Standards for Wave Data Analysis, Archival and Presentation · D2.9 Standards for Wave Data...

WP2: Marine Energy System Testing - Standardisation and Best

Practice

Deliverable 2.9

Standards for Wave Data Analysis, Archival and

Presentation

Marine Renewables Infrastructure Network

Status: Final

Version: 01

Date: 31-Mar-2015

EC FP7 Capacities: Research Infrastructures

Grant Agreement No. 262552, MARINET

D2.9Standards for Wave Data Analysis, Archival and Presentation

Rev. 01, 31-Mar-2015

of 42

ABOUT MARINET

MARINET (Marine Renewables Infrastructure Network for emerging Energy Technologies) is an EC-funded network

of research centres and organisations that are working together to accelerate the development of marine renewable

energy - wave, tidal & offshore-wind. The initiative is funded through the EC's Seventh Framework Programme (FP7)

and runs for four years until 2015. The network of 29 partners with 42 specialist marine research facilities is spread

across 11 EU countries and 1 International Cooperation Partner Country (Brazil).

MARINET offers periods of free-of-charge access to test facilities at a range of world-class research centres.

Companies and research groups can avail of this Transnational Access (TA) to test devices at any scale in areas such

as wave energy, tidal energy, offshore-wind energy and environmental data or to conduct tests on cross-cutting

areas such as power take-off systems, grid integration, materials or moorings. In total, over 700 weeks of access is

available to an estimated 300 projects and 800 external users, with at least four calls for access applications over the

4-year initiative.

MARINET partners are also working to implement common standards for testing in order to streamline the

development process, conducting research to improve testing capabilities across the network, providing training at

various facilities in the network in order to enhance personnel expertise and organising industry networking events

in order to facilitate partnerships and knowledge exchange.

The initiative consists of five main Work Package focus areas: Management & Administration, Standardisation & Best

Practice, Transnational Access & Networking, Research, Training & Dissemination. The aim is to streamline the

capabilities of test infrastructures in order to enhance their impact and accelerate the commercialisation of marine

renewable energy. See www.fp7-marinet.eu for more details.

Partners

Ireland

University College Cork, HMRC (UCC_HMRC)

Coordinator

Sustainable Energy Authority of Ireland (SEAI_OEDU)

Denmark

Aalborg Universitet (AAU)

Danmarks Tekniske Universitet (RISOE)

France

Ecole Centrale de Nantes (ECN)

Institut Français de Recherche Pour l'Exploitation de

la Mer (IFREMER)

United Kingdom

National Renewable Energy Centre Ltd. (NAREC)

The University of Exeter (UNEXE)

European Marine Energy Centre Ltd. (EMEC)

University of Strathclyde (UNI_STRATH)

The University of Edinburgh (UEDIN)

Queen’s University Belfast (QUB)

Plymouth University(PU)

Spain

Ente Vasco de la Energía (EVE)

Tecnalia Research & Innovation Foundation

(TECNALIA)

Belgium

1-Tech (1_TECH)

Netherlands

Stichting Tidal Testing Centre (TTC)

Stichting Energieonderzoek Centrum Nederland

(ECNeth)

Germany

Fraunhofer-Gesellschaft Zur Foerderung Der

Angewandten Forschung E.V (Fh_IWES)

Gottfried Wilhelm Leibniz Universität Hannover (LUH)

Universitaet Stuttgart (USTUTT)

Portugal

Wave Energy Centre – Centro de Energia das Ondas

(WavEC)

Italy

Università degli Studi di Firenze (UNIFI-CRIACIV)

Università degli Studi di Firenze (UNIFI-PIN)

Università degli Studi della Tuscia (UNI_TUS)

Consiglio Nazionale delle Ricerche (CNR-INSEAN)

Brazil

Instituto de Pesquisas Tecnológicas do Estado de São

Paulo S.A. (IPT)

Norway

Sintef Energi AS (SINTEF)

Norges Teknisk-Naturvitenskapelige Universitet

(NTNU)

D2.9 Standards for Wave Data Analysis, Archival and Presentation

Rev. 01, 31-Mar-2015

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DOCUMENT INFORMATION

Title Standards for Wave Data Analysis, Archival and Presentation

Distribution Work Package Partners

Document Reference MARINET-D2.9

Deliverable Leader

José Cândido WAVEC

Contributing Authors

Matthew Finn EMEC

Keith Dampney EMEC

John Lawrence EMEC

Lucia Margheritini AAU

REVISION HISTORY

Rev. Date Description Prepared by

(Name & Org.)

Approved By

(Task/Work-

Package

Leader)

Status

(Draft/Final)

01

ACKNOWLEDGEMENT

The work described in this publication has received support from the European Community - Research Infrastructure

Action under the FP7 “Capacities” Specific Programme through grant agreement number 262552, MaRINET.

LEGAL DISCLAIMER

The views expressed, and responsibility for the content of this publication, lie solely with the authors. The European

Commission is not liable for any use that may be made of the information contained herein. This work may rely on

data from sources external to the MARINET project Consortium. Members of the Consortium do not accept liability

for loss or damage suffered by any third party as a result of errors or inaccuracies in such data. The information in

this document is provided “as is” and no guarantee or warranty is given that the information is fit for any particular

purpose. The user thereof uses the information at its sole risk and neither the European Commission nor any

member of the MARINET Consortium is liable for any use that may be made of the information.


Rev. 01, 31-Mar-2015

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EXECUTIVE SUMMARY

The definition of standards is a dynamic process that follows closely the development of technology, in a constant

interchange of information. A continued update and reorientation of recommendations and guidelines to track the

evolution of wave energy towards the market is of the essence. The work developed in the scope of the MaRINET

project, and in particular the present deliverable, is strategically timely. This report intends to provide an up-to-date

contribution to the definition of a set of standards to be applied in the handling of wave data, based on the

experience and expertise of MaRINET’s consortium and ensemble of world-class wave test facilities.

The report covers a brief review of the standardization efforts carried out to date, the description of the type of

wave data commonly considered for wave energy purposes and the typical data processing outputs, common and

suggested practices in wave measurement and data analysis, as well as data archival and presentation approaches to

be followed.

The document uses the MaRINET experience to provide its contribution towards wave data standardization.

Methods currently adopted by two open sea test facilities within MaRINET are taken to be up-to-date operational

procedures and suggested as recommended approaches.

It is concluded that binned tables are a preferable means to present data and one that technology developers

commonly use to create the necessary interface between technology performance and available resource, in order

to report device efficiency. Specific recommendations for the creation of contingency tables are provided.


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CONTENTS

1 INTRODUCTION .............................................................................................................................................3

1.1 CONTEXTUALIZATION OF THE DELIVERABLE ......................................................................................................... 3

1.2 RELATION TO PREVIOUS WORK ................................................................................................................................ 3

2 WAVE DATA ..................................................................................................................................................5

2.1 CHARACTERIZATION OF OCEAN WAVES ..................................................................................................................... 5

2.2 WAVE DATA PROCESSING OUTPUTS ....................................................................................................................... 10

3 WAVE MEASUREMENTS AND DATA ANALYSIS .............................................................................................. 11

3.1 RAW WAVE MEASUREMENTS DATA ........................................................................................................................ 11

3.2 WAVE DATA ANALYSIS PROCEDURES ...................................................................................................................... 15

4 WAVE DATA ARCHIVAL AND PRESENTATION ................................................................................................ 19

5 CONCLUSIONS AND RECOMMENDATIONS .................................................................................................... 37

6 REFERENCES ................................................................................................................................................ 38


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1 INTRODUCTION

1.1 CONTEXTUALIZATION OF THE DELIVERABLE

The need for a consensual set of standards in wave energy, from the several stages of development (numerical

modelling, wave flume and/or tank testing, sea trial) to the design of wave energy converters (WECs) itself, has been

widely discussed and treated in publications and a variety of research projects (e.g EquiMar). In the scope of

MaRINET, in particular, Deliverable 2.14 (MaRINET, 2012a) addressed data storage, including storage requirement

and data availability, and wave data representation, focusing on common nomenclature and graphs, both at

laboratory facilities and test centres. Deliverable 2.22 (MaRINET, 2014), on the other hand, focused on identifying

commonalities between the different methodologies across the MaRINET facilities for data retrieval, storage,

processing and presentation, through the collection of the results of a specific survey, thus preparing the field for

possible avenues for confluence of approaches.

The present document picks up on the findings of these initial efforts and builds towards a tentative proposal of

wave data standards, in particular with respect to analysis, archival and presentation. The definition of priority areas

where efforts should be focused is a common concern of Deliverable 2.14 and Deliverable 2.22. A common relevant

outcome seems to be that the need for standards lies not so much in the laboratory environment, where conditions

are controlled or produced on demand and wave data handling relies heavily on client customization, as in the field

environment, where conditions must be accepted and there is a wider dispersion of the type of data that is

measured and the possible measuring techniques. Furthermore, as highlighted in Deliverable 2.22, obvious

similarities exist in the sort of data that is presented and the way it is presented throughout the different test

facilities in MaRINET, from laboratories to test sites. Therefore, Deliverable 2.09 focuses primarily on common

practices and standards with regard to wave data in the field environment. In other words, measurements, analysis

techniques, typical archival procedures and presentation methods in test sites are the prime target of the present

report. In this context, MaRINET’s comprehensive ensemble of world-class facilities, and in particular in-sea scale

test sites, offers the possibility to develop such intents.

