Renewable Energy 44 (2012) 296e304
Contents lists available at SciVerse ScienceDirect
Renewable Energy
journal homepage: www.elsevier.com/locate/renene
Quantifying the global wave power resource
Kester Gunn*, Clym Stock-Williams
E.ON New Build & Technology, Technology Centre, Ratcliffe-on-Soar, Nottingham, England, UK
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 19 August 2011
Accepted 26 January 2012
Available online 23 February 2012
Justifying continued development and large-scale deployment of Wave Energy Converters (WECs)
requires quantification of the potential resource. Currently, estimates are available for individual countries or, at low accuracy, for global resource. Additionally, existing estimates do not provide insight into
potential future markets, i.e. the location of the resource.
Here, NOAA WaveWatch III data are analysed for a 6-year period to calculate wave energy potential.
The global market is then quantified by calculating the energy flux across a line 30 nautical miles
offshore. Results are presented by country, continent, hemisphere and for the globe.
Confidence values are also presented in the form of 95% confidence intervals. These limits provide
insight into the uncertainty associated with the length of dataset used and the variability of the resource.
This enables direct comparison with other resource assessment studies, whether using numerical model
or measured data. An extensive survey of previous global and regional resource estimates is also conducted, in order to compare both results and methods.
Supplementing this, extractable resource is estimated by considering the deployment of an illustrative
WEC (Pelamis P2). The global wave power resource is 2.11 0.05 TW, of which 4.6% is extractable with
the chosen WEC configuration.
Ó 2012 Published by Elsevier Ltd.
Keywords:
Wave
Wave energy
Wave power
Wave resource
Resource assessment
Site finding
1. Introduction
Interest in the generation of electricity from waves has been
sustained in the past decade by rising oil prices and the threat of
climate change. From a sector driven mainly by experimentation,
concerted efforts have recently begun to transform it into an
industry, capable of delivering a significant proportion of the
world’s electricity needs. To achieve this, funding is required on
a sustained and substantial basis from governments, venture
capital funds and the energy industry. These bodies require estimates of the long-term potential market for the technology in order
to determine the value of investing in wave energy.
Currently, wave energy is being sold to potential customers on
the basis of wave resource estimates for the world, supplemented by
more detailed studies for particular countries. In general, the world
wave energy resource is quoted to be either “1e10 TW” [40] (or its
equivalent in TWh/year) or “2 TW” [37]. An extensive literature
survey has been required to trace these numbers to their original
sources. Both these figures come from derivations pioneered by
Kinsman [25], who comments openly on the lack of rigour in his
methods, which are essentially inspired guesswork. More details are
* Corresponding author.
E-mail addresses: [email protected]
eon.com (C. Stock-Williams).
(K.
Gunn),
clym.stockwilliams@
0960-1481/$ e see front matter Ó 2012 Published by Elsevier Ltd.
doi:10.1016/j.renene.2012.01.101
given in Section 5, along with comparisons and discussion of later
work presenting global and regional wave power estimates.
The present authors intend to re-establish the economic justification for wave power. A data-based methodology is described and
given with clear discussions of assumptions in Sections 2e3,
enabling the calculation of both mean wave resource and an estimate
of the error on that value. The new figure for global wave resource
presented in Section 4 can therefore be assessed against future
studies which calculate confidence using this methodology, in order
to identify whether the estimates are consistent or in disagreement.
More detailed studies of specific countries (reviewed in Section
5) often consider “theoretical” and “technical” resource. The
intention of this additional calculation is to assess how much of the
total resource is actually extractable, by applying restrictions based
on the contemporary state of Wave Energy Converter (WEC)
technology. This study applies the concept of an illustrative WEC
array, built parallel with the coastlines of the world, to provide an
initial estimate of the proportion of theoretical power which could
be converted into useful electricity.
2. Power estimation
Power estimates were made using outputs from the NOAA
WaveWatch III (WW3) global model [41]. The outputs are provided
K. Gunn, C. Stock-Williams / Renewable Energy 44 (2012) 296e304
by NOAA at a spatial resolution of 30 arc-minutes and a temporal
resolution of 3 h. Spectra are only available for selected geographical
points and so it was necessary to use spectral parameters to quantify
the global wave power resource. The outputs used were: peak
period ðTp Þ; significant wave height ðHs Þ; and mean direction of the
waves ðQm Þ.
2.1. Calculating power density and WEC power
In order to calculate power from these three spectral parameters
it was necessary to assume a dominant spectral shape for the
world’s oceans. The PiersoneMoskowitz (PM) spectrum was
chosen since locations with high wave power (which are of most
interest) will be exposed to long fetch. The spectrum defined
according to the Bretschneider formulation (rather than as a function of wind speed as for PM) was used for this study:
Sðf Þ ¼
A
B
exp
f5
f4
(1)
where
B ¼
5
4Tp4
(2)
A ¼
Hs2
B
4
(3)
The nth spectral moment of the spectrum is defined as:
ZN
mn ¼
f n Sðf Þdf
(4)
0
which, for n 4, can be calculated [42] by:
mn ¼
A n1 n
B4 G 1 4
4
(5)
297
The wave power per unit length of wave crest (“power density”)
can then be calculated:
p ¼
rg 2
m
4p 1
(6)
where the density of water was taken as r ¼ 1025 kg m3 ; and
g ¼ 9:81 ms2 is the acceleration due to gravity.
