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Marine Renewable Energy

Zhaoqing Yang

Andrea Copping Editors

Resource Characterization

and Physical Effects

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Marine Renewable Energy

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Zhaoqing Yang ⋅ Andrea Copping

Editors

Marine Renewable Energy

Resource Characterization and Physical Effects

123

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Editors Zhaoqing Yang

Marine Sciences Laboratory, Pacific Northwest National Laboratory Seattle, WA

USA

Andrea Copping

Marine Sciences Laboratory, Pacific Northwest National Laboratory Seattle, WA

USA

ISBN 978-3-319-53534-0 ISBN 978-3-319-53536-4 (eBook)

DOI 10.1007/978-3-319-53536-4

Library of Congress Control Number: 2017932430

© Springer International Publishing AG 2017

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Printed on acid-free paper

This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG

The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

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Preface

Facing the Challenges of Resource Characterization and Physical System Effects of Marine Renewable Energy Development

Many nations have expanded their national energy portfolio to ameliorate the effects of climate change and to ensure the security and certainty of energy avail- ability. These efforts have led to scrutiny of marine renewable energy (MRE) as one of several viable new renewable energy sources. In addition to the need to prove the reliability and efficiency of current and wave energy converters, effective siting and operation of MRE devices requires detailed and accurate characterization of the tidal stream, ocean current, and wave resource, as well as assessments of the potential risk to the physical marine environment from MRE development.

The desire to understand the many challenges to characterizing marine energy resources and the effects of energy extraction on physical systems motivated the compilation of the chapters in this book, which represent research and review efforts that address these two important topics. Chapters Wave Energy Assessments: Quantifying the Resource and Understanding the Uncertainty through Marine Hydrokinetic Energy in the Gulf Stream Off North Carolina: An Assessment Using Observations and Ocean Circulation Models address resource characterization of wave, tidal stream, and ocean current energy using laboratory experiments,field measurements, and numerical models. ChaptersEffects of Tidal Stream Energy Extraction on Water Exchange and Transport Timescalesthrough Planning and Management Frameworks for Renewable Ocean Energycover topics related to the effects of energy extraction on physical systems, such as water exchange in coastal estuaries and bays, sediment transport, underwater noise, and marine spatial planning for MRE development.

In many parts of the world, harvesting wave energy seems very promising because of the very large potential resource located near many coastlines. Chapters Wave Energy Assessments: Quantifying the Resource and Understanding the Uncertainty through Analyses of Wave Scattering and Absorption Produced by WEC Arrays: Physical/Numerical Experiments and Model Assessmentare devoted

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to techniques and methodologies for wave resource characterization. In Chap.

Wave Energy Assessments: Quantifying the Resource and Understanding the Uncertainty, Robertson provides an overview of wave resource characterization and assessment using field measurements and numerical modeling approaches. The popular state-of-the-art, third-generation, phase-average spectral wave models that are suitable for wave resource characterization are reviewed by model framework, physical processes, computational requirements, and their applications to wave resource assessment at global, regional, and local scales. Techniques and methodologies for conducting baseline and high-fidelity resource assessments are presented, and the challenges of predicting extreme sea states and the uncertainty associated with wave resource characterization are discussed. The International Electrotechnical Commission (IEC) Technical Specification (TS) for wave resource characterization is also described in the chapter. The six parameters recommended by the IEC for characterizing wave energy resources are described—omnidirec- tional wave power, significant wave height, energy period, spectral width, direction of maximum directionally resolved wave power, and the directionality coefficient.

The Atlantic coast of Europe has some of the highest wave power resources in the world. In Chap.Wave Energy Resources Along the European Atlantic coast, Gleizon et al. present a joint effort by several European countries, including the UK, Portugal, France, Spain, and Ireland, to estimate the potential wave energy resource along the European Atlantic coast. Long-term hindcasts with high-resolution spectral wave models can greatly improve the accuracy of wave resource charac- terization and reduce the uncertainty associated with those estimates. A unique numerical modeling approach used in their study combines the regional-scale spectral wave model WaveWatch III (WWIII) for the continental shelf with high-resolution and the unstructured-grid Simulating WAves Nearshore (SWAN) model for the nearshore regions. Specifically, wave resource characterization was conducted based on 7-year high-resolution spectral wave hindcasts atfive distinct coastal regions: Scotland (UK), Ireland, France, Galicia (Spain), and Portugal.

Spatial and temporal variabilities in the wave climate are discussed. This study provides detailed information about the wave resource along the European Atlantic coast to help identify optimal areas for pilot-scale tests and commercial-scale development of wave energy converters (WECs).

While phase-averaged spectral wave models are commonly used in wave resource characterization, laboratory experiments and phase-resolving models enable the investigation of the dynamic interactions between WEC arrays and wave fields. In Chap. Analyses of Wave Scattering and Absorption Produced by WEC Arrays: Physical/Numerical Experiments and Model Assessment, Ozkan-Haller et al. evaluate the wave scattering and absorption induced by WEC arrays through laboratory and numerical experiments. The experimental study described was carried out with 1:33-scale commercial WECs under different array configurations subject to a range of regular waves and random sea states. Numerical experiments were carried out with the phase-resolving model WAMIT and the phase-averaged SWAN model. Model validations were conducted using data collected from the laboratory study. Their study results suggest that the environmental effects of WEC

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arrays can be minimized by designing WECs to operate optimally when the sig- nificant wave energy lies at periods near, or larger than, the period of peak energy extraction.

Chapters Hydrokinetic Tidal Energy Resource Assessments Using Numerical ModelsthroughWave-Tide Interactions in Ocean Renewable Energyfocus on tidal stream resource characterization and wave–tide interactions. ChapterHydrokinetic Tidal Energy Resource Assessments Using Numerical Modelsby Haas et al. and Chap. Tidal Energy Resource Measurements by Thomson et al. present method- ologies and techniques for tidal stream energy resource assessment and include case study examples from modeling and measurement perspectives, respectively. Both chapters discuss the importance of incorporating standards recommended by the IEC TS in the process of tidal energy resource characterization. These IEC stan- dards include model grid resolution, bathymetric resolution, number of tidal con- stituents for the open boundary condition, measurement and simulation periods, and impacts of energy extraction.

