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List of Figures
2.1 Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Correction of wave series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Correction of wave series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 Wave Power Maps for the grids corresponding to the Colombian Caribbean . 12
3.4 Wave Power Maps with the approximation to the Atlantico and Magdalena
Departments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.5 Wave Power monthly means for a chosen location near Barranquilla . . . . . 14
1
List of Tables
2.1 Calculated values of K-means Algorithm . . . . . . . . . . . . . . . . . . . . 7
3.1 Characteristics of Buoys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Contents
1 INTRODUCTION 1
1.1 Wave Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 METHODOLOGY 3
2.1 Swan Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Joint Probability of Hs And Tp . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Maintaining the Representative Power Percentiles . . . . . . . . . . . 5
2.1.3 K-Means Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 APPLICATION OF THE METHODOLOGY 8
3.1 Wind Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Bathymetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Buoy Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 ADVANTAGES 15
5 LIMITATIONS 16
6 FUTURE SCOPE 17
7 CONCLUSIONS 18
Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Chapter 1
INTRODUCTION
Wave power is one of the renewable sources of energy. It mainly benefits the coastal
and island communities rather than fossil fuels which has many disadvantages. There have
been a large amount of studies to assess the wave potential in different places of the world,
but very few have been conducted in the Caribbean Sea. This is mainly because marine
instrumentation in the Caribbean is scarce, and if existent, the wave records usually regis-
ter a very short period of time, insufficient to assess the resource in the long term. This
methodology creates artificial long term wave records from the use of numerical models and
database reanalysis winds, and process this information to assess the wave power present in
different places in the Caribbean. We also consider social, geographical, technical, economic
and enviromental variables for the selection of the wave farm. It acts as an identification
tool for assessing the wave resource without the need of any instruments.
1.1 Wave Energy
Ocean wave energy is the energy that has been transferred from the wind to the ocean.
As the wind blows over the ocean, air-sea interaction transfers some of the wind energy to
the water, forming waves, which store this energy as potential energy (in the mass of water
displaced from the mean sea level) and kinetic energy (in the motion of water particles). The
size and period of the resulting waves depend on the amount of transferred energy, which
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
is a function of the wind speed, the length of time the wind blows (order of days) and the
length of ocean over which the wind blows (fetch). Waves are very efficient at transferring
energy, and can travel long distances over the ocean surface beyond the storm area and are
then classed as swells. The most energetic waves on earth are generated between 30 and 60
latitudes by extra-tropical storms. Wave energy availability typically varies seasonally and
over shorter time periods, with seasonal variation typically being greater in the northern
hemisphere. Annual variations in the wave climate are usually estimated by the use of
long-term averages in modelling, using global databases with reasonably long histories.
Wind energy has potential for use as an energy source in the agricultural sector, specif-
ically for irrigation. With furrow irrigation proving to be very inefficient and many water
sources in the Caribbean situated in valleys, it is necessary to pump water for sprinkler or
drip irrigation systems. Since most farms are outside of the area of the electricity grid, small
wind turbines can be an efficient method of pumping water for irrigation purposes. The
small wind turbine can also be used for pumping water for livestock use. Wind energy can
therefore be competitive. It also offers the opportunity for cleaner electricity generation,
greater versatility in use especially in the agricultural sector for irrigation, and can provide
a standby source of electricity to reduce vulnerability.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Chapter 2
METHODOLOGY
The methodology is based on numeric simulations of a third generation wave propagation
model that uses bathymetries and reanalysis winds in the Caribbean Sea, and it aims to
generate spatial and temporal wave information in zones with scarce instrumentation. Once
there is interest in knowing the wave power potential in a particular location, the first step of
the methodology is to run the wave model on an oceanic scale in the Caribbean Sea, and then
downscale the results using nested runs until the desired detailed work scale is reached. As
a result of these nested runs is a wave information series (with hourly data) near the chosen
location. A similar procedure must be done in parallel, aimed to generate wave information
in the nearest instrumented location, in order to compare the quality of the synthetic series
and to make necessary corrections.
