

spectral third generation models. WWIII has been developed

at the Marine Modeling and Analysis Branch (MMAB) of the

Environmental Modeling Center (EMC) of the National

Centers for Environmental Prediction (NCEP) and SWAN

(Simulating Waves Nearshore) was developed at Delft

University of Technology. Both are widely used and have

been validated in a wide range of situations. These models are

governed by the same principle, where the evolution of the

wave spectrum in space and time is described by conservation

of action density being balanced by source terms representing

generation, dissipation, and wave-wave interaction processes.

σ

S

Dt

DN= (1)

The action density (N), is the energy density (E) divided

by the relative frequency ( ).

This formula can be written in a transport equation form,

or in the conservation form. The conservation form is valid for

the vector wavenumber spectrum N(k,x,t) only, whereas valid

equations of the latter form can be derived for arbitrary

spectral formulations and the corresponding jacobian

transformation is well behaved [16].

Balance equation for the spectrum N(k, ;x,t) used in the

SWAN is given as:

σ

θθ

σσ

SNNNy

yNx

xt

N=

∂

∂+

∂

∂+

∂

∂+

∂

∂+

∂

∂ (2)

The rate of change of N in time is given by the first term

of (2), 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, as

expressed in equation (3).

...ln ++++= dsnlin SSSSS (3)

WWIII tends to be more efficient at global scales, whereas

SWAN offers advantages at smaller scales and for shallow

water processes. Recent developments in SWAN allow it to be

used quite successfully for sub oceanic scales.

The wave hindcast system implemented uses the WWIII

model for wave generation, covering almost the entire North

Atlantic basin, as illustrated in Figure 5, whereas SWAN’s

domain covers UK’s southwest coastal environment and

connects the large scale to the coastal simulations.

WWIII is used for wave generation, covering almost the

entire North Atlantic basin,. Its outputs are then used as

boundary conditions for SWAN that will then simulate wave

conditions for the coastal environment.

Fig.5 Implementation area for WAVEWATCHIII

Bathymetry from NOAA’s GEODAS database and wind

fields taken from ECMWF’s ERA-40 data set, with time steps

of 6 hours (4x daily data), where implemented in WWIII . The

results are generated with a time step of 3 hours. Afterwards,

WWIII outputs are used as boundary conditions for SWAN.

For the SWAN runs, the wind fields considered are the same

as in WWIII, but the bathymetries were taken from GEBCO’s

database. The characteristic for the computational grids, for

both WWIII and SWAN domains, are displayed in Table I.

TABLE I

COMPUTATIONAL GRIDS FOR THE WAVE HINDCAST SYSTEM

Figure 6 illustrates the domains specified for the SWAN

model.

Fig.6 Bathymetry of Southwest UK. Nesting areas in black: Pembrokeshire

(North) and Cornwall (South)

III. VALIDATION TESTS IN THE TIME DOMAIN

Buoy data from the British Oceanographic Data Centre

(BODC) were used. Their location is specified in Table II and

illustrated in Figure 7.

Fig.7 Location of the offshore and nearshore buoys

TABLE II

COORDINATES AND DEPTH OF THE BUOYS CONSIDERED

Coordinates Depth

Buoy 1 (Offshore)

50.67º N,7.5º W 107 m

Buoy 2

(Nearshore) 50.07º N, 6.07º W 61 m

Comparisons in the time domain were carried out for the

simulations performed against the in situ measurements. For

these validations, the time period considered was from

1977/04/4 at 00h to 1977/05/31 at 12h. The time resolution in

question was of 3h for both buoys. Notice that some data from

this time period may not be included due to buoy failure.

Time series for Significant Wave Height (Hs) can be seen

in Figures 8 and 9. Figures 10 and 11 show the time series for

Mean Wave Period (Tm). Each compares the buoys 1 and 2

results with SWAN’s output.

For the analyses of the significant wave height, scatter

plots are presented in the Figures 12 and 13, for the two buoy

locations.

Fig.8 Hs time series of Buoy 1 vs SWAN results.

Fig.9 Hs time series of Buoy 2 vs SWAN results.

Limits

Latitude Longitude Resolution

North Atlantic

(WWIII) (15ºN-72ºN) (66ºW-7ºE) 1º x 1º

Southwest UK (SWAN)

(49ºN-53ºN) (8ºW-3ºW) 3’ x 6’

Cornwall (SWAN)

(50.15ºN-50.7ºN) (5.7ºW-5ºW) 0.5’ x 0.5’

Pembrokeshire (SWAN)

(51.5ºN-52ºN) (5.7ºW-5ºW) 0.5’ x 0.5’

Fig.10 Hs time series of Buoy 1 vs SWAN results.

Fig.11 Hs time series of Buoy 1 vs SWAN results

Fig.12 Hs scatter plot for buoy 1

Fig.13 Hs scatter plot for buoy 2

As can be seen in the time series presented for buoys 1

and 2, Hs have the same behaviour as the buoys, keeping track

of the various oscillations. In terms of magnitude, model

results for buoy 2 are better than for buoy 1, this can be a

consequence of the difference of depths between each location.

For Tm, SWAN’s outcome was not as good as desired,

especially for the offshore location.