1.2 RELATION TO PREVIOUS WORK

Throughout the last decade, the lack of specific codes of practice, standards or guides in wave energy, as a

consequence of the relatively new and unproven technology in the field, has been recognized. As a reaction to this

circumstance, and also thanks to the relatively slow but steady path to commercialization, a few works and

initiatives contributing to the development of a set of standards in the sector have recently come to light. In this

context, the efforts under the EU FP7 project EquiMar and a few publications (e.g. Saulnier et al., 2006, Pitt, 2009a

and Tietje et al., 2011) stand out. The insufficient maturity of the technology and the consequent scarcity of data

recorded by WECs in actual open sea conditions have no doubt limited the ability of these efforts to produce truly

binding results and limited their universal adoption. The reality is that standards and guidelines are bound to

continuously evolve as the findings from ongoing research and development lead to their refinement. Such reality is

particularly evident in the case of a fast-developing pre-commercial technology, as is the case of wave energy. A

continued update and reorientation of recommendations and guidelines to track the development of wave energy

towards the market is of the essence. In the light of this, the work developed in the scope of the MaRINET project,

and in particular the present deliverable, is strategically timely.

A significant part of the work on wave energy standards and guidelines developed to date focus on the actual WEC

performance assessment. However, the definition of common methodological avenues for the handling of the

underlying environmental data is equally crucial to move the sector forward towards economic competiveness.

Although a work of this nature may not directly reflect the standpoint and needs of the technology developer, it will

be essential to facilitate the comparison between approaches across different test sites. The resulting harmonized

comparative procedures will contribute to strengthening the necessary bridge between developers and test site


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operators, thus enabling the comparison of concepts performance and ultimately facilitating the market uptake of

the technologies. This is precisely the focus of the present document.

In the scope of the EquiMar project, protocols for wave energy resource assessment have been produced in

Deliverable 2.7 (EquiMar, 2010a). The document provided recommendations for resource assessment at different

stages of a wave energy project development, by resorting both to in-situ measurements and numerical modelling

results. EquiMar’s Deliverable 4.2, on the other hand, focused on the design of a methodology for the analysis and

presentation of data obtained from sea trials of ocean energy converters (wave and tidal). The document was

elaborated with a view to describe a logical and widely-applicable method to analyze and present data obtained

from sea trials. The main focus was placed on the establishment of the foundations for the presentation of results

obtained from sea trials in a uniform and clear way, thus making it possible to provide an indication of the

uncertainty involved with the stated performance. The ultimate objective was to contribute to a more accurate and

credible comparison between the performance of devices and to an expeditious application of results to alternative

locations.

The European Marine Energy Centre (EMEC) has been developing extensive work on the design of standards in wave

energy. The report on Assessment of Wave Energy Resource (Pitt, 2009b), in particular, provides guidelines for the

storage of wave data. The recommendations can be summarized in the following:

• Data archive shall have a common basic structure and content (independently of the instrument), although

the details may vary;

• Data records shall be consolidated into data files typically containing one month’s worth of data records

and/or no-data records;

• Data files should contain a series of data and no-data records and these shall be preceded by a header

containing information detailing the sampling configuration, data processing and recording of the data.

According to this report, each sample data record should contain the following elements:

i) Date and time stamp;

ii) Depth in metres (variations associated with tides should be included if they lead to > 5 % changes in group

velocity, referred to the maximum energy value of Te in the expected (Hs, Te) scatter diagram);

iii) A frequency listing containing information about the variance spectrum and its directional characteristics as

well as the power spectrum;

iv) A number of derived parameters including power, mean wave direction, wave height and wave period;

v) Quality control flags.

Such requirements are further expanded in the document.

This document focuses on standards for the procedures surrounding the analysis, archival and presentation of wave

data. Based on previous work on this matter, the expertise and experience of the project’s consortium, the

agreements found during the project’s execution and the current state-of-the-art of wave energy as a whole,

tentative proposals will be presented. The document does not include an exhaustive review of wave data archival

and presentation, covered in MaRINET’s Deliverable 2.14, nor an in-depth analysis of the methodologies for data

retrieval, storage, processing and presentation applied by the different MaRINET facilities, addressed in Deliverable

2.22. Likewise, details on wave measurement techniques, the different types of equipment and the respective

working principles were discussed in Deliverable 2.1 (MaRINET, 2012b). Consequently, these aspects are not

considered in Deliverable 2.9, apart from a few occasional exceptions required to elaborate on the matters

addressed.

Section 2 provides a description of the raw data and parameters typically measured and retrieved in the test sites.

The following section describes typical procedures for wave measurements and data analysis. Section 4 addresses

common approaches for wave data archival and presentation. In the final section, some conclusions are drawn and a

few key recommendations provided.


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2 WAVE DATA

2.1 CHARACTERIZATION OF OCEAN WAVES

The characteristics of ocean waves in the time domain are determined through a wave-by-wave analysis of the

surface elevation at a given location (time records). Through this type of analysis it is possible to determine both

individual and integrated wave parameters.

In the frequency domain, the determination of wave parameters is obtained from the spectral analysis of the wave

records, based on the energy spectrum of the records. Parameters are computed through a Fourier analysis of the

time series data, typically with a spectral resolution of 0.05 Hz, as recommended in Tucker, 1993.

On a scale of tens of kilometres and minutes, the local state of the sea surface in deep water conditions may be

accurately described by a stationary Gaussian random process. The local behaviour of the waves is then determined

by the 2D wave spectrum S(f,θ). Spectral information is typically condensed in mean height, period and direction

wave parameters, expressed as a function of the n-th moment spectral moment

∫∫∞

=0

2

0

),( θθπ

dfdfSfm nn .

[ 1 ]

The significant wave height Hs is the most widely used wave height parameter. It is defined as the average of the

highest one third of the trough to crest wave heights. The respective wave height spectral parameter is

sHmHm ≅= 2/1

040

,

[ 2 ]

where 0m is the zero-th spectral moment.

As regards wave period, several parameters are commonly used. Spectral parameter

2/1

2

0

02

=

m

mTm

[ 3 ]

reasonably corresponds to the mean zero-crossing period (the average time elapsed between two sequential crests).

Since it depends on m2, 02mT is very sensitive to the high frequency spectral tail, which typically presents significant

variability and low energy contents.

The mean energy period Tm-10, commonly used for wave energy resource assessment purposes, is defined by


Rev. 01, 31-Mar-2015

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0

110

m

mTm

−− = .

[ 4 ]

Since fT /1= , Tm-10 provides an average value of T weighted by the spectral distribution. This parameter mainly

depends on the lower frequency band of the spectrum where most of the energy is concentrated.

The peak period Tp is the inverse of the peak frequency, fp, to which corresponds the maximum spectral density

value, so that

p

pf

T1

= .

[ 5 ]

The wave power level or flux of energy per unit crest length is given by

∫ ∫∞

=π

θθρ2

0 0

),(),( dfdhfcfSgP g ,

[ 6 ]

where ρ is the water density and g the gravity acceleration. The group velocity cg, corresponds to the velocity at

which the energy propagates and is defined by

kcg

∂

∂=

ω.

[ 7 ]

In deep water conditions (in practice when the water depth h is larger than half wavelength) cg simplifies to

f

gcg

π4=

[ 8 ]

so that the wave power is given by

1

22

0 0

12

4),(

4−

∞− == ∫ ∫ m

gdfdffS

gP

π

ρθθ

π

ρ π

.

[ 9 ]

This relation may be expressed in terms of Hm0 (i.e., Hs) and Tm-10 by

10

2

0

2

64−= mm TH

gP

π

ρ.


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[ 10 ]

Assuming that the sea water density is 1025=ρ kgm-3, if Hm0 is expressed in meters and Tm-10 in seconds, the power

level in kWm-1 is given by

10

2

04906.0 −= mm THP .

[ 11 ]

To overcome the limitations of equation [ 11 ], an alternative TTV (Transport of Total Variance) method to calculate

the wave power is additionally used by EMEC (Pitt, 2005). This method provides a better representation in shallower

water conditions, which is the case of EMEC’s Billia Croo site. The power level estimation using this method is given

in kW/m by

2

62860 seg ,h)H(Tc.P = .

[ 12 ]

This expression in full turns to

22

1

2sinh

21tanh

2

16286.0 sH

kh

khkh

k

gP

+

=

[ 13 ]

with

+=

kh

khccg

2sinh

21

2

1,

[ 14 ]

in which the phase velocity is given by the dispersion relation

2

1

tanh

= kh

k

gc

[ 15 ]

A method based on Mollison (1986) to provide an indication of the effect of directionality on the wave spectra is also

applied by EMEC. This provides firstly an estimate of the net power flux, Pflux , in direction θ , by multiplying the

energy of each spectral component resolved in direction θ by the group velocity gc ,

∫ −= fffSfcgP gflux d))(cos()()()( θψρψ

[ 15 ]


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where ψ is the directional alignment to the waves.