The power density is converted into a directional power density
vector taking its direction from Qm :
p ¼
p,sin Qm
p,cos Qm
(7)
In addition to the power density, the power output ðJÞ from an
illustrative WEC, the Pelamis P2, was calculated at each point on the
WW3 grid by linearly interpolating the published Pelamis power
matrix [4] to each Tp and Hs value.
2.2. Initial statistical data compression
The method used to calculate the power incident on each land
mass (Section 3) cannot be performed for each 3-h time-step from
the WW3 model due to its computational expense. Therefore, mean
values were calculated for each one-month period: pðy;mÞ and Jðy;mÞ
(where y and m denote the year and month).
Means of longer time periods were subsequently calculated
using the methodology outlined in Section 3.3. Fig. 1 shows the
global distribution of annual mean power density. The arrows on
the plot show the mean best direction (i.e. the direction of the
means of the power density vectors). This demonstrates that the
locations of most interest for wave power are on the west coast of
land masses, as waves flow primarily from west to east. This figure
compares well to those produced by Cornett [13] and Barstow et al.
[7]. Wave power is predominantly found between the 40th and
60th lines of latitude north and south, with a larger proportion in
the southern hemisphere.
An interesting result of applying the WEC power matrix to
calculate J is that the locations of the best extractable resource are
Fig. 1. Annual mean wave power density (colour) and annual mean best direction (/). The land buffers used to quantify the resource are also shown, coloured by continent (see
Section 3). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
298
K. Gunn, C. Stock-Williams / Renewable Energy 44 (2012) 296e304
sometimes not obvious from maps of raw mean power density.
Fig. 2 illustrates this for Hawaii. The annual mean power density
shown in Fig. 2a would suggest that the best locations for the
development of WECs are on the north side of Hawaii. However, the
map of J given in Fig. 2b demonstrates that the optimum location
to deploy the illustrative WEC is likely to be to the south of Hawaii.
Certainly, if a different power matrix (whether from different
control or device design) were chosen, the position of maximum
extraction might well move: this highlights the need to design the
WEC for each wave climate in which it is deployed.
The calculation of the total power flowing onto land masses is
achieved by summing the power density over a “buffer” line offset
from the land.
subsequent islands. For this reason, small islands were largely
excluded from this study.
Second, locations in the Arctic and Antarctic are of no interest
for wave energy extraction, given that deployment in these locations is not feasible and there is little need for electricity. These
locations were therefore also excluded.
Finally, it is necessary to check that no sections of the buffer are
counted twice, due to multiple political claims registered in the
VLIZ database. The most significant example of this is the dispute
between Chile and Peru. Where this is the case, the segment was
assigned to the country with the larger resource (Chile in the above
example) and duplications removed.
Each line segment was additionally assigned to a continent and
a hemisphere to allow power availability to be calculated for these
geographical regions. Fig. 1 shows the land buffer used in this study,
coloured by continent.
3.1. Defining the World’s coastline
3.2. Calculating total power crossing the buffer
Due to the resolution of the WW3 model (300 of arc) the
minimum distance offshore from which data can be used is 30
nautical miles (nm). For this reason, a buffer was created 30 nm
from the land masses given in the Natural Earth 1:50 m coastline
dataset [2].
One aim of this work was the quantification of power for individual countries. This was achieved by cutting the 30 nm buffer into
segments by the Exclusive Economic Zones (EEZs) of each country,
as defined by the VLIZ Maritime Boundaries Geodatabase [5].
Although it would now be possible, using these methods, to
calculate the energy flux across the entirety of the 30 nm buffer,
this would not yield a result of practical use.
First, the use of the entire buffer would result in double counting
of the energy flux. Consider an archipelago of small islands. The
30 nm buffer would extend far past the individual islands, thereby
counting energy that would flow past the islands. This same energy
would then be re-counted as it flowed across the buffer for
The global power density estimates generated from the WW3
data were used to calculate the energy flux over the buffer lines. A
similar approach was used to estimate power extraction if WECs
were to be installed along each buffer.
3. Power quantification
a
3.2.1. Energy flux over a line
Nodes were defined at 1 km intervals along each line segment.
At each of these nodes, the power vector was interpolated from the
WW3 grid using a nearest neighbour lookup. Thus, each node
consisted of:
Nlðy;mÞ ¼
n
plðy;mÞ ; Jlðy;mÞ ; ^sl
o
(8)
where l denotes the lth node on the line and ^sl is a unit vector
tangential to the line at the node. ^sl is defined in a left-handed
(clockwise) sense, such that the land is always to the right of the
line (Fig. 3).
b
Fig. 2. Comparison of annual mean power density and annual mean power extractable by Pelames in the Northeast Pacific Ocean.
K. Gunn, C. Stock-Williams / Renewable Energy 44 (2012) 296e304
299
Fig. 3. Illustration of the calculation of power flowing across the land buffer.
The total line power was then calculated by summing the power
across the line at each node. This flux at each node was calculated
assuming a unidirectional spectrum (the effects of which are
considered in Section 3.2.3).
^ l Þ was generated perpendicular to ^sl (Fig. 3):
A unit vector ðn
^l ¼
n
0
1
1
^sl
0
(9)
and the power across the line was calculated as:
L
X
PLðy;mÞ ¼ 1000,
l ¼ 1;cl >0
^l
plðy;mÞ ,n
^l
plðy;mÞ ,n
cl ¼ cosðqÞ ¼ plðy;mÞ Fig. 4. Comparison of the power flux over a line for different spectral spreading
functions.