In Chap. Hydrokinetic Tidal Energy Resource Assessments Using Numerical Models, Haas et al. provide clear definitions for theoretical, technical, and practical resources at different scales of resource assessment. Concepts and modeling approaches for tidal energy resource assessment at individual turbine, regional, and project scales are discussed in detail. Finally, model results from a case study in the Piscataqua River, located between the border of Maine and New Hampshire (USA), illustrate the processes of tidal resource assessment at turbine, project, and regional scales using the Regional Ocean Modeling System.

In Chap.Tidal Energy Resource Measurements, Thomson et al. address tidal energy assessments conducted using analytical and numerical models that should be complemented by information fromfield measurements, especially at large regional scales. High-qualityfield measurements can be used to characterize current spatial and temporal variations and site-specific tidal resource assessment, as well as to validate models that are used for tidal resource assessment at various scales. A full suite of parameters that can be obtained from field measurements, such as tidal harmonic constituents, turbulence spectra and intensity, current histograms, lateral shear and current asymmetry, power density, and annual energy production, are noted, and their application to resource assessment is described. In a case study in Admiralty Inlet of Puget Sound in Washington State (USA), the authors demon- strate thatfield measurements collected at high sampling frequencies and over long periods of time are required to resolve stochastic and deterministic components of tidal currents.

High wave and tidal energy resources may coexist in some coastal regions, such as the seas of the northwest European continental shelf, the Gulf of Alaska, New Zealand, northwest Australia, and the Atlantic seaboard of Argentina. In these coastal regions, wave–tide interaction may be an important factor in resource characterization. In Chap. Wave-Tide Interactions in Ocean Renewable Energy, Hashemi and Lewis evaluate the potential effects of wave–tide interactions on resource characterization using simple analytical methods and coupled wave–tidal modeling techniques. Their study shows that tidal stream energy resources may be

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reduced due to wave–tide interactions under extreme wave conditions, and wave properties may be altered as a result of wave–tide interactions. The authors rec- ommend that wave–tide interactions be considered in either wave or tidal stream resource assessment in regions where high wave and tidal energy exist.

ChaptersUse of Global Satellite Altimeter and Drifter Data for Ocean Current Resource CharacterizationthroughMarine Hydrokinetic Energy in the Gulf Stream Off North Carolina: An Assessment Using Observations and Ocean Circulation Models address the current state of the science and research on ocean current energy. Unlike waves and tides, which propagate in a form of gravity waves, strong ocean currents are mainly generated by wind and the Coriolis force, which result in

“western intensification,” a phenomenon occurring along the western boundaries of large-scale open-ocean basins. In Chap. Use of Global Satellite Altimeter and Drifter Data for Ocean Current Resource Characterization, Tseng et al. examine the large-scale ocean current resource using long-term global satellite altimeter data and SVP drifter data. They quantify averaged surface velocities in the global oceans based on long-term data sets and evaluate long-term-averaged velocity maximums in the four strongest western boundary currents (WBCs): the Agulhas Current in the Indian Ocean, the Gulf Stream in the Atlantic Ocean, and the Mindanao Current and the Kuroshio Current in the Pacific Ocean. Specific locations of the velocity maximums for these four WBCs are identified, and the temporal variability influ- enced by monsoon winds and the El Niño Southern Oscillation are investigated.

Further detailed analysis is conducted to evaluate potential sites for ocean current power generation in the North Pacific, South China Sea, and Oceania, based on a set of criteria including current speed and frequency, water depth, and distance from the shore.

Meyer et al. examine the potential for energy extraction from the Agulhas Current along South Africa’s East Coast in Chap. Mapping the Ocean Current Strength and Persistence in the Agulhas to Inform Marine Energy Development using an integrated approach that combines state-of-the-art satellite remote sensing, predictive modeling, and in situ observation techniques. They evaluate two specific locations, one at mid-shelf and one at offshore, for potential ocean current power generation. Current spatial and temporal variability and power density at these two potential sites are analyzed. Meyer et al. show that data generated from these combined methodologies can provide useful insight into the unique challenges encountered in resource assessment for the Agulhas Current. Finally, considerations of the technical challenges for energy extraction from the Agulhas Current and potential environment impacts are discussed.

Chapters Ocean Current Energy Resource Assessment for the Gulf Stream System: The Florida Currentand Marine Hydrokinetic Energy in the Gulf Stream Off North Carolina: An Assessment Using Observations and Ocean Circulation Modelsare two companion chapters about resource assessment in the Gulf Stream, each focusing on different geographic locations and different methodologies. In Chap. Ocean Current Energy Resource Assessment for the Gulf Stream System:

The Florida Current, Haas et al. evaluate the theoretical resource in the Florida Current portion of the Gulf Stream System, based on idealized and realistic

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numerical model simulations using the Hybrid Coordinate Ocean Model. Their study indicates that while the mean power in the Florida Current was found to be over 22 GW, extraction of only 5 GW of power from the Florida Current would require deployments of thousands of turbines under undisturbed flow assumption.

In their study, Haas et al. demonstrate the importance of incorporating the addi- tional dissipation due to the presence of turbines in model simulations for ocean current resource assessment, the result of which is a smaller level of technically extractable power.

In Chap.Marine Hydrokinetic Energy in the Gulf Stream Off North Carolina: An Assessment Using Observations and Ocean Circulation Models, Lowcher et al.

assess the theoretical energy resource in the portion of Gulf Stream off the North Carolina Coast, based on a combination of observations and numerical model simulations. Current observation data were collected from moored and shipboard acoustic Doppler current profilers as well as from high-resolution ocean surface-current radars. Model simulations were generated from a high-resolution regional ocean circulation model for the Mid- and South Atlantic Bight. While it is challenging to accurately predict the high-frequency variability in spatial and temporal scales, the model estimates are in good agreement with the observed mean currents. Annual power density along three transects off the North Carolina Coast was calculated based on model outputs.

Chapters Effects of Tidal Stream Energy Extraction on Water Exchange and Transport TimescalesandThe Impact of Marine Renewable Energy Extraction on Sediment Dynamics address the effects of MRE extraction on physical ocean processes, such as water exchange and sediment transport. In Chap.Effects of Tidal Stream Energy Extraction on Water Exchange and Transport Timescales, Yang and Wang review the concept of transport timescales and numerical models for assessing tidal energy potential and its effect on volume flux and flushing time.

Model results from idealized and realistic case studies show that the change in flushing time is linearly correlated with the volume flux reduction when the change in volume flux is small, but with a greater rate of change. Their study demonstrates the importance of using three-dimensional models in tidal stream energy resource assessment, as well as the importance of using flushing time as a transport timescale to quantify the effect of tidal energy extraction on transport processes.