In practical terms this can be considered as the power available in the waves from all directions projected on to a

given WEC heading or directional alignment (ψ). The limits to the integration recognise that waves from opposite

directions pass through each other, but only those within 2/)( πθψ ±=− are able to transmit power. For each

hourly record, it is then calculated (in W/m) by

∑=

=

∆−=64

1

)())(cos()(i

iiigiiflux ffcfSgP θψρψ

[ 16 ]

where )( ig fc is the group velocity at the ith frequency, Si is the corresponding spectral density estimate, )( ifθ is the

spectral wave direction at the ith frequency, if∆ is the ith frequency increment (slice thickness) and )( ifθψ − is

limited to ± π/2.

In order to derive a more useful expression of directionality, the above calculation is repeated for ψ = 0 to 360° in 1°

increments, and the power flux for every direction and the best direction Dδ (i.e. the calculated ψ which maximises

the power flux Pflux) are obtained by this means.

Another useful quantity is the directionality coefficient

/Pδ = Pflux .

[ 17 ]

The best direction and the directionality coefficient are calculated for a given period of time. In EMEC’s monthly data

reports they are calculated for each 30 min record and for all of the monthly records combined, and are thus

referred to as the half-hourly or monthly best direction or directionality coefficient.

The overall mean wave direction may be obtained from the 2D spectrum by

∫ ∫

∫ ∫

∞

∞

=π

π

θθθ

θθθ

θ2

0 0

2

0 0

)cos(),(

)sin(),(

arctan

dfdfS

dfdfS

.

[ 18 ]

The Alliance for Coastal Technologies (ACT)1 has found that the majority of coastal users collecting wave data require

the first five Fourier coefficients (Alliance for Coastal Technologies, 2007). This report suggests that wave monitoring

instrumentation should be able to provide at least the first five coefficients, which, nevertheless, are insufficient to

fully characterize the directional spectrum. Additional equipment may be required to provide further Fourier

moments.

1 The ACT (www.act-us.info) comprises research institutions, resource managers and private sector companies to aid the development and adoption of effective

ocean sensors and platforms


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Typical post-processing of directional buoys’ measurements provides only frequency spectra )( fS , related to the

directional spectrum by

∫=π

θθ2

0

),()( dfSfS ,

[ 19 ]

the mean direction per frequency band )( fθ and its spreading for each frequency band )( fθσ . Mean wave direction

is then computed by

∫

∫

∞

∞

=

0

0

))(cos()(

))(sin()(

arctan

dfffS

dfffS

θ

θ

θ .

[ 20 ]

As suggested by a few authors (e.g. Saulnier et al., 2006), recent technological advances have made clear that the

optimization of ocean energy conversion requires the detailed knowledge of additional sea state characteristics,

such as spectral width and wave grouping.

The energy spectral broadness parameter (or narrowness parameter)

2/1

2

1

200 1

−

⋅=

m

mmε

[ 21 ]

is often used to characterize spectral bandwidth due to its weak sensitivity to the cut-off frequency and its focus on

the section of the spectrum with higher energy content (low-frequency waves). It provides an indication of the

degree of tuning (or resonance) that a WEC will require to maximize energy extraction from the sea-state.

Wave groupiness may be assessed using the wave correlation parameter K, which is related to group formation and

is obtained from (Battjes et al., 1984)

2/1

2

0

2

00

)2sin()()2cos()(1

+

= ∫∫

∞∞

dffTfSdffTfSm

K zz ππ

[ 22 ]

The wave correlation parameter and Hs govern the bivariate Rayleigh distribution which has been used by Kimura

(1980) for modelling the dependence of two successive (zero up-crossing) wave heights in offshore applications. The

envelope theory (Longuet-Higgins, 1984) may also be used, although this is applicable only to very narrow spectra.

Spectral peakedness may also be a quantity of interest, in particular to relate wave group length statistics to spectral

shape. Goda’s Peakedness parameter (Goda, 1970) is given by


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∫= ffSfm

Qp d)(2 2

20

.

[ 23 ]

2.2 WAVE DATA PROCESSING OUTPUTS

Typical wave data processing outputs for a detailed wave climate characterization and resource assessment in the

test site may include average values of wave height, period, power and direction, scatter tables of Hs, Te and θ , a

wave power exceedance curve, as well as seasonal and inter-annual variability tables. Generally, scatter tables

present the frequency of occurrence of pairs of Hs, Te and θ . Additionally, energy distribution tables presenting the

percentage of the total energy that occurs for each bin of (Hs, Te), (Hs, θ ) and (Te, c) may be computed.

Table 1 summarizes long-term statistics commonly used to characterize the wave climate and energy resource in the

test sites.

Tables Plots Seasonal and Inter-annual Variability

• Frequency of occurrence of Hs

• Frequency of occurrence of Te

• Frequency of occurrence of Tp

• Exceedance of P

• Bivariate frequency table of (Hs,Te)

• Bivariate frequency table of (Hs,Tp)

• Bivariate frequency table of (Hs, θ )

• Bivariate frequency table of (Te, θ )

• Bivariate frequency table of (Tp, θ )

• Distribution of energy per (Hs,Te) bin

• Distribution of energy per (Hs,Tp) bin

• Distribution of energy per (Hs, θ ) bin

• Distribution of energy per (Te, θ ) bin

• Distribution of energy per (Tp, θ ) bin

• Probability density of Hs

• Probability density of Te

• Probability density of Tp

• Probability density of P

• Exceedance curve of P

• Wave roses

• Bivariate probability

density (scatter

diagram) of (Hs,Te)

• Bivariate probability

density (scatter

diagram) of (Hs,Tp)

• Plot and/or table of monthly mean

value of Hs (with confidence limits)


value of Te (with confidence limits)


value of P (with confidence limits)


value of θ (with confidence

limits)

• Plot and/or table of yearly mean,

minimum and maximum value of

Hs (with confidence limits)



Te (with confidence limits)



P (with confidence limits)



θ (with confidence limits)

Table 1 Typical wave data post-processing outputs


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3 WAVE MEASUREMENTS AND DATA ANALYSIS

3.1 RAW WAVE MEASUREMENTS DATA

According to EquiMar’s Deliverable 2.7 (EquiMar, 2010a), physical wave measurements should be performed using

either wave measurement buoys or acoustic Doppler profilers (ADPs). As suggested by the document, other

measurement methods such as remote sensing or pressure transducers are not recommended due of their lack of

validation for wave energy resource assessment purposes.

Directional buoys, such as Pitch-Roll-Heave (PRH) buoys, follow the surface slope of the waves, measuring time

series of the vertical (heave) acceleration and two orthogonal components of the surface slope (pitch and roll). From

each triplet of time series wave measurements, a directional spectrum can be estimated using the theory of

Longuet-Higgins (Longuet-Higgins et al., 1963) to calculate the auto- and cross-spectra between the records

(MaRINET, 2012b). Spectral parameters can thus be computed. Data is typically processed on-board. Both raw and

processed data may be stored or transmitted to shore via a radio or satellite link.

ADCPs (Acoustic Doppler Current Profilers or simply Acoustic Doppler Profilers) measure the wave orbital velocities

below the sea surface. The ADCP measures the flow velocity of the water by transmitting short sound pulses of

known frequency and measuring the Doppler shift of the signal reflected in scatterers assumed to be passively

following the flow (MaRINET, 2012b). ADCPs use piezoelectric oscillators to transmit and receive the acoustic signals.

Since at least 3 vector components have to be estimated to measure 3D velocities, ADCPs typically include 4

transistors: 3 for measuring velocity (u, v, and w) and a 4th redundant transducer for error checking. For wave

measurement purposes, ADCPs are bottom mounted, upward facing and they include a pressure sensor for

additional non-directional wave measurement. ADCPs feature the capacity to measure flow velocity at several depth

levels, typically up to 128 levels, with each series of pulses. The along-beam component of the orbital velocity for

each depth cell is used to construct a virtual array (Strong et al., 2003). In other words, each cell in each beam is

taken as an independent sensor in an array. The wave measurement uses the phase differences on the spatially

separated virtual array. Cross-spectra, to which the directional spectrum is linearly related for a given frequency, are

calculated between every sensor. Linear wave theory is used to translate the measurement from velocity spectra at

various depths to surface displacement.

As identified in MaRINET (2012a), the large majority of the open sea test facilities pooled in MaRINET use wave

buoys to assess the wave climate and provide developers with real wave conditions in the test site, in order to

support device design, marine operations and performance assessment. As a consequence, for the purposes of the

discussion on data standardization and in the scope of the examples that will be provided, without loss of generality,

this report will focus on wave data measured by this type of equipment.

EMEC has currently deployed on test sites four Datawell directional Waverider MkIII (DWR-MkIII) buoys. The DWR-

MkIII measures wave height by means of an accelerometer mounted onto a platform within the buoy that remains

horizontal under any movement expected to be experienced at sea. Wave direction is measured by correlating

horizontal motion of the buoy with the vertical motions. Two perpendicular sensors are used, one for horizontal

motion when the buoy is upright and another for when the buoy is in tilt. A fluxgate compass converts the

acceleration measured in the buoy to north-west coordinates (Datawell, 2014). In total the DWR-MkIII motion

sensors measure 8 observables (see Figure 1).


