UNIVERSITY OF GOTHENBURG
Department of Earth Sciences
Geovetarcentrum/Earth Science Centre
Mapping Wave Energy
Resources outside
the Norwegian Coast
Adam Nord
ISSN 1400-3821
Mailing address
Geovetarcentrum
S 405 30 Göteborg
Address
Geovetarcentrum
Guldhedsgatan 5A
B780
Bachelor of Science thesis
Göteborg 2013
Telephone
031-786 19 56
Telefax
031-786 19 86
Geovetarcentrum
Göteborg University
S-405 30 Göteborg
SWEDEN
Abstract
The interest in wave energy as a renewable energy resource has increased in the last few
years. This paper primarily describes the wave energy resources for areas outside the
Norwegian coast as the main area of interest. However, the Swedish west coast, the Baltic Sea
and areas in the North Atlantic including the North Sea and the coast of the United Kingdom
are included as well. This study is done by using NORA (Norwegian reanalysis) data and the
transport of wave energy is calculated by using significant wave height and significant period.
The maximum available wave energy resources at the Norwegian coast vary from 3050kW/m for off-shore points and 10-30kW/m for near-shore. For the Baltic Sea the energy
resources are in the range of 7-9kW/m located between Gotland and the Baltic states. Outside
the Swedish west coast this figure is 8-10 kW/m.
ii
Contents
1. Introduction ............................................................................................................................ 1
2. Theory and Method ................................................................................................................ 2
2.1 The NORA archive........................................................................................................... 2
2.2 Deep water waves ............................................................................................................. 2
2.3 Wave spectrum ................................................................................................................. 3
2.3.1 Significant wave height ............................................................................................. 3
2.3.2 Energy and Significant periods ................................................................................. 4
2.3.3 Wave energy flux ...................................................................................................... 6
3. Results .................................................................................................................................... 7
3.1 Significant wave height .................................................................................................... 7
3.2 Energy period ................................................................................................................... 9
3.3 Wave energy ..................................................................................................................... 9
4. Summary and Discussion ..................................................................................................... 15
5. Acknowledgment ................................................................................................................. 16
References ................................................................................................................................ 17
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1. Introduction
Renewable energy is an important political question today and may become significant for our
world’s survival. Ocean energy is one possible part of this. The ocean covers about 70% of
the earth; the water is in constant movement and can be used as an energy source. Oceans
contain a vast amount of energy in different forms (Beels et al, 2007; Bernhoff et al, 2006),
however we will focus on wave energy only. Wave energy is a renewable energy source of
high energy density and the global wave power potential is estimated to be in the order of 1
TW (Leijon et al, 2008). The amount of wave energy is an important factor when determining
the location of wave energy conversion i.e. equipment used to extract wave energy. However,
another factor is the survivability of the conversion tool. If the wave climate is too severe, the
waves might destroy the equipment, therefore it is not always better to have larger waves even
if they contain more energy.
In this study the aim is to investigate the wave energy resource using NORA10 (Norwegian
Reanalysis) data that covers the years 1958 – 2010 with a resolution of 10 kilometers. Our
major point of interest is outside the coast of Norway (figure 1). However, the Baltic Sea, the
Swedish west coast and areas in the North Atlantic, including the North Sea and the coast of
the United Kingdom, are included as well. Wave energy should in principle be calculated
from integration over the wave spectrum. However, in this study we will examine if it is
possible to base the analysis on significant wave height and significant wave period as these
data is a standard output from wave models.
Figure 1. Depth (the maximum depth of 200 meters is selected since in practice it is the maximum depth that
influences the wave fields) and position of points outside the Norwegian coast. Special attention will be paid to
the four points which are two near-shore points (station 1 and 3) and two off-shore points (station 2 and 4)
1
2. Theory and Method
2.1 The NORA archive
During this study we use NORA10 (Norwegian Reanalysis) data that cover the years 19582010. The atmospheric forcing is acquired from the 10 kilometers High-Resolution Limited
Area Model (HIRLAM10) (Furevik et al, 2012). Interpolation of ERA-40 dataset or the ice
data archive at the Norwegian Meteorological Institute is used to determine sea surface
temperature. Also wind velocity, temperature, specific humidity and water for the boundary
zones are relaxed towards ERA-40 (Aarnes et al, 2012).
