Hydrokinetic Resource Assessment of the Florida Current

A HYDROKINETIC RESOURCE ASSESSMENT OF THE FLORIDA CURRENT

Alana E. Smentek-Duerr

A Dissertation Submitted to the Faculty of

The College of Engineering and Computer Science

in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

Florida Atlantic University

Boca Raton, Florida

August 2012

ACKNOWLEDGEMENTS

I would like to thank the Southeast National Marine Renewable Energy Center at

Florida Atlantic University for their support of this research as well as providing the in situ ADCP data. I would also like to heartily thank Dr. Manhar Dhanak for his advice, guidance, and meticulous editing throughout the past three years. Thank you to Dr.

Frederick “Rick” Driscoll for his vision and passion. Additionally, thank you to my committee members, Drs. Howard Hanson, P. Ananthakrishnan, Richard Granata and

Eric Chassignet for their time and guidance. I would also like to thank Dr. James Van

Zwieten for the chance to do collaborative research, and being a sounding board whenever I needed it.

Thank you to my friends and family, especially my parents who have supported me every step of the way in all of my endeavors. And thank you to my loving and supportive husband, Phillip, who challenges me, keeps me grounded, and always offers encouragement whenever it is needed.

iv ABSTRACT

Author: Alana E. Smentek-Duerr

Title: A Hydrokinetic Resource Assessment of the Florida Current

Institution: Florida Atlantic University

Dissertation Advisor: Dr. Manhar Dhanak

Degree: Doctor of Philosophy

Year: 2012

The Straits of Florida has been noted as a potential location for extraction of the hydrokinetic energy of the Florida Current, in view of the strength of the current and its proximity to the shore. In the 1970’s, estimates were made of the hydrokinetic power within the Florida Current. William von Arx suggested that the Florida Current had 25

GW of power; however, for more than 30 years, no definitive research on the viability of the extraction of ocean energy was conducted. This research explores the Florida Current as a potential renewable energy source. By utilizing historical data, in situ observations of the Florida Current, and computer model data, the hydrokinetic resource of the Florida

Current is characterized both spatially and temporally. Subsequently, based on the geographic variability of the hydrokinetic power and other factors that impact the economy of a hydrokinetic turbine array installation, the ideal locations for turbine array installation within the Florida Current are identified. Using this information, estimates of potential energy extraction from turbine arrays are obtained for over 2000 different

turbine array configurations. The trends of the array extraction based on various array parameters are identified. Additionally, an interactive tool has been developed in which array parameters are input—including installation location, turbine diameter, turbine cut- in speed, etc.—and array extraction estimates, ideal installation position, and water depth at the installation points are output. As ocean model data is prominently used in this research, a discussion about the limitations of the ocean model data and a method for overcoming these limitations are described. Globally, the distribution of hydrokinetic power intensity is evaluated to identify other currents that have a high hydrokinetic resource. Finally, the tools developed in considering the Florida Current resource,, are used to analyze two other global ocean currents—Kuroshio and Agulhas—for their hydrokinetic energy potential. The locations with the highest potential within the

Kuroshio and Agulhas Currents are subsequently compared to the hydrokinetic energy potential for the ideal turbine installation location within the Florida Current.

A HYDROKINETIC RESOURCE ASSESSMENT OF THE FLORIDA CURRENT

List of Figures ...... x

List of Tables ...... xx

1. Introduction ...... 1

1.1 Florida’s Energy Landscape ...... 2

1.2 Ocean Renewable Energy ...... 5

2. Objectives ...... 7

3. Background ...... 9

3.1 Literature review ...... 9

3.1.1 The Gulf Stream ...... 9

3.1.2 Florida Current Geography and Climate ...... 9

3.1.3 Florida Current Oceanographic Principles ...... 17

3.1.4 Volumetric Transport ...... 23

3.1.5 Florida Current for Useable Energy ...... 31

3.1.6 Tidal Components of the Florida Current ...... 35

3.1.7 Resource Assessments of Other Forms of Ocean Energy ...... 35

3.2 HYCOM and Observational Data ...... 40

3.2.1 HYCOM Data ...... 40

3.2.2 Observational Data ...... 42

4. Approach ...... 44

vii

4.1 Data Analysis ...... 44

4.1.1 Ocean Model Data ...... 46

4.1.2 Historical Data ...... 49

4.1.3 Present Data ...... 55

4.2 Identification of Optimal Areas for Hydrokinetic Extraction ...... 59

4.3 Turbine Array Energy Extraction Estimation ...... 62

4.4 Identifying Data Limitations ...... 66

4.5 Global Assessment ...... 68

5. Results ...... 71

5.1 Data Analysis ...... 71

5.1.1 HYCOM ...... 71

5.1.2 Historical Data Sets ...... 85

5.1.3 Explorer of the Seas Data Sets ...... 86

5.1.4 ADCP Data ...... 91

5.1.5 NOAA Cable Data ...... 105

5.1.6 Case Studies ...... 106

5.2 Optimal Array Installation Regions ...... 117

5.3 Array Extraction Estimation ...... 124

5.4 Data Limitations ...... 134

5.5 Global Assessment ...... 144

6. Conclusions ...... 159

Appendix A ...... 167

viii

Appendix B ...... 170

Appendix C ...... 181

Appendix D ...... 197

Appendix E ...... 202

References ...... 209

LIST OF FIGURES

Figure 1: Renewable Energy as a Share of Total Primary Energy Consumption, US

Energy Information Administration (EIA) 2012 ...... 1

Figure 2: Gulf Stream Surface Current ...... 10

Figure 3: Straits of Florida Geography ...... 11

Figure 4: Loop Current Flow ...... 12

Figure 5: Bathymetry of Straits of Florida in fathoms—Stommel Page 42 of Gulf

Stream ...... 13

Figure 6: Straits of Florida Bathymetry ...... 14

Figure 7: Profile of Florida Straight Between Cutler, Florida and Gun Cay ...... 16

Figure 8: Profile of the Core of the Gulf Stream due east of Ft. Pierce, Florida ...... 16

Figure 9: Geostrophic Current Illustration ...... 19

Figure 10: Global Thermohaline Circulation ...... 23

Figure 11: Cross-section velocity structure at 27°N from 1982-1984 as observed in

STACS ...... 26

Figure 12: 24-years of Florida Current Transport Data at 27°N Measured by

Submarine Cable ...... 28

Figure 13: Annual Cycle of the Cable Derived Transport ...... 29

Figure 14: Florida Current velocity structure and variation at 27º N (m/s) ...... 30

Figure 15: HYCOM Raw Cross-Sectional Velocity Structure at 26.5°N on January 1,

2009...... 48

Figure 16: HYCOM Interpolated Cross-Sectional Velocity Structure at 26.5°N on

January 1, 2009 ...... 48

Figure 17: Mean downstream isotachs (cm/s), Fowey Rock ...... 51

Figure 18: Mean downstream isotachs (cm/s), Miami...... 51

Figure 19: Mean downstream isotachs (cm/s), Fort Pierce...... 52

Figure 20: Mean Summer downstream isotachs (cm/s), Miami ...... 52

Figure 21: Mean Fall downstream isotachs (cm/s), Miami ...... 53

Figure 22: Mean Winter downstream isotachs (cm/s), Miami ...... 53

Figure 23: Mean Spring downstream isotachs (cm/s), Miami ...... 54

Figure 24: ADCP Deployment Locations ...... 57

Figure 25: Average Cross-Sectional Velocity Structure off the Florida Coast at

25.5°N from 2009-2010 ...... 72

Figure 26: Average Cross-Sectional Velocity Structure off the Florida Coast at 26°N

from 2009-2010 ...... 72

Figure 27: Average Cross-Sectional Velocity Structure off the Florida Coast at 27°N

from 2009-2010 ...... 73

Figure 28: Average Cross-Sectional Velocity Structure off the Florida Coast at

27.75°N from 2009-2010 ...... 73

Figure 29: Average Cross-Sectional Velocity Structure off the Florida Coast at

28.5°N from 2009-2010 ...... 74

Figure 30: Power Fluctuation at 25.5°N from 2009-2010 ...... 75

Figure 31: Power Fluctuation at 26°N from 2009-2010 ...... 75

Figure 32: Power Fluctuation at 27°N from 2009-2010 ...... 76

Figure 33: Power Fluctuation at 27.75°N from 2009-2010 ...... 76

Figure 34: Power Fluctuation at 28.5°N from 2009-2010 ...... 77

Figure 35: Average depth distribution of hydrokinetic power at each longitudinal

cross-section within the study ...... 78

Figure 36: a) Mean vertical distribution of hydrokinetic power over longitudinal

range of study and b) mean vertical distribution of hydrokinetic power at 27°

N ...... 79

Figure 37: Average longitudinal distribution of hydrokinetic power at each constant-

latitude cross-section within the range of study ...... 80

Figure 38: Mean longitudinal distribution of power over a) entire latitude range and

b) at 27°N ...... 81

Figure 39: The fluctuation of the average hydrokinetic power along the east coast of

Florida from 2009-2010 ...... 82

Figure 40: Average hydrokinetic power density up the east coast of Florida from

2009-2010 ...... 83

Figure 41: Average cross-sectional area over which the power density is within a

given threshold from 2009-2010 ...... 84

Figure 42: The average position of the Florida Current’s core and boundaries from

2009-2010 ...... 85

xii

Figure 43: Explorer of the Seas Eastern Route, 2003-2004 ...... 87

Figure 44: Explorer of the Seas western route, 2003-2004 ...... 87

Figure 45: Outbound and Inbound Explorer of the Seas Cruise from July 2003

(Cruise 326) ...... 89

Figure 46: Outbound and Inbound Explorer of the Seas Cruise from June 2004

(Cruise 424) ...... 89

Figure 47: Current speed over the B2-1 ADCP Deployment, February 2009-March

2010...... 92

Figure 48: a) Northward and b) eastward component of velocity over the B2-1

ADCP Deployment, February 2009-March 2010 ...... 93

Figure 49: Eastward component of velocity over the B2-1 ADCP Deployment,

February 2009-March 2010 ...... 93

Figure 50: Mean, absolute minimum, and absolute maximum velocity profiles

during the B2-1 ADCP deployment ...... 94

Figure 51: Average power density as a function of the depth during the B2-1 ADCP

deployment ...... 95

Figure 52: Current speed from July 19-23, 2009 from the B2-1 ADCP deployment ...... 96

Figure 53: Frequency analysis of the B2-1 ADCP deployment with tidal constituents

indicated ...... 96

Figure 54: A) Northward and b) eastward components of the tidal velocities ...... 97

Figure 55: De-tided data sets from ADCP Deployment B2-1 a) over the entire data

set and b)from July 19-23, 2009 ...... 98

xiii

Figure 56: Layered histogram of the B2-1 ADCP Deployment ...... 99

Figure 57: Weighted power density curves for the B2-1 ADCP Deployment ...... 100

Figure 58: Current speed at a) B3-1 ADCP deployment and b) B2-1 ADCP

deployment over same time range ...... 101

Figure 59: Difference in current speed from B2-1 to B3-1 ADCP deployments ...... 102

Figure 60: Shear between the ADCP B2-1 and B3-1 deployments ...... 103

Figure 61: Current reversal at 32 m during the B3-2 ADCP deployment, November

4-5, 2011 ...... 104

Figure 62: Current reversal at 32 m during the B3-2 ADCP deployment, November

9-10, 2011 ...... 104

Figure 63: Mass transport fluctuation of the Florida Current at 27°N from 2009-2010

as measured by the NOAA submarine cable ...... 105

Figure 64: Air and water temperature from 2009-2010 from the Fowey Rocks

Lighthouse weather station compared to power fluctuation ...... 107

Figure 65: Atmospheric pressure from 2009-2010 from the Fowey Rocks Lighthouse

weather station compared to power fluctuation ...... 108

Figure 66: Time series where the atmospheric pressure measured at the Fowey Rocks

Lighthouse weather station was greater than 102.5 kPa for at least three days

in a row and the corresponding power calculations ...... 109

Figure 67: Time series where the atmospheric pressure measured at the Fowey Rocks

Lighthouse weather station was less than 101 kPa for at least three days in a

row and the corresponding power calculations ...... 110

xiv

Figure 68: Wind data measured at the Fowey Rocks Lighthouse weather station from

2009-2010 with power fluctuations ...... 111

Figure 69: Correlation coefficient between the northern component of velocity of the

wind and the power ...... 112

Figure 70: Comparison of the components of the Fowey Rocks wind velocity and

ADCP current velocity data ...... 112

Figure 71: Transport from NOAA submarine cable compared with HYCOM power

estimates at 27° N ...... 114

Figure 72: Correlation coefficient between the transport and power data ...... 114

Figure 73: ADCP current speed at 32 meters compared with the HYCOM power

estimations ...... 115

Figure 74: Correlation coefficient between the ADCP 32-m bin velocity data and

power data ...... 115

Figure 75: UM WERA surface current data from 2009 compared to HYCOM power

fluctuations ...... 116

Figure 76: a) Partial WERA 2009 data set plotted with the HYCOM power

fluctuations, and b) the correlation coefficient between the WERA data and

HYCOM power data ...... 117

Figure 77: The average depth at the Florida Current’s core and boundaries from

2009-2010 ...... 118

Figure 78: Normalized average hydrokinetic power and power density up the Florida

Coast 2009-2010 ...... 119

Figure 79: Normalized average depth at the Florida Current’s core and distance of

the Florida Current’s core from the shore up the Florida Coast 2009-2010 ...... 119

Figure 80: Location Factor based on HYCOM data from 2009-2010 ...... 120

Figure 81: Average Velocity Structure at 27.16°N from 2009-2010 ...... 121

Figure 82: Hydrokinetic power fluctuation at 27.16°N from 2009-2010 ...... 121

Figure 83: Transport fluctuation at 27.16°N from 2009-2010 ...... 122

Figure 84: Weighted Location Factor based on HYCOM data from 2009-2010 ...... 123

Figure 85: Array extraction fluctuation varying installation depth, holding number of

turbines, diameter, and cut-in speed constant ...... 126

Figure 86: Array extraction fluctuation varying cut-in speed, holding number of

turbines, diameter, and installation depth constant ...... 127

Figure 87: Array extraction fluctuation varying number of turbines, holding number

diameter, cut-in speed, and installation depth constant ...... 127

Figure 88: Array extraction fluctuation varying turbine diameter, holding number of

turbines, cut-in speed, and installation depth constant ...... 128

Figure 89: Screenshot of the MATLAB array extraction estimation program ...... 133

Figure 90: ADCP in situ measurements compared to HYCOM data over the same

time period ...... 135

Figure 91: ADCP and HYCOM average velocity profile at ADCP B2-1 ...... 136

Figure 92: a) ADCP and b) HYCOM Normalized Velocity Data at the B2-1 ADCP

Location ...... 137

xvi

Figure 93, a) ADCP and, b) HYCOM Normalized Velocity Data with Linear

Regressions ...... 137

Figure 94: a) Adjusted HYCOM velocity data and b) resulting mean velocity profile

at the B2 ADCP Site ...... 138

Figure 95: Average power density curves from ADCP measurements, HYCOM, and

gain term adjusted HYCOM data sets ...... 139

Figure 96: Squared-error metric of HYCOM and adjusted HYCOM data compared to

the ADCP measurements ...... 140

Figure 97: Volumetric transport data from NOAA cable compared to HYCOM and

adjusted HYCOM calculated mass transport ...... 141

Figure 98: Squared Error Metric between the mass transport measured by NOAA

Cable in situ data set and the HYCOM and adjusted HYCOM data set...... 142

Figure 99: Two-year average of the global surface currents using HYCOM data ...... 144

Figure 100: Global power intensity at 50 m ...... 145

Figure 101: Regions of high hydrokinetic power potential, a) Gulf Stream off the

southeast coast of Florida, b) Alguhas Current off east coast of South Africa,

c) Northern Equatorial, Southern Equatorial and Equatorial Counter Current

mixing near the Philippines, Indonesia and Malaysia, and d) Kuroshio

Current off the south and east coast of Japan, in kW/m2 ...... 147

Figure 102: Kuroshio Current power fluctuation up the northeast coast of Japan ...... 148

Figure 103: Kuroshio Current Power Density Fluctuation up the Northeast Coast of

Japan ...... 149

xvii

Figure 104: Normalized power and power density of the Kuroshio Current along the

northeast coast of Japan ...... 149

Figure 105: Array location factor of the Kuroshio Current along the northeast coast

of Japan ...... 150

Figure 106: Kuroshio Current Average Velocity Structure off the coast of Japan at

35.5°N from 2009-2010 ...... 150

Figure 107: Kuroshio Current Average Velocity Structure from 2009-2010 over

which power was calculated off the coast of Japan at 35.5°N ...... 151

Figure 108: Kuroshio Power Fluctuation at 35.5°N from 2009-2010 ...... 151

Figure 109: Kuroshio Current surface current magnitude at 35.5°N from 2009-2010 ....152

Figure 110: Kuroshio Current hydrokinetic power distribution at 35.5°N from 2009-

2010...... 153

Figure 111: Fluctuation of the average power in the Agulhas Current along the east

coast of South Africa ...... 153

Figure 112: Agulhas Current power density fluctuation along the east coast of South

Africa ...... 154

Figure 113: Normalized power and power density of the Agulhas Current along the

east coast of South Africa ...... 154

Figure 114: Array location factor of the Agulhas Current on the east coast of South

Africa ...... 155

Figure 115: Agulhas Current average velocity structure from 2009-2010 off the

South African Coast at -33.6°N ...... 156

xviii

Figure 116: Agulhas Current average velocity structure from 2009-2010 over which

power was calculated off the South African Coast at -33.6°N ...... 156

Figure 117: Agulhas Power Fluctuation at -33.6°N from 2009-2010 ...... 157

xix

LIST OF TABLES

Table 1: Miami to Bimini Transect Statistics from Richardon, Niiler and Brooks

Data Collection ...... 50

Table 2: ADCP Deployment Statistics ...... 56

Table 3: Hydrokinetic power statistics at specified constant latitude cross-sections ...... 77

Table 4: Estimated power and transport from Lee, Brooks, and Düing data sets ...... 86

Table 5: Estimated power and transport from average STACS transect ...... 86

Table 6: Power and transport from Explorer of the Seas average velocity structure ...... 88

Table 7: Power and flow rate from example Explorer of the Seas transects ...... 89

Table 8:Power and flow rate from 2003-2004 Explorer of the Seas transects ...... 90

Table 9: Explorer of the Seas compared to HYCOM Data ...... 91

Table 10: Tidal constituents seen in ADCP Deployment B2-1 ...... 97

Table 11: Florida Current mass transport statistics from 2009-2010 ...... 106

Table 12: Optimal Array Installation Location Statistics ...... 123

Table 13: Maximum Array Characteristics Evaluated at 27.16°N ...... 124

Table 14: Maximum Array Statistics at 27.16°N, Including Betz Limit Efficiency ...... 125

Table 15: Specific Array Parameters ...... 126

Table 16: Representative Array Extraction Estimation at an installation depth of 65

m without inclusion of Betz Limit Efficiency ...... 131

Table 17: Representative Array Extraction Estimation at an installation depth of 65

m with inclusion of Betz Limit Efficiency ...... 131

Table 18: Comparison of Specific Array Statistics at Five Different Locations ...... 132

Table 19: Array Boundaries and Depth at Array Boundaries ...... 132

Table 20: Volumetric transport statistics from cable, HYCOM, and adjusted

HYCOM data ...... 141

Table 21: Power intensity statistics from global regions of hydrokinetic potential ...... 146

Table 22: Power and power density comparison of three global currents with

hydrokinetic potential ...... 157

xxi

1. INTRODUCTION

Globally, the demand for clean renewable energy is rising. This increased demand has been the product of both the rising cost of oil and its recognized positive impact on climate change. The desire for energy independence has also stimulated the alternative energy industry. As non-traditional energy production schemes are being developed, the validity of these schemes is called into question. While questions about the environmental impact of these new schemes arise, the bottom line still remains—will these schemes be cost effective and provide much needed power? Before commercial development of any type of alternative energy, a company—and its investors—must have full understanding of the power production potential of that system in the site-specific operating conditions. The United States is heavily reliant on non-renewable energy sources—petroleum, natural gas and coal. Renewable energy sources only makeup 7% of the energy landscape.

Figure 1: Renewable Energy as a Share of Total Primary Energy Consumption, US

Energy Information Administration (EIA) 2012

1.1 FLORIDA’S ENERGY LANDSCAPE

In Florida, the leading fuels for energy production are coal and natural gas.

Natural gas typically accounts for 40% of energy production and coal typically 30% of energy production (EIA, 2010). The rest of energy production is mainly dependent on petroleum-fired and nuclear plants. Florida leads the nation in the generation of petroleum fired energy. Florida has very small reserves of natural gas and crude oil and no coal reserves, which means that more than 70% of its fuel for electricity generation is imported into the state. This puts Florida in a vulnerable position if the supply chain were to be interrupted by a severe storm or hurricane, and also sends billions of dollars out of the state’s economy to pay for the fuels. Florida also has the highest per capita residential energy demand in the nation. With the population of the state projected to rise to 30 million people by 2030 (U.S. Census Bureau, 2005), and following the trend of electricity consumption increasing by 3.8% per year, the energy production in Florida will need to increase by at least 30% in the next 10 years (2006 Florida Energy Act,

2006). This adds up to an increase of approximately 17,000 MW of electricity production over the next 10 years. Florida needs to diversify and expand its energy production to meet the demands of its rapidly increasing consumer base.

Florida’s geography does not lend itself well to many different types of traditional renewable energy sources like wind and hydroelectric dams. Solar electricity production may become more feasible as the solar cell technology advances. Looking to the ocean for implementation of renewable energy may be the key to Florida’s energy future.

The 60 million square kilometers of tropical oceans absorb the energy equivalent of 245 billion barrels of oil in solar energy each day. Tapping into this resource and extracting even a small amount of that resource reserve could supply a large portion of electricity to end users. Florida has over 1,400 miles of coastline, and 70% of its population lives within 10 miles of its coast. Harnessing renewable energy from the ocean would put energy production near the end users, so transmission of the energy would not be the prohibitive factor in utilizing the ocean as a renewable resource.

Since the 1970s, the Florida Current—a part of the Gulf Stream—has been observed for the development renewable energy (MacArthur, 1974). The Florida Current has both a thermal and a kinetic resource that could be exploited for the development of

Ocean Thermal Energy Conversion (OTEC) systems, Sea Water Based Air Conditioning

(SWBAC), and hydrokinetic energy conversion systems. The flow of the Florida Current has been estimated to have a total energy flux of 25 GW (Von Arx, 1974). While the power production potential of all of these systems has not been fully evaluated, it has been suggested that the hydrokinetic resource alone could create 1 (Von Arx, 1974) to 10 gigawatts of power (Lissaman et al., 1980); however, the difference between 1 and 10 gigawatts is immense when it comes to development of an extraction scheme. Not only would the scheme be completely different, but the cost effectiveness of a system designed for 10 GW operating in a site with only the potential for 1 GW of extraction could be extremely low. It is important, therefore, to have a full understanding of the operating conditions and the power production potential of a resource before attempting to exploit it.

The Florida Current has a relatively constant current, with small seasonal fluctuations, although daily fluctuations due to tides, weather and the periodic meanders affect the current velocity at any given location. The variations in the current impact the amount of power that can be extracted at any point in time.