The elements of the block diagram includes SWAN model ,wave series, wave farm site
choice and its simulation in the chosen site. First is the generation of the wave series for
wave simulation. Database winds and bathymetries are the datas given to the wave model
as the input. The wave model used is the Simulating Waves Nearshore Model which is a
third generation propagation model specially designed for nearshore propagation based on
energy balance with source and sink terms. After the generation of the wave series ,it is then
compared with the existing wave records mainly the significant wave height(Hs) and peak
period(Tp) variables. The comparison is mainly done in three domains-time, frequency and
probability. Both series are graphed and a linear adjustment between them is carried out to
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Figure 2.1: Block Diagram
analyze them in the desired time domain. In the probability domain, the series are fitted to
a Gumbel distribution and compared. In the frequency domain, the longest uninterrupted
period of recording must be taken and a spectral analysis through a Fourier transform in
conducted, and the same procedure is made to the corresponding period of the simulated
series. The analysis in these domains helps to enlighten how well the simulated series adjust
to reality, and will quantify the errors of the modeling. If the instrumental wave record is
long enough, a calibration process of the model can be carried out in order to improve the
quality of the series, if not; other correction procedures may be applied.
2.1 Swan Model
Simulating Waves Nearshore Model (SWAN) is used for generation of wave series. It is
developed by Delft university of Technology[2]. It is used to compute random ,short-crested
waves in coastal regions with shallow water. SWAN is the most widely used computer model
to compute irregular waves in coastal environments, based on deep water wave conditions,
wind, bottom topography, currents and tides (deep and shallow water). SWAN explicitly
accounts for all relevant processes of propagation, generation by wind, interactions between
the waves and decay by breaking and bottom friction. One of the advantages of SWAN is
that it provides options to produce pictures of the computed wave parameters directly from
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
the program itself. SWAN can operate in first-, second- and third-generation mode.
∂N
∂t+∂cxN
∂x+∂cyN
∂y+∂cσN
∂σ+∂cθN
∂θ=
n∑i=1
Si (2.1)
This is the equation for the SWAN model.Next we have the construction of the wave po-
tential maps. They are constructed by propagating characteristic sea states of the simulated
series. They are chosen using three different criteria-joint probability, representing power
percentiles, k-map algorithm.
2.1.1 Joint Probability of Hs And Tp
The probability that a specific sea state occurs with a determined Hs and Tp is calculated
for the simulated series. The sea states with more probability of occurrence are identified
and wave maps are constructed by propagating them. That way the most common cases are
considered. ∫x
∫y
fx,ydydx = 1 (2.2)
2.1.2 Maintaining the Representative Power Percentiles
The wave power in the sea states are calculated either using the values of Hs and Tp, or
using the numerical model. Once there is a series of wave power, representative percentiles
of its value are selected. The power P is given by
P =ρg3Hs2T
64π(2.3)
where P is the power
ρ is the density
g is the acceleration due to gravity
Hs is the significant wave height
T is the Period
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
2.1.3 K-Means Algorithm
Inorder to count with representative cases of the wave series the k-means clustering algo-
rithm [1] was used. This algorithm divides the set of n observations (in this case sea states)
in the series in k different subsets or clusters, each cluster having a mean that represents
it. Each observation goes to the cluster where its distance to the mean is minimum. This
procedure provides a self organization of the wave series, where a subset of sea-states is rep-
resented by each of the cluster means. The sea-states closer to each of the means are chosen
to create the wave power maps.
Cluster analysis or clustering is the task of assigning a set of objects into groups (called
clusters) so that the objects in the same cluster are more similar (in some sense or another)
to each other than to those in other clusters. Clustering is a main task of explorative
data mining, and a common technique for statistical data analysis used in many fields,
including machine learning, pattern recognition, image analysis, information retrieval, and
bioinformatics. There are different types of clustering algorithms.Algorithm used here is k-
means clustering algorithm. The k-means algorithm assigns each point to the cluster whose
center (also called centroid) is nearest. The center is the average of all the points in the
cluster that is, its coordinates are the arithmetic mean for each dimension separately over
all the points in the cluster. The main advantages of this algorithm is its simplicity and
speed which allows it to run on large datasets. The algorithm steps are
• Choose the number of clusters, k
• Randomly generate k clusters and determine the cluster centers, or directly generate
k random points as cluster centers..
• Assign each point to the nearest cluster center, where ” nearest” is defined with respect
to one of the distance measures discussed above.
• Recompute the new cluster centers.
• Repeat the two previous steps until some convergence criterion is met (usually that
the assignment hasn’t changed).