In Chap. The Impact of Marine Renewable Energy Extraction on Sediment Dynamics, Neill et al. provide a detailed review of sediment dynamics and sediment transport processes in coastal and estuarine systems due to tidal current, wave action, or their combined effect. Impacts on morphodynamics of offshore sand banks as a result of tidal stream energy extraction, and on beach erosion and replenishment due to wave energy conversion are explored. The scale of impacts resulting from MRE extraction on sediment transport processes and coastal mor- phodynamics under extreme wave and storm, compared to scales of natural vari- ability, is discussed.

Like other anthropogenic sources of sound, underwater noise can act as a stressor to marine animals in the marine environment and is an inevitable byproduct of energy generation. Chapters Assessing the Impacts of Marine-Hydrokinetic

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Energy (MHK) Device Noise on Marine Systems by Using Underwater Acoustic Models as Enabling Toolsand Challenges to Characterization of Sound Produced by Marine Energy Convertersaddress the issue of underwater noise on the marine environment. In Chap. Assessing the Impacts of Marine-Hydrokinetic Energy (MHK) Device Noise on Marine Systems by Using Underwater Acoustic Models as Enabling Tools, Etter provides a comprehensive review of the theory of underwater acoustics and describes the background noise fields arising from natural and anthropogenic sounds as well as from MRE devices. A suite of underwater acoustic models is evaluated, and potential applications of different models toward under- standing the impact of anthropogenic noise induced by MRE devices on the marine environment are discussed.

In Chap.Challenges to Characterization of Sound Produced by Marine Energy Converters, Polagye discusses the challenges of characterizing underwater noise generated by MRE devices and the role of field measurements in quantifying acoustic emissions from MRE devices and arrays. Specifically, this chapter addresses the factors influencing sound generation by an MRE device, methods for distinguishing device sound from ambient noise, and masking of the device sound by flow noise. Field measurements of spectrograms and annotated periodograms from a WEC are presented to illustrate these challenges. Potential solutions to overcome these challenges are also discussed.

Marine spatial planning (MSP) is a relatively new approach to analyzing and allocating parts of marine spaces for specific uses or objectives in order to achieve ecological, economic, and social objectives. In Chap. Planning and Management Frameworks for Renewable Ocean Energy, O’Hagan provides an overview of how the requirements of the ocean energy sector are taken into account when designing marine planning systems, how scientific information is reflected in the process, and the tools used to implement MSP. The chapter also identifies how possible or currently experienced conflicts between different sectors or users are managed. The chapter concludes with a section on the key limiting factors to implementation of MSP.

This book presents only part of the ongoing effort to enhance our understanding of the challenges of and barriers to MRE development. By no means does it cover every aspect of resource characterization and physical system effects in MRE development. We hope this book will serve as a useful tool to researchers, industry, and members of the general public who are interested in understanding the current state of the science in MRE development, especially the challenges and approaches to improving resource characterization and reducing system effects.

Finally, we thank the chapter authors for their hard work and contributions to the book, and the many reviewers for their valuable comments and input that improved the quality of the chapters. We also thank Ms. Susan Ennor of Pacific Northwest National Laboratory for technical editing of all of the chapters.

Pacific Northwest National Laboratory Zhaoqing Yang

Seattle, WA, USA Andrea Copping

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Contents

Wave Energy Assessments: Quantifying the Resource

and Understanding the Uncertainty. . . 1 Bryson Robertson

Wave Energy Resources Along the European Atlantic Coast. . . 37 Philippe Gleizon, Francisco Campuzano, Pablo Carracedo,

André Martinez, Jamie Goggins, Reduan Atan and Stephen Nash Analyses of Wave Scattering and Absorption Produced by WEC

Arrays: Physical/Numerical Experiments and Model Assessment. . . 71 H. Tuba Özkan-Haller, Merrick C. Haller, J. Cameron McNatt,

Aaron Porter and Pukha Lenee-Bluhm

Hydrokinetic Tidal Energy Resource Assessments Using

Numerical Models. . . 99 Kevin Haas, Zafer Defne, Xiufeng Yang and Brittany Bruder

Tidal Energy Resource Measurements . . . 121 Jim Thomson, Brian Polagye and Vincent S. Neary

Wave-Tide Interactions in Ocean Renewable Energy. . . 137 M. Reza Hashemi and Matt Lewis

Use of Global Satellite Altimeter and Drifter Data for Ocean

Current Resource Characterization. . . 159 Ruo-Shan Tseng, Yu-Chia Chang and Peter C. Chu

Mapping the Ocean Current Strength and Persistence

in the Agulhas to Inform Marine Energy Development. . . 179 I. Meyer, L. Braby, M. Krug and B. Backeberg

Ocean Current Energy Resource Assessment

for the Gulf Stream System: The Florida Current. . . 217 Kevin Haas, Xiufeng Yang, Vincent Neary and Budi Gunawan

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Marine Hydrokinetic Energy in the Gulf Stream Off North Carolina: An Assessment Using Observations

and Ocean Circulation Models. . . 237 Caroline F. Lowcher, Michael Muglia, John M. Bane, Ruoying He,

Yanlin Gong and Sara M. Haines

Effects of Tidal Stream Energy Extraction on Water Exchange

and Transport Timescales . . . 259 Zhaoqing Yang and Taiping Wang

The Impact of Marine Renewable Energy Extraction

on Sediment Dynamics. . . 279 Simon P. Neill, Peter E. Robins and Iain Fairley

Assessing the Impacts of Marine-Hydrokinetic Energy (MHK) Device Noise on Marine Systems by Using Underwater Acoustic

Models as Enabling Tools. . . 305 Paul C. Etter

Challenges to Characterization of Sound Produced

by Marine Energy Converters. . . 323 Brian Polagye

Planning and Management Frameworks for Renewable

Ocean Energy. . . 333 Anne Marie O’Hagan

Index . . . 385

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About the Editors

Dr. Zhaoqing Yang is a chief scientist for coastal ocean modeling at the US Department of Energy’s Pacific Northwest National Laboratory (PNNL) and a distinguished faculty fellow in the Department of Civil and Environmental Engineering at the University of Washington in Seattle, Washington. Dr. Yang’s research covers broad areas related to coastal hydro- dynamics and transport processes using advanced numerical models. His recent research has focused on marine renewable energy resource assessment and the impacts of extreme events and anthropogenic distur- bances on coastal infrastructure and ecosystems.