(10)
(11)
where the factor of 1000 converts from power density to the total
power across the 1 km of line accounted for by each node. Values
for which cl < 0 were excluded in order that only power flowing
towards the land is counted.
3.2.2. Power from an array of illustrative WECs
In order to calculate the power extracted by the illustrative WEC
(Pelamis) at the line buffer, some further assumptions were
required. First, it was assumed that the direction of the waves could
be neglected, since the Pelamis is designed to align itself with the
direction of highest power. A decision also needed to be taken on
the array layout. Two lines of Pelames spaced at 400 m intervals
was chosen, giving a packing density (D) along the buffer of 5
Pelames per km. The final assumption, which is likely to be valid
given the wide spacing in the array configuration chosen, was that
neighbouring Pelames do not interact to affect each other’s power
absorption.
The extractable power along the line can, therefore, be calculated as:
JLðy;mÞ ¼ D,
L
X
Jlðy;mÞ
(12)
l¼1
Thus, for each line segment there are two monthly time series of
power values (energy flux over the line and the power generated by
the WEC array). These data were then summed to produce monthly
time series for larger regions: i.e. countries, continents, hemispheres and the planet.
3.2.3. Considering the effect of directional spread
It was assumed that the entirety of the power in the spectrum
was flowing in the mean direction. In reality this is unlikely to be
the case. However, directional spread is not available as a spectral
parameter from WW3. It is, therefore, worth examining the effect
that this assumption has had on the power estimates.
Fig. 4 shows three possible methods for representing directional
spectra. First, the method applied here e unidirectional seas e is
shown. This demonstrates that the power flowing across the line
reduces from 100% when it impinges at 0 to the normal, to 0% at
90+ . Outside of this range, power is flowing away from land and
was therefore set to 0. Second, spread seas are illustrated using the
cosine spreading function suggested by Pierson et al. [33] 1:
Sðf ; qÞ ¼ S0 ðf ÞS00 ðqÞ;
S00 ðqÞ ¼ cos2 q
(13)
This shows that, for locations where the wave direction is normal to
the shore, the method used here will overestimate the power by
approximately 15%. Conversely, at locations where the waves travel
along the shore (at the 30 nm buffer), the applied method underestimates by up to 20%. With reference to Fig. 1, it is clear that
predominately the mean best direction is between these extremes.
Thus, the results given in this work are likely to be overestimated by
less than 15%. This is a considerable improvement over the third
option in Fig. 4, illustrating the assumption applied in previous
studies (see Section 5.2.1) of omnidirectional spectra: where
direction is not taken into consideration.
3.3. Calculating long-term statistics
The next stage of resource assessment is to turn the many mean
values for different months obtained above into long-term statistics. The methodology outlined in this and the next sections has
been chosen to be robust. It can be applied equally easily to data
from numerical models or measurements, enabling resource
assessment figures to be directly comparable. There are also some
additional benefits, which are highlighted in the relevant
subsections.
3.3.1. Methodology for assessment of average resource
When conducting a wave resource assessment it is important
that all available valid, consistent wave data are used. Data records
1
This spreading function has been shown to overestimate the energy spread,
thus it is used here as a worst case.
300
K. Gunn, C. Stock-Williams / Renewable Energy 44 (2012) 296e304
often do not exactly span full calendar years; and, particularly in the
case of measured data, particular time periods can be corrupted or
missing. Either of these instances could lead to collateral data loss
in avoiding generating a biased resource estimate.
It is proposed that mean monthly power estimates (P m ) should
be fundamental to resource calculations in order to avoid this
eventuality. All other statistics for longer time periods can therefore
be derived from these by a weighted mean:
P n ¼ Pn
1
n
X
m¼1 dm m ¼ 1
dm P m
(14)
where dm is the number of days in each month (here assigning to
February 28:25).
Essentially, this is an Analysis of Variance approach using the
m
model Py;m ¼ P m þ εm
y . In this model, for each location, εy is an
two did not have high wave power levels, therefore the results
presented here can only be marginally affected by these countries.
This indicates that this requirement is largely met.
Given that the residuals are normally distributed, mutual
independence can be determined from non-correlation. To test this
fourth criterion, therefore, correlation coefficients were calculated
jan
feb
between each εm
y (e.g. the correlation between εy and εy ) for each
country. Each 12 12 symmetric matrix was then reduced to
a single test value by summing the number of pairwise correlation
coefficients which were significantly different from 0 (have a pvalue less than 0.05) and dividing by the total number of pairs
tested (66). On average only 5% of residual pairs were correlated
(and any one country had at most 12% correlated residuals). It can
therefore be assumed that this final criterion is also fulfilled.
array of residuals for month m, e.g. εy ¼ ½ε2005 ; ε2006 ; ε2007 ; ..
For this model to be valid it must satisfy four criteria:
3.3.2. Resource statistics and parameters
The mean power data ðPLðy;mÞ Þ for each month of each year can
now be used to generate the following long-term statistics:
1. The random residuals for each month are normally distributed;
2. The expected value of each month’s random residual is zero;
3. The random residuals for each month all have the same standard deviation (“homoscedasticity”); and
4. The random residuals for each month are mutually independent.
1. the mean power for each month ðP m Þ;
2. the power for other periods (quarters or years) using Eq. (14);
and
3. other statistics used to assess the variation in power over the
annual cycle.
The first criterion can be empirically tested using the data here.