The Straits of Florida is an ideal location to explore the possibilities of OTEC and hydrokinetic ocean energy conversion. Before commercial development of ocean energy conversion systems can occur, the overall amount of energy that can be converted into useable electricity must be quantified. Both resources—kinetic and thermal—need to be assessed for their individual potential. Once a thorough assessment is conducted, a more accurate estimate of how much energy can be extracted from the Florida Current can be obtained. This estimate would help determine whether ocean energy conversion at the chosen location is feasible. Based on resource assessments that have been previously completed, the Florida Current is considered to be a viable energy source of ocean energy. While these resource assessments provide valuable information, the degree of specificity of most of these assessments is low. Previous resource assessments have predominantly focused on the overall mass transport of water through the Straits of

Florida. Knowing the average mass transport of the Florida Current, and having an estimate for the overall surface current speed, have shown that the Florida Current has the potential to be a good overall energy resource. Resource assessments that provide concrete power production potential—based on velocity profiles, mass transport, and their potential variations—are needed for the development of effective hydrokinetic

energy extraction system. To definitely characterize the kinetic resource potential of the

Florida Current, the temporal and spatial variations of the current need to be identified.

1.2 OCEAN RENEWABLE ENERGY

The Florida Current provides a relatively steady current in a relatively steady direction compared to river and tidal currents. River currents can have extreme seasonal variation which could be problematic for any sort of energy extraction scheme. Most engineered systems are designed to be optimized at certain conditions; in this case, a hydrokinetic energy converter is optimized for a certain range of current speeds. If a river current flow has seasonal variation it would lead to inefficiencies in the hydrokinetic energy converter scheme during certain seasons. Additionally, the volume flow of the Florida Current is 30 times greater than the flow of all of the freshwater rivers in the world, combined.

Open ocean currents have received relatively less attention than tidal and river currents with regards to energy extraction. This is not without reason, of course. To understand the energy resource available from any current is a daunting task, but finding the best locations for tapping into the ocean’s energy is far more difficult and requires more extensive research. Once the current resource is assessed, however, an open ocean current could have the energy production potential that far exceeds the potential of a river or tidal current. While some ocean currents have a variable flow rate—which would not make them any better for energy extraction than river currents—some ocean currents have a relatively constant flow rate year round.

The open ocean renewable energy field is in its infancy. Many different technologies are being developed to harness the energy in the ocean. For harnessing ocean current energy, many companies have designed hydrokinetic turbines. These hydrokinetic turbines range in size, design and operation. Vertical axis, horizontal axis, and shrouded turbines have all been developed for ocean energy conversion among others. Conversion of open ocean energy is likened to conversion of wind energy—both technologies use a device to convert the kinetic energy in one fluid—air or water—into useable electricity. The main difference, of course, is the working fluid. One of the best places to start in a nascent industry is to start with existing technology and adapt it to a new purpose. Because the wind industry has demonstrated that the turbine is the best technology to harness wind energy, the logical place for ocean energy technology to start development was with developing a turbine technology, which is what continues today.

As companies continue their development of these technologies, the benefits and limitations of each technology will become apparent..

2. OBJECTIVES

The goal of this research is to provide an assessment of the hydrokinetic resource potential of the Florida Current. The goal is accomplished by meeting the following objectives:

1. Characterize the hydrokinetic energy resource of the Florida Current, including its

variability using the HYbrid Coordinate Ocean Model (HYCOM)

The HYbrid Coordinate Ocean Model (HYCOM) is a global ocean model that

provides a daily “snap-shot” of various oceanographic properties including water

velocity, temperature and salinity. Utilizing the model’s velocity data around

Florida’s East Coast, the Florida Current’s hydrokinetic energy resource can be

evaluated and characterized.

2. Identify optimal locations off Florida’s East Coast for hydrokinetic energy

extraction

As the area encompassed by the Florida Current is large, identification of optimal

locations for hydrokinetic extraction prior to in situ data collection, or installation

of extraction arrays, is beneficial. By recognizing various technical and economic

factors that contribute to the success of a hydrokinetic energy extraction scheme,

locations that are better suited for energy extraction can be determined.

3. Develop tools for assessing and estimating power resource of ocean currents,

optimization and assessing performance of turbine arrays

Tools are developed for assessing the Florida Current’s hydrokinetic energy

resource, as well as optimization and assessment of the performance of turbine

arrays. While the primary goal of this dissertation is to assess the Florida

Current’s hydrokinetic resource potential, the methodology used within the toolset

can be applied to other ocean currents that have hydrokinetic energy potential.

4. Provide a procedure for validating energy density estimates based on HYCOM

through comparison with observations of current velocities

While HYCOM data provides a wealth of knowledge regarding the hydrokinetic

resource assessment of the Florida Current, the prediction of ocean models is not

perfect. By comparing the HYCOM predicted velocities to observational in situ

current measurements, the energy density measurements based on HYCOM can

be validated.

5. Extend application of the approach to characterize global hydrokinetic energy

resources

The number of global locations suited for open ocean hydrokinetic energy

extraction is small. By utilizing the global HYCOM data, global regions with

hydrokinetic energy resources can be identified for further study.

3. BACKGROUND

3.1 LITERATURE REVIEW

3.1.1 The Gulf Stream

The Gulf Stream is one of the most examined and researched ocean currents. The

Gulf Stream was initially noted by early explorers of North America and has been studied by oceanographers and scientists for its physical aspects and for its impact on the North

Atlantic circulation. The Florida Current is an integral component of the Gulf Stream, constituting the current flow through the Straits of Florida. . The Florida Current’s volumetric transport and fluid velocity have been the subject of many studies. The goal of these studies has been to understand the nature of the Florida Current as part of the Gulf

Stream system.

3.1.2 Florida Current Geography and Climate

The Florida Current is part of the Gulf Stream, which is the intense western boundary current of the North Atlantic Gyre. The Florida Current is defined as the current from the Tortugas to Cape Hatteras (Iselin, 1936) as shown in Figure 2.

Figure 2: Gulf Stream Surface Current

Source: http://oceancurrents.rsmas.miami.edu/caribbean/florida.html

Stommel (1966) defined the Florida Current as simply the current that flows through the Straits of Florida, which is the definition used in this dissertation.

Geographically, the Straits of Florida are defined as the channel between Cuba and the

Florida Keys, continuing as the channel between the southeastern coast of Florida and the

Bahamas as seen in Figure 3.

Figure 3: Straits of Florida Geography

Source: http://oceanexplorer.noaa.gov/explorations/05deepcorals/background/mission_plan/medi

a/map_600.gif

The Florida Current has two sources, the Loop Current and the Antilles Current.

The Loop Current flows from the Yucatan Current through the Yucatan channel, but its flow is variable after that; either it flows in a very direct path into the Straits of Florida, or it flows slightly into the Gulf of Mexico and back down through the Straits of Florida as shown in Figure 4.

Figure 4: Loop Current Flow

Source: http://oceancurrents.rsmas.miami.edu/atlantic/loop-current.html

The Antilles Current flows east of the Antilles, and northward until it joins the Florida

Current past the outer Bahamas.

The water flows through a channel that is bounded by Cuba and the southern tip of Florida, flowing east, and then makes a turn toward the north through a channel bounded by the southeast coast of Florida and the Bahamas. The size of the channel between Key West and Havana is 140 km wide with a greatest depth of 1500m, while the size of the channel off of Miami is 80 km wide with a greatest depth of 800m (Stommel,

1966). The Florida Current continues to flow north as it hugs the continental shelf until it deviates from the coast at Cape Canaveral, approximately 33º N. The Florida Current increases in mass transport as it flows toward Cape Hatteras.

The climate in Southern Florida is subtropical, with a wet season and a dry season. The wet season occurs during the summer months (May-October), and the dry

season occurs during the winter months (November-April). Southern Florida has a hurricane season from June through November. Statistically, major hurricane occurrence is higher in September and October.

The bottom composition of the Straits of Florida off of the southeast coast of

Florida is a small layer of sand—a few inches—on top of a limestone floor.

The bathymetry (submerged topography) of the Straits of Florida is variable with location. Previous studies have noted that the bottom, along 80º W, has a positive slope as the distance north increases (Hurley, et al. 1962). Large scale bathymetry of the Straits of Florida can be seen in Figure 5:

Figure 5: Bathymetry of Straits of Florida in fathoms—Stommel Page 42 of Gulf Stream

In order to study the Florida Current for its ocean thermal resource, Leland (2009) conducted bathymetric studies of four different locations off of the Southeast Florida coast shown in Figure 6.

Bathymetry along 27 11’N Bathymetry along 26 38’N 0 0

-100 -100

-200 -200

-300 -300

-400 -400

Depth [m]Depth [m]Depth -500 -500

-600 -600

-700 -700

-800 -800 -80.2 -80.1 -80 -79.9 -79.8 -79.7 -79.6 -79.5 -79.4 -80.1 -80 -79.9 -79.8 -79.7 -79.6 -79.5 Longitude Longitude

Bathymetry along 26 05’N Bathymetry along 25 32’N 0 0

-100 -100

-200 -200

-300 -300 -400 -400

-500

Depth [m]Depth [m]Depth -500 -600

-600 -700

-700 -800

-800 -900 -80.2 -80.1 -80 -79.9 -79.8 -79.7 -79.6 -79.5 -79.4 -80.2 -80.1 -80 -79.9 -79.8 -79.7 -79.6 -79.5 -79.4 Longitude Longitude

Figure 6: Straits of Florida Bathymetry

Source: Leland, 2009

Through these bathymetric studies it is clear that the bottom features differ greatly in different locations throughout the Straits of Florida as the bottom features in the southern transects are far more prominent than those in the northern transects.

However, to generalize the western bathymetry off the southeastern coast of

Florida, the continental slope is broken up by two plateaus—the Miami and Pourtalès

Terraces (Reed, et al. 2005). The Miami Terrace extends 65 km along the Florida coastline at depths between 200 and 400 m, and is approximately 5 km off of the shoreline and has a width of 20 km. The Pourtalès Terrace follows the Florida Keys for approximately 210 km, has a maximum width of 32 km, and is at a depth between 200 and 450 m. The Bahama Banks make up the eastern boundary of the Straits of Florida, while Cuba is the southern boundary.

The core of the Florida Current ranges in its position from the shore. Off of Fort

Lauderdale, the core of the current is approximately 20 nautical miles offshore. Different profiles of the Straits of Florida and the position of the core of the current can be seen in

Figures 7 and 8.

Figure 7: Profile of Florida Straight Between Cutler, Florida and Gun Cay

Source: “On the Extraction of Kinetic Energy from Oceanic and Tidal River Currents,”

W.E. Heronemus, et al. MacArthur Workshop

Figure 8: Profile of the Core of the Gulf Stream due east of Ft. Pierce, Florida

Source: “On the Extraction of Kinetic Energy from Oceanic and Tidal River Currents,”

W.E. Heronemus, et al. MacArthur Workshop

3.1.3 Florida Current Oceanographic Principles

The Florida Current is a complex, dynamic structure. Physical parameters, such as the density of the water—affected by both the temperature and salinity—and the

Coriolis force—induced by the earth’s rotation—have a distinct effect on the overall structure of the Florida Current’s dynamics.

The Florida Current, as stated before, is part of the Gulf Stream. The Gulf Stream is part of the North Atlantic Gyre system. The North Atlantic Gyre is a wind driven circulation that is driven by the Westerlies and the North East Trade Winds. These winds drive the current in a clockwise direction in the Northern Hemisphere due to the Coriolis effect. The North Atlantic Gyre is made of four distinct currents: the North Atlantic

Current, the Canary Current, the North Equatorial Current and the Gulf Stream. The Gulf

Stream is the western boundary current of the North Atlantic Gyre.

Western boundary currents are typically strong, narrow flows that have a higher velocity than their eastern boundary counterparts, in the Northern Hemisphere. These fast flows are due to the change of the Coriolis Parameter with change in latitude and the conservation of planetary vorticity. The Coriolis parameter is

(1) f  2sin where  is the angular velocity of the earth’s rotation, and  is the latitude in degrees.

The Coriolis parameter increases as the latitude increases. The Coriolis parameter influences the potential vorticity in a column of water as shown below:

 z  f (2) h

where h is the height of the water column and  z is the local vorticity. Assuming that the height of the water column remains constant, that potential vorticity must be constant, and that as the current moves north the Coriolis parameter increases, the local vorticity term must decrease as a current moves north. This decrease in local vorticity leads to an increase in the flow velocity.

Geostrophic currents are driven by the Coriolis force and its opposing pressure gradient, governed by the momentum equation:   (3)  ( p  gz)  (2u)  0 where p is the pressure,  is the fluid density, g is the force of gravity, z is the water  depth, and u is the velocity vector. This pressure gradient is the result of a sloped sea surface height (barotropic), a spatial change in the density structure (baroclinic), or a combination of both. The Florida Current has both barotropic and baroclinic aspects to its structure, complicating the overall dynamics.

The sea surface height (SSH) is sloped positively from the eastern Florida coast as distance is increased to the east. The slope of the sea surface to maintain the surface velocity of the Gulf Stream System is 1:100,000; practically, this means that the SSH in

Bermuda is about 1m higher than on the East Coast of the United States (Knauss, 111).

This sloped surface is due to a the wind-driven Ekman transport causing the surface water of the North Atlantic Gyre to the middle of the gyre where a mound of water is essentially created in the middle of the North Atlantic Gyre, as shown in Figure 9. The surface water at the top of the mound starts to flow toward the bottom of the mount. The

Coriolis force and the horizontal pressure gradient due to the sea surface slope develop a balance, causing a geostrophic current flow.

Figure 9: Geostrophic Current Illustration

Source: http://www.atmos.washington.edu/2006Q1/211/Lecture10_notes.html

This SSH slope results in a pressure-gradient force in the westward direction. The pressure gradient keeps the core of the Florida Current from hugging the western side of

Bimini, Bahamas and pushes it toward Florida’s east coast. Using leading order approximation, the momentum equation governing geostrophic, flow is simplified into its x, y, and z component:

(4)

(5)

(6)

where u and v are the x- and y-components of the velocity, respectively, where the x- component is in the East-West direction, and the y-component is in the North-South direction. Using these equations, the induced velocities can be solved.

(7)

(8)

(9)

where  is the slope of the sea surface from east to west. The induced northern velocity, v, is caused by a slope in the east-west direction. Similarly, the equations for the eastern velocity, u, can be derived:

(10)

(11)

(12)

where is the slope of the sea surface in the north-south direction. Again, a slope in the north-south direction induces a velocity in the east-west direction. This approximation does not include any friction or wind stress terms, which is a decent approximation for calculating the v-component of velocity, but is not a good approximation for the u- component of velocity (Pond and Pickard, 99). Adding the wind stress and friction to the approximation would yield the following equations:

(13)

(14)

Additionally, the density structure of the Florida Current impacts the overall dynamics. As the distance increases from the Florida coast, the density of the water in the Florida current decreases. This is due to mixing of the water from the Gulf Stream with the Sargasso Sea. The Sargasso’s water is warmer than the water in the Gulf Stream; therefore, since the density is inversely related to the temperature, the density of the

Sargasso water is less dense than that of the Gulf Stream. This variation of density also affects the geostrophic equations as the density is no longer constant.

∫ ∫ ∫ (15)

∫ (16)

  where dx is the sea surface slope tan and 0 is the density at the surface. Based on the leading order approximation of the momentum equation,

(17)

therefore;

∫ (18)

If the density were a constant, this equation would reduce to the simple barotropic equation for the v. Similarly, the velocity in the x-direction can be found:

∫ (19)

The overall magnitude of geostrophic currents is directly related to the sea surface slope at constant latitude. As the sea surface slope increases, the magnitude of the resulting current also increases. This can explain what has been observed in the past that the current velocity increases during the summer months. During the summer months the sea surface temperature increases, resulting in a lower density. This means, that the amount of water that can be “piled-up” on the Bahamas—due to the constant Coriolis force—must increase. This will result in an overall increase in the slope angle, which will result in a greater overall induced velocity during the summer.

While most of the transport in the Florida Current is a result of the geostrophic and wind driven circulation of the North Atlantic Gyre, a portion of the flow is also due to the deep ocean circulation, or the thermohaline circulation. The thermohaline circulation is likened to a conveyor belt that connects the surface current circulation and deep ocean circulation systems. The combination of sea-ice formation, evaporation and chilling of surface waters near Greenland lead to the formation of North Atlantic Deep

Water (NADW), which is cold water with a high saline content. This cold water sinks and flows southward along the continental slope of North America and South America.

The circulation beyond the Americas can be seen in Figure 10. The heat transport due to the thermohaline circulation is a crucial part of the temperate winters in Europe. Of the total transport of the Florida Current, 13 Sv are due to the thermohaline flow (Lee, et al.

1996). This northward flow is balanced by a 13 Sv southward deep western boundary current on the eastern side of the Bahamas escarpment.

Figure 10: Global Thermohaline Circulation

Source: http://upload.wikimedia.org/wikipedia/commons/4/4c/Thermohaline_Circulation_2.png

3.1.4 Volumetric Transport

The volumetric transport through the Florida Current has been studied through various means: dropsonde, submarine telephone cables, subsurface current meters, and velocity profilers. The observed annual mean transport through the Straits of Florida varies depending on the specific study, as both the location in the Florida Current and the duration of the study will affect the overall results. The location of these transport studies have historically ranged between 26º and 27ºN; although more recent studies have chosen

locations near 27ºN where NOAA’s submarine cables collecting transport data are located.

Before a full evaluation of the Florida Current was conducted, the mass transport of the Florida Current was estimated to be 26 Sv (Stommel, 1966). At the time of

Stommel’s writing, submarine cables were also collecting volume transport data between

Key West and Havana for approximately two years. The data from the combined

Western Union Telegraph Company and Woods Hole Oceanographic Institution experimental set up led to a calculated transport of 26 Sv in that region (Wertheim,

1954). This 26 Sv measurement does not account for the total transport in the Florida

Current as there is inflow through island passages downstream of the observed channel.

From 1964-67, Schmitz and Richardson collected transport data using dropsondes across several sections of the Florida Current (Schmitz and Richardson, 1968). This was the first detailed study of the Florida Current transport. The transport estimated by this study was 32 Sv and suggested that nontidal fluctuations in the Florida Current caused less than a 10% variation in the overall transport.

Using a fuller data set than previously analyzed by Schmitz and Richardson

(1968), Niiler and Richardson (1973) found that the mean transport of the Florida Current is 29.5 Sv at 26º N using data collected from 1964 to 1970 (Niiler and Richardson, 1973).

This mean transport was found by using 90 transport transects, which were collected using the dropsonde procedure; however, the data collection was scattered over several years. The transport variation reached its maximum in the early summer at 33.6 Sv and

its minimum of 25.4 Sv in the early winter. This asymmetric annual cycle was verified by cable measurements at the time.

In the 1971 SYNOPS project, energetic flow reversals on times scales of 4 to 10 days were noted (Düing, 1975), which prompted further studies of these subinertial motions. Assuming that two years of current and temperature data from a single subsurface mooring would represent the fluctuation of the Florida Current on large and small periods, Düing et al. (1977) found that energy maxima for the northern component of velocity were found in three period bands: 8 to 25 days, 4 to 5 days, and 2 to 3 days.

A cross stream array verified these observations. Data from the cross stream array also showed that in all locations across the Florida Current showed a maximum northern velocity component at the 12-day period.

The perturbations of the Florida Current are caused by horizontal wave-like meander and eddies, and the tide and wind induced motions are masked by the meanders and eddies (Lee, 1975). The reversals of energy flow—increased or decreased—are not impacted by the shifting tides and winds.

Lee and Mayer (1977) also studied the low-frequency current variability of the

Florida Current. Using data from an eight-current meter array, the northward velocity had the most variability with broad-band spectrum peaks at periods of 2.3, 3.1, 9.3, and

18.7 days. These velocity oscillations occurred at the southern current meters first and then propagated northward. In the cross-shelf direction, the significant spectrum peaks were at 2.2 days.

NOAA’s Subtropical Atlantic Climate Study (STACS), was a rigorous study of the Florida Current between 1982 and 1984. Data collected included seven-months of current meter readings and 16 cross-sections of the Florida Current using PEGASUS velocity profilers along 27º N (Leaman et al, 1987). Nine PEGASUS profiler stations were spaced across 27º N. At each of these stations, the PEGASUS profiler was deployed, collecting two-velocity profiles at each station—one during decent and one during ascent. Velocity cross-sections were then interpolated based on the location of each profiler station, and from those cross-sections a transport value was calculated. The average transport during these cruises—which lasted approximately two weeks—was

31.7±3.0 Sv. The two-year average velocity structure at 27° N, from 1982-1984 can be seen in Figure 11.

Figure 11: Cross-section velocity structure at 27°N from 1982-1984 as observed in

STACS

Source: Leamen et al, 1987

A full transect would take between 16-20 hours and were subjected to tidal variations, although tidal variations were not removed from Leaman et al (1987) data set.

These tidal variations were studied by Mayer et al (1984) by using the current meters upstream of the PEGASUS stations, which showed that the northward velocity variation due to the shifting tides was approximately 3.9 X 10-2 m/s.

Further evaluation of the data collected by the STACS program led to the study of the meandering of the current and its relation to the transport variations of the Florida

Current. Dominating meander periods were observed at 5 and 12 days using the current meter array, although meandering motions were noted over a range of different time scales (Johns and Schott, 1987). This study also suggested that there is not a strong correlations of the meandering of the Florida Current with the variation in the transport.

Transport variations due to along-channel wind stress were found to lag the wind stress by approximately a day.

Using the STACS current meters and the observed vertical shear at the locations to interpolate the current to the surface, Schott, Lee and Zantopp found that the mean transport was 30.5±3.0 Sv (1988). Although the yearly standard deviation was found to be ±3 Sv, the mean of the monthly transport only deviated from the yearly mean by ±1

Sv.

From all of the studies that used the STACS data the overall conclusions that were drawn was that the annual cycle of the variations of the Florida Current were asymmetrical—with a peak transport in the summer and a minimum transport in the fall.

Since 1982, NOAA has been collecting cable data across 27º N and has found that the

annual mean transport of the Florida current is 32.2 Sv (Baringer and Larsen, 2001). At

8-year intervals, the annual cycle of the transport was evaluated—both in 2001 by

Baringer and Larsen, and in 2010 by Meinen et al. In 2001, Baringer and Larsen showed that the two different 8-year cycles that were evaluated resulted in completely different annual cycles. This methodology was reprised in 2010 by Meinen et al, when nearly 25 years of transport data collection (Figure 12) was analyzed. As seen in Figure 13, the three different multi-year cycles are not the same, and the 25-year average suggests another annual cycle. The reason for this drastic change in the transport is unclear, although it illustrates the fact that the annual cycle of the Florida Current transport cannot be expected to be identical year after year.

Figure 12: 24-years of Florida Current Transport Data at 27°N Measured by Submarine

Cable

Source: Meinen et al, 2010

Figure 13: Annual Cycle of the Cable Derived Transport

Source: Meinen et al, 2010

The transport through the Yucatan Channel of the Gulf Stream system was measured over a 10-month period, and was found to be 23.8±1 Sv (Sheinbaum et al.

2002). This exit for this transport from the Gulf of Mexico is through the Straits of

Florida. A ssuming that the transport between Havana and Key West is approximately equal to the transport through the Yucatan Channel, and that the average transport of the

Florida Current is between 30-32 Sv, this means that additional transport flows into the

Florida Current at various locations. Hamilton et al. moored several arrays of current meters to study the inflows into the Florida Current (2005). The arrays were located at six different sections: Key West to Havana, Cay Sal Bank, Miami to Bimini, Jupiter to

Settlement Point (27º N), Northwest Providence Channel, Santaren Channel, and Old

Bahama Channel. Data was collected between November 1990 and November 1991.