Dr. Yang leads PNNL’s modeling effort on wave and tidal energy resource characterization as well as asso- ciated environmental impact assessment. He holds a Ph.D. in Physical Oceanography from the School of Marine Sciences at the College of William and Mary.

Dr. Yang is a member of the Journal of Renewable Energy Editorial Board and served on the National Academy of Sciences—National Research Council’s Committee on Marine and Hydrokinetic Energy Assessment.

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Dr. Andrea Copping is a senior research scientist and program manager for Pacific Northwest National Laboratory (PNNL) and a distinguished faculty fellow in the School of Marine and Environmental Affairs at the University of Washington in Seattle, Washington.

Dr. Copping’s research focuses on the environmental effects of development of wave and tidal energy and offshore wind installations, and the role that these effects play in technology development and project initiation across the nation. Andrea leads international projects under International Energy Agency agree- ments on the environmental effects of marine energy development (Annex IV) and of wind (WREN) that share environmental effects information in order to benefit from progress made around the world. Prior to joining PNNL, Dr. Copping was the associate director of the Washington Sea Grant Program. Although trained as a blue water biological oceanographer, Andrea has spent most of her professional career examining the interactions of humans and the marine environment. Andrea holds a Ph.D. in Biological Oceanography from the University of Washington. Dr.

Copping is an associate editor of the Coastal Man- agement Journal, and on the Editorial Board of the International Journal of Marine Energy.

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Wave Energy Assessments: Quantifying the Resource and Understanding

the Uncertainty

Bryson Robertson

Introduction

Raw wave energy and the associated potential power production from wave energy converters hold great promise as an abundant, carbon-neutral source of electricity generation for generations to come. The International Energy Agencies (IEA) Ocean Energy Systems (OES) (OES 2015) estimates that the global wave resource could provide up to 29,500 TWh of carbon-neutral electrical energy annually through the use of wave energy conversion (WEC) technologies. Sub- stantial efforts are being made to understand coastal and offshore wave energy resources, expand methods to quantify and characterize the measurements, and provide wave energy companies with the necessary knowledge to design WEC technologies (Cornett and Zhang2008; Dunnett and Wallace2009; Kim et al.2012;

Reikard et al.2015; Robertson et al.2013; Hiles et al.2014).

Highly resolved and accurate assessments of the gross wave resource are required for the wave energy industry to mature and begin to provide power to electrical grids. Wave resource assessments are the foundation for the architectural design of a wave energy converter (WEC), a project developer’s unit cost calcu- lations, a utility’s reserve costing plans, and for a regulator’s cost-benefit analyses of large-scale WEC activities. The importance of the resource assessment in pro- viding an accurate and precise representation cannot be overstated.

Wave energy can be described as a concentration and moving reservoir of solar energy. As the world heats differentially from incoming solar irradiance, air masses heat and cool, moving air from high pressure to low pressure areas, thereby creating wind. When this wind blows over vast stretches of unobstructed ocean fetch, waves are generated. If the wind blows with sufficient speed, over a large enough fetch and

B. Robertson ()

Institute for Integrated Energy Systems, University of Victoria, Victoria, Canada e-mail: bryson@uvic.ca

© Springer International Publishing AG 2017

Z. Yang and A. Copping (eds.), Marine Renewable Energy, DOI 10.1007/978-3-319-53536-4_1

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for extended portions of time, ocean swells develop. The longer and harder the wind blows, over increasing fetches, the more the wave height and wave period increase. Once generated, ocean swells are able to propagate vast distances with negligible dissipation or dependence on the wind that generated them. As a result, ocean waves arriving at any shoreline globally are the culmination of the local wind conditions, as well as the hysteresis effect of hundreds of storms across the millions of square kilometers of surrounding ocean. As a result, ocean swells are moving reservoirs of concentrated wind and solar energy. The stores feature high power density and are well predicted. Excluding tidal energy resources, ocean waves are the most energy dense form of renewable energy sources. For example, solar energy flux is measured in kilowatts per square meter and reaches a maximum of 1 kW/m2 at high noon on the equator, while relatively benign regular wave sea state of 2-m wave height with a ten second period features ∼20 kW/m of wave energy flux (Falnes2002; DNV 2010).

The goal of this chapter is to provide an introduction to the vast, complex, and engaging research area of wave resource assessments. The objectives, methods, and outcomes of various wave resource methodologies will be discussed. The intrica- cies of a resource assessment and the implications forfinal WEC power production will be quantified. Recommendations and further work in future research avenues will be presented as the topics are discussed and analyzed; a brief introduction to extreme wave analysis and the siting of future WEC farms is included. Ultimately, the goal of this chapter is to provide an overview of the present state of the art in wave resource assessment methodologies, recommendations for best practices, and help illuminate the true nature of this vast resource for future renewable energy generation.

Wave Data Sources

The development and accuracy of a robust wave resource assessment methodology rely intrinsically on the input data sources. Hence, the collection of high-resolution observations, or measurements, of the wave conditions and a detailed and validated numerical model is of utmost importance. As will be shown throughout this chapter, the present level of the accuracy and robustness of the resource assessment is limited by the availability of necessary data sources; however, as the industry evolves over time, more data will be collected and the resource assessment methodology will become increasingly robust and accurate.

Wave Measurements

Waves are generally either directly measured, through deployed in situ measure- ment devices, or remotely measured through backscatter and Doppler shifts by

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radar and satellites. As noted, the most common direct measurement of wave conditions is through the deployment of in situ wave measurement devices; gen- erally moored wave buoys, seafloor-mounted acoustic measurement devices, or statically mounted wave poles.

Wave buoys float on the ocean surface and follow the three-dimensional varying ocean surface over time. Wave buoys are deployed across the globe and provide continuous measurements of wave conditions to metrological organizations, ship- ping traffic, and recreational ocean users such as surfers. Buoys can either be permanently moored or free-floating measurement devices. Moored buoys provide a clean consistent record of wave conditions at a specific location, with depths ranging from 10 s to 1000 s of meters. However, buoys are susceptible to breaking wave loading and are unsuitable for shallow water deployments where breaking waves are expected. Through detailed analysis of the recorded buoy accelerations, the buoys’ heave (vertical motion) and horizontal movements can be calculated and are generally presented as a time-dependent Heave-Northing-Easting record. Using the same input data, a representation of the incoming directional wave spectrum is created (a detailed explanation of directional wave spectra is presented later).