First, the residual values were calculated and then the Lilliefors’ test
was applied since this test accepts small samples. The MATLAB
implementation Lillie test requires two inputs: a vector of εm
y values
for each month and a significance value. A Boolean is returned
indicating whether the values entered are significantly different
from the null hypothesis that the data are normally distributed. Of
the 1416 monthly values tested (12 months for 118 countries) 25
were non-normal to 1% significance. These individual months displaying non-normality of residuals were not concentrated in one
particular country or month: the maximum number of such months
for any one country was 2; and August was the worst offender with
6 instances. This indicates that the first requirement is sufficiently
satisfied to permit the use of the method outlined here.
The second criterion is met since the expected value ðP m Þ is
taken as the mean of the data. Thus, by definition, as the residuals
are normally distributed, the expected values of the residuals will
be zero.
The truth of the third criterion can also be tested using the data
from this study. Heteroscedasticity can be assessed using Cochran’s
test, which can be stated as:
In order to perform calculations for continents, hemispheres
etc., the PLðy;mÞ values were summed first. Mean values and associated standard deviations for each calendar month were then
calculated. This order of calculation is important since, for instance,
adjacent lines forming a single continent’s coastline buffer are
likely to have correlated power values. Although there would be no
impact on mean values, combining standard deviations would
require consideration of cross-correlation.
This process is also applied to WEC power, by substituting
JLðm;yÞ and Jm .
jan
maxðSm Þ
>Cna;k ;
Pk
ðS
Þ
m
m¼1
Sm ¼
vþ1
P
y¼1
Py;m P m
2
jan
jan
jan
(15)
The critical point ðCÞ above which the data exhibit heteroscedasticity depends on the significance level ðaÞ, the number of
degrees of freedom (n, here 11 since there are twelve months in
each year) and the number of variances (k, here 5 since only the
years 2006e2010 with full data were used). Statistics textbooks
recommend taking a very low value of a [22] since abandoning this
model requires that “there should be substantial evidence of
a considerable degree of heteroscedasticity”. Applying a conservative value of a ¼ 0:01 allows the calculation of the critical point
from the inverse F cumulative distribution, giving a value of 0.456.
Applying this to data from the 118 countries included in the study
revealed that only 4 had heteroscedasticity to 1% significance. Of
these, two countries were only just above the limit. The remaining
3.4. Estimating errors
Estimates of mean power are useful, however, point estimates
are best complemented by a discussion of their likely accuracy. This
paper has sampled a model of a stochastic process and therefore
the total accuracy is a combination of:
the natural variability of the process;
the accuracy of the model; and
the length of the finite sample.
The first of these has been widely covered in the wave resource
literature, e.g. by Cornett [13], and is calculated using the standard
deviation of all the sea state data available.
The prediction errors in the WaveWatch III model have also
been discussed elsewhere, with a previous study [9] indicating that,
in summer, the r.m.s. error on Hs is 0.33 m, and for Tp is 2.06 s. This is
corroborated by results from NOAA’s participation in an ongoing
study [3], which indicate that the r.m.s. error on Hs varies on an
annual cycle, within bounds of approximately 0.3 m and 0.7 m.
In this section the third consideration will be tackled, complementing the earlier discussion on using all available data.
3.4.1. Quantifying confidence
Although some numerical oceanographic models are available
covering multiple decades [38,43], it is often necessary, as in this
instance, to use data which cover a shorter period. It is therefore
important to assess the likelihood that an estimate of the mean
power (taken from a finite sample) is within a certain distance from
K. Gunn, C. Stock-Williams / Renewable Energy 44 (2012) 296e304
the true mean power. This can be achieved by use of the “confidence interval” [23]:
Pr½xL ðx1 ; .; xn Þ < x < xH ðx1 ; .; xn Þjx ¼ 1 a
(16)
where the confidence coefficient ð1 aÞ gives the probability that
the true value (x) being estimated lies between the bounds xL and
xH. These bounds are determined from the samples xi ,ði ¼ 1.nÞ.
In order for the confidence limit to be applied in practice to the
problem of wave resource assessment, the population being
sampled must be normally distributed, and sampling must be
independent. For this to be achieved, one must classify the samples
as the mean power of a particular month in a particular year. By the
central limit theorem, these data form a normally distributed
population, which has already been shown to be independent
(Section 3.3). Quantified confidence intervals can be obtained as
follows, taking all independent measurements of the power for e.g.
January:
1
n
m ¼ x pffiffiffitðn1;1a=2Þ s
(17)
where the true mean (m) is estimated by the measured mean ðxÞ
and standard deviation (s) of the samples, along with the number
of samples n. In this publication a ¼ 0:05 is taken in order to
estimate the 95% confidence intervals. The MATLAB function tinv
was used to evaluate the inverse Student’s t cumulative distribution tðn1;1a=2Þ .
The confidence interval has been mentioned previously in
relation to wave resource assessment by Mollison [28]. There, it was
first applied to a short period (z1 year) of wave data, where the
samples were the measured sea state power values. The application
of confidence statistics was then correctly dismissed as inappropriate, given the non-independence of these selected sea states in
estimating annual power. Monthly mean values were also derived
for a much longer period, and used to re-estimate mean power and
a confidence interval; however exactly how this latter value was
calculated was not explained. If all the monthly means were used,
these are also not independent (or indeed likely to follow a normal
distribution).