The mean transport found between Key West and Havana using these current meters was

25.2 Sv, which agreed well with the previous measurements by Sheinbaum et al (2002).

The difference between the transport between Key West and Havana, and along 27º N was partially accounted by the 2 Sv inflow through the Old Bahama Channel and the 1 Sv inflow through the Northwest Providence Channel. Hamilton et al. concluded that the inflow through the Santeren Channel had been previously underestimated, and amounted to approximately 2 Sv of transport. Additionally, the overall fluctuations of the transport at 27º N were smaller than at the Key West to Havana section.

The University of Miami and NOAA mounted two ADCP to the Royal Caribbean cruise ship Explorer of the Seas to study the Florida Current structure and transport.

Over a five-year period—May 2001 to May 2006—the cruise ship made one transect a week across 26º N. The average data for the five years of data collecting are seen in

Figure 14.

Figure 14: Florida Current velocity structure and variation at 27º N (m/s)

Source: Beal et al., 2006

Using cross-sectional velocity data from the ADCPs, the resulting transport was 31.0±4

Sv (Beal et al, 2008). The mean transport calculated from the NOAA cable at 27º N over the same period of time was 32.4±3.2 Sv, which implies that an average of 1.4 Sv flowed into the Florida Current from the Northwest Providence Channel over that duration.

3.1.5 Florida Current for Useable Energy

Using the Florida Current as a potential ocean energy source is not a newly devised idea. In 1974, the MacArthur Workshop was held to discuss the feasibility of extracting energy from the Florida Current (Stewart, 1974). Not only were various ocean energy conversion schemes presented, but the Florida Current was evaluated for its power producing potential. Von Arx, et al (1974) discuss the general oceanographic characteristics of the Florida Current, citing a 30 Sv flowrate, with a maximum surface velocity of 2.5 m/s and a vertically averaged velocity of 0.9 m/s (Von Arx, 1974). They estimated that the Florida Current’s motion held approximately 25 GW of total power.

Assuming that an array of ducted turbines were placed in the current—between 30 m and

130 m below the surface, and extending 20 km across the Miami Terrace—they predicted that 1 GW of power could be extracted from the Florida Current, about 4% of the total available power. Von Arx conjectured that any more than 4% extraction could have a serious impact on the climate downstream of the Florida Current.

The variability of the transport of the Florida Current is also discussed in the

MacArthur Report. Using the SYNOPS project, the Florida Current was studied to understand its vertical structure and how it changes. Transient waves, with several-day

periods, occur frequently and cause the current to meander (Düing, 1974). The simplest meander case shifts the current parallel to its axis, while more complicated meanders cause the cross-stream velocity profile to change. Occurring phenomenon—current meanders, transport variation, deep-flow reversals, and temperature fluctuations— exemplified periodicity over a 4 to 10 day range. The directionality of the transport deviates by approximately ±3º in the upper layers of the water column, and the cross- stream volume transport is approximately 5% of the downstream transport. This study agreed with the Schmitz and Richardson results, yielding a steady-state transport of 32 ±3

Sv. This study noted the occurrence of subsurface jets that increased the velocity in the upper 100m of the water column. This acceleration of the flow would last between hours up to one day. Attempts to correlate this acceleration with local wind data were not successful. Speculation that these “jets” were caused by eddies that could not be properly observed by the experimental set up. What was shown by these jets is the fact that the kinetic energy in the upper regions of the water column—above 250m—fluctuates more than the kinetic energy in lower regions of the water column. This study drew a lot of attention to the deep southward flow of the Florida Current. It was thought to vary based on tidal fluctuations; however, the periodicity of the deep flow reversal was on the order of four to six days, leading to the conclusion that the flow reversal was not due to tidal fluctuations.

An in depth study of the Florida Current specifically for power production potential was not attempted immediately after the MacArthur Workshop as the national energy crisis that prompted the workshop seemed to resolve itself; however, as energy

prices started to rise, renewable energy sources gained interest once again. The Florida

Current became the focus of open ocean renewable energy, which prompted a thorough study of the Florida Current for its kinetic energy potential.

Using both ship-mounted and permanently moored ADCPs, as well as additional data from previous studies, Raye studied the characteristics of the Florida Current at a specific mooring location for the Aquantis C-Plane (2002). Nineteen months of data were collected by a moored 75 kHz ADCP located at 26.11º N 79.5º W moored at 330 meters below the sea surface. This was approximately 13 miles from the shore on the

Miami Terrace. This specific location was predetermined by Aquantis as a location that would be reasonable for installing and maintaining the C-Plane, but also as a location that would be close enough to shore for cost effective power transmission to shore. The

ADCP would remain deployed for 95 days at a time, and the ADCP would ping approximately every 8 seconds and would be compiled into 15-minute ensembles. There were 100 bins at 3.25 m per bin. The moored ADCP data provides a good view of the temporal variability in the water column, but spatial variability is not captured by an

ADCP at a single location; therefore, a ship mounted 300 kHz RDI Workhorse ADCP was used to capture spatial variability in the velocity structure across the Straits of

Florida. It was mounted to Florida Atlantic University’s R/V Stephan. For this ADCP, the bin size was 1 meter with 128 bins, with an approximately 2 meter blanking distance.

Single ping data was collected and subsequently processed. By resolving the ADCP single ping data to the navigational data, the velocity data was transformed from its local coordinate system into a global coordinate system. Two transects were completed.

The study found that the current velocity reached a maximum during the summer months, with typical surface currents that would exceed 1.5 m/s for periods of days or weeks at a time. From February through November 2001, the velocity in the upper 100 m of the water column showed little variation, with velocities that rarely fell below 1.5 m/s.

The minimum current speeds, less than 1 m/s throughout the entire water column, happened occasionally during the summer months but with higher frequency during the winter. The absolute maximum velocities exceeded 2 m/s in the upper 100 m of the water column, and can potentially exceed 1.8 m/s in the upper 200 m of the water column; however, the velocity can decrease to 0.135 m/s around 100 m. At 300 m, a zero velocity was recorded, with an average velocity of 0.19 m/s.

Statistically, the variation of the velocity throughout the water column was found to be largely Gaussian. The variability of the current was noted over short periods of time showing that within half of a day the velocity could go from over 2 m/s in a large portion of the water column to less than 1 m/s in the entire water column. These extreme fluctuations are important to understand if subjecting a turbine to that environment.

Although the wind and tides may not significantly impact the energy flow of the Florida

Current, they could cause temporary fluctuations in highly localized environments. In studying a pinpointed area, Raye looked at the energy density and its fluctuations, and how varying velocities and rotor diameters changed the ideal power output; however, since this was a local study for a specific ocean current energy conversion device, it still does not provide an overall Florida Current energy assessment.

3.1.6 Tidal Components of the Florida Current

The tides in the Gulf of Mexico are small, which results in a semidiurnal progressive tidal wave. This wave moves upstream from Miami, and studies have shown that the tidal range along the United States coast is higher than the range along the coast of Cuba and the Bahamas (Stommel, 1966). The tidal currents can reach a velocity of 12 cm/s, and the transport variability of the Florida Current can be, in part, attributed to the tidal currents (Mayer et al., 1984). The tides can produce a transport of up to 5.1 Sv, although that was only recorded twice by Mayer et al.; however, the RMS transport was approximately 1.5 Sv, which is approximately half of the RMS transport variability of 3.0

Sv found in other studies (Leaman et al, 1987). The average northward tidal velocity was

3.9 X 10-2 m/s across the Straits of Florida, while the eastward velocity was less than

10% of the northward velocity (Leaman et al., 1987). These velocities are due to the major tidal constituents (K1, O1, and M2).

3.1.7 Resource Assessments of Other Forms of Ocean Energy

While the hydrokinetic resource of the Florida Current has not been extensively studied and assessed, the US Department of Energy has sponsored the resource assessment of offshore wind, tidal and wave energy off of the US coastline. The goal of each individual resource assessment varies—building a resource database or a geographic information system (GIS) tool—though the steps within the resource assessment are very similar. Each assessment starts by developing a model of the specific resource—wind speed, tidal currents, or wave characteristics. The model is then validated through

comparison to observational data. If the difference between the model and observational data is below a certain threshold, the model is deemed appropriate for estimating the resource; however, if the difference between the model and observational data is too large to resolve, then the model is modified. Then, utilizing the model data, power predictions are made. Typically, each resource assessment differentiates between theoretical power and extractable or realistic power.

3.1.7.1 US Offshore Wind Resource Assessment

The “Assessment of Offshore Wind Energy Resources for the United States” was prepared by the National Renewable Energy Laboratory (NREL) in June 2010. The offshore wind resource was measured up to 50 nm off the coastline, and was broken up into specific geographic regions. The goal of this resource assessment was to build wind resource GIS database. Using a wind resource model developed by AWS Truepower

(AWST), annual average wind speeds at 90 m were calculated to populate the GIS database. The model values were validated by NREL using ocean buoys, marine automated stations, lighthouses, and satellite derived winds speeds measured based on the sea-state detected using microwave imaging. Based on these measurements, AWST adjusted the model.

Based on the wind resource map, areas over which the average wind speed is above 7 m/s are calculated. These geographic areas are also broken down into regions where the wind speed is within a certain threshold, i.e. between 7.5 and 8 m/s. This differentiation areas with average wind speeds ranges from 7 m/s to 10 m/s, with a final

area representing all regions that have average wind speeds over 10 m/s. Furthermore, by assuming that 5 MW of installed capacity can be implemented in 1 km2, the resource potential is estimated. Using this rational, the US Offshore Wind Resource is 4,150 GW.

What is peculiar about this resource assessment is the assumption that if the average wind speed is greater than 7 m/s, then the installed potential is 5 MW/km2; however, presumably a region with an annual average wind speed of 9m/s would have a greater potential than a region with an annual average wind speed of 7 m/s. Additionally, the assumption that a region with wind speeds greater than 7 m/s has the extraction potential of 5 MW/km2 is not rationalized within the resource assessment.

3.1.7.2 US Tidal Resource Assessment

The “Assessment of Energy Production Potential from Tidal Streams in the

United States” was prepared by the Georgia Tech Research Corporation in June 2011.

The goal of the resource assessment was to create a GIS tool that was usable by those within the tidal energy industry. The report identifies the following as criteria for an ideal tidal extraction location: high current velocity and flowrate, beneficial specific site characteristics including bathymetry, sea floor depth, and geology of the seabed, the ability to connect to a local electrical grid, and the regional cost of energy.

The tidal resource assessment uses regional ocean modeling systems (ROMS) to model specific coastal regions. The numerical model is then calibrated by available observational measurements of the current speeds and sea level height. Oakridge

National Laboratory performed the validation of the numerical model to meet the EMEC

guidelines that: “ model predictions are considered adequate when predicted maximum current speeds are within 30% of those estimated from tidal monitoring station measurements” (Hass et al, 2011). By comparing the model data to observational data, the model over-predicts velocities within regions where there is a high power density, and under-predicts velocities within regions where there is a low power density. Within medium and high power density regions, the mean current speed is over-predicted by

24%, and the mean current speed is over-predicted by 21%. The mean and maximum current speeds are under-predicted within low power density regions by 18% and 13%, respectively. The model’s tidal elevation predictions are much better than the tidal current predictions.

The regional models then identify “hot spots” that are ideal for tidal energy extraction. The characteristics of these hot spots are that the region must have a maximum average power density of 500 W/m2 that is sustained over an area greater than

0.5 km2, occurring at a depth greater than 5 m. The tidal resource assessment differentiates between the total theoretical power (measured in GW), and the theoretical available power density, measured in kW/m2. The theoretical power is calculated using the method prescribed by Garrett and Cummins (2005), and results in an estimated tidal resource for the US of 50.8 GW. The theoretical available power density is measured for specific tidal basins, and the results are presented in detail within the report. Neither the total theoretical power nor the theoretical available power density assumes anything about particular technologies.

3.1.7.3 US Wave Resource Assessment

The “Mapping and Assessment of the United States Ocean Wave Energy

Resource” was prepared by the Electric Power Research Institute (EPRI) in cooperation with Virginia Tech Advanced Research Institute and NREL in December 2011. The goal of the research was to estimate the naturally available and technically recoverable wave energy resource of the US. Again, as in the other resource assessments, a distinction between the available and technically recoverable resource was made.

Using a 51-month Wavewatch III hindcast database, the wave resource up to 50 nm off of the US coastline was estimated. The Wavewatch III database provides, every three hours, a complete directional wave spectrum at 257 different global locations. At the other global grid points, with a longitude and latitude spacing of 4 minutes, the significant wave height, peak wave period, and mean direction of peak spectral energy are calculated. Of the 257 global locations where the complete directional wave spectrum is calculated, 15 of those are within the US Wave Assessment boundaries. Using these spectra, shape coefficients are calculated for the grid points nearest the full spectrum to adjust the shape of the spectral density predicted at each location. Once these shape coefficients are calculated, the wave statistics are reconstructed. Subsequently, the significant wave height, period, and power density at each grid point is calculated, leading to the resource assessment. The model was validated by NREL using wave statistics observed by 44 buoys from NOAA’s National Buoy Data Center (NBDC).

Overall, the model tends to under-predict the wave power density more than it over-

predicts. The ratio of the predicted mean annual wave power density value to the measured value ranges between 73 and 113% over the 51-months of study.

The wave resource assessment predicts that the US has a wave resource of 2,640

TWh/year, which would result in a power of around 300 GW. Based on the state of the art, and assuming a 15 MW/km coastline array capacity packing density, the technically recoverable wave resource is 1,170 TWh/year, approximately 134 GW.

3.2 HYCOM AND OBSERVATIONAL DATA

3.2.1 HYCOM Data

The HYbrid Coordinate Ocean Model (HYCOM) is a real-time global and basin scale ocean prediction system (Chassignet et al, 2009). It is an evolution of the Miami

Isopycnic-Coordinate Ocean Model (MICOM) developed by Rainer Bleck and colleagues at the University of Miami. HYCOM was developed to resolve issues with

MICOM’s vertical coordinate scheme (Halliwell 2002). MICOM employed an isopycnic—constant density—vertical coordinate scheme except in the top layer, which was non-isopycnic slab layer.

HYCOM is a 3-dimensional model. The x-(east-west coordinate) and y-(north- south coordinate) direction resolution is 1/12°. The z- (vertical coordinate) has a varying resolution according to the region of the ocean. The model runs in real time at the Naval

Oceanographic Office at the John C. Stennis Space Center in Mississippi. For each day a global data set is produced and includes the u- and v-velocities, salinity, and ocean

temperature. Additionally, ocean regional (Atlantic and Pacific) and basin (Gulf of

Mexico and Japan/East Sea) models have been produced. These smaller models use the global model’s output for boundary conditions.

What stands out about HYCOM is its vertical coordinate scheme (Chassignet

2007). Typically ocean models employ discrete intervals of depth, density or will follow the terrain for the vertical coordinate structure. However, these schemes are not best suited to all portions of the ocean. An isopycnal structure is best for deep ocean modeling. Constant depth or pressure schemes are best for mixed layer modeling.

Terrain following coordinates are best suited for coastal regions. For very shallow water modeling, level coordinates are suitable. HYCOM uses all four different vertical coordinate schemes in the regions where they are best suited. A smooth transition occurs between each region.

HYCOM assimilates observational data into the ocean model. Historical measurements and present measurements are exploited for this purpose. The data includes sea surface temperature and sea surface height—from different satellites as well as in situ data—temperature and salinity profiles from CTD’s and moorings, and Special

Sensor Microwave Imager (Chassignet 2009).

The model is run once daily, and completes a five day forecast and hindcast, which takes around 15 hours to run on parallel computers. The global model provides the boundary conditions for the regional basin models. In the future, the ocean model will continue to evolve and will include tides, increase the resolution to 1/25°, and more data are included into the model’s data assimilation.

3.2.2 Observational Data

The mass flow rate of the entire Florida Current is not descriptive enough to know how much energy one hydrokinetic turbine—or other ocean energy conversion device— is able to extract. Knowing shape of the current’s velocity structure below the sea surface is crucial to understanding the power potential as well as the operating conditions of current turbines. Depending on the location, the velocity decay from the ocean surface to the ocean floor varies: observations have shown that in certain locations there can be a strong countercurrent in lower layers of the water column. For hydrokinetic devices, the velocity of the current in specific locations is critical information.

Velocity data has been measured using both moored and shipboard ACDPs, and the data is available for analysis. The shipboard ADCP data was collected aboard the

Explorer of the Seas by the University of Miami (Beal et al, 2006), and the moored

ADCP data was collected by the Southeast National Marine Renewable Energy Center

(SNMREC). There are advantages and disadvantages to using both types of ADCPs.

Moored ADCPs have the advantage that they are able to record data for a long period of time; therefore, current variation with respect to time is clearly documented. Moored

ADCPs are limited by the fact that they are only able to be in one location, limiting the scope of the currents observed. Even though there may be a string of ADCPs moored across a current, the velocities between the buoys must be interpolated. With vessel mounted ADCPs, a full cross-section of the current is able to be measured creating a snapshot in time of the current structure. This snapshot will show the entire velocity

structure without needing interpolation between geographic points; however, the temporal variability is difficult to discern using a vessel mounted ADCP.

Although data averages—and their statistical variations—can help provide a first estimate of the energy available in the Florida Current, understanding the long term

(yearly) fluctuations to the shorter term variability (seasonally, monthly, daily, hourly), are crucial to a full estimate of the power production of the Florida Current. A rational and statistical approach must be taken.

4. APPROACH

In order to fulfill the objectives of this dissertation, the approach taken is multi- faceted. This approach establishes a logical progression of research in order to maintain a cohesive body of work.

4.1 DATA ANALYSIS

The first step in this resource assessment is to identify data that is pertinent to the study, and subsequently conduct, over an extended period, a study and analysis of the data. Different data sets are used to determine hydrokinetic energy density in the water column and to characterize its spatial distributions and temporal variability over the period of study. Additionally, the limitations of each data set are identified, and a procedure is developed for using each data set in a complementary way. In this way, appropriate information are extracted from each data set.

For a channel flow, the power flux Pf across a cross-section plane is given by:

(20) ( ) ‖ ⃗⃗ ‖ ( ⃗⃗ ⃗ )

where | ⃗⃗ |, ⃗ is the unit normal vector to the cross-sectional plane, y,z denote coordinates in the cross-stream plane, and ρ is the water density; this approximation assumes that the principal velocity component is along the streamwise direction, and that

the cross-stream components are small. The total power of the stream P is obtained by integrating over the cross-sectional area of the channel:

̅̅̅ ̅ ∫ (21)

This assumption also applies to estimating turbine extraction, as hydrokinetic turbines will tend to pivot into a plane normal to the direction of the flow; therefore, using the velocity magnitude is the appropriate estimate for the power that an array of current turbines could extract.

As transects of the Florida Current have been taken along a constant-latitude, and assuming that nothing is known about the flow direction, the theoretically correct way of assessing the hydrokinetic resource along a constant-latitude cross section would be to use the following equations:

(22) ( ) ‖ ⃗⃗ ‖ ( ⃗⃗ ⃗ )

(23)

∫ ̅ ̅

where U is the velocity magnitude, v is the northward component of velocity (with a constant latitude cross-section). However, in the case that only the current speed—or the dominant component of velocity—is known, the methodology shown in (20) and (21) is used.

Based on this methodology, current velocity data is pertinent to the hydrokinetic resources assessment of the Florida Current. Additionally, the study of climatological data that may have an impact on the current speed is pertinent. The data that are studied

includes: ocean model data (HYCOM) for the Straits of Florida, available historical data sets, and data from recent observations.

4.1.1 Ocean Model Data

As this is a new industry, no clear standards for resource assessment have been established; although, many lessons have been learned through wind energy development and expansion. Typically, for siting wind turbine installations, the winds are monitored by meteorological stations for a year or more (Manwell). In this vein, two years of

HYCOM model data are used to evaluate the hydrokinetic power resource. The HYCOM model data for 2009-2010 are considered.

HYCOM provides a daily snapshot of the velocity, temperature and salinity on a global scale. The latitude and longitude scale of the model are 1/12°, while the vertical spacing is variable. The velocity data are linearly interpolated from a variable vertical spaced grid to a uniform grid with a constant vertical spacing of 10 m. The HYCOM data are pared down to the area around the Florida Current spanning from 25 to 30°N, and -

78.2 to -81.28°E. With this data, the average velocity structure of the Florida Current at different locations is determined. Additionally, the location of the core and its meander can be determined using the HYCOM data.

The hydrokinetic power and mass transport of the Florida Current is assessed along constant-latitude cross-sections:

(24) ∑ ∑

(25) ∑ ∑

where i is the latitude, j is the longitude, k is the depth, and Ai is the cross-sectional area.

The cross-sectional area is dependent on latitude as HYCOM has a constant longitude- latitude grid, which, therefore varies in size (in the east-west direction) depending on the latitude.

The daily hydrokinetic power and transport is calculated from the available velocity data set at various locations over the above latitude range and the spatial and temporal variability of the resource is studied. While seasonable variability cannot be ascertained based on a two-year data set, the variation of power and transport over the two-year data set still provide valuable insight to resource characterization. The relationship between the transport and the hydrokinetic power is determined.

The velocity interpolation may have an impact on the calculated transport and power values as calculated using Eq. (24). As the power and transport are calculated using discrete summations, interpolating the velocities between HYCOM grid points will change the vertical structure of the values from the raw HYCOM data. The difference between a transect using raw HYCOM data and a transect using interpolated HYCOM data can be seen in Figures (15) and (16).

Figure 15: HYCOM Raw Cross-Sectional Velocity Structure at 26.5°N on January 1,

2009

Figure 16: HYCOM Interpolated Cross-Sectional Velocity Structure at 26.5°N on

January 1, 2009

Using the raw HYCOM data, the calculated hydrokinetic power and mass transport at 26.5°N on January 1, 2009 were 16.2 GW and 32.3 Sv, respectively. Using the data that had been interpolated to a finer depth grid, the corresponding power and transport are 14.8 GW and 27.5 Sv, respectively. Thus, the impact of interpolating the velocities to the finer depth spacing results in a lower prediction of the hydrokinetic power and transport; however, it is not realistic to assume, based on previous ADCP data collected within the Florida Current, that a given velocity is maintained for an entire 25 m vertical grid space. If the coarse gridding model is used, then different methods of numerical integration—based on the trapezoidal or Simpson’s rule—are required instead of integration based on direct summation..

4.1.2 Historical Data

Various historical data sets can be used to estimate the hydrokinetic power resource of the Florida Current. These data sets also give context to the HYCOM prediction. In 1977, the University of Miami published a technical report entitled “The

Florida Current: Structure and Variability,” by Thomas Lee, Irving Brooks, and Walter

Düing. This report combines data collected by Düing, Lee, Richardson, and Brooks and

Niiler between 1964 and 1974, and information about the individual data collections and their conclusions has been disseminated (Düing, 1974, 1975, Düing et al. 1977, Lee

1975, Schmitz and Richardson, 1968, Niiler and Richardson, 1973).

Within the report, average velocity transects are published from the Richardson,

Niiler and Brooks dropsonde data collection. Average transects were constructed at six

different sites—Key West, Marathon, Fowey Rock, Miami, Bal Harbor and Fort Pierce.