Rev. 01, 31-Mar-2015

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Figure 1 Axes and signs of the DWR-MkIII motion sensors

Raw displacement data are generated by the buoy at a rate of 1.28Hz and stored within an onboard data logger flash

card. These raw data as well as additional processed data from the DWR-MkIII are transferred ashore. At EMEC the

data are transferred via a high frequency (HF) radio link although there is capability to pass this data ashore via

satellite or GSM link. From the HF radio link data are logged straight onto EMEC’s SCADA network and a non-quality

controlled wave data feed is supplied directly from the SCADA and passed onto the EMEC website (EMEC, 2015). The

DWR-MkIII’s onboard batteries have autonomy in continuous operation of up to 3 years. Recalibration of the

measurement systems is recommended on a regular basis every 3 to 6 years.

The internal wave spectrum is calculated at a sampling rate of 1.28Hz. Every 200s a total number of 256 heave

samples are collected. In total 8 sets of 256 translational data samples are processed per half-hour to produce a

wave / direction spectrum. A Fast Fourier Transform (FFT) is applied to obtain the spectrum in the frequency range 0

to 0.64 Hz, with 0.005Hz resolution. For the wave directional spectrum, the north, west and vertical displacements

are included in the processing to give the wave direction, the directional spread, the wave ellipticity and the power

spectral density.

The Datawell real-time format refers to hexadecimal vectors with vertical, north and west displacements which,

compiled, generate a spectrum. The resulting hexadecimal (*.hxv) files contain real-time displacements, full wave

spectrum data, a system status data and timings. For each half an hour record, eight spectra with a 200s interval are

collected and averaged at the end of the 30 minutes, thus providing a usable smoothed estimate of the spectrum.

The transmission of each 30 minute record from the buoy takes 255s. During the following half an hour the file is

transmitted 8 times for redundancy.


Rev. 01, 31-Mar-2015

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The *.hxv files are processed using the Datawell W@ves21 v2.1.18 software (see Figure 2) where raw displacements

(*.raw), spectral data (*.spt), waves statistics (*.wvs), spectrum history (*.his), statistics history (*.his) and 3D

spectrum (*.dat) files are produced. The resulting files can be used for further processing using customized software

routines.

Figure 2 Screenshot of Datawell W@ves21 software

The Danish Wave Energy Center (DanWEC), on the other hand, has a non-directional Datawell directional Waverider

MkII buoy deployed in their test site (located off Hanstholm, in the northwest coast of Denmark). The buoy provides

both time and frequency domain parameters for 30 minutes interval. The files containing these parameters are

automatically generated by the software provided with the Datawell buoy.

Table 2 provides an overview of the typical time domain parameters obtained from the processing of thirty minutes

wave records (wave elevation time series) such as the one presented in Figure 3 (Lavelle et al., 2012). As seen in this

figure, the wave height is defined as the crest to trough distance and the wave period as the time elapsed between

two successive crests or troughs.

In the light of this, the Hmax and Tmax parameters in Table 2 respectively are the maximum wave height and the

maximum wave period in the thirty minute sample period. H1/3 and H1/10 are respectively the average heights of the

top one third and the top one tenth of the highest individual wave heights (i.e., H1/3 is the significant wave height).

T1/3 and T1/10 are respectively the average periods of the top one third and the top one tenth of the highest individual

wave heights.


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Field Unit Description

Date and time

Hmax

Tmax

H1/10

T1/10

H1/3

T1/3

Hav

Tav

Eps

#Waves

-

cm

s

cm

s

cm

s

cm

s

-

-

Start of acquisition (Format: YYYY-MM-DD hh:mm)

Height of the highest wave

Period of the highest wave

Average height of 10% highest waves

Average period of 10% highest waves

Average height of 33% highest waves

Average period of 33% highest waves

Average height of all waves

Average period of all waves

Bandwidth parameter

Number of waves

Table 2 Time domain wave parameters provided a Datawell non-directional buoy

Figure 3 Wave elevation time series sample from the DanWEC test site buoy (individual wave shaded in pink).

Frequency domain parameters are computed from the wave spectrum which, in turn, is obtained from the time

domain data using Fast Fourier Transform (FFT). Table 3 provides an overview of the typical frequency domain

parameters obtained from wave spectra such as the one presented in Figure 4 (Lavelle et al., 2012). The parameters

in the table are described in section 2.1.


Rev. 01, 31-Mar-2015

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Symbol Unit Title Moment definition

Hm0 m Significant wave height 2/1

04m

Te s Mean energy period 01 / mm−

Tm01 s Mean period 10 / mm

Tm02 s Mean zero-crossing period 02 / mm

Tp s Peak period -

ε - Spectral bandwidth 2/140

2

2 )/1( mmm−

Lp m Peak wavelength -

P W/m Wave power -

Table 3 Frequency domain wave parameters obtained from a Datawell non-directional buoy

Figure 4 Example of wave spectrum from the DanWEC test site buoy

3.2 WAVE DATA ANALYSIS PROCEDURES

Measurement errors can occur due to instrument (e.g. electronics malfunctioning, knocks from floating object) or

transmission failures resulting in ‘spikes’ (large erroneous values) or ‘flat spots’ (reading remains constant for a few

samples). Consequently, data filtering and quality control (QC) are key procedures and, as a standard approach,

should be carried out before any other data processing. Discriminating the erroneous from the accurate data values

may be challenging. Errors can be detected by range and rate of change checks on the time history. They also have

an effect on the spectrum, resulting in anomalously high values at low and high frequencies.

There is a variety of quality control and wave data filtering procedures that can be adopted with satisfying results,

depending on user’s customization. Pitt (2009b) provides an overview of several quality control methodologies. In


Rev. 01, 31-Mar-2015

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the scope of this report, the methods currently adopted by EMEC and DanWEC are taken to be up-to-date

operational procedures and, as such, are suggested as recommended approaches.

DanWEC adopts a data filtering method developed by Tucker et al. (2001) which is based on the identification of

erroneous values using the inspection of elevations and velocity of the waves (Lavelle et al., 2012). The diagram in

Figure 5 top right plots velocity versus elevation. Velocity is given by

dtv ii

i1−−

=ηη

,

[ 24 ]

where iη is the elevation of the i-th sample and dt is the sampling interval.

Figure 5 Top left: selection of se surface elevation time series. Top right: scatter plot of elevation versus velocity for the full 30

min time series. Bottom right: histogram of wave elevations. Bottom right: wave velocity and wave elevations transformed to

new coordinates using SVD

Real ocean waves have normally distributed values of η and v. The values of the η and v vectors shown in Figure 5

top right are decomposed into orthogonal vectors (i.e. factorized) using Scalar Vector Decomposition (SVD), as

shown in Figure 5 bottom right, thus rendering easier the discrimination of erroneous values. The standard deviation

of both the x and y coordinates are calculated. Values greater than four standard deviations in both x and y are

identified as erroneous. The erroneous values in η are replaced as with the interpolation of the two adjacent values.

The Shapiro test for normality (Shapiro et al., 1965) is then applied to the x and y coordinates of the new elevation

and velocity vectors (with erroneous values corrected). The Shapiro test gives a metric with values close to 1 for


Rev. 01, 31-Mar-2015

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normal distributions. With values inferior to 0.95 for the x or the y coordinate, the time series is rejected and the

respective parameters are not added to the database.

Data files from EMEC’s DWR-MkIII buoys undergo reception quality and screening checks which are automated by

the W@ves21 software. In addition to this, EMEC routinely carries out additional quality control on all data sources

in order to determine whether the information that has been recorded is a valid representation of the test site

conditions, thus ensuring that a data feed that is free from erroneous observations is being received.

The in-house quality control routine developed by EMEC uses MATLAB software to assess the data files before

further use. The quality control routine requires that the *.hxv files first be analysed in W@ves21 and makes use of

the resulting processed file types. There are two steps in the quality control process: visual QC Part1 and visual QC

part 2.

In visual QC part 1 a MATLAB script is run which creates a user interface (UI). The UI table is populated with

parameters from the *.raw, *.spt and *.his 30 minute records (see 6). Parameters include the number of valid

records in each file, Hmax and a number of heave statistics. Two plots are generated for the user to consider. The

topmost is the heave, north and west displacements of the buoy with a status indication and a guideline box within

which the displacement values should be retained. The lower plot is the power spectral density with direction and

directional spread from the same 30 minute time period.

Users are invited to select a ‘flag’ value dependant on what the displacements records indicate. A number of flag

types are generated automatically such as reception errors (flag 7) or periods where the DWR-MkIII was otherwise

unavailable (flag -2). A selection of other flag types which users can select are ‘Data OK’ (flag 1), ‘Filter error’ (flag 2)

and ‘Spikes’ (flag 6). The software automatically detects when a heave displacement has exceeded the expected

boundary and the user is prompted to select the ‘Spikes’ flag. When the user reaches the end of the records there is

a save function that records the information recorded in visual QC Part 1 out with the MATLAB UI.