The confidence interval implicitly combines both natural variability between independent measurements of the power in
a particular recurring time period and the uncertainty associated
with a limited sample size. In wave resource assessment, therefore,
the value of the confidence interval for the particular confidence
coefficient chosen is unlikely to continue decreasing once a certain
sample size is reached. The sample size at which this occurs will
depend on the true standard deviation (s) at the location of
interest.
3.4.2. Combining confidence intervals
In Section 3.3 it was proposed that the mean values for each
month are combined to create annual and seasonal statistics. It is
also possible to do this for confidence intervals, since they can be
considered errors and can be combined in the usual manner for
independent variables:
"
dP ¼
2
n X
vP
dPm
vPm
m¼1
301
4. Results
Selected results are included in this section: either for
comparison with earlier studies; or to be of use to the wave energy
industry for the reasons outlined in the introduction. The statistics
available e which can be presented monthly, quarterly and annually e include:
mean wave power density;
total mean wave power;
power extracted by the chosen array of Pelamis WECs; and
95% confidence intervals on the above.
Each buffer line has been used to calculate these values for
countries, continents, hemispheres, and the whole world.
4.1. Global resource estimate
The total wave power incident on the ocean-facing coastlines of
the world (neglecting certain islands and the poles) is:
2:11 0:05 TW
to 95% confidence.
Using the array of illustrative WECs described in Section 3.2.2,
the total extractable wave power is calculated to be:
96:6 1:3 GW
This represents an “efficiency” (i.e. the proportion of the
resource extracted by the Pelames) of:
hJ ¼ 4:6%
4.2. Hemisphere power estimate
Fig. 5 illustrates the monthly variation in power between north
and south hemispheres. The expected seasonal variation can be
seen for both hemispheres. The annual means are given in Table 1.
4.3. Continental resource estimate
The incident wave power on each continent is shown in Fig. 6.
For comparison, the latest electricity consumption figures from the
CIA World Factbook [1] are also presented. Table 2 also presents the
power extracted by the illustrative Pelamis array and the extraction
efficiency.
4.4. Country resource estimate
Annual mean statistics for selected countries are given in
Table 3. These give an indication of the mean wave power resource
for each country, along with the degree to which the wave climate
is matched to the Pelamis power matrix.
#1
2
(18)
where dP indicates the error (or confidence interval) on the
measurement P.
Since P is given by Eq. (14), the partial derivative for each month
equals its length as a proportion of the total year.
5. Analysis
Observations are now extracted from the resource figures presented in Section 4. It is also essential that these results are
compared with those from earlier studies, so this is subsequently
performed on a global and country-by-country basis, where
possible, to assess the methods and data used in this study.
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K. Gunn, C. Stock-Williams / Renewable Energy 44 (2012) 296e304
800
Annual mean wave resource
Electricity consumption
700
600
Power (GW)
500
400
300
200
100
0
Fig. 5. Hemisphere power fluctuation. The error bars show the 95% confidence
intervals.
5.1. Distribution of wave resource
It appears surprising that, given the strength of the southern
hemisphere’s resource as shown in Fig. 1, the quantities of wave
power reaching coastlines in the northern and southern hemispheres are equal, to 95% confidence. This highlights the fact that
high wave power results from long fetch, which requires no
coastline to interrupt the flow of power: thus the power cannot be
extracted at coasts.
At first glance, the values for extractable power from the illustrative WEC are even more surprising, since the southern hemisphere is calculated to have approximately 40% less power than the
northern hemisphere. From an examination of the 3-hourly record,
however, it appears that this is because the power matrix made
publicly available by PWP is designed for a site in the UK. A large
proportion of the most energetic wave conditions experienced in
the southern hemisphere exceed the maximum values in the power
matrix and so zero power is extracted. The P2 would instead be
designed for, and tuned to, each installation site.
While it has been a useful exercise to apply this power matrix
across the world’s oceans, it is recommended that this set of results
is used with extreme caution. Any hypothesis about the potential
contribution of wave energy to a region’s electricity generation
should require a far more detailed study of local conditions,
including consideration of physical barriers to consent and
construction. In the judgement of the authors, however, this
method represents an improvement on the simple assumption of
a capacity factor or capture width.
North
South
Ocea
nia
rica
Ame
Afric
a
rica
Asia
Ame
Euro
pe
Fig. 6. Wave power available compared to electricity consumption for continents. The
error bars show the 95% confidence intervals.
wave power market. Tracking down the derivation of the various
figures generally quoted has not been a trivial task, due to a paucity
of references to the original sources of each resource estimate.
Methods for calculating global wave resource have historically
used one of three methods, which shall here be named M1, M2 and
M3. The first two were pioneered by Kinsman [25], who points out
the assumptions in his derivation at each step and prepends the
section with the following discussion of its likely accuracy:
“In this footnote we are again going to misapply an oversimplified relation to get an estimate that will be dressed up to
look as though it said something about the real ocean.”
The three methods are:
5.2. Global wave power
M1 Guesses are made for the mean global wave height and period.
These are used, assuming monochromatic Airy waves, to
calculate the power density. This is then multiplied by the
length of the global coastline.
M2 A mean wave height value is guessed for the entire surface of
the ocean. This is used (again assuming monochromatic Airy
waves) along with the total surface area of the oceans to estimate the total instantaneous wave energy across the planet.
Finally, by assuming a value for the number of times this
energy runs ashore per year, an estimate for power is obtained.
M3 Boud and Thorpe [10] take a different approach, by quantifying
the deep-water global wave resource using various sources of
power density data. This is close to the approach used here.