Increasingly common for shallow water applications with breaking waves, seafloor-mounted devices can take acoustic measurements of the water surface and record the orbital velocities of particles near the surface and/or the time-varying water pressure. Single-point-of-measurement pressure devices provide a time-history of the sea surface elevation but provide no details about the direc- tionality of the incoming waves. Acoustic measurement devices featuring multiple acoustic beams will recreate the full incoming wave spectra through detailed analysis of these multiple beam time-histories. Measurements derived from seafloor-mounted devices provide extremely precise measurement of the sea surface but are generally limited in application to shallow water locations. Point mea- surements from wave buoys or acoustic measurement devices are widely under- stood, and their deployments are easily achieved. However, they provide limited knowledge of the spatial variability in the resource.

Remote measurements from aircraft, satellites, or tall coastal structures are better suited for giving larger spatial distributions of the wavefield. The resulting mea- surements of the sea surface from these remote methods are developed through detailed analysis of the radar backscatter or recorded imagery pixel intensity. As a result, wave measurements obtained using remote methods generally lack the high level of precision and accuracy that in situ measurements provide and are generally of shorter duration than existing in situ measurements.

The suitability of a certain wave measurement technique depends on the goal of the measurement campaign; each method has advantages and disadvantages. For the wave energy industry, the current standard is wave buoys—primarily due to their ease of deployment and the availability of long-term data sets.

It is important to note that a wave measurement sample is only one realization of the underlying spectrum; slight variations in timing, frequency bands, and record length will result in variations in thefinal spectrum. Direct measurement of wave conditions, from wave buoys, acoustic wave and current (AWAC) profilers, radar,

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etc., are not without systematic biases and random errors. Each measurement platform and technique includes a range of inherent assumptions in the recreation of the sea state, and, if possible, these assumptions should be quantified prior to their detailed use for wave resource assessments. For example, the Joint WMO-IOC Technical Commission for Oceanography and Marine Meteorology (JCOMM) (JCOMM2014) provides a database of buoy intercomparisons and quantifies the accuracy of measurements for permanent wave buoys around the globe. The results from the JCOMM project and other similar studies (Robertson et al.2015) provide the necessary quantitative information to help correct and improve the accuracy of wave measurement records. These sorts of analyses should be performed in parallel with numerical model development to ensurefinal numerical model validation is compared against the most accurate measurements of wave conditions possible.

Numerical Wave Models

Wave measurements from buoys, satellites, or radars are not wholly sufficient for characterizing wave conditions across an area of interest. Robust wave resource assessments require detailed knowledge of wave conditions across significant spatial areas and over long time frames. Numerical wave propagation models provide the bulk of the data required for a wave resource assessment because they provide the necessary temporal and spatial scope to allow for a detailed under- standing of the wave climate. A wide range of numerical models is available for simulating surface wave processes, based on different physical formulations, assumptions, and numerical frameworks. Wave models can be divided into two major categories: phase-resolving models and phase-averaged models.

Phase-resolving models are based on fundamental wave equations that involve rigorous approximations. The propagation and evolution of each phase-resolved wave must be computed on a grid with a resolution finer than the wavelength.

Phase-resolving models solve for the water surface elevation and account for the horizontal and vertical flow velocity. These types of models are suitable for resolving radiation and diffraction over 10 s of kilometers or short time periods (Hiles et al. 2014) but are too computationally expensive for large-scale or long-term analyses.

Phase-averaged spectral models compute the evolution of the wave spectrum in space and time, based on the wave energy balance equation, and are currently the only practical models for assessing large-scale wave resources (i.e., ocean basin scale). The oceanographic community has developed many spectral wave models, and recent wave resource assessment is almost exclusively based on third-generation (3G) version of these models. The most popular 3G wave models are the Wave Action Model (WAM) (WAMDI1988), WAVEWATCH III (WWIII) (Tolman 2014), Simulating WAves Nearshore (SWAN) (SWAN 2006), TOMA- WAC (Benoit et al.1996), and MIKE-21 SW (DHI2012).

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The 3G wave models resolve the nonlinear interactions through the spectral wave action density (N) equation (Eq.1) and balance the equation across the full frequency and direction domain (Tolman2014). Wave action density is defined as wave energy density divided by frequency of occurrence ðN = E ̸ σÞ. Action density is conserved in the presence of ambient current, whereas energy density (E, to be discussed in detail later) is not, hence the use of action density (SWAN2006).

The evolution of the wave spectrum is calculated by implicitly solving the action balance equation (Eq.1) to predict wave conditions across a computational grid.

∂N

∂t +∂ ðCg, x+ UÞN

∂x + ∂ ðCg, y+ VÞN

∂y +∂Cg,σN

∂σ +∂Cg,ϑN

∂ϑ = S ̸ σ ð1Þ The wave action density evolves as a function of time (t), distance (shown in the Cartesian coordinates (x, y)), depth and current induced refraction (θ), and fre- quency (σ). Frequency-shifting is related to the Doppler effect and is due to the presence of ambient current. Relative frequency (σ) is due to variation in depths and currents; Cgdenotes the wave action propagation speed in (x, y,σ, and θ) space (see Eq. (9)); U and V are the depth-averaged current velocities in (x, y) space, while S denotes the generation and dissipation terms within the model.

Each model is dependent on a computational spatial grid, a series of nodes and cells that define the geographic space over which the model will compute the propagation and evolution of the wave action density. Grids are eitherfixed size (or

“structured”) or variable size (or “unstructured”).

Structured grids can either be uniform rectilinear or curvilinear quadrilateral grids. Rectilinear grids are based on uniform-distributed nodes, and the cell dimensions are based on Cartesian coordinates. Curvilinear grids are also based on uniform cell discretization but are based on spherical coordinates to better represent the spherical nature of the planet. Given that these are both types of quadrilateral grids, four cells are required to meet at internal nodes within structured grids.

Unstructured grids allow for variable resolution in the grid spacing and cell shape. Unstructured grids can be combination of triangles and quadrilaterals, a so-called hybrid grid. The goal of an unstructured grid is to improve grid resolution in spatial areas of interest, while reducing the computational overhead.

WAM

WAM—the first 3G spectral wave model to be widely adopted—is one of the most well-tested wave models and is widely used internationally, especially in the European wave modeling communities. Developed by the WAMDI Group (1988), WAM simulates spectra of random wind-generated waves by solving the action density equation, including nonlinear wave–wave interactions. It has since been further developed by different organizations but without a centrally maintained version. WAM has proven to be reliable for deep-water open-ocean applications

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over regular grids, yet it does not contain the necessary shallow water physics for application in depth-limited locations.