Figure 6 EMEC’s Visual QC Part 1 Screenshot

In visual QC Part 2 a second MATLAB script is initiated creating a UI generating a plot of the significant and maximum

wave heights and wave periods with the associated flags that were generated as part of visual QC part 1. The

parameters and flags also populate the table below in 7. Users can change the status of the error flag during visual

QC part 2 as the record can be compared with the records immediately proceeding and preceding any suspected

error. Users are prompted to save any changes made here and then generate an output file that makes a record file


Rev. 01, 31-Mar-2015

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of each 30 minute records and the associated flag. This file can then be used on an ongoing basis to determine which

wave records are useable and which contain potential errors.

Figure 7 EMEC’s visual QC Part 2 showing instances of error flags

As mentioned above, ensuring that measurements are reliable and free of spurious data is a crucial step in wave

data analysis. Besides quality control and data filtering, other procedures are typically carried out, in particular

concerning the more useful spectral analysis (frequency domain). Pitt (2009b) provides an overview of the steps to

be followed, which the author summarizes in the following:

1. The basic Fourier transform is done using the Fast Fourier Transform (FFT) which is fundamentally a binary

algorithm so that the number of data values in the input time history should be a binary number.

2. The frequency width of the variance estimates in the final spectrum (the frequency resolution) should ideally

be 0.005 Hz or less, and certainly no greater than 0.01 Hz.

3. The frequency range of the spectrum should ideally be 0.04 Hz to 0.5 Hz. The upper frequency limit of the

range may be lower if constrained by the instrumental technique, but should not be less than 0.3 Hz.

4. To avoid aliasing, the input should be low pass filtered with a cut-off of 1/(2Δt), where Δt is the sampling

interval. It may be convenient to sample the signal at a much higher rate than is required for the calculation

of the spectrum and apply a digital filter before analysis.

5. Contamination of one part of the spectrum by ‘leakage’ of variance from other parts of the spectrum should

be minimized. This requires that the section of data which is Fourier transformed is ideally no shorter than

1000 seconds. This is particularly important for pressure and other subsurface records in which

contamination of the higher frequency estimates should be minimized.

6. The statistical variability of the spectral estimates should be as low as is practicable. It turns out that each

estimate should be defined with a minimum of 20 degrees of freedom (d.f.) and ideally with 40 d.f..

These recommendations are applicable to the many different principles upon which wave measuring systems are

based and not only to wave buoys.


Rev. 01, 31-Mar-2015

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4 WAVE DATA ARCHIVAL AND PRESENTATION

Archival and presentation are priority areas within the wave data standards context. The definition of the storage

requirements of the data, how it can be accessed and the format in which it is archived should be the first step in the

efficient preparation for wave data collection. Pitt (2009b) establishes a set of recommendations to be followed in

data archival procedures, notably:

• Whatever the type of instrument, the data archive shall have a common basic structure and content,

although the details may vary. The information arising from an individual sample measurement is referred to

as a data record and these shall be ascribed a series of nominal times which will usually be on the hour, one

hour apart. Where the data record for a particular nominal time is missing, a specially formatted ‘no-data’

record shall be substituted.

• The data records shall be consolidated into data files typically containing one month’s worth of data records

and/or no-data records. This is not a fixed requirement, but monthly files have proved to be a useful length

to handle.

• The data files shall thus contain a series of data and no-data records and these shall be preceded by a header

record. The file header shall contain details of the measurement, processing and recording of the wave data.

The documentation should be sufficiently comprehensive to ensure the intelligibility of the data to all

interested parties.

This report further includes details on the recommended information content of the data records and, in particular,

a suggestive listing of the spectral and non-spectral data quantities that should be recorded.

The EquiMar project also provides a few key recommendations on wave data archival (EquiMar, 2010a). In

particular, it is recommended that time series data are recorded and archived for validation. The elaboration of

periodic summary reports including metadata should be carried out at appropriate intervals. These reports should be

produced on a monthly basis in the case of buoy measurements where data are transmitted to shore. This is, in fact,

aligned with the report periodicity suggested by Pitt (2009b). In the cases of wave instrumentation requiring in loco

data recovery, longer periods between reports should be acceptable.

In light of the above, the monthly wave report template developed at EMEC is here suggested as a standard format

against which wave data can be presented across different test facilities. As a consequence, key elements of this

report template are included and described in the present report.

EMEC’s template report is based on wave data collected using the Datawell MIII Directional Waverider buoy

deployed at the Billia Croo test site and its scope is derived from the performance assessment methods outlined in

Pitt (2009a). It is suggested that, although the reported parameters and categorisation of results are focussed on the

parameters found relevant at the Billia Croo test site, the template should be easily extended at sites where other

parameters are shown to be of relevance. It is stressed that notwithstanding the methods outlined in the report

being in review with respect to the updated performance assessment methods described in International

Electrotechnical Commission (2012), the overall pattern of reporting remains the same. The summary analyses of the

prevailing wave and meteorological conditions in the test site provided below refer to October 2014.

The following summarizes data analysis procedures adopted by EMEC for the elaboration of the monthly report.

Data processing and data files

All figures and data for the tables have been generated by code written in Matlab by EMEC. Where possible, efforts

have been made to automate the report writing process as much as possible, but some measure of manual

intervention is required.


Rev. 01, 31-Mar-2015

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The wave data used in this report are generated from the raw (.hxv) files recorded by the wave buoys using file

regeneration in W@ves21 (version 2.1.18) software. Met data is as recorded from the Met Station at Billia Croo.

Missing data records

None of the data files contain indicators for missing records. Thus, prior to processing, a data structure which

assumes a record every 30 minutes for every day of the month is generated, and then explicitly filled record by

record according to the date and time for each. In this way missing records are identified, and a missing data record

is one anticipated at that time on that day but which is not present, or which is only partially complete.

The detection of missing records and the correct time allocation for all records is aggravated in the case of data from

the buoys whose transmission may be interrupted resulting in the drifting of the time date stamps. Special routines

have been incorporated to handle this and provide additional safeguards. As a matter of protocol all tabular outputs

explicitly account for the number of records, and these plus the number of missing records must equal the number

of anticipated records for the month (being 48 * number of days in the month).

30 minutes records

While the 30 minute record from the buoy data files is a summary of the time series captured during the preceding

half-hour, for the met station (with the exception of rainfall) it contains values captured at that instant. Most

processing of this data is simple data summarising, finding the maxima, minima and mean values for the day and

month for the parameter concerned from the 30 minute records. Missing records are excluded from these, but only

prevent their daily summary presentation where a whole day’s data is missing.

Excluded records

In many of the monthly data reports there is no need to exclude any of the 30 minute records. However, in certain

months (for example when maintenance work on the buoys is undertaken, while still recording) the resulting record

will contain anomalous data. These data are removed and treated as missing records, with the monthly narrative

report describing the timing and nature of any maintenance undertaken.

Additionally where EMEC considers a record to be an anomalous outlier (or simply unreliable) it will require that it is

excluded from the analysis. While the code also treats these as missing data records, the monthly narrative report

will identify any excluded records and provide an explanation for their exclusion by EMEC.

Key elements of the template monthly report developed by EMEC are presented below.

Summary statistics

Table 4 below provides a summary of monthly mean wave statistics.

Table 4 Summary of monthly wave statistics

Table 5 provides a summary of the monthly minimum, maximum and mean values for the characteristics of wave-

height (Hs), wave period (Tz) and peak direction, together with the derived estimates of wave power. The values

Month Year Tz (s) Hm0 (m) Peak

direction (o)

Spread (o) Mean

power

(kW/m)

No. of data

points

buoy E

October 2014 8.47 2.17 299.1 26.7 34.73 48


Rev. 01, 31-Mar-2015

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contained within each of the rows are selected as discrete values for each characteristic and do not necessarily

relate to the same half-hour record.

Characteristic Wave height

[Hm0 (m)]

Wave period

[Tz (s)]

Direction (o) Wave Power Estimate

(Daily mean – kW/m)

Minimum 0.37 2.77 141.8 0.42

Maximum 7.57 10.01 357.2 332.50

Mean 2.14 6.00 299.1 34.73

Table 5 Summary of mean, min and max wave characteristics

When available, meteorological data may be of use. The monthly report must state: During [Month] there was a

meteorological data capture rate of [perc.].

Table 6 provides a summary of the monthly mean meteorological statistics, together with the sea surface

temperature, sourced from the Waverider buoy data.

Month Year Air

Temp.

(oC)

Wind

velocity

(m/s)

Pressure

(mbar)

No. of data

points

Sea surface

temp (oC)

October 2014 10.8 6.75 1001 4464 12.38

Table 6 Summary of monthly mean meteorological statistics

Table 7 provides a summary of the monthly minimum, maximum and mean values for the meteorological statistics.