However, it is unclear which areas have been excluded for
having too low a wave power; or what length of coastline was
used and from what distance to shore the power is taken.
It is now necessary to consider whether these figures alter or
confirm the marine energy sector’s general view of the potential
Table 2
Resource and yield estimates for continents (95% confidence intervals).
Table 1
Resource and yield estimates for hemispheres (95% confidence intervals).
Hemisphere
P (TW)
J(GW)
hJ(%)
North
South
1.07 0.03
1.05 0.02
60.7 1.0
35.9 0.6
5.7
3.4
Continent
P (GW)
North America
Oceania
South America
Africa
Asia
Europe
427
400
374
324
318
270
18
15
16
12
14
20
J (GW)
20.5
14.9
13.5
12.9
20.3
14.6
0.5
0.4
0.3
0.3
0.7
0.5
hJ (%)
4.8
3.7
3.6
4.0
6.4
5.4
K. Gunn, C. Stock-Williams / Renewable Energy 44 (2012) 296e304
Table 3
Resource and yield estimates for selected countries (95% confidence intervals).
Country
P (GW)
Australia
United States
Chile
New Zealand
Canada
South Africa
United Kingdom
Ireland
Norway
Spain
Portugal
France
280
223
194
89
83
69
43
29
29
20
15
14
13
12
11
16
7
4
4
4
4
3
2
3
J (GW)
8.3
3.59
4.62
3.51
5.13
2.17
2.44
1.13
1.67
0.65
0.49
0.57
0.2
0.17
0.17
0.16
0.19
0.08
0.14
0.09
0.12
0.05
0.04
0.06
hJ (%)
3.0
1.6
2.4
4.0
6.2
3.1
5.7
3.8
5.7
3.3
3.2
3.9
Table 4 presents original estimates from the literature (i.e. those
which are not cited to earlier work). The fact that Kinsman’s two
estimates are close, bounding the value calculated here, does not
really tell us anything. As Kinsman [25] says of his two methods:
“The above is an example of the “razzle-dazzle” or “guessingfrom-both-ends” ploy. If done rapidly, it can be pretty impressive, but it doesn’t prove anything except your ability to make
two guesses come out in the same place. If you use it, be careful
not to have the two estimates exactly equal. Equal estimates
make the listener suspect that he is being one-upped.”
To prove his point, the mean of all the values in the table (if one
excludes 1e10 TW and 0.8 TW, which are not true resource estimates) happens to be equal to Kinsman’s M2 value (2.22 TW). Such
numerology, however, does not improve understanding of whether
the final global wave resource estimate presented in this paper is
accurate. The previous estimate which differs most from the value
presented here is the one which uses the closest method, and it is
obviously impossible to assess the reason for differences in those
values which have been stated without being derived. The accuracy
of the global values presented here can therefore only be tested by
comparison with regional studies.
5.2.1. Wave power by region
Comparisons are now made with previous studies of wave
resource in specific regions or countries. These are summarised in
Table 5 and discussed in the text below.
Table 4
Comparison of results with previous global resource studies.
Previous
estimate (TW)
Method
Reference
1.87
2.22
2.5
2.5
2.6
1e10
2
1.3
2
3
0.8
M1
M2
M1
Not stated
M1a
M1b
M2
M3
Not stated
Not stated
See noted
Kinsman, 1965 [25]
Inman and Brush, 1973 [20]
Isaacs and Seymour, 1973 [21]
Panicker, 1977 [31,32]
Pond and Pickard, 1978 [34] c
Boud and Thorpe, 2003 [10]
Strange et al., 1993 [37]
Hemer and Griffin, 2010 [18]
Thorpe, 2011 [40]
a
Panicker [31] gave a value of 5.3 TW, however Jonsson [24] responded to correct
this by a factor of 2 to 2.6 TW, which Panicker [32] accepted.
b
Panicker [31] states 1e10 TW as the rate of renewal of wave energy by wind
(not the power available at the coast), a range chosen to contain the (incorrect)
5.3 TW value presented in the paper and 2.2 TW by Kinsman [25]. It is presented
here due to a later reference to it as a global resource estimate [16].
c
Pond and Pickard [34] attribute this to Arthur [6].
d
Thorpe [40] provides this estimate, referencing it to Cornett [13]. However, this
paper contains no quantification of the global resource.
303
Table 5
Comparison of results with previous regional resource studies.
Region
Previous
estimate
(GW)
New
estimate
(GW)
Reference
Europea
Portugal
Ireland
290
10
25
237 10
15 2
29 4
WERATLAS, 1998 [35]
Mollison and Pontes, 1992 [30]
Gallachóir [17] quoting Mollison,
1982 [29],
Clément et al. [11] quoting Lewis,
1999 [26]
ESBI, 2005 [27]
Winter, 1980 [45]
Thorpe [39] quoting Whittaker,
1992 [44]
Thorpe [39] quoting ETSU,
1985 [15]
Cornett, 2006 [12]
21.4
U.K.
4.25 80
30.8
68 80
43 4
U.K. incl. Ireland
120
72 6
Canada, East coast
Canada, West coast
U.S.A., East coast
U.S.A., West coast
Chile
Australia
146.5
37
14
50
164.9
146
67.7
36
34
19
57
194
280
4
4
2
6
11
13
EPRI, 2005 [8]
Garrad Hassan, 2009 [14]
Hemer and Griffin, 2010 [18]
Hughes and Heap, 2010 [19]
a
Estimates given here are for Europe as defined by Pontes [35], i.e., excluding
Iceland and including Madeira, the Azores and the Canary Islands. Thus, this value
differs from that given in Table 2.