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Consider a series of numbers Eg:(2,4,10,12,3,20,30,11,25) Suppose k=2 and we assign
means as m1=2 and m2=4.The numbers nearer to m1 are taken as one cluster and numbers
nearer to m2 is taken as another cluster. So k1=(2,3) and k2=(4,10,12,20,30,11,25). Again
the mean is calculated for respective clusters m1=2.5,m2=16. Next cluster is k1=(2,3,4) and
k2=(10,12,20,30,11,25) and the process continues. Table shows how the mean converges
Table 2.1: Calculated values of K-means Algorithm
m1 m2 k1 k2
3 18 2,3,4,10 20,30,25
4.75 19.6 2,3,4,10,11,12 20,30,25
The variables included in each of the sea states may vary, for this research 5 vari-
ables were taken into account: Hs, Tp, Dir(Direction), U wind(component of wind) and
V Wind(component of wind). The sea states closer to each of the means are chosen to create
the wavepower maps. Thus this map shows the availability of wave resource. For the wave
farm site we have to consider the technical, social, economic, environmental, and geographic
restrictions. Finally when locations are chosen and correction equations of wave series are
known ,there is a last simulation to generate a wave series in the place where the wave farm
will be located. The correction equations are applied to the series, and the wave power and
its variation is quantified in different time scales. The data used as input for the simulation
comprehends reanalysis database winds, and bathymetries for the Caribbean Sea. The wind
and bathymetry data were interpolated to match the dimensions of the nested grids used in
the simulation.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Chapter 3
APPLICATION OF THE
METHODOLOGY
The methodology was applied to assess the wave power resource in a region of the Colom-
bian Caribbean, near the Atlantico and Magdalena Departments. Following the proposed
methodology, wave simulations must be done from an oceanic scale to a local scale. The
model chosen for making the wave simulations is the SWAN Simulating Waves Nearshore
model, developed by the Delft University of Technology. The data used as input for the sim-
ulation comprehends reanalysis database winds, and bathymetries for the Caribbean Sea.
The wind and bathymetry data were interpolated to match the dimensions of the nested
grids used in the simulation.
3.1 Wind Data
NCEP North American Regional Reanalysis NARR. These are 10m wind in a 3-hour
resolution with a record length of 30 years . Members of Grupo OCEANICOS trimmed the
data in a domain defined in longitude 90 W to 64 W and latitude 6 N to 22 N. Data have a
spatial resolution of 0.25.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
3.2 Bathymetries
The bathymetry for the Caribbean Sea was taken from the ETOPO1 model from NOAA[3].
The detailed bathymetries were elaborated by the Direccin General Martima DIMAR, and
are available in the software Sistema de Modelado Costero SMC, developed by Universidad
de Cantabria
3.3 Buoy Data
The instrumental data corresponds to two buoys belonging to the Direccin General Mar-
tima DIMAR located in Puerto Bolivar and Barranquilla, in the Colombian Caribbean
Coast[4].
Table 3.1: Characteristics of Buoys
Buoy Latitude(N) Longitude(W) Depth(m) Measurements Period
Barranquilla 11.161 N 74.681 W 150 m Hs,Tp,Dir,Temp Mar2006-Dec2008
Puerto Bolivar 12.351 N 72.218W 150 m Hs,Tp,Dir,Temp Nov2007-Dec2008
The series are compared in the time,frequency and probability domains according to
the methodology. In the time and probability domain, the modeled and measured wave
series are found to be very similar, but Hs is lightly overestimated, contrasting with the
large underestimation of Tp. The analysis shows that the probability distribution of the
Hs is similar in the modeled series and the buoy measurements, but there are significant
differences when it comes to the comparison of the Tp. In the frequency domain, due to
the short length of the continuous records, there are no conclusive results. The probability
of occurrence of the extreme wave periods, comprehending the periods over 10 seconds, is
completely different to the rest of the set of Tp. This suggests that the model fails to
represent the extreme wave periods.In the frequency domain, due to the short length of the
records, there are no conclusive results.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Figure 3.1: Correction of wave series
After the comparisons, the synthetic wave series are corrected in the probability domain,
using a quantile analysis. As there are 2 buoys along the coast there are 2 set of expressions
for correcting the wave series, depending on the area that it they are located. A large
geographical accident, Sierra Nevada de Santa Marta, separates the correction zones: North
of Sierra Nevada is corrected using the Puerto Bolivar buoy and south of Sierra Nevada is
corrected using the Barranquilla buoy. The corrections graphs for the Barranquilla buoy are
presented in Figure 3.1
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Figure 3.2: Correction of wave series
After the correction of series, a total of 30 wave power maps maps were produced prop-
agating 5 cases chosen with the joint probability, 5 chosen with power percentiles and 20
chosen using the k-means clustering algorithm criteria. These maps show both the wave
power and the direction of propagation of the waves.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Figure 3.3: Wave Power Maps for the grids corresponding to the Colombian Caribbean
Figure3.2 and Figure3.3 shows an example of this power maps for 2 nested grids, chosen
using the representative power percentile of 75 percentage.The maps in Figure 3.2 and Figure
3.3 shows that larger wave resource is located at the center of the Colombian Carribean. By
analyzing the power distribution on these maps and taking into account restrictions such as