WAM was the first operational wave model to be fully coupled to an atmo- spheric model and later to an ocean circulation model. This work was carried out at the European Centre for Medium-Range Weather Forecasts (ECMWF). Further documentation on the current ECMWF WAM model can be found in (ECMWF 2013). Coupling to a hydrodynamic model was first carried in the PRO-WAM version, and a recent version of WAM (4.5.4) was also made available as part of the MyWave project (http://mywave.github.io/WAM/). For additional detail, see chapter“Wave Energy Resources Along the European Atlantic Coast”.

WWIII

WWIII is a popular wave model for global analyses and is continually developed by the Marine Modeling and Analysis Branch at the National Centers for Environ- mental Prediction and by an international team of developers. Similar to WAM, WWIII solves the random phase spectral action density balance equation. The current version 4.18 of WWIII, which is available to the public, allows for various grid options and physics packages. WWIII generally uses an explicit numerical scheme to solve the governing equation on traditional structured rectilinear or curvilinear grids. Hence, the model run time-step is constrained by the Courant– Friedrichs–Lewis (CFL) stability criteria (CFL ≤ 1), which simply states that wave energy may not travel more than one geographic computational grid cell per time-step. Further documentation on the current WWIII model can be found in (Tolman2014).

WWIII and WAM are excellent examples of wave models suited for global wave resource assessments; they are able to provide the necessary long-term hindcasts of wave conditions, over large spatial domains, with sufficient resolution to precisely and accurately quantify the wave resources. These sorts of standardized meteoro- logical office wave products provide an excellent resource for identifying geo- graphical regions that have sufficient wave energy transport resources for future development. However, when attempting to identify specific locations for deployment and assessment of the wave resource, additional spatial resolution in the model computational grid and resolution within the model wave parameter output are required. For these applications, nested or multigrid WAM or WW3 models could be employed, or boundary conditions from a global model could be used within models specifically designed for coastal applications, such as SWAN, TOMAWAC, or MIKE-21 SW. Note that both WAM and WWIII have current and in-development model implementations that have all of the necessary physics and numerical schemes to handle coastal applications.

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SWAN

The basic scientific philosophy of SWAN is identical to that of WAM, but with applications for shallow water. SWAN is an open-source wave model that was developed at the Delft University of Technology and was built as an extension of the 3G WAM model. The fundamental difference between SWAN and WWIII/WAM is the numerical scheme used to solve the spectral action balance equation. SWAN only uses an implicit formulation, which allows for larger com- putational time-steps and efficient simulations of high spatial resolution areas (<1 km). Designed to simulate the propagation of waves in shallow nearshore areas (depth <½ wavelength), SWAN is often applied for wave resource assessments (Ruehl2013; Dykes et al.2002; Rusu and Soares2009; Choi et al.2009; Robertson et al.2014). As an example of the generation and dissipation terms, noted in Eq. 1 and expanded in Eq.2, SWAN breaks the S term down to account for input by wind (Sin), triad and quadruplet nonlinear wave-wave interactions (Snl), and wave dis- sipation through white-capping (Swc). In shallow water, S includes the effects of bottom friction (Sbf) and shoaling-induced breaking (Sbr) (SWAN 2006).

S = Sin+ Snl+ Swc+ Sbf+ Sbr ð2Þ SWAN can solve the steady form of the action balance equation by running in the stationary mode, which greatly reduces computational requirements and run times, yet should only be applied when the model domain is sufficiently small (∼100 km).

Further documentation of the base SWAN model is available online (Tolman2014).

TOMAWAC

TOMAWAC is the coastal wave propagation sub-module of the commercial inte- grated TELEMAC modeling system (Telemac-Mascaret 2015). TOMAWAC/

TELEMAC is managed and developed by Artelia, BundesAnstalt fur Wasserbau, Centre d’Etudes Techniques Maritimes at Fluviales, Daresbury Laboratory, and Electricité de France R&D and HR Wallingford. TELEMAC is a modeling tool used for free-surface flows; it is based on afinite element method and can be solved over both structured and unstructured grids. Similar to SWAN, TOMAWAC models the sea states by solving the balance equation of the action density direc- tional spectrum.

MIKE-21 SW

MIKE-21 SW is the spectral wave modeling sub-module of the MIKE-21 suite (DHI2016), developed by DHI International. MIKE-21 SW is also a 3G spectral

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wind-wave model and based on a cell-centeredfinite volume formulation. The time integration is performed using a fractional step approach where a multi-sequence explicit method is applied for wave propagation (DHI 2012). MIKE-21 can be formulated as either a fully directional spectral formulation or a parametric for- mulation. It includes shallow water physics and works on both structured and unstructured grids.

The use of localized coastal wave models, such as SWAN, TOMAWAC, or MIKE-21, allows wave energy developers to run high-resolution, long-term hind- casts of wave conditions without having access to significant high-powered com- puting resources. SWAN, TOMAWAC, and MIKE-21 SW are not constrained to run on structured computational girds; they are able to run on unstructured com- putational grids that have more flexibility on grid resolution and format. Depending on the application, these models still rely on global wave models, or in situ instruments, for spatially invariant wave and wind boundary conditions. If the model domain is larger than 10 s of kilometers, it is suggested that wind forcing fields should be included in the local model to more accurately recreate locally generated wind seas and, hence, improve the representation of the true sea surface conditions.

Table1 provides a quick overview of the main characteristics of the models discussed. Global and regional wave models are still models and do not exactly replicate the true sea conditions. Models are known to underpredict extreme wave conditions, overpredict low-energy wave conditions, and provide a smoother rep- resentation of wave conditions. In contrast to wave measurements, which are a single realization of the underlying wave spectrum, wave models provide an estimate of the underlying spectrum. Hence, it is nearly impossible to get a zero root mean square error (RMSE) between a measurement and a model. Regardless, data from an in situ measurement device should be thoroughly checked for errors and consistent biases.

Any model used for wave resource assessment should be validated against numerous independent wave measurements prior to use, preferably measurements obtained using calibrated wave measurement devices (JCOMM2014).