Comparing the methodology used for this study with those of
earlier reports, three key differences become apparent, which
qualitatively can account for differences in resource estimates:
1. The coastline buffer used differs between studies (and
frequently it is not stated or not obvious).
(a) Shallow water processes will significantly reduce the estimated resource where nearshore data are used, as in the
studies of Australia by Hemer and Griffin [18] (at the 25 m
isobath) and of Ireland by Lewis [26].
(b) By contrast, the study of Canada [12] presents resource
estimates both for the 1000 m isobath (given in the table)
and the 200 nautical mile limit. Both of these are far
offshore, inflating the power.
2. Almost all previous reports have used omnidirectional power
(see Section 3.2.3) summed along the length of coastline, with
the notable exception of Winter [45].
(a) This is true for the resource estimates of Europe [35] and
Chile [14].
(b) The case of the Canadian Atlantic east coast [12] study is
most interesting, as the 1000 m isobath is far offshore. Here
the waves are being generated by westerly winds (travelling east across the Atlantic) and so are not impinging on
the Canadian coastline. This means that they are not available to WECs, which will necessarily be nearer the shore.
This results in an overestimation by about 300%.
3. The data source used may be inaccurate, of short time-scale, or
of low geographical or temporal resolution.
(a) Since no previous studies have calculated confidence
intervals on their estimates, it is difficult to determine
whether results are consistent or not. However, frequent
comments in the contemporary literature (e.g. Snodin [36])
on results from older studies [30,35] indicate that the
numerical models used may underestimate swell wave
height.
(b) The oldest studies, where original papers (and therefore the
methods) are difficult to obtain, are likely to have used
visual observations [15] or sparse buoy measurements and
short time periods of model data [29].
304
K. Gunn, C. Stock-Williams / Renewable Energy 44 (2012) 296e304
In summary, good agreements are achieved when like-for-like
comparisons are made (U.S.A. coasts, Canadian west coast,
Europe, Chile and Ireland). However, many resource estimates in
wide currency today (particularly for the U.K., where the estimate is
based on the 1980s Met Office model) appear to be of low accuracy
and new estimates should be made now that numerical wave
hindcast models are well-developed and more widely available.
6. Conclusions
Data for 2005e2011 from the WaveWatch III global model run
by NOAA have been used to quantify the wave power experienced
by the world’s oceanic coastlines. The power is calculated at
a buffer line running 30 nautical miles offshore. Power from a WEC
array using the published Pelamis P2 power matrix is also applied
to give an indication of extractable power.
The world’s theoretical wave power resource is estimated to be
2:11 0:05 TW to 95% confidence, with equal amounts in the
northern and southern hemispheres. As a worldwide average, 4.6%
of this is estimated to be extractable by the illustrative WEC array
chosen. However, this number is to be treated with caution since
the array is sparse and the device is not tuned to each wave climate.
On the other hand, this approach has qualitative value since it
reveals that the best areas for wave power generation may not be
exactly correlated with the best areas for raw resource.
Comparisons to previous studies of results for specific regions
indicate a degree of agreement which raises confidence in the
overall figure. The global result is also close to the estimate in wide
currency today of 2 TW, which is generally referenced to Strange
et al. [37]. However, that report does not cite any further authority
or present any derivation for the resource estimate stated, which is
understandable given that it is an industry summary paper.
The robust assessment methodology presented here results in
resource values which have quantified confidence and which can
be queried to various levels of spatial and temporal detail. It is
therefore recommended that the wave energy sector begins to use
these estimates, which will increase the status of wave energy in
the eyes of those bodies able to provide financial and political
support. It is also recommended that this methodology guides
future studies, which should use longer periods of data at finer
spatial resolution.
Acknowledgements
Thanks are due to Prof. David Ingram of the University of
Edinburgh for his statistical advice.
References
[1] CIA world factbook [Website], www.cia.gov/library/publications/the-worldfactbook/rankorder/2042rank.html; June 2011.
[2] Natural earth [Website], www.naturalearthdata.com; June 2011.
[3] NOAA WW3 validation [Website], polar.ncep.noaa.gov/waves/validation.
shtmlUþ003F-wave-rmse-glo-HIND-large-; June 2011.
[4] Pelamis. Local resource assessment [Website], www.pelamiswave.com/
project-development/local-resource-assessment; June 2011.
[5] VLIZ. Maritime boundaries geodatabase, version 6.0 [Website], www.vliz.be/
vmdcdata/marbound/; March 2011.
[6] Arthur. Lecture notes.
[7] Barstow S, Mørk G, Lønseth L, Mathisen JP. Worldwaves wave energy resource
assessments from the deep ocean to the coast. In: 8th European wave and
tidal energy conference. Fugro: OCEANOR; 2009.
[8] Bedard R, Hagerman G, Previsic M, Siddiqui O, Thresher R, Ram B. Final
summary report, project definition study, offshore wave power feasibility
demonstration project. Technical Report, EPRI; 2005.
[9] J.R. Bidlot, J.G. Li, P. Wittmann, M. Fauchon, H. Chen, J.M. Lefèvre, et al. Intercomparison of operational wave forecasting systems. In 10th International
workshop on wave hincasting and forecasting, Oahu, Hawaii, 2007.