In NORA10 wave simulations are achieved by using a modified version of wave modeling
(WAM) cycle 4 model (Komen et al, 1996). WAM cycle 4 is the third generation wave model
which integrates the basic spectral transport equation without any presumptions on the shape
of the wave spectrum, also it is tuned for infinite depth, i.e. deep water waves (see below)
(Hasselmann, 1988). This setup of WAM run on the same grid as the HIRLAM10 and is
forced with ERA-40 wind fields (Reistad et al, 2011)
It is important to note that the ERA-40 dataset only spans the period September 1957 to
August 2002, however NORA10 is being extended by the use of operational analyses for the
European Centre for Medium-Range Weather Forecasts (ECMWF) as boundary and initial
conditions (Aarnes et al, 2012; Reistad et al, 2011) .
This data-set produce a 3-hourly wave field with a resolution of 10 kilometers and covers the
northeast Atlantic, including the North Sea, the Norwegian Sea and the Barents Sea (Aarnes
et al, 2012). WAM produces a two dimensional ocean wave spectrum (Hasselmann, 1988;
Semedo et al, 2011). From the dataset, the significant wave height , and significant
period (see below for definitions) are available. Also, full spectrum is accessible at some
prescribed locations.
2.2 Deep water waves
In this study we assume deep water waves. This approximation is valid if the water depth, d,
is much greater than the wave length,  i.e.
(Stewart, 2008). For deep water wave
approximation the dispersion relation becomes:
where
is the angular frequency and is the wave period, is gravitational
acceleration and
is the wave number. Using equation (1) we find the wave speed
2
Since the significant wave period is available from the NORA archive the angular
frequency can be rewritten as the wave period. Thus, the wave speed becomes:
For wave energy the group velocity is of greater significance. It can be described as the speed
at which a group of waves travel, but it is also the propagation velocity of wave energy
(Stewart, 2008). For deep water waves the approximation of the group velocity is:
2.3 Wave spectrum
A wave spectrum is used to describe the surface variations of the ocean and provides us with
the distribution of wave energy for different frequencies (Stewart, 2008). The concept of the
wave spectrum is based on Fourier transform.
Wave models contain large amounts of information which can be difficult to store and one
needs to condense the data for long model runs. Often the condensed data is in the form of an
integration of the full wave spectrum. The integrated quantities are found by integration over
the wave spectrum:
∫
where
is called the nth-order moment,
is the frequency and
is the wave spectrum.
In a wave model that is based on finite frequency, the integral in equation (5) is in the form of
a summation i.e.
∑
Also notice that the variance of the surface elevation is:
∫
2.3.1 Significant wave height
The significant wave height is defined from the zero-order moment of the wave spectrum:
√
3
2.3.2 Energy and Significant periods
The energy period is defined as (Laing et al, 1998):
The energy period is used during wave energy calculations since
is proportional to the
energy flux. However, from the NORA archive the significant period is available and it is
defined as:
√
It should be noted that
. However, to determine how
other we consider two model wave spectra.
and
relate to each
The Pierson-Moskowitz spectrum is denoted such as:
[
( ) ]
where
,
of 19.5 meter above the sea.(Stewart, 2008)
and
is the wind speed at a height
A Pierson-Moskowitz spectrum is presented in figure 2. We see that the spectral density is
higher at low frequencies and thereby for faster waves.
4
Figure 2. Typical wave spectrum, here a Pierson-Moskowitz spectrum for different wind speed varying from 10
to 22 m/s
The Joint North Sea Wave Observation Project (JONSWAP) spectrum is denoted as
(Stewart, 2008):
[
where
[
( ) ]
(
)
]
is the peak frequency, the peak enhancement factor
and
{
By using these two spectra and obtaining the significant period and the energy period from the
integral and summation (equations 5 and 6) a ratio between
was found to be
approximately 1.21 for wind speeds above roughly 3 m/s for both JONSWAP and PiersonMoskowitz-spectra (figure 3)
5
Figure 3. Ratio between
varying from 1 to 25 m/s.
and
for JONWSAP and Pierson-Moskowitz spectrum at different wind speed
Thereby we obtained a relationship between significant period and energy period such as:
√
Thus, we can replace with
output from the NORA archive.
for wave energy calculations and then use the standard
2.3.3 Wave energy flux
The transport of wave energy is defined as:
where
is the total energy given by:
In a spectral formulation this can be written as:
∫
6
Using equation (8) and equation (9); the wave energy flux can be calculated from the
energy period and significant wave height i.e.
By using the relationship between
energy transport to:
and
(equation 13) we approximate the
Transport of wave energy will be estimated by equation (18) and the use of the
significant wave height and the significant period from the NORA archive.
