methodology for estimating wave power potential in places with scarce instrumentation in the...

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

Department of Electronics & Electronics Engineering Page 1


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.



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



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



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



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).



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.



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.



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.



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



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.



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.



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.



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.



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.



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.



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



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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coastal regions”, Journal of Geophysical Research. - C4 : Vol. 104. - pgs. 7649-7666

[3] Gonzlez M. “ An integrated coastal modeling system for analyzing beach processes and

beach restoration projects.”,Computers & geosciences.pp916-931,June2008

[4] Doug Wilsonand Eric Siegel “Evaluation of Current and Wave Measurements from a

Coastal Buoy”, OCEANS 2008,pp1-5,sept 2008



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