[10] Boud R, Thorpe TW. Wavenet: results from the work of the European thematic
network on wave energy [chapter D, pages 307e308]. European Community;
2003.
[11] Clément A, McCullen P, Falcão A, Fiorentino A, Gardner F, Hammarlund K,
et al. Wave energy in Europe: current status and perspectives. Renewable and
Sustainable Energy Reviews 2002;6:405e31.
[12] Cornett AM. Inventory of Canada’s marine renewable energy resources.
Technical Report, Canadian Hydraulics Centre; 2006.
[13] Cornett AM. A global wave energy resource assessment. In ISOPE; 2008.
[14] Cruz J, Thomson MD, Stavroulia E. Preliminary site selection e Chilean marine
energy resources. Technical report, Report for Inter-American Development
Bank by Garrad Hassan & Partners; 2009.
[15] ETSU. The department of energy’s R&D programme 1974e1983. Technical
Report, ETSU; 1985.
[16] Falnes J. A review of wave-energy extraction. Marine Structures 2007;20:
185e201.
[17] Gallachóir BÓ. Ireland’s wave power resource [Website], www.
aislingmagazine.com/aislingmagazine/articles/TAM17/Wave.html; 1995.
[18] Hemer MA, Griffin DA. The wave energy resource along Australia’s southern
margin. Journal Of Renewable And Sustainable Energy 2010;2:1e10.
[19] Hughes MG, Heap AD. National-scale wave energy resource assessment for
Australia. Renewable Energy 2010;35:1783e91.
[20] Inman DL, Brush BM. The coastal challenge. Science 1973;181:20e32.
[21] Isaacs JD, Seymour RJ. The ocean as a power resource. International Journal of
Environmental Studies 1973;4:201e5.
[22] Johnson NL, Leone FC. Statistics and experimental design in engineering and
the physical sciences, vol. 2. John Wiley & Sons, Inc.; 1964 [chapter 13 53e54].
[23] Johnson NL, Leone FC. Statistics and experimental design in engineering and
the physical sciences, vol. 1. John Wiley & Sons, Inc.; 1964 [chapter 7
187e192].
[24] Jonsson IG. Power resource estimate of ocean surface waves: discussion.
Ocean Engineering 1977;4:211e2.
[25] Kinsman B. Wind waves [chapter 3, pages 150e154]. Prentice-Hall; 1965.
[26] Lewis T. A strategic review of the wave energy resource in Ireland. In: wave
energy e moving towards commercial viability. London, UK: IMechE Seminar;
1999.
[27] McCullen P. Accessible wave energy resource atlas: Ireland. Technical Report,
Report by the ESBI for the Marine Institute and Sustainable Energy Ireland;
2005.
[28] Mollison D. Power from Sea waves, chapter the prediction of device performance [pages 135e172]. Academic Press; 1980.
[29] Mollison D. Ireland’s wave power resource. Technical Report, National Board
for Science and Technology and the Electricity Supply Board; 1982.
[30] Mollison D, Pontes MT. Assessing the Portuguese wave power resource.
Energy 1992;17:255e68.
[31] Panicker NN. Power resource estimate of ocean surface waves. Ocean Engineering 1976;3:429e39.
[32] Panicker NN. Power resource estimate of ocean surface waves: closure. Ocean
Engineering 1977;4:213.
[33] Pierson WJ, Neumann G, James RW. Practical methods for observing and
forecasting ocean waves by means of wave spectra and statistics. Washington:
Govt. Print. Off; 1955.
[34] Pond S, Pickard GL. Introductory dynamic oceanography; 1978 [Pergamom].
[35] Pontes MT. Assessing the European wave energy resource. Journal of Offshore
Mechanics and Arctic Engineering 1998;120:226e31.
[36] Snodin H. Scotland’s renewable resource 2001-volume i: the analysis. Technical Report, Report for the Scottish Executive by Garrad Hassan and Partners;
2001.
[37] Strange DLP, Tung T, Baker GC, Hagerman G, Lewis LF, Clark RH. Renewable
energy resources: opportunities and constraints 1990e2020 [chapter 6].
World Energy Council; 1993:321e58.
[38] Swail VR, Cardone VJ, Ferguson M, Gummer DJ, Harris EL, Orelup EA, et al. The
MSC50 wind and wave reanalysis. In: 9th international workshop on wave
hindcasting and forecasting; 2006 [Victoria, B.C. Canada].
[39] Thorpe TW. A brief review of wave energy. Technical Report, ETSU; 1999.
[40] Thorpe TW. 2010 survey of energy resources [chapter 11]. World Energy
Council; 2011:562e3.
[41] Tolman HL. User manual and system documentation of WAVEWATCH III
version 3.14. Technical report, U.S. Department of Commerce e National
Oceanic and Atmospheric Administration e National Weather Service e
National Centers for Environmental Prediction e Environmental Modeling
Center, Marine Modeling and Analysis Branch; 2009.
[42] Tucker MJ, Pitt EG. Waves in ocean engineering. Elsevier Science; 2001.
[43] Uppala SM, Kallberg PW, Simmons AJ, Andrae U, Da Costa Bechtold V,
Fiorino M, et al. The ERA-40 re-analysis. Quarterly Journal of the Royal
Meteorological Society 2005;131:2961e3012.
[44] Whittaker TJT. The UK’s shoreline and nearshore wave energy resource,
Technical report. Report by Queen’s University Belfast for ETSU; 1992.
[45] Winter AJB. The UK wave energy resource. Nature 1980;287:826e9.