3. Results
In the following section, many results are illustrated as seasonal averages; this is
accomplished by a mean value of months for the four seasons respectively. This
approximation is done since mean values of months are easier available and it should result in
a fairly good estimate. For example, the winter average would be calculated as:
where
and
contain values for each month respectively.
3.1 Significant wave height
Since the wave height plays a crucial role when discussing wave power, not just for the wave
energy itself but also for the survivability of equipment used when extracting energy; the
significant wave height is illustrated in figure 4 which includes one plot of the entire area
(upper four panels) and one plot focusing on the area of interest (lower four panels).
As seen in figure 4 the wave height is highest in the North Atlantic outside the coast of the
United Kingdom. Even though the wave height declines as we go north there are large wave
heights outside the Norwegian coast as well. During the winter they vary in the range of 3-4
meter while during the summer they are significantly lower and vary in the range of 1-2
meters. The sheltering effects of the United Kingdom, the Shetland Islands and even the Faroe
Islands have an effect on the spreading and thereby explaining declination of wave height.
The change in wave height is more significant when we get closer to the coast; this probably
depends on the small fetch length when the wind blows out towards the sea.
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Figure 4. Significant wave height (m) for the different seasons. The four upper panels illustrate the whole area
while the lower four panels are close-ups on our points of interest. Black dots are the stations shown in figure 1.
8
3.2 Energy period
The wave energy period is obtained by using the significant wave period from the NORA
archive and the relationship between the significant period and the energy period (equation
13). Wave energy period is illustrated in figure 5 which includes one plot of the entire area
(upper four panels) and one plot focusing on the area of interest (lower four panels).
As suspected, figure 5 shows that the energy period follow same pattern as the
significant wave height. It is longest during winter when there are high waves and
shortest during summer. Also the longest wave energy periods are found in the North
Atlantic outside the coast of the United Kingdom where it can reach 11 seconds.
Outside the Norwegian coast the wave energy period varies from 8-9 seconds during
the winter and 6-7 seconds during the summer.
3.3 Wave energy
All figures and values of wave energy flux presented in this section are the energy resources
that exist, not the possible energy that can be extracted. That value would be significantly
lower because the efficiency of a wave energy converter is less than 100 %. Also, the
direction of the wave energy flux will influence the amount of energy that can be extracted.
Here, the directions are not illustrated or taken into account.
The wave energy transport is calculated from equation (18) using NORA data and is
illustrated as a spatial distribution. Figure 6 presents the wave energy during the four seasons.
The four upper panels illustrates the whole area while the lower four panels are close-ups on
our points of interest. Note that the maximum scale bar value (100 kW/m) is not the
maximum value in reality. Outside the coast of the United Kingdom a more exact number is
120 kW/m, the cutoff is done because our point of interest is not the United Kingdom but the
Norwegian coast.
Since wave energy is extracted during the whole year an annual mean value of wave energy
estimation is of interest. This is presented in figure 7 which includes one plot of the entire
area and one plot focusing on the area of interest.
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Figure 5. Energy period (s) for the four different seasons. The four upper panels illustrates the whole area while
the lower four panels are close-ups on our points of interest. Black dots are the stations shown in figure 1.
10
Figure 6. Transport of wave energy (kW/m) for the different seasons. The four upper panels illustrates the whole
area while the lower four panels are close-ups on our points of interest. Black dots are the stations shown in
figure 1.
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Figure 7. Annual mean value of wave energy flux (kW/m). Left panel illustrates the whole area while the right
panel is a close-up on our points of interest. Black dots are the stations shown in figure 1. Note the different
scale from previous figures.
As suspected, the wave energy flux follows the same pattern as the wave height and the
energy period. The maximum amount of energy flux is found in the North Atlantic during
winter. Also, as we can see in the lower four panels on figure 6, the transport of wave energy
have a significant variation during seasons. The sheltering effects of the United Kingdom, the
Shetland Islands and even the Faroe Islands are notable (upper four panels in figure 6 and left
panel in figure 7). The sheltering effect has a slight impact on the energy conditions at the
Norwegian coast. However, its impact is strongest at northern North Sea and southern
Norwegian Sea.
The annual mean of wave energy is, as suspected, highest in the North Atlantic outside the
coast of the United Kingdom while it declines as we get closer to the Norwegian coast.
However, the wave energy outside the coast of Norway is still substantial, varying from 3050kW/m for off-shore points and 20-40kW/m for near-shore.