Characteristic Air temp. (oC) Wind velocity

(m/s)

Pressure

(mbar)

Sea surface temperature

(oC)

Minimum 4.9 0.47 975 11.6

Maximum 17.4 19.71 1021 13.05

Mean 10.8 6.75 1001 12.38

Table 7 Summary of mean, max and min meteorological statistics

Table 8 contains basic summary information from the wave buoy data, giving daily minima, maxima and mean

values, and a monthly summary of these. Summarised data for Hs, Tz, Te, peak direction and spread are taken

directly from regenerated files provided by the buoy software for the month, or calculated from these. The number

of records is determined explicitly from the presence or absence of each expected 30 minute record. The data

coverage is calculated as a percentage of the actual records to the expected records for the month.

Table 9 contains basic summary information from the met station data, giving daily minima, maxima and mean

values, and a monthly summary of these. Summarised data for air temperature, rainfall, wind velocity and pressure

are taken directly from the logged data. The summary column of average surface sea temperature is taken from the

history file for the buoy data processed during that month.


Rev. 01, 31-Mar-2015

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Table 8 Monthly summary of basic wave statistics

Day min max mean min max mean min max mean min max mean min max mean min max mean

1 2.31 4.91 3.21 6.40 9.22 7.19 9.03 12.08 9.95 271.5 301.2 284.9 15.1 37.9 23.7 7 27.81 165.66 59.34 48

2 3.15 5.09 4.09 6.90 9.56 8.47 10.41 13.50 11.78 272.6 305.9 286.6 16.0 33.5 22.7 7 59.71 169.44 112.54 48

3 2.57 4.63 3.32 6.24 8.38 7.34 8.73 11.32 10.12 276.7 305.8 284.9 15.5 36.4 22.9 7 32.99 131.52 63.83 48

4 1.89 3.80 2.73 6.27 9.49 7.69 9.23 11.63 10.34 270.4 298.4 281.7 15.6 32.4 22.0 7 19.70 95.53 44.17 48

5 1.79 3.39 2.46 6.06 7.90 6.99 8.60 11.45 9.83 270.1 299.4 286.4 15.5 33.5 24.3 7 15.30 67.44 33.95 48

6 0.87 2.14 1.50 3.56 7.07 4.84 6.26 11.32 8.44 265.2 295.8 281.8 15.7 52.0 30.6 7 4.80 27.20 11.17 48

7 0.91 1.80 1.22 3.40 6.69 4.59 6.08 11.06 8.27 262.6 298.0 280.2 14.3 50.2 29.1 7 3.32 14.55 7.08 48

8 0.71 1.08 0.86 3.38 6.35 4.91 6.23 7.99 7.05 270.4 344.6 314.4 21.6 47.7 33.7 7 1.91 4.81 2.77 48

9 0.87 1.78 1.10 4.17 6.36 5.37 6.03 8.34 7.20 307.8 349.7 334.9 15.4 45.5 28.4 7 2.78 10.73 4.59 48

10 1.18 1.99 1.50 4.38 7.20 5.53 5.87 9.28 7.43 326.3 354.3 341.2 14.1 43.2 27.9 7 4.63 18.62 9.03 48

11 0.98 2.09 1.43 4.60 6.79 5.46 6.10 8.61 7.06 314.1 357.2 339.0 20.3 39.3 28.4 7 3.34 19.84 7.84 48

12 0.75 1.64 1.16 4.03 5.25 4.61 5.25 6.66 5.83 319.8 356.5 336.9 16.9 43.8 29.3 7 1.52 8.99 4.20 48

13 0.68 0.89 0.78 4.18 5.19 4.72 5.36 6.41 5.94 316.9 351.3 336.6 18.0 47.0 28.2 7 1.35 2.49 1.79 48

14 0.52 0.96 0.68 4.10 5.46 4.78 5.34 6.75 6.09 318.9 352.3 337.6 20.6 41.1 29.3 7 0.87 2.86 1.43 48

15 0.37 1.16 0.60 3.73 10.01 5.76 6.09 15.43 9.48 272.4 353.5 314.4 15.8 46.9 30.2 7 0.42 11.75 2.52 48

16 0.57 1.16 0.81 2.97 8.27 4.71 5.89 13.78 9.85 272.5 305.0 285.6 18.7 49.1 30.4 7 1.10 10.29 4.16 48

17 0.53 0.77 0.65 2.78 3.77 3.12 4.82 8.17 6.13 261.5 300.0 283.4 26.1 57.3 38.6 7 0.81 2.00 1.40 48

18 0.43 1.14 0.78 2.91 4.84 3.46 3.85 8.78 5.83 141.8 309.8 248.8 14.1 51.6 33.1 7 0.72 6.05 1.91 48

19 1.00 4.73 2.15 3.99 7.03 5.07 6.28 8.39 7.26 262.8 300.0 277.2 14.9 44.1 28.3 7 4.38 91.38 21.32 48

20 1.53 4.29 2.76 5.28 6.96 6.08 6.86 8.77 7.73 268.6 309.1 287.0 13.1 32.3 21.1 7 9.21 77.93 33.82 48

21 1.53 7.69 4.30 4.98 8.73 6.90 6.79 10.44 8.65 276.1 319.8 293.6 15.1 39.5 24.3 7 8.75 342.27 110.21 47

22 2.43 4.52 3.65 6.66 7.79 7.29 8.79 10.34 9.44 282.4 318.5 295.9 15.7 35.0 24.1 7 32.92 108.65 69.70 48

23 2.42 4.39 3.58 6.86 8.53 7.44 9.03 10.54 9.63 264.2 305.9 283.8 13.4 33.4 23.7 7 31.26 95.33 68.46 48

24 2.86 4.44 3.60 6.78 7.89 7.27 9.00 10.18 9.64 271.9 299.0 282.1 15.5 30.9 21.9 7 43.99 103.96 68.99 48

25 2.65 5.63 3.77 6.33 7.98 7.19 8.42 10.44 9.44 268.9 292.4 281.3 13.6 35.5 21.1 7 39.03 165.40 76.97 47

26 4.03 6.42 5.19 7.22 8.83 8.15 9.25 11.68 10.63 266.5 294.6 281.4 14.6 32.5 22.2 7 97.95 256.48 161.43 48

27 2.17 4.48 3.08 7.02 8.49 7.75 8.95 10.88 10.05 271.1 308.2 284.5 14.6 26.7 21.0 7 26.62 111.31 54.39 48

28 1.73 3.38 2.38 5.33 7.39 6.14 6.93 9.90 8.18 272.5 314.7 287.1 16.0 38.2 25.4 7 14.76 46.63 24.66 48

29 1.60 3.53 2.36 5.86 7.39 6.48 7.42 9.08 8.31 269.3 322.9 296.5 16.4 39.0 28.7 7 11.88 48.05 24.94 48

30 1.06 2.02 1.36 4.34 9.18 6.50 7.58 10.70 9.13 281.8 349.1 331.5 14.3 42.6 25.5 7 4.71 18.45 9.25 48

31 0.91 1.51 1.14 4.21 7.59 5.41 7.07 10.29 8.75 280.1 349.9 329.7 14.8 46.3 28.6 7 3.68 11.60 6.31 48

Monthly Summary

Battery Records

min 0.37 2.78 3.85 141.8 13.1 7 0.42 47

max 7.69 10.01 15.43 357.2 57.3 7 342.27 48

mean 2.20 6.04 8.50 299.1 26.7 7 35.62 48

Total 1486

1488

99.87%

Total possible records

Actual coverage

Power (kW/m) Number of

records

Hm0 (m), monthly Tz (s), monthly Te (s), monthly Direction, monthly Spread, monthly Power (kW/m)

Hm0 (m), daily Tz (s), daily Te (s), daily Peak direction, daily Peak spread, daily Battery

status


Rev. 01, 31-Mar-2015

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Table 9 Monthly summary of met statistics