Additionally, the seasonal average velocity structure at the Miami site was calculated and published. Based on the geographic area of study, the transects that are most important to this study are the Fowey Rock, Miami, Bal Harbor and Fort Pierce transects; however, the data collection statistics of the Bal Harbor transects are not published within the report. Without the number of transects taken and the date range over which the transects were performed, the Bal Harbor average velocity plot is incomplete; therefore, only the

Fowey Rock, Miami, and Fort Pierce average, and Miami seasonal average transects are studied. Data collection statistics for the Fowey Rock, Miami, and Fort Pierce sites can be seen in Table 1:

Table 1: Miami to Bimini Transect Statistics from Richardon, Niiler and Brooks Data

Collection

Number Transect Geographic Site of Time Range Transects Fowey Rock Light to Cat Cay 11 May-June 1965 6 July-August 1966 Ft. Pierce to Matanila Shoal 5 May-June 1967 5 August-December 1964 12 May-June 1965 3 March-December 1966 4 November-December 1967 Miami to Bimini 17 January-May 1968 21 April-December 1969 18 January-November 1970 50 March-August 1974

Additionally, the transects can be seen in Figures 17 to 23:

Figure 17: Mean downstream isotachs (cm/s), Fowey Rock

Source: Lee, Brooks, Düing, 1977, Page 54

Figure 18: Mean downstream isotachs (cm/s), Miami

Source: Lee, Brooks, Düing, 1977, Page 55

Figure 19: Mean downstream isotachs (cm/s), Fort Pierce

Source: Lee, Brooks, Düing, 1977, Page 57

Figure 20: Mean Summer downstream isotachs (cm/s), Miami

Source: Lee, Brooks, Düing, 1977, Page 62

Figure 21: Mean Fall downstream isotachs (cm/s), Miami

Source: Lee, Brooks, Düing, 1977, Page 63

Figure 22: Mean Winter downstream isotachs (cm/s), Miami

Source: Lee, Brooks, Düing, 1977, Page 64

Figure 23: Mean Spring downstream isotachs (cm/s), Miami

Source: Lee, Brooks, Düing, 1977, Page 65

By utilizing AutoCAD, the isotachs can be integrated. The area encompassed by each isotach can be used to estimate the power at each transect. By calculating the power and mass transport that is represented by the average cross-sectional velocity structures, these can be used as a comparison to the HYCOM predictions.

Additionally, the hydrokinetic power based on the 2-year average velocity structure produced by the STACS study (Figure 11), and the 5-year average velocity structure from the Explorer of the Seas study (Figure 14), is evaluated in the same way.

The pertinent shipboard ADCP data from the Explorer of the Seas is also analyzed at each individual transect. Due to difficulties in data collection and the sporadic nature of fully populated data sets, the data that has been analyzed in this research spans 2003-

2004.

The cruise ship did not transect the Florida Current on a directly east-west line.

The cruise ship started at a 25.7° N, and would travel northeast; the ship would typically finish traveling across the Straits of Florida around 26.2° N. The average latitude of the crossing was 26° for all of the data sets. Although the latitude is not constant, for the purpose of this research, the data is projected onto a grid along the mean latitude of 26°

In addition to the velocity data, the mass transport data from the NOAA submarine cable is utilized. The cable has been collecting data for nearly 30 years, all of which is available on NOAAs Atlantic Oceanography and Meteorological Laboratory

(AOML) website. While the transport cannot be directly compared to the hydrokinetic power, the overall trends seen in the transport should be similar to the trends in the hydrokinetic power. Also, the mass transport determined from HYCOM can be compared to the cable data as a point of validation.

4.1.3 Present Data

The Southeast National Marine Renewable Energy Center (SNMREC) at Florida

Atlantic University (FAU) have deployed moored, upward facing ADCPs over various time scales and at different locations between 2009 and 2012. The first ADCP was deployed at deployment point B2 (26º 4.3.’ N, 79º 50.5’ W) at a depth of 340 m, and collected velocity data from late-February 2009 to late-March 2010. Another moored

ADCP, was deployed at a depth of 260 m along the same latitude at deployment point B3

(26º 4.3.’ N , 79º 55’ W) 8 km west of the previously mentioned B2 ADCP deployment.

This ADCP was deployed from late-February 2009 to late-March 2009. In 2011, another

ADCP was deployed at location B3, and collected data from August to November, 2011.

In November 2011, two additional ADCPs were deployed at location B3 and B2b (26º

4.3.’ N, 79º 51’ W). and collected data through the beginning of April 2012. A table of deployment specifications can be seen in Table 2.

Table 2: ADCP Deployment Statistics

Deployment Dates Depth Ensemble Deployment Coordinates Length, Designation Start End m min 27 Feb. 25 Mar. 26º 4.3’ N, 79º 50.5’ B2-1 2009 2010 340 W 30 27 Feb. 19 Mar. 26º 4.3’ N, 79º 55’ B3-1 2009 2009 260 W 30 23 Aug. 16 Nov. 26º 4.3’ N, 79º 55’ B3-2 2011 2011 260 W 1 16 Nov. 5 Apr. 26º 4.3’ N, 79º 51’ B2b-3 2011 2012 340 W 10 16 Nov. 31 Mar. 26º 4.3’ N, 79º 55’ B3-3 2011 2012 260 W 10

The location of the ADCP deployments can be seen in Figure 24.

Figure 24: ADCP Deployment Locations

Velocity and hydrokinetic power flux statistics can be analyzed using the ADCP data. Additionally, frequency analysis will indicate periodicity in the current. When

ADCPs are simultaneously collecting data at different locations, the horizontal shear between the two locations can be evaluated.

Beyond the basic statistical analysis, the data can be manipulated in a way that provides a broader understanding of the data as it relates to hydrokinetic energy extraction. For example, a typical way of analyzing moored ADCP data is to organize the water column into vertical bins. Subsequently, a histogram of the velocities within that bin can be constructed and analyzed. However, depth-dependent histograms are not indicative of the velocity structure and behavior within the entire water column. By layering the depth dependent histograms in a 2-d plot provides a full picture of the velocity statistics at a given ADCP deployment site. Using the velocity statistics, as well

as the relationship of velocity to power, statistical evaluation of the power flux at each

ADCP location is performed.

As both the mass transport and the hydrokinetic power are functions of the velocity, it would seem reasonable that fluctuations seen in one would be apparent in the other data set. In order to determine if there is any correlation between the two variables,

HYCOM power data is compared to the mass transport from the NOAA submarine cable data. The Florida Current cable and section data are made freely available on the Atlantic

Oceanographic and Meteorological Laboratory web page and are funded by the NOAA

Office of Climate Observations (Florida Current Transport, 2010). Overall trends are noted, and case studies comparing the two data sets are conducted in order to verify any observed trends.

The University of Miami Rosenstiel School of Marine and Atmospheric Sciences presently operates four WERA High Frequency radars in order to capture surface current measurements (UM/RSMAS HF Radar Operations, 2012). These shore based WERA radars are located in Key Largo, Key Biscayne, Virginia Key, and Dania Beach and provide surface current measurements over a large area off of Florida’s east coast. The surface current data is publically available on their website. The purpose of analyzing the surface current data is to attempt to find a correlation between surface current measurements and the available power as calculated using HYCOM. If such a relationship is found, then surface current measurements could potentially be used to estimate the hydrokinetic power of the Florida Current. The surface current is evaluated over 2009, as there are many data sets missing from 2010.

The final data to be analyzed is atmospheric data. Using a similar rationale as evaluating surface current data, if a correlation between readily accessible atmospheric data and the available power could be found, then the availability of hydrokinetic power could be estimated based on weather conditions. Wind, temperature and atmospheric pressure data from the Fowey Rocks Lighthouse Weather Station are used as the source of data. This atmospheric data is made publically available by NOAA’s National Buoy

Data Center (NDBC). Case studies of the atmospheric data and the power data are conducted in order to find any relationships between the power and atmospheric conditions.

4.2 IDENTIFICATION OF OPTIMAL AREAS FOR HYDROKINETIC EXTRACTION

The footprint of a hydrokinetic array will be much smaller than the expanse of an entire hydrokinetic resource. Within a given region, there will be locations that are better suited for hydrokinetic energy extraction than others. A method for finding optimal spatial locations within the Straits of Florida for hydrokinetic extraction within the

Florida Current is devised. Knowing where regions are better suited for energy extraction is beneficial to developers as it potentially reduces the amount of site surveys that need to be done.

In order to find optimal locations, the factors that are important for successful extraction are identified. These contributing elements are determined as beneficial or detrimental to the economics of the array. How the power and mass transport change temporally and geographically are also contributing largely to the success of an array. A

combination of the factors important for successful extraction and the power availability are considered in identification of optimal locations within the Florida Current for optimal extraction locations.

The two main factors that will impact the overall economic viability of an array are the power extraction potential and the site characteristics. The power extraction potential can be measured in the total power available in the cross-section, and the availability of a given power density over the cross-section. The total available power in the cross-section is calculated at constant-latitude cross-sections up the Florida Coast as discussed previously and temporally averaged over the data set. At each cross-section, the area over which a threshold power density of 0.5 kW/m2 is met—a current speed of 1 m/s—is determined. Again, this value is temporally averaged to show how the available power and power density vary up the Florida Coast. Both the available power and power density are beneficial economic factors; namely, the increase in quantity will increase the economic viability of the site.

The physical site characteristics will also impact economic viability. These characteristics include distance of the core and its boundaries from shore, and the seafloor depth at the core and its boundaries. As the distance from shore increases, so does the electrical cabling length. Additionally, any maintenance that needs to be performed will take longer—and be more expensive—as service boats or ships will have to travel further. As the seafloor depth over increases, so does the complexity of mooring systems, which will have a direct impact on the installation time and difficulty. As depth

and distance from shore increase, more capital will be spent on the array installation, operation and maintenance; therefore, these are considered negative economic factors.

In order to compare geographic regions, all of these factors must be considered.

One way of doing this to look at the plot of each different factor as it varies up the

Florida Coast, determining what factors are most important, and then choosing a potential installation site. Another way is to create a design matrix. Each of the factors that have been temporally averaged—power, power density, distance from shore, and depth of the sea floor—are normalized by their maximum value as seen in Eq. (26 ) to (29 ):

(26)

(27)

(28)

(29)

where a is the normalized power within the cross-section, b is the normalized area above the threshold power density, c is the normalized distance from shore, and d is the normalized sea floor depth. Both c and d can be evaluated at the core, or the eastern or western boundaries of the core. Both a and b are positive factors, while c and d are negative factors. By normalizing each of the factors, a location factor can be calculated:

(30)

By plotting the location factor as a function of latitude, regions where the location factor is the highest will indicate where optimal extraction sites are located.

Additional weighting factors can be added to the location factor calculation. This way, importance can be placed on different elements. For example, if one assumes that the power and power density available throughout the entire Florida Current are suitable for energy extraction, then more weight may be placed on the physical site characteristics. Most likely, the factors that will have the most importance, however, are the power and available power density, followed by the depth and distance from shore.

By introducing weighting factors, the location factor can be customized:

(31)

where α is the power weighting factor, β is the power density weighting factor, λ is the distance from shore weighting factor, and η is the depth weighting factor. By plotting the un-weighted and weighted location factors side by side, the influence of different weighting factors can be quantified. Through this evaluation, an optimal location for hydrokinetic energy extraction within the Florida Current—based on HYCOM data—are identified.

4.3 TURBINE ARRAY ENERGY EXTRACTION ESTIMATION

While understanding of the available resource is beneficial, open ocean current extraction within the Florida Current will require arrays of turbines to extract enough energy to be profitable; therefore, a method is devised for estimating energy extraction of

an array of turbines placed within the Florida Current. First, a realistic method of predicting the performance of an array is determined. This method is used to predict the performance of an array at the optimal location found in the previous assessment. As a point of comparison, the performance of this array is analyzed at four other distinct locations from the optimal location.

In addition to the estimation of the performance of the initial array, a sensitivity study is performed. A number of arrays are considered at the five previously determined locations. The impact of changing the turbine diameter, cut-in speed, and installation depth in turn is assessed. Over 2000 array configurations are considered—five different locations, three different turbine diameters (20, 30 and 40 m), 11 different cut-in speeds

(0.3 to 1.3 m/s by steps of 0.1 m/s), five different number of turbines (100, 250, 500,

1000 and maximum array), and three different hub installation depths (45, 65, 85 m).

Two different methodologies can be used for evaluating array performance: a user defined number of turbines and a “maximum array” based on the cut-in speed. A

MATLAB tool is developed that will allow the user to decide which methodology will be employed. The tool will allow users to input the turbine installation latitude (°N between

25 and 30°N), turbine diameter, turbine cut-in speed, turbine spacing within the array, turbine hub installation depth. For the user defined number of turbines, the number of turbines within the array will be specified by the user.

Regardless of the method to be employed, HYCOM data is used to determine the

2-year average velocity structure at a specified latitude. If the maximum array methodology is employed, the longitudinal boundaries of a maximum array is identified

based on the hub installation depth, the turbine cut-in speed, and the average velocity structure. For example, if a turbine is to be installed at a depth of 50 m, and its cut in speed is 1 m/s, it would be sensible to find the area over which—on average—the velocity is equal to or greater than 1 m/s at the hub installation depth; therefore, the extreme east and west longitudes, within the boundaries of the HYCOM data set, that have average velocities that meet the cut-in speed are found.

After determining the array’s longitudinal boundaries, the number of turbines within the array is calculated using the turbine diameter and spacing. As this methodology uses HYCOM data, the number of turbines within the maximum arrays is set by the number of grid spaces where the cut-in speed requirement is met, therefore, highly dependent on the horizontal grid spacing. If the grid spacing is altered in some manner, the number of turbines in the maximum array will vary. The hub installation depth, longitudinal boundaries—whether the maximum array or the user specified array—and turbine diameter are used to define the “working area.”

If the user specified number of turbines methodology is employed, the HYCOM grid point that has the highest average velocity at the hub depth is found. This point will act as the midpoint of the user specified array. Using the turbine diameter and the spacing parameter, the width of the array can be calculated; therefore, defining the

“working area” of the array.

The two-year average of the structure of the current speed at a specified latitude, the power within the entire cross-section over two years, calculated using Eq. (24), the power within the array’s working area, and the array power output based on Betz’ limit

efficiency can be plotted, to provide visual statistics at the location of the array. The

MATLAB tool developed also outputs the array parameters, core statistics—where the center of the core is, and the maximum and minimum boundaries of the core—power statistics over the entire cross-section, working area statistics—width, depth range of the working area, longitudinal boundaries, power within the working area—number of turbines, packing fraction, and the power production estimate—with and without Betz’ limit.

These statistics and plots are beneficial for the first estimate of the extraction potential of a given array; however, this methodology does not include efficiencies beyond Betz’ limit and does not include turbine interaction effects. The goal of this array performance estimation is to illustrate the impact of changing geographic locations, turbine size, number of turbines, and the cut-in speed on the power that is available for turbine arrays to extract. There has been much debate that revolves around the applicability of Betz’ limit to ocean energy extraction devices; therefore, for this estimation of the extraction potential to be more accurate, user specified turbine efficiencies that are functions of the inflowing velocity should be added.

Garret and Cummins (2005) provide a method for predicting the hydrokinetic power extraction of a turbine array in a tidal flow, suggesting that the extractable energy from a tidal flow is related to the volumetric flow rate and tidal height amplitude, not the hydrokinetic flux through a channel:

(32)

where γ is a parameter, ρ is the density of seawater, a is the amplitude of the tidal level constituent, Qmax is the corresponding maximum tidal flow rate. This method assumes that the tidal flow is through a restricted channel; however, for the case of open ocean, the currents are typically only bounded on one side. Even in the case of the Florida

Current, where the Bahama Banks bound portions of the current, channel width is large compared to the size of a turbine array so that this assumption does not apply.

Additionally, the Garrett and Cummins method adds a component of potential energy by using the tidal height amplitude and gravitational coefficient. Even though the tidal influence in the Florida Current is identifiable, the tidal current is not the current’s driving force. Therefore, for this evaluation, it is assumed that the extractable energy is a function of the hydrokinetic power flux.

The particular methodology described here has been developed for the Florida

Current. However, it could be equally applied to other geographic regions. For processing simplification, local data set for these regions would need to be compiled—as the

HYCOM global data sets are very large and coarse. Also, it would be necessary to do a comparison of the HYCOM data in a different region to in situ observations within that given region, whereby any discrepancies between the data sets can be noted and considered when using the evaluation methodology.

4.4 IDENTIFYING DATA LIMITATIONS

In using ocean model data, it is important to identify the limitations of the model.

For example, if an ocean model over-predicts the velocities, the hydrokinetic power—and

any other quantity that is a function of the velocity—will be over-predicted. Therefore,

HYCOM data is validated against in situ observations within the Florida Current. Hence a correction factor is determined to allow for discrepancy between the HYCOM data and the observed data for energy densities.

HYCOM data is compared to the in situ ADCP data from February 2009 to March

2010 (ADCP B2-1). The HYCOM data are linearly interpolated at locations corresponding to the bins of the ADCP. The ADCP data are filtered so that only data sets that correspond to the HYCOM prediction, namely only the measurements taken at 2400

UTC, are included. Initial assessments between the HYCOM velocity predictions and the

ADCP, and the implications of the differences between the two data sets, are evaluated and quantified.

Even if the current speed prediction of HYCOM differs from the ADCP,

HYCOM may model the shape of the vertical shear well. In order to compare the shape of the vertical shear from the in situ data with the HYCOM data, each day’s data set is normalized by maximum velocity of the day. Comparing the normalized profiles makes it apparent whether the vertical shear represented by HYCOM is a reasonable prediction of the changing velocity throughout the water column. The ratio of the two normalizing terms can be used as a scaling term for the HYCOM data set:

( ( )) (33) ( ) ( ( ))

This scaling term can then be applied to the HYCOM data on a day to day basis. The impact of application of the scaling term is evaluated in terms of the velocity and hydrokinetic power prediction.

In order to understand if the scaling term dependent on one geographic location is applicable to other geographic locations—over the same time period—the scaling term is applied to the HYCOM data set at 27° N. Subsequently, the transport is calculated and compared to the NOAA cable data measurements. If the agreement between the two data sets is improved, then it would suggest that the gain term application may not be geographically constrained, even if it is only calculated at one geographic location. This study helps to determine the suitability of the HYCOM data for predicting the hydrokinetic power resource of the Florida Current.

4.5 GLOBAL ASSESSMENT

The Florida Current is not the only ocean current where hydrokinetic energy extraction has potential. In the context of ocean renewable energy, both the Florida

Current and Kuroshio Current have been the speculative locations for ocean energy extraction. By utilizing the HYCOM data and using the tools developed in this research, locations of global potential can be more easily identified. Once currents, or geographic regions, are identified, local resource assessment can be performed.

The Florida and Kuroshio Currents were identified as having hydrokinetic potential based on their swift surface currents. However, a more robust method of finding global locations that have hydrokinetic potential is to evaluate the quantity

(34)

where PI is the measure of power intensity, ρ is the water density, and U is the current speed at a specific depth. Using the HYCOM global data set, the power intensity can be

calculated at each grid point. The power intensity is calculated at a depth of 50 m, as that is a probable installation depth for an array of current turbines. After calculating the power intensity at 50 m over the 2-year global data set, 2009-2010, the mean power intensity levels can be mapped. The map will include only locations that have a power intensity of greater than 0.5 kW/m2, based on the assumptions used in the US Tidal

Resource Assessment (Georgia Tech Research Corporation, 2011). From this mapping, areas of hydrokinetic potential can be identified; subsequently, a brief resource characterization of two different currents—the Kuroshio and Agulhas—is made as a point of comparison with the Florida Current. Hydrokinetic array extraction potential and HYCOM agreement with in situ data observations within these global currents is not considered.

Unlike the Florida Current resource assessment, the HYCOM data is not resolved into 10 m vertical-bin sizes, and the horizontal resolution remains at 1/12°. In addition, the resource is assessed at 20 HYCOM grid spaces off of the coastline of the two currents because, unlike the Florida Current, there is no natural eastern boundary of the Kuroshio

Current, and the portion of the Agulhas Current that is being evaluated is south of

Madagascar. This results in east-west transects that extend between 82 (151) and 90

(167) nmi (km) offshore depending on the latitude of the transect. Due to the geography of Japan, some of the transects are constant-longitude transects; the resulting north-south transects extend 100 (184) nmi (km) offshore.

The power and power density at the different transects is evaluated, and the geographic and temporal variation of the resource is also studied from 2009 to 2011. As

these transects will have a larger area than the transects of the Florida Current, the only fair comparison of these three resources is to evaluate the power density at each over the run of each current. In addition to comparing the power density, the optimal power and power density location in the Kuroshio and Agulhas current are identified, and the average cross-sectional velocity structure is qualitatively evaluated and compared to the optimal location in the Florida Current. Completing this brief analysis makes it apparent which of the three global currents is better suited for ocean energy extraction.

5. RESULTS

5.1 DATA ANALYSIS

5.1.1 HYCOM

Due to the fluctuating bathymetry of the Straits of Florida, the physical shape of the Florida Current’s transects change along the coastline. In order to better visualize the changing shape of the Straits of Florida and the impact that the changing shape has on the

Florida Current’s velocity structure and hydrokinetic power, five different constant- latitude transects have been evaluated over the HYCOM data set from 2009-2010: 25.5°,

26°, 27°, 27.75°, and 28.5°N. The average velocity structure at each transect is shown in

Figures 25 to 29. The physical bounds of the Straits of Florida are much narrower at

25.5°N than at 28.5°N, which constrains the core of the current to a smaller area.

Additionally, the current speeds within the core of the current increase as the cross- sections proceed from south to north.

Figure 25: Average Cross-Sectional Velocity Structure off the Florida Coast at 25.5°N

from 2009-2010

Figure 26: Average Cross-Sectional Velocity Structure off the Florida Coast at 26°N

from 2009-2010

Figure 27: Average Cross-Sectional Velocity Structure off the Florida Coast at 27°N

from 2009-2010

Figure 28: Average Cross-Sectional Velocity Structure off the Florida Coast at 27.75°N

from 2009-2010

Figure 29: Average Cross-Sectional Velocity Structure off the Florida Coast at 28.5°N

from 2009-2010

Using the 2-year HYCOM data set, the hydrokinetic power at each day was calculated at the different cross-sections using (24). The results of this calculation can be seen in Figures 30 to 34, with average statistics presented in Table3. Evaluating the cross-sections from south to north, the available hydrokinetic power increases as the latitude increases. This is partially due to the fact that the core velocities are intensified within the northern latitudes, but also due to the fact that there is more area over which the power has been integrated.

Figure 30: Power Fluctuation at 25.5°N from 2009-2010

Figure 31: Power Fluctuation at 26°N from 2009-2010

Figure 32: Power Fluctuation at 27°N from 2009-2010

Figure 33: Power Fluctuation at 27.75°N from 2009-2010

Figure 34: Power Fluctuation at 28.5°N from 2009-2010

Table 3: Hydrokinetic power statistics at specified constant latitude cross-sections

Hydrokinetic Power, GW Latitude, Standard °N Mean Maximum Minimum Deviation 25.5 8.1 2.3 16.5 2.9 26.0 9.6 2.8 17.8 3.4 27.0 11.8 3.6 21.9 4.0 27.75 12.2 3.8 24.4 3.4 28.5 12.7 4.5 25.7 2.7

The distribution of the power within the each cross-section is important in characterizing the Florida Current’s power. By understanding the vertical distribution of power, it gives scientists and technology developers a logical depth range in which turbine installation is sensible. By integrating the power from the surface to a specific

depth, and then dividing by the total power within the cross-section 35, the vertical distribution of the power can be visualized:

(35) ∫ ∫

∫

where z is the depth over which the partial cross-sectional power is integrated, and x is the entire longitudinal range over which the partial cross-sectional power is integrated.

The quantity, (35), has been calculated at each depth, for each cross-section on a daily basis. The resulting daily vertical power distributions were temporally averaged, and the vertical power distribution curves for all of the constant-latitude cross-sections have been plotted in Figure 35.