To determine the wave energy at our selected points, a more specific analysis is illustrated in
figure 8 where the probability of different values of wave energy is illustrated. This also
follows the same pattern as describe above. During the summer there is a high probability to
get 20kW/m but almost zero chance to get 40kW/m. On the other hand, during winter there is
still a high probability to find locations with 80kW/m. Also note the more significant
difference on the off-shore (2, 4) and near-shore (1, 3) points.
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Figure 8. Probability for different values of wave energy flux (kW/m) for all seasons. Station 2 and 4
are off-shore points 1 and 3 are located close to the coast (figure 1).
During this study the main focus is outside the coast of Norway. However, the Swedish west
coast and the Baltic Sea are also of interest though the resolution of the data set used (see
section 2.1) is not enough to give satisfying results but it can still be used as an
approximation. Figure 9 illustrates wave energy for the Swedish west coast and the Baltic Sea
for each season while figure 10 represents the annual mean of wave energy. Note the different
scale from previous figures.
The wave energy resources in the Baltic Sea and outside the Swedish west coast are
significantly lower than outside the coast of Norway. Still, it follows the same pattern and
reaches its maximum value during winter even though a large area can be covered with ice. In
the Baltic Sea, the annual wave energy resources reach the maximum value of 7-9kW/m
between Gotland and the Baltic States, probably because of the long fetch length. The highest
energy outside the Swedish west coast is found in Skagerrak between Kungshamn and
Strömstad and varies from 8-10 kW/m. Also notice the low wave energy in the Kattegat
because of the sheltering effects of Denmark.
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Figure 9. Wave energy resources (kW/m) for the Swedish west coast and the Baltic Sea during the different
seasons. Note the different scale from previous figures.
Figure 10. Annual mean of wave energy resources (kW/m) for the Swedish west coast and the Baltic Sea.
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4. Summary and Discussion
During this study we found that the available annual mean of wave energy resources outside
the Norwegian coast vary from 30-50kW/m for off-shore points with higher energy values at
the southern locations and 10-30kW/m at near-shore stations where the lowest is located far
north. For the Baltic Sea the wave energy resources are in the range of 7-9kW/m located
between Gotland and the Baltic states. Outside the Swedish west coast these figures are 8-10
kW/m. Common for all studied areas are, not surprisingly, that the wave energy resources are
highest during the winter and in the open ocean while it is lowest during summer.
The largest amount of wave energy is found outside the coast of United Kingdom where the
annual mean value varies from 50-70 kW/m (figure 6 and 7). This value first appeared too
large to seem reasonable. However, these numbers are similar to that found in other studies
(Semedo et al, 2011).
The wave energy transport outside the Swedish west coast is almost two times higher than
that found in other studies (Waters et al, 2009). However, they use other data for a shorter
time period but the differences are significant. This may be because the resolution for the
NORA-archive is not adapted to the Swedish west coast and another study with higher
resolution might be needed.
The assumption to calculate the wave energy transport from the significant wave height and
significant period using the obtained relation (
gives reasonable results and
therefore seems to be a fairly good approximation. The obtained relation is an estimation but
it is similar to that found in other studies (Beels et al, 2007). This relation could also be
verified by using the available spectral points from the NORA archive. However, this is out of
scope.
The efficiency of wave energy converter is less than 100% therefore not all calculated energy
can be used. With today’s technology we can convert more energy at low energy locations.
For wave energy range from 20-30kW/m the global technical resources i.e. the energy that
can be extracted and used as a resource, are estimated to range from 100-500 TWh/year (~1050 GW) and for lower power range from 10-20 kW/m it is estimated to range from 2001000TWh/year (~20-100 GW) (Beels et al, 2007; Bernhoff et al, 2006).
It is likely that the other factors that might need to be taken into account are the wave length
and the wave height. Different wave lengths may cause the efficiency to change. For example,
if the wave length is much longer than the equipment used to convert the energy we speculate
that it would be more difficult to extract energy than if the equipment is longer than the
average wave length. This also depends on method used for extracting the energy. For the
survivability of the equipment; large wave heights are of importance since too large waves
could destroy it.
As an example, during these 52 years as the dataset covers, waves with heights above 10
meters has occurred 225 times at station 2 during the three winter months (December, January
and February). This tells us that waves above 10 meters happen approximately 4 times a year
on average and therefore the used equipment must be able to withstand such high waves.
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5. Acknowledgment
I would like to thank Norwegian Meteorological Institute for providing access to the NORA
archive. I would also like to thank my supervisor Göran Broström for helpful guidance, great
matlab tricks and support during this project. Finally I would like to thank my girlfriend Sofia
Johansson for patience and understanding.
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