Day min max mean min max mean min max mean min max mean

1 10.9 16.5 12.6 3.01 11.50 8.25 1007 1021 1014 144 12.95 13.05 13.01

2 10.5 14.5 12.8 2.40 9.09 5.96 1003 1021 1016 144 12.90 12.95 12.93

3 10.6 14.7 12.4 1.28 11.52 6.43 999 1007 1004 144 12.85 12.95 12.91

4 8.4 11.8 10.4 0.55 8.22 4.35 1003 1008 1005 144 12.75 12.90 12.85

5 8.5 13.4 11.0 2.87 11.92 6.64 1002 1009 1007 144 12.65 12.85 12.78

6 10.8 12.8 11.8 5.17 16.47 12.26 993 1002 996 144 12.60 12.75 12.70

7 10.0 12.2 11.0 4.30 16.23 11.46 990 998 993 144 12.55 12.70 12.65

8 7.2 12.7 9.9 2.02 11.64 4.43 988 990 989 144 12.55 12.65 12.60

9 8.1 11.7 10.4 1.77 6.60 3.66 987 993 989 144 12.55 12.60 12.56

10 8.0 12.4 10.9 0.58 7.58 4.22 993 1002 998 144 12.50 12.55 12.55

11 7.8 11.4 10.6 1.05 6.56 4.03 1002 1005 1003 144 12.45 12.55 12.51

12 5.8 11.5 9.6 2.06 5.51 3.54 1005 1013 1009 144 12.45 12.55 12.51

13 5.1 10.4 7.7 0.92 3.63 2.41 1013 1015 1014 144 12.40 12.60 12.51

14 6.5 11.2 8.7 1.69 3.89 2.86 1011 1015 1013 144 12.40 12.55 12.48

15 5.1 11.9 8.3 2.60 6.24 4.23 1005 1011 1008 144 12.35 12.55 12.46

16 7.1 12.1 10.1 3.32 9.97 7.33 1002 1005 1003 144 12.20 12.45 12.38

17 10.3 12.3 11.2 6.67 11.08 9.02 999 1003 1002 144 12.15 12.40 12.34

18 12.1 17.4 14.4 1.38 13.20 6.30 990 999 992 144 12.25 12.50 12.39

19 10.5 14.0 12.7 2.98 15.23 9.25 984 995 988 144 12.25 12.40 12.38

20 10.3 12.3 11.4 3.21 15.26 7.71 986 999 996 144 12.20 12.40 12.28

21 7.6 12.8 9.4 4.54 18.28 11.46 975 1007 990 144 12.15 12.35 12.28

22 8.1 12.8 10.7 2.65 11.19 7.02 1000 1010 1006 144 11.95 12.25 12.12

23 10.6 13.2 12.0 2.79 12.27 7.44 996 1001 999 144 11.90 12.20 12.11

24 8.9 11.5 10.2 4.37 12.61 7.46 997 1000 998 144 11.90 12.20 12.08

25 9.1 12.2 10.6 3.89 15.46 8.69 990 997 993 144 11.90 12.15 12.01

26 9.4 13.1 11.3 6.38 19.71 11.58 988 999 991 144 11.80 12.15 12.01

27 8.3 13.4 10.6 1.05 12.02 5.33 995 1001 998 144 11.90 12.10 11.96

28 7.5 10.5 9.2 2.03 13.64 7.71 995 1005 999 144 11.85 12.10 11.95

29 4.9 10.6 8.5 1.28 13.38 5.87 1005 1017 1012 144 11.70 12.05 11.85

30 7.3 11.4 10.1 2.65 11.79 6.55 1006 1016 1010 144 11.60 11.95 11.83

31 11.3 15.6 13.1 0.47 9.02 5.87 997 1007 1001 144 11.70 11.95 11.89

Records

min 4.9 0.47 975 144 11.60

max 17.4 19.71 1021 144 13.05

mean 10.8 6.75 1001 144 12.38

Total 4464

4464

100.00%

Total possible (10 min) met records

Actual coverage

Daily Temperature (oC) Wind velocity (m/s) Air pressure (mbar) Number of

records

Sea surface temperature

Temperature, monthly Wind velocity, monthly Pressure, monthly

Monthly summary

Sea temperature


Rev. 01, 31-Mar-2015

Page 24 of 39

Table 10 is generated by code, which constructs a simple 2-way contingency table using Hs and peak direction.

Column and row names show the binned ranges, using the notation explained above. All records for each Hs and

peak direction range are summed for each cell in the table, so that the sum of rows and columns must equal the

total number of records for the month. Any rows or columns that are empty are excluded from the table for ease of

reading and printing. The complete data space is represented graphically in Figure 8 at a much finer resolution, and

also in a wave rose format in Figure 9.

Table 11 is generated by code, which constructs a simple 2-way contingency table using Tz and peak direction.

Column and row names show the binned ranges, using the notation explained above. All records for each Tz and

peak direction range are summed for each cell in the table, so that the sum of rows and columns must equal the

total number of records for the month. Any rows or columns that are empty are excluded from the table for ease of

reading and printing. The complete data space is represented graphically in Figure 10 at a much finer resolution.

Table 12 is generated by code, which constructs a simple 2-way contingency table using Tz and wave height, Hs.

Column and row names show the binned ranges, using the notation explained above. All records for each Tz and Hs

range are summed for each cell in the table, so that the sum of rows and columns must equal the total number of

records for the month. Any rows or columns that are empty are excluded from the table for ease of reading and

printing. The complete data space is represented graphically in Figure 11 at a much finer resolution.

Table 13 is generated by code, which constructs a simple 2-way contingency table using energy period (also referred

to as the power period), Te and wave height, Hs. Column and row names show the binned ranges, using the

notation explained above. All records for each Te and Hs range are summed for each cell in the table, so that the

sum of rows and columns must equal the total number of records for the month. Any rows or columns that are

empty are excluded from the table for ease of reading and printing. The complete data space is represented

graphically in Figure 12 at the same resolution.


Rev. 01, 31-Mar-2015

Page 25 of 39

Table 10 Monthly occurrence table, Hm0 vs Peak direction

Figure 8 Distribution of the number of 30 minute records by peak direction and significant wave height

Height [Hm0] in m

(140,150] (150,160] (160,170] (170,180] (180,190] (190,200] (200,210] (210,220] (220,230] (230,240] (240,250] (250,260] (260,270] (270,280] (280,290] (290,300] (300,310] (310,320] (320,330] (330,340] (340,350] (350,360] TOTAL

(0.0,0.5] 0 0 0 0 0 0 0 0 0 0 0 0 1 1 4 1 0 0 1 6 9 1 24

(0.5,1.0] 3 1 0 2 1 0 0 1 0 0 0 1 11 43 59 38 10 10 28 79 55 4 346

(1.0,1.5] 2 3 0 0 0 0 0 0 0 0 0 0 7 39 40 14 4 8 29 83 64 6 299

(1.5,2.0] 0 0 0 0 0 0 0 0 0 0 0 0 2 17 15 18 15 4 5 15 16 4 111

(2.0,2.5] 0 0 0 0 0 0 0 0 0 0 0 0 2 14 51 41 16 6 1 1 1 0 133

(2.5,3.0] 0 0 0 0 0 0 0 0 0 0 0 0 1 42 63 17 2 5 0 0 0 0 130

(3.0,3.5] 0 0 0 0 0 0 0 0 0 0 0 0 5 49 72 26 3 3 0 0 0 0 158

(3.5,4.0] 0 0 0 0 0 0 0 0 0 0 0 0 7 26 55 20 3 0 0 0 0 0 111

(4.0,4.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 20 33 21 4 1 0 0 0 0 79

(4.5,5.0] 0 0 0 0 0 0 0 0 0 0 0 0 1 15 19 6 2 1 0 0 0 0 44

(5.0,5.5] 0 0 0 0 0 0 0 0 0 0 0 0 1 4 11 3 2 0 0 0 0 0 21

(5.5,6.0] 0 0 0 0 0 0 0 0 0 0 0 0 1 4 7 1 0 0 0 0 0 0 13

(6.0,6.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 6 2 2 0 0 0 0 0 0 10

(6.5,7.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 1 0 0 0 0 0 6

(7.0,7.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(7.5,8.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1

TOTAL 5 4 0 2 1 0 0 1 0 0 0 1 39 280 432 213 62 38 64 184 145 15 1486

Peak Direction (degrees)


Rev. 01, 31-Mar-2015

Page 26 of 39

Figure 9 Wave rose

10%

20%

30%

W E

S

N

0 - 0.5

0.5 - 1

1 - 1.5

1.5 - 2

2 - 2.5

2.5 - 3

3 - 3.5

3.5 - 4

>=4

Significant Wave Height (m)


Rev. 01, 31-Mar-2015

Page 27 of 39

Table 11 Monthly occurrence table, Tz vs Peak direction

Figure 10 Distribution of the number of 30 minute records by peak direction and period Tz

Period [Tz] in seconds

(140,150] (150,160] (160,170] (170,180] (180,190] (190,200] (200,210] (210,220] (220,230] (230,240] (240,250] (250,260] (260,270] (270,280] (280,290] (290,300] (300,310] (310,320] (320,330] (330,340] (340,350] (350,360] TOTAL

(0.0,0.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(0.5,1.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(1.0,1.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(1.5,2.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(2.0,2.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(2.5,3.0] 0 0 0 1 1 0 0 1 0 0 0 0 3 5 2 6 0 0 0 0 0 0 19

(3.0,3.5] 5 4 0 1 0 0 0 0 0 0 0 1 6 15 23 17 3 0 0 0 0 0 75

(3.5,4.0] 0 0 0 0 0 0 0 0 0 0 0 0 4 15 23 14 4 0 1 0 4 1 66

(4.0,4.5] 0 0 0 0 0 0 0 0 0 0 0 0 3 18 20 10 1 6 13 33 20 0 124

(4.5,5.0] 0 0 0 0 0 0 0 0 0 0 0 0 5 9 9 4 2 5 20 69 42 5 170

(5.0,5.5] 0 0 0 0 0 0 0 0 0 0 0 0 2 15 18 8 8 5 12 39 33 4 144

(5.5,6.0] 0 0 0 0 0 0 0 0 0 0 0 0 2 19 21 21 10 5 7 20 18 3 126

(6.0,6.5] 0 0 0 0 0 0 0 0 0 0 0 0 9 18 33 18 9 5 9 7 15 2 125

(6.5,7.0] 0 0 0 0 0 0 0 0 0 0 0 0 2 41 62 30 9 5 1 6 6 0 162

(7.0,7.5] 0 0 0 0 0 0 0 0 0 0 0 0 1 43 100 37 8 6 1 0 2 0 198

(7.5,8.0] 0 0 0 0 0 0 0 0 0 0 0 0 2 46 59 24 5 1 0 2 2 0 141

(8.0,8.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 27 41 12 3 0 0 5 2 0 90