minimum distance to ports and cities, and avoidance of natural parks and merchant ship
routes, a spot was selected near the city of Barranquilla.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Figure 3.4: Wave Power Maps with the approximation to the Atlantico and Magdalena
Departments
The last step of the methodology was to run the model once more to generate wave series
at this location and correct according to the wave series analysis. Hs and Tp were corrected
after finding the equation and the equation found was applied with the corrected figures to
determine the wave power transport. Numerical processes were conducted to quantify the
resource in different time scales.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Figure 3.5: Wave Power monthly means for a chosen location near Barranquilla
It was found that the wave resource has a very clear annual cycle, with grater waves in
the months of December to April, and a small peak during June coinciding with the windy
summer season.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Chapter 4
ADVANTAGES
This methodology presents an effective way to assess the wave power potential in regions
with scarce instrumentation with a reasonable confidence. One of the advantages of the
methodology is that it offers an integral description of the availability of the resource, because
the maps serve to understand the spatial distribution and the wave series can be used to
describe the temporal availability in different time scales. This methodology serves as an
interesting identification tool. It may be most useful in the first stage of a feasibility study or
a regional wave power analysis, where it will overcome the need for instruments in a particular
area in the Caribbean, saving economic resources and providing long term information of
the wave climate.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Chapter 5
LIMITATIONS
The synthetic wave series can trustfully represent the average wave climates, but they
are not able to reproduce the extreme wave climates caused by the storms and hurricanes
that occur in the Caribbean Sea. The main reason for this is that even though the NARR
reanalysis winds offer an excellent representation of the mean wind patterns in the Caribbean,
they systematically underestimate the hurricane winds. Because of this, the model responded
by giving inaccurate results for the storms, especially when evaluating the extreme wave
periods. From a wave power harnessing point of view, it is more important to characterize
the mean wave climates because it is during these that the wave power is produced, while
the extreme wave climates are taken into account for survivability.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Chapter 6
FUTURE SCOPE
One of the advantages is that it offers description of availability of the wave resource,
because the maps serve to understand the spatial distribution and the wave series can be
used to describe the temporal availability in different time scales. One of its drawback is
that they are not able to represent the extreme wave climate caused by the storms and
hurricanes that occur in the carribean sea. Even though the NARR reanalysis winds offer
an excellent representation of the mean wind patterns in the Caribbean, they systematically
underestimate the hurricane winds. Because of this, the model responds by giving inaccurate
results for the storms, especially where evaluating the extreme wave periods. From a wave
power harnessing point of view, it is more important to characterize the mean wave climates
because it is during these that the wave power is produced, while the extreme wave climates
are taken into account for survivability. Another method has to be developed which involves
the characterization of the extreme wave climates, using a similar scope of wave modeling
but correcting the hurricane winds by different methods. Moroever if a technology designed
for this power potential in particular appears and becomes commercially competitive, it is
possible that wave power becomes important in the Colombian electric market or represent
a solution for non grid-connected communities
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
Chapter 7
CONCLUSIONS
This research provides a methodology to evaluate wave potential in zones with scarce
instrumentation with reasonable confidence. The power potential map describe the distri-
bution of wave power in a selected area, and the wave series provide long term behavior
of the resource. This methodology presented serves as an interesting identification tool. It
may be most useful in the first stage of a feasibility study or a regional wave power analysis,
where it will overcome the need for instruments in a particular area in the Caribbean, saving
economic resources and providing long term information of the wave climate. It is impor-
tant to keep in mind that these results reflect very well the mean wave climates, but fail
to represent the extreme wave conditions caused by hurricanes, mainly because the extreme
winds are underestimated in the NARR winds. These results become a powerful tool in
identifying possible sites, that later would be instrumented as a first step for developing a
wave farm project. As a sub product, the wave information can be also used for different
coastal engineering applications.
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
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Coastal Buoy”, OCEANS 2008,pp1-5,sept 2008
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Methodology for Estimating Wave power Potential in places with scarceInstrumentation in the Caribbean Sea
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Department of Electronics & Electronics Engineering Page 20
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