Figure 35: Average depth distribution of hydrokinetic power at each longitudinal cross-

section within the study

The visualization of the vertical distribution of power shows that between 72% and 89% of the total hydrokinetic power within all of the constant-latitude cross-sections resides above 200 m. If the geographic average of these curves is taken, the result shows that on average, 82% of the total hydrokinetic power resides above 200 m (Figure 36a), and at

27°N, 85% of the total power resides above 200 m (Figure 36b). This suggests that hydrokinetic turbines should be installed within the top 200 m of the water column.

Figure 36: a) Mean vertical distribution of hydrokinetic power over longitudinal range of

study and b) mean vertical distribution of hydrokinetic power at 27° N

Additionally, the visualization of the longitudinal distribution of power across the constant-latitude cross-sections helps further characterize the Florida Current’s hydrokinetic resource. By integrating the power over the entire depth range, but over just one longitudinal grid space, and then dividing by the total power within the cross- section (36), the longitudinal distribution of the power can be calculated and subsequently plotted as seen in Figure 37,

(36) ∫ ∫

∫

where again, z is the depth range, and x is the longitude at which the partial power is calculated.

Figure 37: Average longitudinal distribution of hydrokinetic power at each constant-

latitude cross-section within the range of study

As with the vertical distribution of power, this can be geographically averaged, provide an average longitudinal distribution of power over the entire range of the Florida Current from 25 to 30°N (Figure 38a). Additionally, the longitudinal distribution is better evaluated at a single longitude, providing specific information for where the high regions of power within the cross-section reside (Figure 38b).

Figure 38: Mean longitudinal distribution of power over a) entire latitude range and b) at

27°N

The final geographic distribution of power is show by plotting the fluctuation of the available power from south to north. As shown in Figures 25 through 34, the trend seems to be that as the Florida Current progresses northward through the Straits of

Florida, the core velocities intensify and the available hydrokinetic power also increases.

However, a much easier way to visualize the power increase is in Figure 39, where the average hydrokinetic power at each constant-latitude cross-section is plotted against the increasing latitude. This figure shows that the hydrokinetic power over the geographic range that has been studied increases from 25° to 29°N. The decrease in power north of

29°N is simply due to the fact that the core starts to move further east, and is not always within the geographic bounds of the study.

Figure 39: The fluctuation of the average hydrokinetic power along the east coast of

Florida from 2009-2010

As seen in Figures 25 through 29, the area over which the power is integrated fluctuates.

In order to remove the variability in the area over which the power is integrated, the average power density over each cross-section is calculated (20), and subsequently averaged, and can be seen in Figure 40. As turbine arrays will not create a dam across the

Florida Current, and most likely will only occupy a small portion of the total cross- sectional area, it is important to know not only the regions where the available hydrokinetic power is high, but also where the hydrokinetic power density is high. The purpose of this plot is to show the regions in which there is a higher density of power.

Figure 40: Average hydrokinetic power density up the east coast of Florida from 2009-

2010

While regions of high power density are important to note, the power density has been averaged over the entire cross-section. However, as shown in Figure 35, the majority of the power resides within the upper 200 m of the water column. By taking the average power density over the entire cross-section, the power density is skewed as most of the area is not usable area for turbine installation purposes. Another way of evaluating the power density fluctuation along the coastline is to evaluate how much area of each constant-latitude transect has a power density within given bounds. As seen in Figure 41, the average cross-sectional area where the power density ranges from 500-1000 W/m2,

1000-1500 W/m2, 1500-2000 W/m2, and 2000+ W/m2 at each transect is plotted. This

indicates the average amount of installation area within a cross-section in the Straits of

Florida for a turbine array with a given operating power density threshold.

Figure 41: Average cross-sectional area over which the power density is within a given

threshold from 2009-2010

Finally, the relative position of the core of the current—the location where the most intense velocities reside—to the shore indicates how far offshore the high power densities are. The east and west boundaries of the core are found by finding the range over which the surface velocity is less than once standard deviation away from the maximum surface velocity. The average position of the center of the core, and its eastern and western boundaries, are shown in Figure 42. As the Florida Current progresses northward from 25°N, the core stays relatively near the Florida Coast; however, progressing northward from 27°N, the core shifts further offshore.

Figure 42: The average position of the Florida Current’s core and boundaries from 2009-

2010

5.1.2 Historical Data Sets

By integrating the isotachs seen in Figures 17 to 23, the power and the transport can both be estimated. As seen in Table 4, the power ranges from 7.6 to 16.1 GW, with a corresponding transport of 22.1 to 28.8 Sv.

Table 4: Estimated power and transport from Lee, Brooks, and Düing data sets

Data Set Power, GW Transport, Sv Miami Mean 11.2 25.6 Spring 16.1 28.8 Summer 15.5 28.8 Fall 7.6 22.1 Winter 8.3 22.3 Fowey Rocks Mean 12.5 27.7 Fort Pierce Mean 15.5 25.7

In a similar fashion, the isotachs from the STACS transect (Figure 11) have been integrated to estimate the average power and transport at 27°N.

Table 5: Estimated power and transport from average STACS transect

Data Set Power, GW Transport, Sv STACS Mean 19.0 31.0

As these power and transport estimates were based on average cross-sectional velocity structures, they may be slightly skewed; however, they provide a baseline to compare the power calculated by the HYCOM data set. Overall, the HYCOM predicted power is lower than the estimated power based on these various historical data sets; however, the orders of magnitude of both data sets agree.

5.1.3 Explorer of the Seas Data Sets

ADCP data from the Royal Caribbean cruise ship Explorer of the Seas has been evaluated for its power potential and core position, much like the HYCOM data. The

Explorer of the Seas collected data for six years in and out of Port Everglades. Due to difficulties in data collection and the sporadic nature of fully populated data sets, the data that have been analyzed in this research span 2003-2004. At the time, the Explorer of the

Seas operated two different routes, an eastern and western route, as seen in Figures 43and

44.

Figure 43: Explorer of the Seas Eastern Route, 2003-2004

Figure 44: Explorer of the Seas western route, 2003-2004

The eastern route transected the Straits of Florida on its departure and arrival into port while the western route did not. Because the ship was operating on this schedule, transects of the Straits of Florida were taken approximately twice every two weeks. Over the two year period from 2003-2004, 69 of the Florida Current transects warrant evaluation.

Before evaluating each individual transect, the isotachs of the average transect

(Figure 14) were integrated to establish a baseline power and transport estimate as seen in

Table 6.

Table 6: Power and transport from Explorer of the Seas average velocity structure

Data Set Power, GW Transport, Sv Explorer of the Seas Mean 13.7 27.4

Based on order of magnitude comparison, these estimates agree with both the Lee, et al. data, and the STACS data. However, as stated previously using averaged data only provides a baseline estimate for the power prediction; therefore, the velocity structure captured on individual cruises were evaluated for their power and transport. An example of outbound and inbound transects can be seen in Figures 45a and b and 46a and b. The power and transport from these individual transects is shown in Table 7.

Figure 45: Outbound and Inbound Explorer of the Seas Cruise from July 2003 (Cruise

326)

Figure 46: Outbound and Inbound Explorer of the Seas Cruise from June 2004 (Cruise

424)

Table 7: Power and flow rate from example Explorer of the Seas transects

Cruise Power, Transport, Number Direction Date GW Sv 326 Outbound 07/11/03 16.3 24.3 326 Inbound 07/18/03 14.1 24.2 424 Outbound 06/12/04 7.4 19.2 424 Inbound 06/19/04 10.1 20.3

Over the 69 transects from 2003 and 2004 that were evaluated, the average power and transport are seen in Table 8. The power and transport calculated from the individual cruises can be seen in Appendix A. Additionally, the data from the Explorer of the Seas transects has been compared to HYCOM data from 2009-2010. Although these two data sets have a different time history, they both represent two-year temporal averages. Overall, the HYCOM predicted transport and power are less than what is predicted by the Explorer of the Seas data; however, considering that the data sets are six years apart, it is not expected that the data would compare perfectly. While the power and transport are seemingly under-predicted by the HYCOM data set, the position of the core, and the eastern and western boundaries of the core compare very well. The

HYCOM predicted core, and eastern and western boundaries of the core are further east than what is seen by the Explorer of the Seas data; however, the maximum difference is

0.06° longitude, which at the given latitude is approximately 6 km—which is also less than one HYCOM grid space away. This suggests that the shape of the velocity structure represented by the HYCOM data is very near the structure that was seen by the Explorer of the Seas cruise ship. Additionally, it would suggest that the temporally averaged velocity structure is relatively constant.

Table 8:Power and flow rate from 2003-2004 Explorer of the Seas transects

Data Set Power, GW Transport, Sv Explorer of the Seas 2003-2004 12.2 22.8

Table 9: Explorer of the Seas compared to HYCOM Data

Explorer of the Seas, 2003-2004 HYCOM, 2009-2010 Power, Transport, Core Power, Transport, Core GW Sv Position, °E GW Sv Position, °E Mean 12.3 23.0 -79.78 9.6 21.3 -79.76 Max 30.1 33.1 -79.56 17.8 26.8 -79.52 Min 5.4 14.9 -79.98 3.5 14.8 -79.92

5.1.4 ADCP Data

As shown in Section 4.1.3, five ADCP deployments have been completed by the

SNMREC at Florida Atlantic University from 2009 to 2012. The date ranges and locations of these deployments are seen in Table 2. In this section, the results and trends seen in each of the deployments is discussed, but only figures from the first two deployments B2-1 and B3-1 is presented in this section. The figures for the remaining three deployments are presented in Appendix B.

The current speed is plotted in Figure 47. As expected using the HYCOM data set, the most intense current speeds are located within the upper portions of the water column and decay as the depth increases. The surface current is intensified over a prolonged period of time during the month of July.

Figure 47: Current speed over the B2-1 ADCP Deployment, February 2009-March 2010

The current magnitude only shows a portion of the current, as the directionality of the current will play a large role in the deployment of turbine arrays. In Figure 48, the northward and eastward component of velocity are plotted side by side. Additionally, they are plotted on the same scale so that the order of magnitude of both can be visually compared. The eastward component of velocity is also shown in Figure 49, and plotted on a more appropriate scale. From Figure 48, the northward component of velocity is much more intense than the eastward component of velocity. The data show that the predominant flow direction is northward with a slight eastward velocity component. The mean northward flow nearest the surface is 1.56 m/s, while the mean eastward flow is

0.38 m/s, with a mean direction of 13.6 ° east of north.

Figure 48: a) Northward and b) eastward component of velocity over the B2-1 ADCP

Deployment, February 2009-March 2010

Figure 49: Eastward component of velocity over the B2-1 ADCP Deployment, February

2009-March 2010

The mean, minimum and maximum velocity profiles are shown in Figure 50.

While the average velocity profile sets a baseline for standard operating conditions for a

turbine, the absolute minimum and maximum profiles indicate the velocity range over which a turbine would operate in over the 13-month deployment. Knowing the absolute maximum velocity profile also allows for the estimation of the forces acting on a turbine array.

Figure 50: Mean, absolute minimum, and absolute maximum velocity profiles during the

B2-1 ADCP deployment

Over each day, the power density was calculated at each individual depth bin.

This value was then averaged to arrive at an average power density plot, seen in Figure

51. It is important to calculate the power density at each day as opposed to using the average velocity profile to construct this power density curve, as the power density curve will then be skewed.

Figure 51: Average power density as a function of the depth during the B2-1 ADCP

deployment

Although it is not easily seen by plotting the entire data set, by focusing on a small portion of the ADCP deployment, the current speed shows the influence that the tidal fluctuations have on the velocity. As seen in Figure 52, the current speed increases for approximately 12 hours, reaches a peak, and then decreases for approximately 12 hours. By performing spectral analysis of the current speed, as seen in Figure 53, the tidal constituents O1, K1, N2, M2, S2 are apparent. The properties of the tidal constituents seen within the ADCP data set are seen in Table 10.

Figure 52: Current speed from July 19-23, 2009 from the B2-1 ADCP deployment

Figure 53: Frequency analysis of the B2-1 ADCP deployment with tidal constituents

indicated

Table 10: Tidal constituents seen in ADCP Deployment B2-1

Period, Constituent Name hours Principal Lunar O1 Diurnal 25.82 K1 Luni-solar Diurnal 23.93 N2 Larger Lunar Ecliptic 12.66 M2 Principal Lunar 12.42 S2 Principal Solar 12.00

As the tidal influence is easily seen, in both Figures 52 and 53, the magnitude of the tidal current becomes an important quantity to understand. By using the T-Tide

MATLAB toolbox, the tidal currents were evaluated. By inputting the complex current into t_tide, the tidal velocities are extracted from the data. The northward and eastward components of the tidal velocity are seen in Figure 54a) and b). At a depth of 100 m, there is a distinct break in the tidal velocities as predicted by the T-Tide toolbox. The cause of this is unknown; however, using the t-tide tool box with all of the ADCP data sets has shown that tidal velocities in the northward direction can reach up to ±0.5 m/s, while the eastern tidal velocities can reach up to ±0.2 m/s.

Figure 54: A) Northward and b) eastward components of the tidal velocities

By subtracting the tidal velocities from each velocity component, and plotting the current speed, the de-tided data sets can be seen in Figures 55a and b.

Figure 55: De-tided data sets from ADCP Deployment B2-1 a) over the entire data set

and b)from July 19-23, 2009

What is important about understanding the tidal induced velocities is that they will have an impact on the arrays and array extractions. By investigating ADCP data, the tidal influence is clearly seen; however, because tidal forcing is not included in the

HYCOM model, and due to the temporal resolution of the model, tidal influences in the velocity could be missed if solely model data were relied upon for resource assessment.

In the past, ADCP data was used to construct velocity histograms in order to better understand the probabilistic distribution of velocities; however, these histograms are typically depth dependent. By layering depth-dependent histograms, a visual of the velocity probability throughout the entire water column can be constructed, as seen in

Figure 56. Given a certain cut-in speed, this layered histogram shows where a turbine should be installed within the water column to take advantage of the high probability that

a given cut-in speed will occur. Conversely, if a turbine is to be installed over a certain depth range, the turbine can be optimized to work within the operating conditions at that depth.

Figure 56: Layered histogram of the B2-1 ADCP Deployment

By multiplying the layered histogram—the probability of occurrence of a given velocity—by the power density that would be present operating at the given velocity, a weighted power density is calculated (37).

(37) ( )

Using the weighted power density, the power available to a turbine operating at a specific depth, at a specific velocity can be calculated. In other words, at an operating depth of 50

m, a turbine can be expected to experience availability of approximately 170 W/m2 of power with an operating speed V = 1.4 m/s. If a current turbine were located at 50 m/s, and had a cut in speed of 1 m/s, the expected power density that the turbine could expect to incur would be 1880 W/m2, which is the sum of the individual expected power density values over the range of operating velocities, from 1 m/s to 2.5 m/s. This also helps visualize the distribution of power throughout the water column.

Figure 57: Weighted power density curves for the B2-1 ADCP Deployment

Finally, the B2-1 and B3-1 deployments were simultaneously collecting data for three weeks during the beginning of the B2-1 deployment. By comparing these data sets, some information can be learned about the horizontal shear between the two deployment sites; however, the information is limited as there are only three weeks of simultaneous data collection, and there are only two points over which to make any horizontal shear

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calculations. In Figure 58, the two data sets are plotted side by side, with the inshore deployment (B3-1) on the left, and the offshore deployment (B2-1) on the right.

Although the surface velocities seem more intense for the B3-1 deployment, over the entire span of the water column, the velocity intensity is greater at lower depths in the water column for the B2-1 deployment.

Figure 58: Current speed at a) B3-1 ADCP deployment and b) B2-1 ADCP deployment

over same time range

In Figure 59, the difference in the current speed for the two data sets is seen. The current speed from B3-1 was subtracted from the B2-1 data set. The figure clearly shows that at deeper points within the water column, the current speed at B2-1 is much higher.

The average horizontal shear between the two data sets was calculated using the following equation:

̅̅̅̅(̅ ̅̅ ̅ ̅)̅̅ ̅̅̅ ̅̅̅(̅̅ ̅ ̅ ̅̅) (38) ̅

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where U is the current speed, and Δx is the distance between the two deployment sites.

The result of this calculation is shown in 19. Within the upper 100 m of the water column, the horizontal shear between the two locations is small; however, below 100 m in the water column, the horizontal shear increases between the two deployment sites. In terms of turbine deployment between these two locations, this would suggest that if the turbines were installed in the upper 100 m of the water column, the turbines would be experiencing very similar operating conditions in terms of the current speed.

Figure 59: Difference in current speed from B2-1 to B3-1 ADCP deployments

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Figure 60: Shear between the ADCP B2-1 and B3-1 deployments

As for the other three ADCP deployments, many of the same trends are present.

Various figures that have been presented in this section have been replicated and presented in Appendix B for the other three deployments, B3-2, B2b-3 and B3-3. The mean velocity profile maintains its nearly linear structure throughout all of the ADCP deployments. Additionally, the horizontal shear between B2b-3 and B3-3 is approximately the same shear curve that was calculated for the B2-1 and B3-1 deployment. This suggests that the mean current structure is fairly consistent between those two geographic locations regardless of the duration of the data collection, and regardless of the time of year. The tidal influence is seen in all of the ADCP data sets.

There were two current reversals that were seen throughout the duration of all of the deployments. They occurred during the B3-2 deployment, during early November

2011. The plots of the current reversals can be seen in Figures 61 and 62. These quiver

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plots were made at the 32 m depth bin; however, the depth of influence of these reversals was up to 110 m.

Figure 61: Current reversal at 32 m during the B3-2 ADCP deployment, November 4-5,

2011

Figure 62: Current reversal at 32 m during the B3-2 ADCP deployment, November 9-10,

2011

These current reversals provide another degree of complication for the installation of current turbines within the Florida Current. The fact that eddies can create current reversals, and can be seen up to 110 m deep, needs to be carefully taken into consideration when designing or installing an array of current turbines. However, these

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reversals were two very isolated incidences; in 773 days of data collection, only two current reversals were seen. Taking the scarcity of these occurrences into consideration, no definitive conclusion can be made regarding the periodicity of current reversals; however, current reversals can happen and should be a design consideration.

5.1.5 NOAA Cable Data

The data from the NOAA submarine cable that collects mass transport data of the

Florida Current at 27° N from 2009 to 2010 has been plotted in Figure 63. The two-year data statistics can be seen in Table 11. The maximum, minimum, and standard deviation of the mass transport have been presented in absolute terms, as well as in terms of the mean mass transport. This is done in order to see if the average fluctuation of the estimated power fluctuates in the same manner in which the mass transport fluctuates.

Figure 63: Mass transport fluctuation of the Florida Current at 27°N from 2009-2010 as

measured by the NOAA submarine cable

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Table 11: Florida Current mass transport statistics from 2009-2010

Transport, Sv % of Mean Mean 31.0 -- Standard Deviation 3.4 11% Max 40.0 129% Min 19.8 64%

5.1.6 Case Studies

Various case studies comparing readily accessible observation data with the hydrokinetic power estimated through use of HYCOM data have been completed in the attempt to find a relationship between these quantities. If the hydrokinetic power can be related to readily accessible measurements, then the fluctuation of the resource could be estimated by the fluctuation of other observational data. Even if the observational data and the power estimations are not related on a measurement-by-measurement basis, overall trends are noted. Different atmospheric conditions are compared with the power including the temperature of both air and water, the atmospheric pressure, and the wind.

Additionally, the wind data are compared to the top bin within the ADCP data set.

Transport and surface current data—from both the UM WERA high frequency radar operations and from the uppermost bin of the ADCP data set—are compared to the fluctuating power as well. The fluctuating power used for the case studies is the average power of the HYCOM transects between 26 and 28°N over the two year data set, except in the case of comparing the power to the transport. The fluctuating power curve for comparison with the transport values is the power calculated from the HYCOM transects at 27° N.

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5.1.6.1 Atmospheric Data

The fluctuation of the air and water temperature was compared to the fluctuating power over the two years study. As seen in Figure 64, there is a pronounced seasonality of both sets of temperature data. The power curve shows some seasonality as the peak power values occur in the summertime, which is when the peak temperatures occur.

Figure 64: Air and water temperature from 2009-2010 from the Fowey Rocks Lighthouse

weather station compared to power fluctuation

On average, the air temperature is 24.4° C, the water temperature is 26.3° C, and the power is 11.3 GW. During the month of July 2009, the average air temperature was

28.6° C, the water temperature was 29.4° C, and the average power was 15.9 GW.

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During the month of July 2010, the average air temperature was again 28.6° C, the water temperature was 29.6° C, and the average power was 13.7 GW. However, with only two years of data, it is impossible to prove seasonality. With additional years of HYCOM and temperature data, it may show that the power has a seasonal periodicity.

The fluctuation in atmospheric pressure and power can be seen in Figure 65.

Overall, there does not seem to be an obvious trend between the power and atmospheric fluctuation.

Figure 65: Atmospheric pressure from 2009-2010 from the Fowey Rocks Lighthouse

weather station compared to power fluctuation

While the plot of each entire data set does not show any trends between the two sets of data, on closer examination there may be some correlation between the air pressure and the power. Between 2009-2010, there were three cases in which the atmospheric pressure was greater than 102.5 kPa for at least three days in a row. In these

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three occurrences, 5-10 days later there was a spike in the hydrokinetic power. These three anomalies are plotted in Figure 66.

Figure 66: Time series where the atmospheric pressure measured at the Fowey Rocks

Lighthouse weather station was greater than 102.5 kPa for at least three days in a row and

the corresponding power calculations

Conversely, there were two cases in which the pressure dropped below 101 kPa for three days in a row. In these two occurrences, there was a drop in the hydrokinetic power 6-10 days later, as seen in Figure 67. As there are a limited number of these

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occurrences, there is not enough evidence to draw any conclusions; however, with more data, this could be evaluated in more detail.

Figure 67: Time series where the atmospheric pressure measured at the Fowey Rocks

Lighthouse weather station was less than 101 kPa for at least three days in a row and the

corresponding power calculations

Subsequently, the wind data from the Fowey Rocks Lighthouse weather station was evaluated in order to find a correlation between not only the power and the wind, but also the top bin of the ADCP current data with the wind. As there is a component of directionality to the wind, the wind speed, northern and eastern wind velocity were all plotted against the power fluctuation in Figure 68.

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Figure 68: Wind data measured at the Fowey Rocks Lighthouse weather station from

2009-2010 with power fluctuations

There is no apparent correlation between the fluctuations in the wind and the power; however, when looking at the correlation coefficient between the fluctuation of the northern component of wind velocity and the power fluctuation, seen in Figure 69, there is a distinct lag between the wind and the power. The wind leads the power by one day; however, the correlation coefficient is not high.

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Figure 69: Correlation coefficient between the northern component of velocity of the

wind and the power

With the ADCP data, the velocity data from the top most bin with good data—at

32 meters—was compared to the different components of wind velocity. Both the north and east velocity components from the ADCP measurements were compared to the north and east velocity components from the wind measurements; resulting, in a total of four different comparisons. Two of the comparisons are seen in Figure 70.

Figure 70: Comparison of the components of the Fowey Rocks wind velocity and ADCP

current velocity data

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The subsequent correlation study between four different velocity comparisons yielded correlation coefficients of less than 0.15, and the maximum correlation coefficients occurred at zero time lag between. As this ADCP measurement is not at the surface, the wind influence may not be seen at this depth within the Florida Current; therefore, a high correlation between these two measurements should not be expected.

5.1.6.2 Transport Data and Power

As both the transport and the power a functions of the velocity, it seems reasonable to think that there would be some correlation between the two measurements; however, since the power is a function of the velocity cubed, the relationship may not be as correlated as initially anticipated. In Figure 71, the transport and power fluctuations are shown. Qualitatively, the data sets seem to exhibit some of the same behaviors. For example, in July 2009, both the power and transport have peaking values; however, the transport seems to increase, and stay very high in July 2010 while the power starts to decrease. A correlation study of the two time signals was done and plotted in Figure 72.