Table 1 Overview of wave model and characteristics

Model General

application

Solver Method Grid Source

WAM Global Explicit Finite

difference

Structured Open source WWIII Global/coastal Explicit/implicit Finite

difference

Structured/

unstructured

Open source

SWAN Coastal Implicit Finite

difference

Structured/

unstructured

Open source

TOMAWAC Coastal Implicit Finite

element

Structured/

unstructured

Open source

MIKE 21 Coastal Explicit Finite

volume

Structured/

unstructured

Commercial

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Analyzing and Quantifying the Resource

Over the past decade, significant effort has been expended on analyzing the data from wave models and wave measurement instruments to quantify the magnitude and distribution of wave energy resources around the world. A nonexhaustive review of published literature indicated the availability of wave resource assess- ments in the contiguous United States (EPRI 2011; Lenee-Bluhm et al. 2011;

Dallman and Neary2014), Hawaii (Stopa et al.2011), Australia (Hughes and Heap 2010; Hemer and Griffin2010), Canada (Hiles et al.2014), (Robertson et al.2014), (Cornett2006), Chile (Monardez et al.2008), Africa (Sierra et al.2016), and across the European Union (Smith et al.2012; Rusu and Soares2012; Rute Bento et al.

2016; Liberti et al.2013; Ayat2013; Folley and Whittaker2009). In the majority of the noted studies, a numerical wave model was validated against wave buoys and was subsequently used to quantify the characteristics of the long-term wave climate.

Precisely quantifying the multi-dimensional characteristics of wave conditions is more complex than for other renewable forms of energy, i.e., wind, tidal, or solar resources. Generally, wind, solar, and tidal resource can be described using a single variable—wind speed, solar irradiation, or water speed, respectively. In contrast, wave energy transport is a multivariable problem and can only be quantified, at a very minimum, through detailed knowledge of both the significant wave height ðHm0Þ and the wave energy period ðTeÞ parameters. This added dimension signif- icantly complicates wave resource assessments and necessitates both a high-resolution wave data set and a detailed understanding of all of the influencing variables.

Wave Spectra and Characteristic Parameterizations

Under the assumption that the sea surface elevation is a stationary and Gaussian process, the short-term (<30 min) characteristics of a single sea state can be characterized, at any particular point in time or space, by a directional variance density wave spectrum, which is more commonly referred to as a directional wave spectrum. A sample directional wave spectrum is presented in Fig.1; the direc- tional wave spectrum plots the sea surface variance densityðEijÞ over a range of wave frequencies (i) and directions (j). As shown, the frequency component of the variance density is represented by concentric rings showing the reducing frequency/increasing wave period values as the rings approach the center. The direction that the variance density is arriving from is represented by the respective angles, with 0° generally representing a swell traveling from the north to the south and 270° generally representing a swell traveling from the west to the east. The magnitude of the variance density for each direction and frequency is represented by the color-intensity map.

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Older wave measurement buoys andfixed in situ instruments, such as pressure sensors, are generally unable to measure the directional content of the variance density spectrum and often only report the nondirectional variance density spectrum.

A sample nondirectional variance density spectrum is shown in Fig.2for the same sea state used in Fig.1. The nondirectional spectrum can be easily generated from the directional wave spectrum by simply integrating all of the directional componentsðθÞ of the variance density within a single frequency band, as shown in Eq. (3):

Ei=∑

j

EijΔθ ð3Þ

When quantifying the long-term wave resource at a location of interest, the use of the full directional wave spectrum is exceedingly cumbersome, impractical, and Fig. 1 Directional spectral

variance density spectrum

Fig. 2 Nondirectional spectral variance density spectrum

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does not allow for quick comparative exercises. For example, a 10-year numerical hindcast of wave conditions at a single location would involve∼87,600 hourly directional wave spectra. It is necessary to parameterize these data into simplified metrics that provide the necessary level of detail for the sea state and are tractable when quantifying the wave climate. This parameterization process inherently introduces uncertainty to the wave resource assessment but is required to keep the wave climate data manageable for both WEC developers and policymakers.

The two dominant parameters used for wave resource assessments are the sig- nificant wave height ðHm0Þ, also known as the zero-moment wave height, and the energy periodðTeÞ. The significant wave height is used to characterize the wave height of a given sea state and, historically, was calculated as the average value for the highest third of waves from a time-series zero-up or zero-down crossing analysis. In the frequency-domain, and more conventionally, it is calculated using the zeroth spectral moment of the wave spectrum, according to Eq. (4). This also equates to the variance or the square root of the standard deviation of the sea surface elevation.

Hm0= 4 ffiffiffiffiffiffi m0

p ð4Þ

where the spectral moment of nth order, mn, uses Eq. (5) when calculating from the nondirectional variance density spectrum using:

mn= ∑

i

finEiΔf ð5Þ

whereΔf is the frequency increment and finis the ith frequency to the nth power.

The energy period is the variance-weighted mean period from the directional or nondirectional variance density spectrum. The energy period is calculated using moments of the wave spectrum according to Eq. (6):

Te=m− 1

m0 ð6Þ

It is still common to see wave resource assessment uses the peak periodðTpÞ and peak direction ðθpÞ to quantify the periodicity and directionality of the wave cli- mate. The peak period and direction correspond to the wave frequency and direc- tion, which feature the maximum variance density; for example in Fig.2, Tp is 11.4 s while Te is 7.2 s. The peak period and direction are independent of the distribution of the variance density across the frequency and direction axis and are prone to chaotic behavior. As a result, the energy period has become the preferred metric for characterizing the periodicity of the wave condition, while θJmax is specified by the International Electrotechnical Commission (IEC) for directionality (θJmax is discussed on the next page). If shape of the wave spectrum follows a known spectral shape, the transform from Tp to Te can be easily calculated. See Table2 for a Pierson–Moskowitz spectral shape. For more detail about the impact of energy values, see (Cahill and Lewis2014) and (Goda2009).

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Table2Pierson–MoskowitzspectrumTpTetransform Peak period2345678910111213141516171819 Energy period1.82.63.44.35.16.06.97.78.69.410.311.112.012.913.714.615.416.3

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An additional wave spectrum parameter often cited is the spectral width. The spectral width characterizes the distribution of the variance density along the fre- quency axis. Saulnier et al. (Saulnier et al.2011) review different published spectral width formulations and found that Eq. (7), which defines the spectral width as the standard deviation of the period variance density normalized by the energy period, provides a robust representation of the width.