Analysing the scatter plots, it can be seen that most of

SWAN results are below the observations line, which means

that the model underestimates the observations.

To better understand the performance of the model, a

statistical evaluation was made. The computed statistics were

the average values of measurements (Bm) and simulations

(Sm), the bias, root mean square error (RMSE), scatter index

(SI) and Pearson’s Correlation Coefficient (r) and can be

expressed by the relationships:

n

X

Bm

n

i

i

== 1 (4)

n

Y

Sm

n

i

i

== 1 (5)

n

YX

Bias

n

i

ii

=

−

= 1

)(

(6)

n

YX

RMSE

n

i

ii

=

−

= 1

2)(

(7)

X

RMSESI ~= (8)

= =

=

−−

−−

=n

i

n

i

ii

n

i

ii

YYXX

YYXX

r

1 1

22

1

)~

()~

(

)~

)(~

(

(9)

Here iX represent the measured values, iY the simulated

values and n the number of observations. The results are

shown in Table III.

TABLE III

STATISTICAL RESULTS FOR HS AND TM

Significant Wave Height

Bm Sm Bias RMSE SI r

Buoy 1

(n=370) 1.768 1.020 0.748 0.902 0.510 0.886

Buoy 2

(n=402) 1.848 1.556 0.292 0.587 0.318 0.793

Mean Wave Period

Buoy 1

(n=371) 7.115 3.042 4.073 4.225 0.594 0.306

Buoy 2

(n=402) 6.361 3.789 2.572 2.761 0.436 0.498

Some comments can be made at this point relative to the

statistical results.

For Hs, in terms of RMSE, the model results are 0.902 for

the offshore location and 0.587 for the nearshore site. Both

correlation coefficients are over 0.75, which shows that the values are well correlated. The Bias shows that the model

mostly underestimates buoy values, confirming what was said

when analysing the scatter plots.

Comparing results between locations, depth can be

recognized has an influence in the ability of the model to

predict wave conditions with minor error. In terms of Tm the results where not as good as for Hs,

but however this is typical of period predictions. It can be

noticed that the model gave worst results for buoy 1, as it

happened for significant wave height, which is located where

the waters are deeper.

IV. WAVE ENERGYASSESSEMENT

Energy transport per unit of wave front (W/m) can be

obtained as an output of the SWAN model. It can be

expressed by the following formula:

( )= θσθσρ ddEcgP xx , (10)

( )= θσθσρ ddEcgP yy , (11)

Here x, y are the problem coordinate system and xc ,

yc are the propagation velocities of wave energy in the

geographical space defined as:

Ucccdt

xdgyx +== ),( (12)

Wave power can afterwards be calculated using the

formula :

22yx PPP += (13)

A case study was considered and analyzed for both wave

energy test sites: Cornwall and Pembrokeshire. The date and

time chosen were 2010/04/22, at 18h, where one of the highest

simulated values for Hs was encountered.

Fig.14 Hs spatial distribution. In the background significant wave height scalar fields and in foreground wave vectors (Cornwall).

Fig.15 Computed Wave power (W/m). In background wave power scalar

fields and in foreground energy transport vectors (Cornwall).

Fig.16 Hs spatial distribution. In the background significant wave height

scalar fields and in foreground wave vectors (Pembrokshire).

Fig.17 Computed Wave power (W/m). In background wave power scalar

fields and in foreground energy transport vectors (Pembrokeshire).

In this case study, waves are coming from SW. In

Cornwall’s case, the peninsula causes wave refraction and the

wave direction changes almost do 270º near coast. At the

Wave Hub location it can be seen that significant wave height

is between 2.5 and 3 m (e.g. Fig 14). Theoretical results show

that with a significant wave height of around 2.5 m, wave

power can measure up to 30 kW/m (e.g. Fig 15). For

Pembrokeshire, the incoming waves have smaller intensity

and, therefore, wave power is lower. In the location planned

for the deployment of the wave dragon, wave power reaches

only 14 kW/m.

V. CONCLUSIONS

Two state-of-the-art spectral models, WWIII and SWAN,

were used to create a wave prediction system to evaluate wave

conditions on UK’s southwest coast.

Knowing that wave power is proportional to the

significant wave height and to the period of motion, by

simulating these parameters, the ability of the model to

simulate wave energy was tested. Validation analysis of the

computed results against buoy measurements gave a

perspective on the accuracy of the numerical wave models and

theoretical values for the energy transport components were

obtained, which gave the absolute values of the energy

transport, denoted also as wave power.

Overall the wave prediction system gave reasonable

results when comparing significant wave height with the buoy

data, showing better accuracy for shallow waters. For

significant wave height the outcome was better than for the

mean wave period, as was expected.

Analysing the results from the two nested areas, taking

into consideration know theoretical mean values for wave

power in that areas and the performance of the wave

prediction system implemented in this work, the results

obtained can be acknowledged as being near to the real

potential of that areas.

ACKNOWLEDGMENT

This work has been performed within the project

MAREN – Marine Renewable Energy, Energy Extraction and

Hydro-environmental Sustainability, which is partially funded

by the Atlantic Area Programme.

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