In this case, the highest correlation coefficient occurs when the transport leads the power by one day, meaning that a transport increase one day will lead to a power increase the next day.

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Figure 71: Transport from NOAA submarine cable compared with HYCOM power

estimates at 27° N

Figure 72: Correlation coefficient between the transport and power data

5.1.6.3 Surface Current Data and Power

Both the ADCP top most bin and the UM WERA Surface Current Radar measurements to compare the surface current speed with the power fluctuations. First, the

ADCP top-most bin was compared to the fluctuating power, as seen in Figure 73.

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Subsequently, the correlation study shows that the highest correlation between the data sets is at zero-lag, with a correlation coefficient of 0.57 (Figure 74).

Figure 73: ADCP current speed at 32 meters compared with the HYCOM power

estimations

Figure 74: Correlation coefficient between the ADCP 32-m bin velocity data and power

data

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Finally, the UM WERA high frequency radar surface current data was compared to the power. As the area range over which surface currents are calculated fluctuates in the UM WERA data, the average surface current over the entire range was calculated each day instead of choosing a specific location to find the surface current. Also, only

WERA data from 2009 was evaluated as there were many missing data sets in 2010; the breaks in the 2009 data can be seen in Figure 75 as well.

Figure 75: UM WERA surface current data from 2009 compared to HYCOM power

fluctuations

Over the portion of the WERA data that was consistent—from late-March 2009 through late-October 2009—a correlation study was done. This specific data set is shown in Figure 76. The highest correlation coefficient was at a 1-day lag, where the surface current was leading the power, also seen in Figure 76.

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Figure 76: a) Partial WERA 2009 data set plotted with the HYCOM power fluctuations,

and b) the correlation coefficient between the WERA data and HYCOM power data

5.2 OPTIMAL ARRAY INSTALLATION REGIONS

The identification of areas of higher realistic potential for array installation, without having to do extensive and expensive site surveys throughout the entire range of the Florida Current, is extremely beneficial to the scientists and stakeholders involved in offshore renewable energy. Finding the optimal location for turbine installation involves the balance of different parameters that impact array installation costs, operation, and energy output.

The fluctuation of the power, power density, and distance of the core from the coastline can be seen in Figures 39, 40, and 42. As discussed previously, the power and power density are both positive site attributes, while the distance from shore is a negative attribute to the success of the array. Additionally, the installation depths over the core boundaries, seen in Figure 77, has a negative impact on the array success as the deeper

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the depth, the more complicated the mooring system becomes to design, build and implement.

Figure 77: The average depth at the Florida Current’s core and boundaries from 2009-

2010

In order to weigh all of these factors into finding the optimal array installation location, each of these factors—power, power density, distance from the center of the core to shore, and depth at the center of the core—have been normalized by their maximum value, as prescribed in Eq. (26)-(29) and plotted in Figures 78 and 79. The normalized positive site attributes are plotted in Figure 78, and the normalized negative site attributes are plotted in Figure 79.

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Figure 78: Normalized average hydrokinetic power and power density up the Florida

Coast 2009-2010

Figure 79: Normalized average depth at the Florida Current’s core and distance of the

Florida Current’s core from the shore up the Florida Coast 2009-2010

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Using Eq. (30), the un-weighted installation location factor has been plotted in

Figure 80. The un-weighted location factor indicates that the best region for turbine array installation is between 26.5° and 28°N, with the optimal location at 27.16°N. The 2-year average velocity structure, power, and transport at the optimal location factor have been plotted in Figures 81 through 82.

Figure 80: Location Factor based on HYCOM data from 2009-2010

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Figure 81: Average Velocity Structure at 27.16°N from 2009-2010

Figure 82: Hydrokinetic power fluctuation at 27.16°N from 2009-2010

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Figure 83: Transport fluctuation at 27.16°N from 2009-2010

Weighting factors can also be introduced into the location factor calculation as seen in Eq. (31). In the specific case evaluated, the weighting factors are: α is 4, β is 3, λ is 1, and η is 2. Using these specific weighting terms, the optimal location for array installation was still 27.16°N. In the future, these weighting terms can be adjusted in order to more closely relate the different factors to the actual installation and operating costs, as well as the price at which electricity produced will be bought.

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Figure 84: Weighted Location Factor based on HYCOM data from 2009-2010

Based on this analysis, the optimal array installation location is considered

27.16°N. The average statistics from this cross-section can be seen in Table 12.

Table 12: Optimal Array Installation Location Statistics

Optimal Location Statistics Latitude 27.16° N Mean Power 12.1 GW Mean Power Density 296 W/m2 Distance of Core from Shore 37.4 km Depth at Core 400 m

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5.3 ARRAY EXTRACTION ESTIMATION

Based on the results from finding the optimal location for turbine installation in the previous section, the maximum array size—dependent on the 2-year current structure at 27.16°N, the cut in speed of the turbine, and the turbine installation depth—has been determined at 27.16° N. The parameters of the turbine arrays can be seen in Table 13.

The step size for the cut-in speed was 0.1 m/s.

Table 13: Maximum Array Characteristics Evaluated at 27.16°N

Diameter 30 m Hub Installation Depth 65 m Spacing (Tip to Tip) 1 Diameter Cut-in Speed 0.3 to 1.3 m/s

Using the given parameters, the maximum array size for each cut-in speed was found. The array bounds, number of turbines, mean array power and mean power per turbine values for each cut-in speed are found in Table 14. The power statistics within the table include Betz’ limit efficiency, but do not include other efficiencies. While an array could certainly be comprised of more turbines than suggested by the maximum array determination, it is sensible to install an array where, on average, a turbine will be operational. Namely, if a turbine with a 1 m/s cut-in speed is installed outside of the 1 m/s maximum array bounds, they may operate on occasion, but on average are in a region where the conditions will not support energy extraction.

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Table 14: Maximum Array Statistics at 27.16°N, Including Betz Limit Efficiency

Maximum Turbine Arrays at 27.2°N Array Bounds, Mean Mean Number Cut-in °E Array Power per of Speed, m/s Power, Turbine, Turbines West East MW kW 0.3 -79.92 -79.16 1254 441 352 0.4 -79.92 -79.24 1122 439 392 0.5 -79.92 -79.24 1122 438 391 0.6 -79.92 -79.32 990 432 437 0.7 -79.84 -79.32 858 424 494 0.8 -79.84 -79.32 858 419 489 0.9 -79.84 -79.40 726 404 557 1 -79.84 -79.40 726 396 545 1.1 -79.84 -79.48 594 355 598 1.2 -79.76 -79.48 462 298 645 1.3 -79.76 -79.56 330 232 703

The overall trends found in the maximum array extraction estimation show that if the cut-in speed is low more cross-sectional area will support energy extraction; therefore, the maximum number of turbines for an array with 0.3 m/s cut-in speed is much higher than the maximum number of turbines for an array with 1.3 m/s cut-in speed. Because the maximum array area is larger with low cut-in speeds, the mean array power extraction is higher for an array with a lower cut-in speed. In general, as the cut-in speed increases, the mean power per turbine increases. This is due to the fact that there are fewer turbines operating in areas with higher velocities; therefore a higher concentration of hydrokinetic power.

In addition to the maximum array, set arrays were evaluated at 27.16°, and the parameters can be seen in Table 15.

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Table 15: Specific Array Parameters

Number of Turbines 100, 250, 500, 1000 Turbine Diameters 20, 30, 40 m Cut-in speeds 0.3 to 1.3 by steps of 0.1 m/s Hub installation depths 45, 65, 85 m

Each of the different parameters has an impact on the turbine array power extraction. In order to understand the impact that each of these parameters has on the array extraction, three of the parameters must be held constant while one varies.

Visually this can be seen in Figures 85 through 88.

Figure 85: Array extraction fluctuation varying installation depth, holding number of

turbines, diameter, and cut-in speed constant

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Figure 86: Array extraction fluctuation varying cut-in speed, holding number of turbines,

diameter, and installation depth constant

Figure 87: Array extraction fluctuation varying number of turbines, holding number

diameter, cut-in speed, and installation depth constant

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Figure 88: Array extraction fluctuation varying turbine diameter, holding number of

turbines, cut-in speed, and installation depth constant

The trends illustrated in Figures 85 through 88 are straight forward. As the installation depth at the hub increases from 45 m to 85 m, as seen in Figure 85, the total array power decreases. This is due to the fact that as the installation depth increases, the velocities decrease, which will in turn impact the array extraction. As the better power resource is closer to the surface, the closer to the surface that arrays can be installed the better; although, realistically a balance will have to be achieved between what is the theoretically best installation depth—based on turbine size, consideration of surface affects, and the marine traffic within the region—and what is feasibly possible.

As seen in Figure 86, as the cut-in speed is increased, the time in which a turbine array is operating in a current cannot that sustain energy production is more frequent; namely, the water velocity is less than the cut-in speed in more instances. In Figure 86,

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only the cut-in speeds above 1 m/s were plotted because the power fluctuation curves within the array area are almost identical with cut-in speeds between 0.3 m/s and 0.9 m/s.

The power extraction potential increases as the number of turbines in the array increases (Figure 87). This is expected and straight forward; however, the average individual turbine productivity decreases as the number of turbines increases. This due to the fact that large arrays may include turbines are operating in regions where the velocity is not as favorable as it is within the core of the current.

Finally, as the turbine diameter increases, the power also increases as seen in

Figure 88. If there is more area occupied by turbines, then there is more potential to convert more energy from hydrokinetic into useable electricity; therefore, installing turbines with larger diameters will be the best option in the future. However, technology needs to improve in order to build a robust, large turbine.

At 27.16°N, nearly 400 different arrays have been evaluated based on the fluctuating cut-in speed, hub installation depth, diameter, and number of turbines. The results from all of these array extraction estimates can be found in Appendix C. These results are different from the results presented in the body of this work as they do not include the Betz’ limit, or any measure of efficiency. Using the numbers reported in these tables, a turbine designer could user the speed-dependent efficiency of the turbine into the results. For example, if the cut-in speed of a turbine is 1 m/s, the efficiency at that given speed could be added to the results presented in the appendix. Additionally, if values including Betz’ limit efficiency are desired then the fixed ratio of 16/27 could be applied to the data.

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Similarly, these 396 combinations of arrays have been evaluated at four other distinct locations: 25.7°, 26.5°, 27.5° and 28.9° N. This is done as a comparison to see if the investigation of the location factor was useful in predicting the output of a turbine array. The results of these nearly 1600 turbine array combinations are also included in

Appendix C.

In order to quickly compare the estimated power output of these arrays in different locations, a representative array was chosen and compared at each of the five latitudes. The results of this comparison can be seen in Table 16 without including Betz limit efficiency, and Table 17. Overall, the arrays at at 27.2° and 27.5° N have the same output for the compared arrays. The other three locations do not have less potential than the two in the 27° region. The location factor at 27.2° and and 27.5° were 1.08 and 0.68, while the location factors at 25.7, 26.5 and 28.9 were 0.29, 0.63 and 0.11, respectively.

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Table 16: Representative Array Extraction Estimation at an installation depth of 65 m

without inclusion of Betz Limit Efficiency

Turbine Array Power Extraction Estimate, MW Cut-in 500, 30 m-diameter turbines Speed, Latitude, °N m/s 25.7° 26.5° 27.2° 27.5° 28.9° 0.3 376 429 495 496 408 0.4 376 429 495 496 408 0.5 376 429 495 496 407 0.6 375 429 495 496 407 0.7 375 429 495 496 407 0.8 374 428 494 495 405 0.9 371 426 493 493 399 1 361 420 489 488 386 1.1 337 401 476 475 362 1.2 292 362 448 448 325 1.3 219 298 396 397 277

Table 17: Representative Array Extraction Estimation at an installation depth of 65 m

with inclusion of Betz Limit Efficiency

Turbine Array Power Extraction Estimate, MW 500, 30 m-diameter turbines Cut-in Speed, m/s Latitude, °N 25.7° 26.5° 27.2° 27.5° 28.9° 0.3 223 254 294 294 242 0.4 223 254 294 294 242 0.5 223 254 294 294 241 0.6 223 254 293 294 241 0.7 222 254 293 294 241 0.8 222 254 293 293 240 0.9 220 253 292 292 236 1 214 249 290 289 229 1.1 200 237 282 282 215 1.2 173 214 265 266 193 1.3 129 176 235 235 164

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By choosing a cut-in speed of 1m/s, the average estimated extracted power at each location are presented in Table 18. In addition to comparing the power output, the boundaries of the 500 turbine array and their corresponding depths are presented in Table

19. Again, the sites at 27.16° and 27.5° N are comparable in both power output, and depth at the array installation locations; however, the distance offshore for the array at

27.5° is considerably further offshore than the array at 27.16°N.

Table 18: Comparison of Specific Array Statistics at Five Different Locations

Comparison of Specific Array at Each Latitude, °N Average Site Power, MW Array Specifics: 25.7 214 Cut-in Speed: 1 m/s 26.5 249 Diameter: 30 m 27.2 290 Number of Turbines: 500 27.5 289 Installation Depth: 65 m 28.9 229

Table 19: Array Boundaries and Depth at Array Boundaries

Western Bounds Mid-Point Eastern Bounds Latitude, °N Distance, Depth, Distance, Depth, Distance, Depth, km m km m km m 25.7 20.0 300 36.1 690 52.1 700 26.5 19.9 300 35.8 590 51.8 700 27.2 27.7 250 43.5 490 59.4 700 27.5 43.4 300 59.2 490 75.0 700 28.9 89.6 400 105.2 590 120.8 700

While all of these comparative studies can be performed, a tool has been developed so that a user may input the desired array installation location, cut-in speed, number of turbines—maximum or user specified—turbine diameter, hub installation

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depth, and turbine spacing—from blade tip to blade tip. The MATLAB program then outputs various figures in a PDF file, as well as an Excel spreadsheet that reports the inputs of the program, as well as various calculated array statistics. As an example, an array located at 27.16° N, comprised of 500, 30-m turbines with a cut-in speed of 1 m/s, turbine spacing of 30 m, and with a hub installation depth of 65 m has been evaluated using the MATLAB program. The PDF output and Excel spreadsheet can be seen in

Appendix D. Additionally, the program tells the user if the number of turbines that has been specified is outside the bounds of the maximum array size, and then adjusts the number of turbines so that the array is operating within an acceptable region. A screen shot of the program is seen in Figure 89.

Figure 89: Screenshot of the MATLAB array extraction estimation program

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5.4 DATA LIMITATIONS

The ocean is a very complicated, dynamic system. Although ocean models have improved significantly with the advances in computing technology, they still are not able to perfectly model the oceans’ dynamics. While ocean models are heavily used in wave and tidal resource predictions, the models are compared to in situ data measurements in order to better understand how the ocean model predictions differ from the real ocean conditions. In addition to understanding how the variables predicted in the ocean model vary from the real conditions, overall model parameters—such as temporal and spatial resolution—and the influence of these parameters should be taken into consideration.

When using HYCOM to predict the hydrokinetic resource of the Florida Current, a few things must be taken into immediate consideration. The temporal resolution of

HYCOM is one daily snapshot. Based on ADCP data evaluation, there is considerable variation in the current speed within the span of a day—especially due to the tidal influences. These fluctuations are not modeled by HYCOM due to the temporal resolution; additionally, tidal forcing is not included in HYCOM. As HYCOM is a global model, the comparisons made in this section will only apply to the Florida Current. For the applicability of HYCOM in other global locations, the data should be compared to in situ measurements within those regions.

In order to better understand the limitations of using HYCOM for hydrokinetic resource assessment in the Florida Current, data from HYCOM are compared directly to the ADCP measurements. In order for the data sets to match, the ADCP data has been filtered so that only the data sets taken at 2400 UTC are included in the data set. The

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HYCOM data was selected at the closest data point to the ADCP deployment. The data set could also be made by interpolating the data set from the nearest four HYCOM grid points. In this case, the difference between the interpolated data and the data at the nearest grid point to the ADCP deployment was minimal. The comparison of these two data sets can be seen in Figure 90. The HYCOM data set is shown with un-interpolated grid spacing.

Figure 90: ADCP in situ measurements compared to HYCOM data over the same time

period

Qualitatively, velocities in the HYCOM data set are less than the velocities in the

ADCP data set, especially within the upper portions of the water column. In Figure 91, the average velocity profile of the ADCP and HYCOM data are compared. On average, the HYCOM data set under-predicts the velocities by 12% over the B2-1 ADCP deployment; due to the cubic relationship of velocity to power, this could lead to a 32% under-prediction of the power.

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Figure 91: ADCP and HYCOM average velocity profile at ADCP B2-1

Although HYCOM may under-predict the velocities, the “shape” of the data both temporally and spatially are similar to the ADCP data. In Figure 90, the intense velocities in July seen in the ADCP data are replicated in the HYCOM data set, and the overall decay of the velocity from the surface to the bottom in a linear fashion is similar.

To compare the shape of the two data sets, each day was normalized by the maximum velocity occurring each day, resulting in a data set ranging between 0 and 1 which is seen in Figure 92. In terms of the maximum velocity, the ADCP shows much more variation in how intense the velocities remain in the lower portions of the water column. The average profile from each of the normalized data are seen in Figure 93.

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Figure 92: a) ADCP and b) HYCOM Normalized Velocity Data at the B2-1 ADCP

Location

Figure 93, a) ADCP and, b) HYCOM Normalized Velocity Data with Linear Regressions

As both mean normalized-velocity profiles have a near linear behavior, a linear regression was applied to each data set. The equations for the linear fit are yADCP=288.2x-

318.6 and yHYCOM=283.3x-317.6. These normalized equations are nearly the same, with approximately a 2% difference—less than the natural fluctuation in the current. Using

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this knowledge, the normalized HYCOM data can be scaled by the maximum velocity data from the ADCP and should yield more accurate velocity predictions.

By calculating the gain term, as in (33), an adjusted velocity for the HYCOM data set can be found by using (39).

( ) ( ) ( ) (39)

Once the gain term is applied, the resulting data set is seen in Figure 94a and b.

Figure 94: a) Adjusted HYCOM velocity data and b) resulting mean velocity profile at

the B2 ADCP Site

The average velocity profile from the adjusted HYCOM data much more accurately represents the average velocities seen by the ADCP. This better prediction of the velocity values has a direct impact on the average power density, as seen in Figure 95.

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Figure 95: Average power density curves from ADCP measurements, HYCOM, and gain

term adjusted HYCOM data sets

Although the average velocity profile is closer to what was seen in the ADCP deployment, on a daily basis it is important that the HYCOM data more closely represent the conditions that were observed. A squared-error metric is established in (40) to show the error between the HYCOM data sets—raw and adjusted—compared to the ADCP data set,

√( )

∑ (40) ( )

where nbins is the number of depth bins within the ADCP and HYCOM data set, n is the depth bin number, i is the day at which the squared error metric is being calculated, hn,i and an,i are the HYCOM and ADCP data points, respectively, at the nth and ith bin, and

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ηa,n is the temporal average ADCP measurement at the nth bin. As seen in Figure 96, the squared-error improves with the gain term adjustment of the HYCOM data. On average, the squared-error term for the original HYCOM data set and the ADCP is 44% of the mean data value and is 27% of the mean data value one the HYCOM data set has been adjusted.

Figure 96: Squared-error metric of HYCOM and adjusted HYCOM data compared to the

ADCP measurements

Finding a gain term based on one particular location is not of much use if it cannot be applied to other locations. In an attempt to validate this gain term application to the HYCOM data, and to ensure that is not geographically specific, the gain term is applied to the HYCOM data transect at 27° N and compared with in situ data collected at that transect. The transport from the cable, HYCOM, and adjusted HYCOM data are shown in Figure 97. While the adjusted data set does not match perfectly with the cable transport data, the HYCOM data transport predictions are improved by the application of

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the gain term. A table of transport statistics can be seen in Table 20. There is still a slight bias in the HYCOM data; however, by understanding this bias, HYCOM predictions can be used properly.

Figure 97: Volumetric transport data from NOAA cable compared to HYCOM and

adjusted HYCOM calculated mass transport

Table 20: Volumetric transport statistics from cable, HYCOM, and adjusted HYCOM

data

Adjusted Cable HYCOM HYCOM Sv (m3/s x 106) Mean 30.8 23.6 27.3 Standard Deviation 3.1 2.3 3.2 Minimum 22.5 15.8 20.0 Maximum 40.0 29.9 34.5

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Another squared-error term was calculated to see the difference between the

HYCOM data set and the adjusted HYCOM data set compared to the cable measured transport:

√ ( ) (41)

where the subscript i indicates the date, Q is the mass transport in Sv, the subscripts H and C indicate HYCOM mass transport and cable mass transport, respectively, and μC is the expected value of the mass transport. This plot of this calculation over the duration of the data set is seen in 98. . The gain term application to the HYCOM data improved the prediction of the transport at 27° N, and the squared error metric improved from an average value of 23% of the mean transport with the original HYCOM data set, to 12.5% of the mean transport with the adjusted HYCOM data set.

Figure 98: Squared Error Metric between the mass transport measured by NOAA Cable

in situ data set and the HYCOM and adjusted HYCOM data set

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This same methodology was applied to the ADCP B3-2 deployment, the results of which can be seen in Appendix E. The gain term application improved the data set, especially the average power density estimate; however the adjustments to the HYCOM predicted transport did not match the measured transport data well. Within the first two weeks of the data set, the adjusted transport data resulted in a transport that was much higher than the cable measured transport. After those two weeks, however, the adjusted

HYCOM transport prediction matches the cable data very well. Overall, the gain term application seems to improve the HYCOM data; although, the results of the gain term application should be thoroughly compared with in situ data sets that were not used to calculate the gain term.

While HYCOM does not show the small scale variability within the current, and typically under-predicts the current speeds within the Florida Current, HYCOM is a good model to begin the resource assessment process. In the future, regional ocean models

(ROMS) should be made for the Florida Current to provide a smaller temporal and spatial grid, to see the tidal influences, and to model the impact that installing turbines into the

Florida Current will have on the Florida Current and Gulf Stream. HYCOM can be used to show that the Florida Current has hydrokinetic power potential as long as the results that are presented include the fact that HYCOM typically under-predicts the current velocities in the Florida Current, thereby impacting the power prediction.

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5.5 GLOBAL ASSESSMENT

Previously, the intensity of the surface current has been used to postulate whether a region has the potential for open ocean energy extraction. The swift surface current of the Florida Current is one of the factors that led scientists to investigate the hydrokinetic energy potential of the Florida Current in the MacArthur Workshop. As seen in Figure

99, the global 2-year average surface current has been calculated using HYCOM data.

Figure 99: Two-year average of the global surface currents using HYCOM data

Looking at simply the surface current plots, areas that look like they could have power potential are the Loop Current and Gulf Stream off the coast of the United States , northern coast of Brazil, the eastern coast of Argentina, the eastern coast of Africa, the east coast of Japan, throughout the Philippines, and the east coast of Australia. However, the surface current is not the best indication of the potential hydrokinetic resource as

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turbines will not be installed on the surface. By calculating and plotting the power intensity, (34), at a given depth, in this case 50 m, a more accurate visualization of the hydrokinetic potential can be seen in Figure 100. In Figure 100, only power intensities above 0.5 kW/m2 have been highlighted, and eight global regions have been identified as potential locations for offshore energy extraction. Regions with power density below 0.5 kW/m2 are shown in gray. Additionally, statistics from each of these eight regions can be seen in Table 21.