ϵ0=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m0m− 2

m2− 1 − 1 r

ð7Þ

The most commonly cited energy parameter is the omnidirectional wave energy transport (J). The omnidirectional wave energy transport provides a measure of the time-averaged energy flux, through an envisioned vertical cylinder of unit diameter extending from the sea floor to the surface, and is the power per meter of wave front that WECs are attempting to capture. It is calculated using:

J =ρg ∑

i

cg, iEiΔf Δθ ð8Þ

where

cg, i=πfi

ki

1 + 2kih sinh 2kih

 

ð9Þ

whereρ is water density, g is gravity, kiis the wave number at the ith frequency, cg is the group velocity, and h is the mean water depth. The wave number is calculated as 2π/L.

The parameters noted thus far are common, standardized oceanographic and marine wave condition parameterizations. Moving beyond these parameters and identifying parameters of interest and necessity to the wave energy community, the IEC works with international experts to develop baseline standards for wave, tidal, and water resource assessments, under the Technical Committee-114 identifier (Piche et al. 2015; International Electrotechnical Commission T C 114 2015).

Based on the cumulative scientific knowledge about wave resource assessments, and first published by Lenee-Bluhm et al. (2011), the IEC has included three additional parameters for wave resource assessments in their current technical specification: the directional wave energy transport, the direction of the direction- ally resolved wave energy transport, and the directionality coefficient.

Resolving the directional components of the omnidirectional wave energy transport requires a measure of the time-averaged energy flux through the same envisioned vertical plane of unit width, extending from the sea floor to the surface, but with its normal vector parallel with direction, θ. This directionally resolved wave energy transport is the sum of the contributions of each component, with a positive component in directionθ and is calculated as follows:

Wave Energy Assessments: Quantifying the Resource 13

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Jθ=ρg ∑

i, j

cg, iEijΔf Δθ cos θ − θj

 

δ δ = 1, cos θ − θj

 

δ = 0, cos θ − θj ≥ 0

 

< 0



ð10Þ

When assessing the directionality of a sea state, the IEC specification recom- mends using the direction of maximum directionally resolved wave energy trans- portðθJmaxÞ, which corresponds to the maximum value of Jθ.

Finally, the directionality coefficient is a characteristic measure of the directional spreading of wave energy transport. It is the ratio of the maximum directionally resolved wave energy transport to the omnidirectional wave energy transport (see Eq. (11)).

d = JθJmax

J ð11Þ

Baseline Resource Assessment

Over the past couple of decades, numerous methodologies have been presented to perform a baseline wave resource assessment—an assessment that provides both the necessary information about the wave resource and sufficient detail for the devel- opment of WEC technologies. International wave energy experts are collaborating with the IEC to develop technical specifications that outline a robust and consistent method for performing baseline wave resource assessments. The technical speci- fications are consistently updated, generally based on published academic research, and can be purchased from IEC (International Electrotechnical Commission T C 1142015).

As noted in the numerical wave models section, one of the major advantages of numerical wave models is their ability to quantify the spatial distribution of wave resources and characteristic metrics. The resulting maps (example shown in Fig.3) allow for the identification of prospective locations of interest and further investi- gation. If the prospective location does not have a direct measurement of the resource (through one of the methods presented in the wave measurements section), researchers have been using measure–correlate–predict (MCP) (Phillips et al.2008) or triple-collocation methods (Robertson et al. 2015) to provide an improved assessment of the resource.

The primary metric used to quantify the wave climate at a prospective wave energy deployment location is a bivariate histogram of Hm0and Te. The histogram illustrates the mean annual occurrence and annual energy contribution of specific wave conditions from a long-term hindcast. A sample histogram is shown in Fig.4.

The values in each bin represent the mean number of hours in a year that a particular wave sea state occurs, while the color scale represents the percentage contribution of each condition bin to the annual omnidirectional wave energy transport (J). The histogram is generally parameterized at a resolution of 0.5 m and

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Fig. 3 Mean annual wave energy transport (J) in the Canadian Pacific

Fig. 4 Wave bivariate histogram for Amphitrite Bank, Canada. Numbers indicate the number of hours each year, while the contour colors indicate the percentage of total energy within that sea state

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1 s, respectively. However, the discretization of Hm0and Tespace into specific bins changes between authors and locations (Liberti et al.2013; Mackay et al.2010).

The histogram provides a simple, tractable representation of the annual wave climate, allowing for quick analyses of the wave climate, and comparison between prospective sites. For example, the details included in Fig.4illustrate that the most frequent sea stateðHm0: 1.25 m, Te: 8.5 s) does not provide the highest annual wave energy contribution ðHm0: 1.75 m, Te: 9.5 sÞ. These characteristics are easily extracted from the histogram and, from the point of view of the WEC developer, indicate the need for a detailed optimization of device architecture to maximize WEC performance under the most frequent or most energetic wave conditions (Bailey et al.2016).

Complementing the histogram and providing details about the directional dis- tribution of the mean annual wave climate is a directional wave rose. The rose discretizes the magnitude of the parameter of interest across differing directions and can be modified to present the distribution of significant wave heights, energy period, omnidirectional wave energy, or any of the baseline wave parameters previously presented. Figure5provides an example of the directional distribution of omnidirectional wave energy.

Wave histograms and wave roses provide simple tractable representations of wave climate, yet they provide no details about the temporal variability of the wave parameters, i.e., how does the parameter vary by seasonal, monthly, and hourly time

5%

10%

15%

20%

WEST EAST

SOUTH NORTH

<5000 5000 - 10000 10000 - 15000 15000 - 20000 20000 - 30000 30000 - 40000 40000 - 50000

>=50000

Wave Energy (W/m)

Fig. 5 Directional wave rose

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frames? The interannual or monthly variation in wave parameters is easily repre- sented by a simple line plot, generally presented in conjunction with the mean ± single standard deviation and various percentiles, as shown in Fig.6. For this location, the November–February period is extremely active, showing 90th per- centile significant wave heights of ∼4.0 m, while during the May–August period, the mean wave height is just 1.6 m.

A cumulative distribution function (CDF) is another frequently used presentation technique for temporally varying parameters. The CDF allows the assessment to provide a simple representation of the distributions of wave parameters across the differing months. Figure7shows that the 98th percentile significant wave height in December is∼6 m but only 1.9 m in July.

The monthly variability plots in Figs.5and6detail the interannual variation, but they provide no details about the short hourly or daily time scales. While numerous Fig. 6 Monthly variability of

significant wave height

0 2 4 6 8 10

Significant Wave Height (m) 0

0.2 0.4 0.6 0.8 1

Cumulative Distributions

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC YEAR

Fig. 7 Cumulative distribution function for significant wave height

Wave Energy Assessments: Quantifying the Resource 17

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