Figure 100: Global power intensity at 50 m

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Table 21: Power intensity statistics from global regions of hydrokinetic potential

Location Average Power Intensity Statistics Maximum, Current Country kW/m2 Coordinates Gulf Stream East coast of United States 1.96 27.87° N, 79.68° W East coast of Agulhas (South) Mozambique, South 1.78 28.79° S, 32.48° E Africa North Equatorial Southeast Asia Current, Equatorial (Philippines, Indonesia, 1.76 6.86° N, 126.72° E Counter Current, South Malaysia) Equatorial Current Kuroshio Southeast coast of Japan 1.65 35.81° N, 142.08° E East coast of Somalia, Agulhas (North) 1.40 5.51° S, 39.52° E Kenya, Tanzania North Brazil Current Northeast cost of Brazil 1.08 4.87° S, 35.04° W Mozambique East coast of Madagascar 0.91 23.99° S, 47.76° E Eastern Australian East coast of Australia 0.75 31.35° S, 153.28° E

If the power intensity is used as the measure for determining the best global locations for hydrokinetic potential, the four regions that have the highest hydrokinetic power potential are the Gulf Stream, with its most intense power located in the Florida

Current, Kuroshio Current, Agulhas Current, and a mixture of different currents in the

Philippines. More detailed plots of these regions can be seen in Figure 101.

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Figure 101: Regions of high hydrokinetic power potential, a) Gulf Stream off the southeast coast of Florida, b) Alguhas Current off east coast of South Africa, c) Northern

Equatorial, Southern Equatorial and Equatorial Counter Current mixing near the

Philippines, Indonesia and Malaysia, and d) Kuroshio Current off the south and east coast

of Japan, in kW/m2

Based on the global analysis, the Kuroshio and Agulhas Currents are evaluated for their hydrokinetic power potential. Unlike the Florida Current’s hydrokinetic power prediction, the HYCOM data will not be modified to have a finer resolution; namely, the depth and longitudinal scales will not be altered. The impact that this has on the power

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prediction can be seen in Section 4.1.1. Additionally, the power integration was performed up to 20 HYCOM grid spaces away from the coast of both Japan and South

Africa. This is larger than the area over which the Florida Current’s power was integrated; therefore, this should be taken into consideration in comparing the hydrokinetic power of both the Kuroshio and Agulhas Current to the Florida Current.

The Kuroshio Current follows the southern/eastern coast of Japan. Due to the geography, it was broken into three distinct sections so that constant latitude and constant longitudinal cross-sections could be constructed. After breaking the current into three distinct sections, it was found that the power potential of the Kuroshio off the northeastern coast of Japan was the best location. The fluctuation of the average hydrokinetic power of the Kuroshio Current along the northeast coast of Japan can be seen in Figure 102. Additionally, the fluctuation of the power density along the northeast coast of Japan can be seen in Figure 103.

Figure 102: Kuroshio Current power fluctuation up the northeast coast of Japan

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Figure 103: Kuroshio Current Power Density Fluctuation up the Northeast Coast of Japan

Similarly to the Florida Current, a location factor—only considering the power and power density—was calculated for the Kuroshio Current as seen in Figure 104. The location factor in this portion of the Kuroshio Current, based on the power and power density, is plotted in Figure 105.

Figure 104: Normalized power and power density of the Kuroshio Current along the

northeast coast of Japan

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Figure 105: Array location factor of the Kuroshio Current along the northeast coast of

Japan

Using this location factor, the best location for array installation in the Kuroshio

Current is at 35.5°N. The entire cross-section of the Kuroshio Current along this latitude is plotted in Figure 106; however, this is larger than the range over which the power was calculated. The area over which the hydrokinetic power was integrated can be seen in

Figure 107. The power fluctuation over 2009 and 2010 can be seen in Figure 108.

Figure 106: Kuroshio Current Average Velocity Structure off the coast of Japan at

35.5°N from 2009-2010

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Figure 107: Kuroshio Current Average Velocity Structure from 2009-2010 over which

power was calculated off the coast of Japan at 35.5°N

Figure 108: Kuroshio Power Fluctuation at 35.5°N from 2009-2010

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In Figure 108, there are a few instances in which the power within the cross- section is nearly zero. This decrease in estimated power is related to the meandering of the Kuroshio Current. The power was only integrated over a region that stretches 140 km offshore the coast of Japan. When the Kuroshio Current meanders outside of that region, the power would inherently decrease. The meander of the Kuroshio Current has been well documented, and the current’s path is also bimodal (Mizuno and White, 1983).

In Figure 109 the surface current has been plotted over time. The black line in the figure represents the eastern boundary of the region over which the power time series was integrated. This illustrates the meander of the current, and shows that during the periods of minimal hydrokinetic power, the surface current within the integrated region is much less than the average surface current. This is reinforced in Figure 110, which plots the distribution of hydrokinetic power off the coast of Japan.

Figure 109: Kuroshio Current surface current magnitude at 35.5°N from 2009-2010

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Figure 110: Kuroshio Current hydrokinetic power distribution at 35.5°N from 2009-2010

Similarly, the same analysis was performed for the Agulhas Current off the southeast coast of Africa. The power and power density plots can be seen in Figures 111 and 112, respectively. The normalized power and power density, and the location factor based on the power and power density can be seen in Figures 113 and 114, respectively.

Figure 111: Fluctuation of the average power in the Agulhas Current along the east coast

of South Africa

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Figure 112: Agulhas Current power density fluctuation along the east coast of South

Africa

Figure 113: Normalized power and power density of the Agulhas Current along the east

coast of South Africa

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Figure 114: Array location factor of the Agulhas Current on the east coast of South

Africa

Based on the location factor calculations, the best location off the coast of South

Africa is at -33.6° N. The average cross-sectional velocity structure over the entire transect, as well as the area over which the power was calculated can be seen in Figures

115 and 116, respectively. The power fluctuation at -33.6° N can be seen in Figure 117.

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Figure 115: Agulhas Current average velocity structure from 2009-2010 off the South

African Coast at -33.6°N

Figure 116: Agulhas Current average velocity structure from 2009-2010 over which

power was calculated off the South African Coast at -33.6°N

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Figure 117: Agulhas Power Fluctuation at -33.6°N from 2009-2010

Basic comparisons of the three different global locations are made in Table 22.

When comparing these global sites to the Florida Current, a fair comparison is the power density as the area over which the power was calculated for the global current evaluation is much larger than the area of the Straits of Florida.

Table 22: Power and power density comparison of three global currents with hydrokinetic

potential

Mean Mean Power Latitude, Location Power, Density, °N GW W/m2

Florida Current 27.2° 12.1±3.4 278±85 Kuroshio 35.5° 22.9±17.3 154±117 Current Agulhas Current -33.6° 24.1±17.6 140±108

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Based simply on the average power within the cross-section, the Agulhas current has the most potential; however, the standard deviation of the power is over 70% of the mean. Also, even though the Kuroshio Current has more power than the Florida Current, the standard deviation of the power is greater than 75% of the mean power. This large standard deviation, in terms of the mean power, indicates that the power at both the

Kuroshio and Agulhas Current vary to a much higher degree than that of the Florida

Current—where the standard deviation is less than 30% of the mean. The fair comparison is the power density of the three currents. Using this as the metric for choosing a location to attempt offshore energy extraction, the Florida has far more potential than either the Agulhas or the Kuroshio Current. Like the power, the fluctuation of the power density is far less in the Florida Current than in either of the other two global locations. Furthermore, the bathymetry of both the Kuroshio and Agulhas

Current are far deeper than the Florida Current. Combining all of these factors and statistics, the Florida Current has the highest hydrokinetic potential of all of the global current locations and is the most sensible location to begin to develop offshore turbine arrays for energy extraction.

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6. CONCLUSIONS

Overall, the Florida Current has a high potential for hydrokinetic energy extraction. Based on the HYCOM data, between 6 and 13 GW of power are available on average at transects between 25° and 30°N, and based on historically collected observational data, there are between 8 and 20 GW within the Florida Current at various transects. Geographically, some of the variability of the resource comes from in flowing currents through the providence channel, and some is due to the variable bathymetry of the Straits of Florida. From the data that has been analyzed, there seems to be a seasonal variability of the power, with the peak power occurring in July; however, since only two years of data have been analyzed, the seasonal variability observations are inconclusive.

This research has shown that some locations within the Florida Current are better than others for energy extraction array installation, and based on the parameters set, the best location for installation in the Florida Current is along 27.16° N. While the resource varies geographically, it also has a degree of temporal variability. The temporal standard deviation of the power is between 28 and 40% of the mean power value over the entire geographic range of study. The areas with less variability—where the standard deviation is less than 33% the average—occur between 25.2 and 27.9° N.

Overall, the case studies to determine if there was any correlation between different in situ observations and the power prediction were inconclusive. The strongest correlation found was the correlation between the transport measured by NOAA cable

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data and the power calculated using HYCOM data, where the power lagged the transport by one day; however, the correlation coefficient was 0.63, which does not suggest strong correlation. Additionally, there may be correlation between the power and the top bin of the ADCP, and the power and the sea surface current data; however, again the correlation coefficients were low.

By utilizing an assortment of different data—including data from moored ADCPs,

NOAA submarine cable, and ship-mounted ADCPs—a better understanding of the dynamics of the Florida Current has been gained. Overall, the transport calculated using the ship-mounted ADCPs is slightly less than the measurements of the submarine cable; however, most of this is due to the fact that the submarine cable is north of the

Providence Channel—where currents are inflowing into the Straits of Florida—and the ship-mounted ADCP data was collected south of the Providence Channel. In previous studies, the ship-mounted ADCP data was mainly used to estimate the transport of the

Florida Current, but is repurposed in order to estimate the hydrokinetic power in the

Florida Current.

Estimates of the energy that an array would extract are provided, based on the available hydrokinetic power, turbine array parameters, and the inclusion of Betz limit efficiency. The optimal array installation location is at 27.16° N. The optimal array would be comprised of large turbines with low cut-in speeds; although, as long as the cut- in speed is less than 1 m/s, the impact of the cut-in speed selection is minimal.

Additionally, turbines should be installed in the upper 200 m of the water column, as 70-

80% of the total hydrokinetic power is in the upper 200 m of the water column.

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Optimally, turbines will be installed at the highest possible point in the water column keeping maritime traffic and free surface effects on the turbine in mind. Determining the number of turbines that comprise an optimal array is an exercise in economics beyond the scope of this dissertation. By adding more turbines to an array, the array has a higher overall extraction potential; however, the power production per turbine decreases as more turbines are added to an array.

The HYCOM data set are compared with in-situ observations, and a method for addressing the observed discrepancies between predicted and measured flow rates is provided. Finally, a global analysis of the hydrokinetic power is made, and the methodologies developed within this research have been applied to the Kuroshio and

Agulhas Currents. Overall, the hydrokinetic resource of the Kuroshio and Agulhas

Currents are larger than the Florida Current; however, the resource variability of the

Kuroshio and Agulhas Currents is much greater than the Florida Current. The standard deviation of the Florida Current’s hydrokinetic resource at its best location is less than

30% of the mean value, while the Kuroshio and Agulhas Current’s standard deviation of the hydrokinetic power are 75% and 70%, respectively. Furthermore, though the hydrokinetic power is greater in the Kuroshio and Agulhas Currents compared to the

Florida Current, the power density found in the Florida Current is nearly double the power density in the Kuroshio and Agulhas Currents. Based on the variability and the power density, the Florida Current is a more promising resource than the Agulhas and

Kuroshio Currents.

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Several observations can be made based on the considerations of this dissertation and as suggestions for future work. First, the relationship between the hydrokinetic power available, the hydrokinetic power extracted from the flow, and the power that is actually converted into useable electricity by the turbine needs to be determined. While a flowing stream has a hydrokinetic power given by ½ρU3A, the presence of the turbine induces a drag force on the current. This drag D results in energy taken out of the system that may be estimated as DU. The actual power that is converted into useable electricity is a quantity that will be dependent on the turbine. Extensive testing and modeling of an entire turbine system within a flow field should be done in order to better understand these principles.

Second, a better understanding of how turbines interact within an array needs to be gained. This requires a better understanding of turbine-turbine, turbine-wake, and wake-wave interactions. This will lead to determination of how closely turbines can be spaced. Depending on the number of turbines within an array, and the depth at which a turbine array is to be installed, this knowledge will give an estimated cross-sectional area in which turbine arrays should be placed.

Third, the effect of the turbine array on the current—both upstream and downstream—must be fully analyzed. Not only will the energy extraction impact the current speed near the turbine, but the energy extraction may impact the current speed upstream or downstream of the turbine array. More turbine arrays should be modeled in the flow to determine how far downstream an array can be installed without feeling direct impact of the turbines upstream.

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Fourth, the effect of multiple arrays on the current system must be well understood. If the installation of turbines disrupts the natural current system, resulting in a decrease in power within the system, then the installation would be counterproductive.

Before any extensive installation and commercialization of hydrokinetic turbines takes place, the impacts to the local and global current system should be modeled and studied.

Of course, the economics of array design, procurement, installation, operation, and maintenance are important to the commercial success of ocean current energy extraction. The economic feasibility of extracting energy from the Florida Current will be one of the driving factors leading to commercialization. Additionally, with advances in turbine technology, installation equipment, and the growth in the knowledge base, the economics will improve. It is possible that the economics of ocean energy extraction may be discouraging at present; however, in time, with the rising price of oil, and the rapid development of former 3rd world countries, the economics may prove to be favorable.

In any resource assessment, the limitations of data sets used—whether they are model data or in situ observations—should be well documented and understood. In the case of the Florida Current, HYCOM under-predicts the velocities; therefore, under- predicting the hydrokinetic power. However, HYCOM provides a starting point in the resource assessment of the Florida Current, and should be utilized in future resource assessments. Ideally, HYCOM would be used in a 5 to 10 year resource characterization study in order to determine any seasonality in the available power.

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Moored ADCP data is also limited in its scope, especially if only two ADCPs are collecting data simultaneously. They are also limited in their bin size and sampling rate.

Turbine developers need to know the forces that will be on their turbine blades, and the temporal and spatial resolution of the ADCP data does not provide the turbulence data that is crucial for blade development.

If offshore hydrokinetic power is to be commercialized, the Florida Current is the best global location to start. Of all of the global ocean currents, it has the highest power density, most consistent power, and shallowest installation depths. Also, with the current near the coastline and near highly populated areas, some of the basic infrastructure—like ports and a power distribution grid—are already in place.

There is a great deal of future work that needs to be done before hydrokinetic energy extraction becomes a reality in the Florida Current. An ideal situation would be to have ADCPs installed permanently throughout the Straits of Florida, simultaneously collecting data, and transmitting the data to shore. Real time conditions could then be seen, and the vast amount of data would provide another source for completing resource assessment. This is a time consuming and expensive enterprise, but would be rewarding.

In addition, in-depth site surveys need to be carried out over the span of at least two years. These surveys include not only capturing the velocity data, but also any environmental data—such as animal species inventories—that are required by regulatory agencies.

The interaction of arrays—both turbine to turbine interaction, as well as the interaction of the turbine with the current—must be realistically modeled in an

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oceanographic model. Presently, turbine arrays are modeled as a drag coefficient in oceanographic models. Using this methodology, one can estimate how much energy is taken out of the current system due to the drag term imposed; however, the relationship of the energy taken out of the system to the actual energy that can be produced is unknown. Additionally, the drag term does not accurately represent the turbine-turbine and turbine wake interactions as the drag term essentially creates a fence across a given area. As the tidal energy industry is much further ahead than the open ocean current industry, there is much to be learned from tidal energy extraction. As the tidal energy industry grows, and more is learned about extraction rates and the influence of turbine arrays on their surrounding areas, this knowledge can be applied to open ocean current systems.

Finally, before considering installation of a commercial energy-producing array of turbines, developers should test a single device first, followed by studies of the impacts of single turbines and a small array of turbines on the ocean current, as these studies will help educate the stake-holders of the potential of ocean energy extraction. Additionally, economic analyses of the turbine installations should be conducted in order to show that the technology is economically viable. Grid connectivity must also be taken into consideration. In general, the public wants to use alternative energies, but only if they are economical and safe to the environment. Economic impacts—namely the price of energy to the consumer—and environmental impacts to the area in which consumers live cannot be ignored.

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It has been suggested that the present state of the ocean energy industry is similar to where the wind energy industry was 30 years ago. There will be many trials and errors, machinery will break, and some small start-up companies will succeed and rise to the top of the industry, while others will be unsuccessful. Great advances in technology—materials, sensors, installation equipment, mooring schemes—have to take place to foster this industry. Public support of the industry will also play a critical role in its future. Through innovation, ingenuity, and perseverance, this industry can play a part in the diversified energy production of the future.

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APPENDIX A

Explorer of the Seas Cruise Ship Supplementary Data

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Table A-1: 2003 Explorer of the Seas Cruise Transect Dates, Calculated Power and

Volumetric Transport

Power, Transport, Power, Transport, Date GW Sv Date GW Sv 01/25/03 15.9 26.5 07/18/03 14.1 24.2 01/31/03 8.4 15.2 07/25/03 14.7 25.1 02/08/03 19.5 27.7 08/01/03 11.2 23.4 02/14/03 30.1 33.1 08/08/03 11.2 22.9 02/28/03 16.3 26.3 08/15/03 15.2 24.4 03/08/03 14.2 25.8 08/22/03 8.2 22.0 03/14/03 9.2 18.8 08/29/03 11.3 21.4 03/22/03 11.7 14.9 09/05/03 11.6 22.0 03/28/03 10.7 20.8 09/12/03 8.2 19.1 04/05/03 17.0 27.0 09/19/03 13.4 23.9 04/18/03 18.3 30.3 09/26/03 10.5 21.0 04/25/03 9.3 18.7 10/03/03 7.5 19.5 05/02/03 17.1 28.4 10/10/03 18.4 28.8 05/09/03 14.8 26.5 10/17/03 9.6 21.7 05/16/03 14.8 23.6 10/24/03 22.7 29.4 05/23/03 13.9 25.7 11/07/03 13.9 25.4 05/30/03 15.8 26.1 11/14/03 14.7 26.4 06/13/03 20.7 26.9 11/21/03 10.8 20.4 06/20/03 13.5 24.8 12/12/03 17.4 28.2 06/27/03 11.6 22.9 12/27/03 10.6 23.5 07/04/03 18.4 26.5 01/02/04 14.5 24.8 07/11/03 16.3 24.3

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Table A-2: 2004 Explorer of the Seas Cruise Transect Dates, Calculated Power and Mass

Transport

Power, Transport, Power, Transport, Date GW Sv Date GW Sv 01/16/04 10.9 23.5 07/10/04 9.6 22.8 02/07/04 12.9 24.1 07/17/04 7.3 19.3 02/13/04 13.4 22.4 08/07/04 9.4 20.3 02/20/04 12.0 22.8 08/14/04 16.9 27.0 03/06/04 9.8 23.1 08/21/04 14.2 24.1 04/03/04 6.6 19.6 08/28/04 12.4 23.7 04/16/04 11.0 24.6 09/19/04 6.5 17.4 04/23/04 12.5 23.2 10/02/04 9.4 20.3 05/08/04 6.6 17.8 10/09/04 13.8 24.2 05/15/04 8.0 19.0 10/16/04 8.5 21.5 05/22/04 9.9 21.7 10/30/04 8.9 20.8 05/29/04 10.6 20.5 11/20/04 7.9 22.1 06/05/04 5.7 15.8 11/27/04 7.6 20.6 06/12/04 7.4 19.2 12/04/04 11.9 24.2 06/19/04 10.1 20.3 12/12/04 13.2 23.9 06/26/04 11.8 22.9 12/26/04 5.4 16.7 07/03/04 8.5 19.9

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APPENDIX B

Supplementary ADCP Data

170

ADCP Deployment B3-2

Figure B1: Current magnitude over ADCP B3-2 deployment

Figure B2: Current mean, absolute maximum and absolute minimum profiles at ADCP

deployment B3-2

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Figure B3: Average power density over ADCP deployment B3-2

Figure B4: Frequency analysis ADCP deployment B3-2

Tidal Constituents Present: O1, K1, M2

172

Figure B5: Layered Histogram for ADCP deployment B3-2

Figure B6: Weighted power density plot over B3-2 ADCP Deployment

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ADCP Deployment B2b-3

Figure B7: Current magnitude over ADCP B2b-3 deployment

Figure B8: Current mean, absolute maximum and absolute minimum profiles at ADCP

deployment B2b-3

174

Figure B9: Frequency analysis ADCP deployment B2b-3

Tidal Constituents Present: O1, K1, N2, M2

Figure B10: Layered Histogram for ADCP deployment B2b-3

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Figure B11: Weighted power density plot over B2b-3 ADCP Deployment

ADCP Deployment B3-3

Figure B12: Current magnitude over ADCP B3-3 deployment

176

Figure B13: Current mean, absolute maximum and absolute minimum profiles at ADCP

deployment B3-3

Figure B14: Frequency analysis ADCP deployment B3-3

Tidal Constituents Present: O1, K1, N2, M2

177

Figure B15: Layered Histogram for ADCP deployment B3-3

Figure B16: Weighted power density plot over B3-3 ADCP Deployment

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Comparing Deployment B2b-3 and B3-3

Figure B17: Current speed over ADCP B3-3 (left) and ADCP B2b-3 (right) deployments

Figure B18: Difference in current speed from ADCP B2b-3 to B3-3

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Figure B19: Horizontal velocity shear from ADCP B2b-3 to B3-3

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APPENDIX C

Turbine Array Power Extraction Estimation Supplemental Tables

181

Table C1: Hydrokinetic Power Available to Turbines Arrays at 25.73°N

Hydrokinetic Power into Turbine Array (Diameter = 20 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 44.9 107.9 209.6 349.9 40.3 97.5 188.3 311.2 35.4 86.1 165.5 270.6 0.4 44.9 107.9 209.6 349.9 40.3 97.5 188.3 311.2 35.4 86.1 165.5 270.6 0.5 44.9 107.9 209.6 349.8 40.3 97.5 188.3 311.2 35.4 86.1 165.5 270.6 0.6 44.9 107.9 209.6 349.8 40.3 97.5 188.3 311.1 35.4 86.1 165.5 270.5 0.7 44.9 107.9 209.6 349.6 40.3 97.5 188.3 310.8 35.4 86.1 165.5 270.1

182 0.8 44.9 107.9 209.4 348.6 40.3 97.5 188.2 309.6 35.4 86.1 165.4 268.4

0.9 44.8 107.7 209.0 345.2 40.2 97.3 187.8 305.5 35.3 85.9 164.9 262.8 1 44.5 106.9 207.0 335.2 39.9 96.4 185.3 293.2 34.9 84.7 161.5 247.5 1.1 43.8 104.5 201.2 315.1 39.0 93.4 178.1 268.9 33.5 80.5 151.6 216.9 1.2 41.6 98.4 187.9 278.7 36.1 85.6 161.2 226.8 29.3 69.6 128.6 168.4 1.3 36.4 84.9 160.6 224.1 29.1 68.4 126.9 165.6 20.6 48.1 86.6 104.6

Table C2: Hydrokinetic Power Available to Turbines Arrays at 25.73°N

Hydrokinetic Power into Turbine Array (Diameter = 30 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 97.2 235.8 420.9 663.9 87.8 211.9 375.5 586.5 77.5 186.2 327.5 507.2 0.4 97.2 235.8 420.9 663.9 87.8 211.9 375.5 586.3 77.5 186.2 327.5 507.0 0.5 97.2 235.8 420.8 663.6 87.8 211.9 375.5 585.9 77.5 186.2 327.5 506.3 0.6 97.2 235.8 420.8 662.7 87.8 211.9 375.5 584.5 77.5 186.2 327.5 504.3 0.7 97.2 235.8 420.6 660.1 87.8 211.9 375.3 581.2 77.5 186.2 327.2 500.3 0.8 97.2 235.7 420.0 653.7 87.8 211.8 374.5 573.6 77.5 186.1 326.0 492.8 0.9 97.0 235.2 417.5 638.7 87.6 211.4 371.4 557.5 77.3 185.4 321.7 475.5 183 1 96.2 232.9 408.6 606.9 86.8 208.5 360.7 523.2 76.2 181.7 308.1 438.6

1.1 94.1 226.5 389.7 554.7 84.0 200.4 337.1 468.3 72.4 170.4 277.5 374.3 1.2 88.6 211.5 352.0 478.5 77.0 181.3 292.1 385.4 62.6 144.4 222.6 283.7 1.3 76.5 180.7 289.5 377.2 61.6 142.7 218.5 277.6 43.2 97.4 140.8 174.5

Table C3: Hydrokinetic Power Available to Turbines Arrays at 25.73°N

Hydrokinetic Power into Turbine Array (Diameter = 40 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.4 172.1 418.0 698.4 880.3 155.8 376.3 622.0 781.5 137.8 331.1 541.6 679.6 0.5 172.1 418.0 698.3 877.4 155.8 376.3 622.0 778.8 137.8 331.1 541.5 676.7 0.6 172.1 418.0 698.2 871.6 155.8 376.3 621.9 772.7 137.8 331.1 541.3 669.8 0.7 172.1 417.9 697.7 864.2 155.8 376.3 621.3 765.1 137.8 331.1 540.5 662.1 0.8 172.1 417.7 695.7 853.2 155.8 376.1 618.8 753.3 137.8 331.0 537.0 650.7 0.9 171.8 416.9 688.9 830.4 155.6 375.3 610.3 728.6 137.5 329.7 525.6 623.7 1 170.4 412.7 668.5 782.8 154.0 370.1 585.6 677.8 135.5 323.0 494.6 568.0 184 1.1 166.5 401.0 627.8 709.5 149.0 355.3 536.5 599.9 128.6 302.5 433.3 479.8

1.2 156.6 374.2 555.7 608.8 136.3 320.9 451.7 489.8 110.8 255.9 337.3 362.4 1.3 134.7 318.6 446.1 477.0 108.7 252.1 330.7 351.5 76.8 173.7 211.9 224.4

Table C4: Hydrokinetic Power Available to Turbines Arrays at 26.52°N

Hydrokinetic Power into Turbine Array (Diameter = 20 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 47.3 118.2 223.5 395.6 43.4 108.4 203.5 355.2 38.8 97.0 180.9 311.7 0.4 47.3 118.2 223.5 395.6 43.4 108.4 203.5 355.2 38.8 97.0 180.9 311.7 0.5 47.3 118.2 223.5 395.6 43.4 108.4 203.5 355.2 38.8 97.0 180.9 311.7 0.6 47.3 118.2 223.5 395.5 43.4 108.4 203.5 355.1 38.8 97.0 180.9 311.6 0.7 47.3 118.2 223.5 395.3 43.4 108.4 203.5 354.9 38.8 97.0 180.9 311.2 0.8 47.3 118.2 223.4 394.3 43.3 108.4 203.4 353.7 38.8 97.0 180.9 309.8 0.9 47.2 118.1 223.0 391.2 43.3 108.3 203.0 350.2 38.8 96.9 180.3 305.6 185 1 47.1 117.7 221.2 383.5 43.1 107.8 201.0 341.7 38.5 96.4 177.8 294.8

1.1 46.3 115.8 215.3 367.1 42.3 105.8 194.0 321.7 37.5 93.7 169.0 270.1 1.2 44.3 110.7 202.4 337.1 39.7 99.3 178.6 286.2 34.1 85.3 149.9 228.6 1.3 39.6 99.1 178.9 289.9 34.3 85.8 151.2 232.7 27.1 67.7 114.5 166.1

Table C5: Hydrokinetic Power Available to Turbines Arrays at 26.52°N

Hydrokinetic Power into Turbine Array (Diameter = 30 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 106.4 262.7 474.9 663.9 97.6 239.5 429.0 588.4 87.3 213.1 378.3 509.7 0.4 106.4 262.7 474.9 663.6 97.6 239.5 429.0 588.1 87.3 213.1 378.3 509.5 0.5 106.4 262.7 474.9 662.8 97.6 239.5 429.0 587.2 87.3 213.1 378.3 508.7 0.6 106.4 262.7 474.9 660.4 97.6 239.5 429.0 584.8 87.3 213.1 378.3 505.9 0.7 106.4 262.7 474.8 655.1 97.6 239.5 428.9 579.4 87.3 213.1 378.1 499.7 0.8 106.4 262.6 474.4 646.5 97.6 239.5 428.3 569.8 87.3 213.0 377.4 488.8 0.9 106.3 262.3 472.7 632.1 97.5 239.2 426.4 554.2 87.2 212.8 375.0 473.1 186 1 105.9 261.3 466.9 609.1 97.0 237.9 420.1 530.2 86.7 211.1 366.5 447.5

1.1 104.3 256.3 451.0 570.9 95.2 232.1 400.8 487.7 84.3 203.7 342.2 401.7 1.2 99.7 244.1 418.5 511.8 89.5 217.3 361.9 425.8 76.8 184.3 294.6 335.0 1.3 89.3 218.4 363.3 431.5 77.3 186.6 297.6 341.6 60.9 143.8 217.0 242.3

Table C6: Hydrokinetic Power Available to Turbines Arrays at 26.52°N

Hydrokinetic Power into Turbine Array (Diameter = 40 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 188.4 445.5 788.7 962.3 173.1 406.4 709.7 852.3 155.2 361.6 623.0 738.1 0.4 188.4 445.5 788.7 960.9 173.1 406.4 709.7 850.6 155.2 361.6 623.0 736.4 0.5 188.4 445.5 788.6 957.5 173.1 406.4 709.7 847.2 155.2 361.6 623.0 733.4 0.6 188.4 445.5 788.6 952.0 173.1 406.4 709.6 842.2 155.2 361.6 622.9 728.5 0.7 188.4 445.4 788.1 942.6 173.1 406.4 709.1 833.4 155.2 361.6 622.1 719.0 0.8 188.4 445.2 785.9 928.7 173.1 406.3 706.7 819.2 155.1 361.5 619.3 703.7 0.9 188.1 444.3 779.6 907.5 172.9 405.4 699.7 796.8 155.0 360.4 610.5 680.9 187 1 187.5 440.6 764.0 874.1 172.2 401.4 682.3 762.1 154.1 355.1 588.3 643.7

1.1 184.5 428.5 730.3 818.6 168.8 387.3 642.0 701.2 149.6 337.3 538.9 577.9 1.2 176.1 402.5 669.9 733.8 158.5 356.3 571.4 611.9 136.1 298.2 454.9 481.0 1.3 157.5 355.3 575.6 618.1 136.4 300.2 463.1 489.3 107.6 227.8 332.4 349.2

Table C7: Hydrokinetic Power Available to Turbines Arrays at 27.16°N

Hydrokinetic Power into Turbine Array (Diameter = 20 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 56.3 140.8 260.9 448.0 52.1 130.2 238.7 404.1 47.2 118.1 214.2 357.3 0.4 56.3 140.8 260.9 448.0 52.1 130.2 238.7 404.1 47.2 118.1 214.2 357.3 0.5 56.3 140.8 260.9 448.0 52.1 130.2 238.7 404.1 47.2 118.1 214.2 357.2 0.6 56.3 140.8 260.9 447.9 52.1 130.2 238.7 403.9 47.2 118.1 214.1 357.0 0.7 56.3 140.8 260.9 447.6 52.1 130.2 238.7 403.6 47.2 118.1 214.1 356.6 0.8 56.3 140.8 260.8 446.9 52.1 130.2 238.6 402.8 47.2 118.1 214.0 355.2 0.9 56.3 140.7 260.5 444.5 52.0 130.1 238.1 399.8 47.2 117.9 213.3 351.4 188 1 56.2 140.4 259.3 438.5 52.0 129.9 237.0 393.3 47.1 117.7 212.1 343.6

1.1 55.6 139.1 255.5 424.7 51.4 128.5 233.0 377.6 46.5 116.2 207.1 324.6 1.2 54.5 136.4 246.8 399.2 50.0 125.0 222.6 348.1 44.8 112.0 194.3 290.9 1.3 51.5 128.8 228.3 356.8 46.8 116.9 202.1 302.0 40.8 101.9 169.9 242.5

Table C8: Hydrokinetic Power Available to Turbines Arrays at 27.16°N

Hydrokinetic Power into Turbine Array (Diameter = 30 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 126.7 308.8 545.7 734.9 117.2 283.3 495.4 653.0 106.3 254.7 440.6 576.3 0.4 126.7 308.8 545.7 734.7 117.2 283.3 495.4 652.9 106.3 254.7 440.6 575.9 0.5 126.7 308.8 545.6 734.3 117.2 283.3 495.4 652.2 106.3 254.7 440.6 574.8 0.6 126.7 308.8 545.6 733.0 117.2 283.3 495.3 650.4 106.3 254.7 440.4 572.7 0.7 126.7 308.7 545.4 729.1 117.2 283.2 495.0 645.8 106.3 254.7 440.1 568.6 0.8 126.7 308.7 544.9 720.0 117.2 283.1 494.5 636.2 106.3 254.5 439.1 559.7 0.9 126.6 308.3 543.6 705.4 117.1 282.7 492.6 620.9 106.1 254.0 436.5 544.0 189 1 126.4 307.5 539.8 682.9 116.9 281.9 488.6 599.9 105.9 253.1 431.6 523.0

1.1 125.2 304.1 528.8 648.7 115.6 278.5 476.1 566.5 104.6 249.2 416.2 486.0 1.2 122.8 297.2 504.4 599.3 112.5 269.4 447.6 514.9 100.8 237.9 382.2 428.7 1.3 116.0 279.3 457.6 528.0 105.3 250.0 395.9 442.1 91.7 213.4 324.3 353.9

Table C9: Hydrokinetic Power Available to Turbines Arrays at 27.16°N

Hydrokinetic Power into Turbine Array (Diameter = 40 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 224.4 520.8 896.3 1072.4 208.0 477.0 807.7 952.0 188.9 428.3 714.3 841.8 0.4 224.4 520.8 896.2 1071.7 208.0 477.0 807.6 951.6 188.9 428.3 714.3 841.2 0.5 224.4 520.8 896.2 1069.3 208.0 477.0 807.6 949.1 188.9 428.3 714.2 838.2 0.6 224.4 520.8 896.0 1064.4 208.0 476.9 807.3 943.4 188.9 428.2 713.8 831.8 0.7 224.4 520.7 895.5 1054.8 208.0 476.8 806.6 932.9 188.9 428.1 712.8 821.7 0.8 224.4 520.6 894.0 1039.6 208.0 476.7 804.9 917.4 188.9 427.9 710.0 806.2 0.9 224.3 519.8 889.1 1017.6 207.8 475.7 798.9 894.8 188.7 426.6 702.4 783.0 190 1 223.9 517.6 877.0 985.3 207.5 473.5 785.8 864.0 188.4 424.0 686.2 751.9

1.1 221.7 509.8 849.2 936.3 205.2 465.1 753.8 815.0 186.0 414.0 648.8 699.3 1.2 217.2 492.0 797.6 864.8 199.7 444.1 694.9 739.8 179.1 387.8 581.5 616.8 1.3 205.0 454.5 712.5 761.7 186.5 402.9 603.3 635.0 162.6 338.3 484.1 508.6

Table C10: Hydrokinetic Power Available to Turbines Arrays at 27.45°N

Hydrokinetic Power into Turbine Array (Diameter = 20 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 57.1 142.8 262.6 443.8 53.1 132.8 241.5 401.6 48.4 120.9 217.5 357.8 0.4 57.1 142.8 262.6 443.8 53.1 132.8 241.5 401.6 48.4 120.9 217.5 357.8 0.5 57.1 142.8 262.6 443.8 53.1 132.8 241.5 401.6 48.4 120.9 217.5 357.8 0.6 57.1 142.8 262.6 443.6 53.1 132.8 241.5 401.5 48.4 120.9 217.5 357.6 0.7 57.1 142.8 262.5 443.3 53.1 132.8 241.4 401.0 48.4 120.9 217.4 357.1 0.8 57.1 142.8 262.4 442.2 53.1 132.7 241.2 399.9 48.3 120.8 217.2 355.4 0.9 57.1 142.7 261.9 439.5 53.0 132.6 240.7 396.4 48.3 120.8 216.6 351.3 191 1 56.9 142.3 260.7 432.8 52.9 132.2 239.6 389.1 48.2 120.4 215.2 342.2

1.1 56.5 141.3 257.2 419.1 52.5 131.3 235.5 372.5 47.7 119.2 210.2 323.1 1.2 55.4 138.6 248.2 393.6 51.3 128.4 225.7 344.6 46.1 115.3 198.0 291.9 1.3 52.3 130.9 229.8 352.5 48.0 119.9 204.7 299.5 42.2 105.5 172.9 243.7

Table C11: Hydrokinetic Power Available to Turbines Arrays at 27.45°N

Hydrokinetic Power into Turbine Array (Diameter = 30 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 128.6 311.6 544.5 719.8 119.6 287.4 496.3 649.1 108.8 259.5 444.1 579.9 0.4 128.6 311.6 544.4 719.6 119.6 287.4 496.3 648.9 108.8 259.5 444.1 579.6 0.5 128.6 311.6 544.4 719.2 119.6 287.4 496.3 648.0 108.8 259.5 444.1 578.3 0.6 128.6 311.6 544.3 717.5 119.6 287.4 496.2 645.8 108.8 259.5 443.9 576.2 0.7 128.6 311.6 544.1 713.2 119.5 287.4 495.9 641.3 108.8 259.4 443.5 572.3 0.8 128.5 311.5 543.3 703.4 119.5 287.2 495.0 632.2 108.7 259.2 442.2 563.6 0.9 128.4 311.0 541.5 687.9 119.4 286.7 492.6 616.9 108.7 258.7 439.4 547.8 192 1 128.1 309.9 537.2 665.9 119.0 285.6 487.9 595.7 108.3 257.4 433.5 524.1

1.1 127.2 307.1 526.6 633.4 118.2 282.5 475.4 559.9 107.3 253.5 418.2 484.8 1.2 124.8 300.0 502.0 585.1 115.5 274.5 448.4 510.8 103.7 242.9 386.7 431.1 1.3 117.8 281.8 456.4 517.9 108.0 254.2 396.8 439.1 94.8 218.6 328.4 356.4

Table C12: Hydrokinetic Power Available to Turbines Arrays at 27.45°N

Hydrokinetic Power into Turbine Array (Diameter = 40 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 227.7 524.1 888.6 1055.3 212.2 482.3 803.1 947.8 193.4 434.7 715.2 848.9 0.4 227.7 524.1 888.6 1054.8 212.2 482.3 803.1 947.4 193.4 434.7 715.2 848.3 0.5 227.7 524.1 888.6 1052.5 212.2 482.3 803.0 944.9 193.4 434.7 715.1 845.5 0.6 227.7 524.1 888.3 1046.6 212.2 482.3 802.7 938.5 193.4 434.7 714.7 839.1 0.7 227.7 524.0 887.6 1036.7 212.1 482.2 801.9 928.1 193.4 434.5 713.5 828.9 0.8 227.6 523.7 885.5 1020.4 212.0 481.8 799.4 911.9 193.3 434.0 710.0 812.4 0.9 227.4 522.7 879.9 996.7 211.9 480.8 792.6 888.4 193.1 433.0 701.5 788.1 193 1 226.8 520.3 866.5 964.7 211.2 478.4 777.5 856.9 192.6 430.1 683.6 754.0

1.1 225.2 513.0 838.6 916.9 209.7 470.2 744.6 805.2 190.7 419.7 645.5 697.4 1.2 220.8 495.0 787.3 846.9 204.8 450.3 688.6 733.9 184.2 395.1 583.6 620.5 1.3 208.3 457.7 705.1 748.8 191.3 407.8 598.5 630.8 168.2 344.6 487.1 512.5

Table C13: Hydrokinetic Power Available to Turbines Arrays at 28.86°N

Hydrokinetic Power into Turbine Array (Diameter = 20 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 48.5 121.2 219.4 370.6 40.3 100.6 191.6 340.1 38.5 96.3 180.7 317.4 0.4 48.5 121.2 219.4 370.6 40.3 100.6 191.6 340.1 38.5 96.3 180.7 317.4 0.5 48.5 121.2 219.3 370.4 40.3 100.6 191.6 340.1 38.5 96.3 180.7 317.3 0.6 48.4 121.1 219.2 370.0 40.2 100.6 191.5 339.8 38.5 96.2 180.6 316.9 0.7 48.4 121.0 218.9 368.9 40.2 100.5 191.3 338.5 38.5 96.2 180.4 315.8 0.8 48.3 120.9 218.2 366.7 40.2 100.5 190.8 335.8 38.4 96.1 179.7 312.8 0.9 48.0 120.0 216.3 361.1 40.0 100.1 188.7 328.5 38.2 95.6 177.7 305.4 194 1 47.3 118.2 212.6 350.5 39.3 98.4 183.8 316.1 37.5 93.8 172.5 291.9

1.1 46.2 115.4 205.5 332.7 37.7 94.4 174.3 295.6 36.0 89.9 162.6 270.7 1.2 44.0 110.1 193.1 304.6 34.6 86.6 158.1 265.4 32.9 82.1 146.1 239.6 1.3 40.9 102.3 174.7 266.6 29.6 74.1 135.5 227.0 27.4 68.4 122.0 198.4

Table C14: Hydrokinetic Power Available to Turbines Arrays at 28.86°N

Hydrokinetic Power into Turbine Array (Diameter = 30 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 109.1 261.3 454.8 624.0 90.6 225.5 407.6 583.8 86.6 213.4 381.9 538.7 0.4 109.1 261.3 454.7 623.6 90.6 225.5 407.6 583.5 86.6 213.4 381.9 538.4 0.5 109.1 261.2 454.6 622.6 90.6 225.5 407.5 582.4 86.6 213.4 381.8 537.3 0.6 109.1 261.2 454.2 620.5 90.6 225.5 407.3 579.5 86.6 213.3 381.6 534.1 0.7 109.0 260.8 453.2 615.2 90.5 225.3 406.6 572.4 86.6 213.2 380.9 527.5 0.8 108.8 260.1 451.2 605.7 90.5 224.9 404.8 560.8 86.5 212.7 378.9 515.1 0.9 108.0 258.1 446.4 587.3 90.1 223.6 399.0 539.6 86.0 211.2 373.0 493.6 195 1 106.4 254.3 437.0 560.4 88.5 219.6 385.7 511.7 84.4 207.1 359.0 464.5

1.1 103.9 247.3 419.2 519.9 85.0 210.3 362.4 471.9 80.8 197.5 334.5 423.7 1.2 99.1 235.1 389.2 466.7 78.0 192.7 325.1 418.1 73.9 179.9 296.1 370.2 1.3 92.2 217.2 345.0 401.7 66.7 164.4 277.0 354.0 61.5 149.3 244.8 303.9

Table C15: Hydrokinetic Power Available to Turbines Arrays at 28.86°N

Hydrokinetic Power into Turbine Array (Diameter = 40 m) Cut-in Hub Depth = 45 m Hub Depth = 65 m Hub Depth = 85 m Speed, Number of Turbines Number of Turbines Number of Turbines m/s 100 250 500 1000 100 250 500 1000 100 250 500 1000 0.3 193.2 438.1 742.0 923.6 160.8 382.5 679.5 862.8 153.9 361.0 633.9 793.4 0.4 193.2 438.1 741.9 922.7 160.8 382.5 679.4 861.6 153.9 361.0 633.9 792.2 0.5 193.2 438.0 741.6 920.0 160.7 382.4 679.3 858.3 153.9 361.0 633.7 789.0 0.6 193.1 437.9 740.8 914.3 160.7 382.3 678.7 851.3 153.9 360.8 633.0 782.1 0.7 193.0 437.1 738.5 902.5 160.6 382.0 676.3 837.9 153.8 360.5 630.8 769.0 196 0.8 192.7 435.6 733.9 884.3 160.5 380.8 670.6 817.5 153.6 359.1 624.6 747.7

0.9 191.3 432.0 722.9 853.2 159.8 376.7 656.2 784.1 152.8 354.8 609.7 714.0 1 188.6 424.6 702.0 812.1 157.1 366.6 631.0 741.0 150.0 344.6 583.1 670.3 1.1 183.7 409.9 665.9 751.9 150.8 347.7 590.1 681.8 143.4 324.5 540.1 610.2 1.2 175.3 385.3 609.6 673.7 138.2 315.3 529.9 602.9 131.0 291.5 477.6 532.3 1.3 163.1 349.1 534.5 580.4 118.0 269.9 452.4 509.3 109.2 243.3 395.7 437.2

APPENDIX D

Turbine Extraction Estimation Tool Output

197

Turbine Extraction Estimation Report

Inputs

Latitute 27.16 °N Cut-in Speed 1 m/s Diameter 30 m Hub Depth 65 m Turbine Spacing 30 m Number of Turbines 500

Outputs

Core Statistics

Center of Core -79.70 ± 0.07 °E

Core Width Mean 43.68 km Maximum 67.30 km Minimum 19.79 km

Power in Transect

Mean 12.08 GW Maximum 22.81 GW Minimum 3.97 GW

Array Area Statistics

Width 30 km Depth Range of Array 50 to 80 m East Boundary -79.49 °E West Boundary -79.79 °E

Power in Array Area Mean 1.48 GW Maximum 3.31 GW Minimum 0.04 GW

198

Turbine Array Statistics

Number of Turbines 500.00 Packing Fraction 0.33

Production Estimate

Power into turbine array (not including Betz Limit) Mean 488.6 MW Maximum 1095.2 MW Minimum 14.0 MW

Power into turbine array (including Betz Limit) Mean 289.5 MW Maximum 649.0 MW Minimum 8.3 MW

Depth at Array Boundaries West Boundary -250 m Mid-point -490 m East Boundary -700 m

199

200

201

APPENDIX E

HYCOM Adjustment Based on ADCP Deployment B3-2

202

Figure E1: ADCP (left) and HYCOM (right) Velocity Current Speed Data over B3-2

ADCP Deployment

Figure E2: ADCP and HYCOM Velocity Profile over B3-2 ADCP Deployment

203

Figure E3: Normalized ADCP (left) and HYCOM (right) Current Speed Data over B3-2

ADCP Deployment

Figure E4: Normalized HYCOM and ADCP Velocity Profile for B3-2 ADCP

Deployment

204

Figure E5: Linear Regressions for ADCP B3-2 (left) and HYCOM (right) Normalized

Velocity Profiles

ADCP: y= 205.6695x – 254.2271

HYCOM: y= 212.3370x – 250.9793

Figure E6: Adjusted HYCOM Data Set over B3-2 ADCP Deployment

205

Figure E7: ADCP, HYCOM and Adjusted HYCOM Velocity Profile over B3-2 ADCP

Deployment

Figure E8: ADCP, HYCOM and Adjusted HYCOM Power Density over B3-2 ADCP

Deployment

206

Figure E9: Squared Error Metric for B3-2 ADCP Deployment and HYCOM and

Adjusted HYCOM Data Set

Figure E10: Cable Measured Transport compared to HYCOM Estimated Transport over

B3-2 ADCP Deployment

207

Figure E11: Cable Measured Transport compared to HYCOM and HYCOM Adjusted

Estimated Transport over B3-2 ADCP Deployment

Figure E12: Squared Error Metric for HYCOM and Adjusted HYCOM Estimated

Transport compared to Cable Measured Transport over B3-2 ADCP Deployment

208

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