(8.5,9.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 7 16 7 0 0 0 3 0 0 33

(9.0,9.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 4 0 0 0 0 1 0 11

(9.5,10.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1

(10.0,10.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1

TOTAL 5 4 0 2 1 0 0 1 0 0 0 1 39 279 432 213 62 38 64 184 145 15 1486

Peak Direction (degrees)


Rev. 01, 31-Mar-2015

Page 28 of 39

Table 12 Monthly occurrence table, Tz vs Hm0

Height [Hm0] in m

(2.5,3.0] (3.0,3.5] (3.5,4.0] (4.0,4.5] (4.5,5.0] (5.0,5.5] (5.5,6.0] (6.0,6.5] (6.5,7.0] (7.0,7.5] (7.5,8.0] (8.0,8.5] (8.5,9.0] (9.0,9.5] (9.5,10.0] (10.0,10.5] TOTAL

(0,0.5] 0 3 7 2 4 7 1 0 0 0 0 0 0 0 0 0 24

(0.5,1.0] 18 63 35 57 85 43 20 9 8 4 3 1 0 0 0 0 346

(1.0,1.5] 0 7 19 58 66 53 26 26 17 6 7 8 4 1 0 1 299

(1.5,2.0] 0 0 0 4 15 26 24 12 16 14 0 0 0 0 0 0 111

(2.0,2.5] 0 0 0 0 2 14 28 32 26 20 7 4 0 0 0 0 133

(2.5,3.0] 0 0 0 0 0 3 17 17 19 35 20 19 0 0 0 0 130

(3.0,3.5] 0 0 0 0 0 0 5 14 45 49 24 17 4 0 0 0 158

(3.5,4.0] 0 0 0 0 0 0 1 8 14 49 21 11 5 2 0 0 111

(4.0,4.5] 0 0 0 0 0 0 0 2 11 16 29 9 6 5 1 0 79

(4.5,5.0] 0 0 0 0 0 0 0 0 2 8 16 9 6 3 0 0 44

(5.0,5.5] 0 0 0 0 0 0 0 0 0 1 13 4 3 0 0 0 21

(5.5,6.0] 0 0 0 0 0 0 0 0 0 1 3 8 1 0 0 0 13

(6.0,6.5] 0 0 0 0 0 0 0 0 0 0 1 4 5 0 0 0 10

(6.5,7.0] 0 0 0 0 0 0 0 0 0 0 1 3 2 0 0 0 6

(7.0,7.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(7.5,8.0] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1

TOTAL 18 73 61 121 172 146 122 120 158 203 145 97 37 11 1 1 1486

Period [Tz] in seconds


Rev. 01, 31-Mar-2015

Page 29 of 39

Figure 11 Distribution of the number of 30 minute records by significant wave height and period Tz

Table 13 Monthly occurrence table, Te vs Hm0

Figure 12 Distribution of the number of 30 minute records by significant wave height and energy period

Height [Hm0] in m

(3.5,4.0] (4.0,4.5] (4.5,5.0] (5.0,5.5] (5.5,6.0] (6.0,6.5] (6.5,7.0] (7.0,7.5] (7.5,8.0] (8.0,8.5] (8.5,9.0] (9.0,9.5] (9.5,10.0] (10.0,10.5] (10.5,11.0] (11.0,11.5] (11.5,12.0] (12.0,12.5] (12.5,13.0] (13.0,13.5] (13.5,14.0] (14.0,14.5] (14.5,15.0] (15.0,15.5] (15.5,16.0] TOTAL

(0,0.5] 0 0 0 0 0 8 13 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24

(0.5,1.0] 1 3 6 23 71 82 51 23 21 10 14 9 3 0 5 6 3 2 2 2 2 4 2 1 0 346

(1.0,1.5] 1 3 1 0 18 40 31 45 41 35 16 15 16 19 4 2 0 0 2 3 4 1 1 1 0 299

(1.5,2.0] 0 0 0 0 0 5 13 13 18 19 28 9 2 4 0 0 0 0 0 0 0 0 0 0 0 111

(2.0,2.5] 0 0 0 0 0 2 8 14 18 12 25 18 14 12 5 5 0 0 0 0 0 0 0 0 0 133

(2.5,3.0] 0 0 0 0 0 2 3 3 18 4 2 16 35 27 15 5 0 0 0 0 0 0 0 0 0 130

(3.0,3.5] 0 0 0 0 0 0 1 5 8 7 9 31 39 41 12 5 0 0 0 0 0 0 0 0 0 158

(3.5,4.0] 0 0 0 0 0 0 1 5 5 3 6 27 26 14 8 8 5 1 1 1 0 0 0 0 0 111

(4.0,4.5] 0 0 0 0 0 0 0 0 6 5 3 15 19 4 5 9 4 3 3 2 1 0 0 0 0 79

(4.5,5.0] 0 0 0 0 0 0 0 0 1 3 0 2 12 7 5 6 4 2 1 1 0 0 0 0 0 44

(5.0,5.5] 0 0 0 0 0 0 0 0 0 1 0 2 6 5 1 3 3 0 0 0 0 0 0 0 0 21

(5.5,6.0] 0 0 0 0 0 0 0 0 0 0 1 2 1 6 2 0 1 0 0 0 0 0 0 0 0 13

(6.0,6.5] 0 0 0 0 0 0 0 0 0 0 0 1 1 3 2 3 0 0 0 0 0 0 0 0 0 10

(6.5,7.0] 0 0 0 0 0 0 0 0 0 0 0 1 2 3 0 0 0 0 0 0 0 0 0 0 0 6

(7.0,7.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(7.5,8.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1

TOTAL 2 6 7 23 89 139 121 109 137 99 105 148 176 146 64 52 20 8 9 9 7 5 3 2 0 1486

Energy period [Te] in seconds


Rev. 01, 31-Mar-2015

Page 30 of 39

Tables 14 and 15 are 3-way contingency tables generated by code, extending Table 10 by a further directional factor

(Mean Wave Direction – MDIR). Each worksheet provides a monthly occurrence table for energy period [Te] against

wave height [Hs] and Direction [MDIR]. Column and row names show the binned ranges, using the notation

explained above, with the title of each indicating the binned ranges for direction. All records for each Te and Hs

range are summed for each cell in the table, so that the sum of rows and columns must equal the total number of

records for the month. As the Mean Wave Direction is factored in 15° bins there is in principle a maximum of 24

tables.

Two tables were selected to include in the present report: one with very few occurrences within the binned

directional range (Table 14) and another with a large number of occurrences (Table 15). Note that, as expected, the

number of occurrences for these two directional bins is in agreement with what can be observed in Figure 9.

Figure 13 presents a preferred graphical representation of the data contained in Table 13 and Figure 12, showing

estimated power contours by both the methods described in equations [12] and [13].

In Figures 14 and 15, the power estimate for each 30 minute record is summed according to the binned range within

which its Hs and Te value falls. The summed results are given in kWh/m for each Hs and Te bin combination in Figure

14 and in parts per thousand (ppt) in Figure 15. The highlighted portion of these matrices must correspond with that

of Figure 13, but the values and colour range will differ.


Rev. 01, 31-Mar-2015

Page 31 of 39

Table 14 Monthly occurrence table, Te vs Hm0 for mean direction (30°,45°]

Table 15 Monthly occurrence table, Te vs Hm0 for mean direction (270°,285°]

Height [Hm0] in m

(0,0.5] (0.5,1.0] (1.0,1.5] (1.5,2.0] (2.0,2.5] (2.5,3.0] (3.0,3.5] (3.5,4.0] (4.0,4.5] (4.5,5.0] (5.0,5.5] (5.5,6.0] (6.0,6.5] (6.5,7.0] (7.0,7.5] (7.5,8.0] (8.0,8.5] (8.5,9.0] (9.0,9.5] (9.5,10.0] (10.0,10.5] (10.5,11.0] (11.0,11.5] (11.5,12.0] (12.0,12.5] (12.5,13.0] (13.0,13.5] (13.5,14.0] TOTAL

(0,0.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(0.5,1.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(1.0,1.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1

(1.5,2.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(2.0,2.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(2.5,3.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(3.0,3.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(3.5,4.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(4.0,4.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(4.5,5.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(5.0,5.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(5.5,6.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(6.0,6.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(6.5,7.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(7.0,7.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(7.5,8.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(8.0,8.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(8.5,9.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(9.0,9.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(9.5,10.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

TOTAL 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1


Height [Hm0] in m

(0,0.5] (0.5,1.0] (1.0,1.5] (1.5,2.0] (2.0,2.5] (2.5,3.0] (3.0,3.5] (3.5,4.0] (4.0,4.5] (4.5,5.0] (5.0,5.5] (5.5,6.0] (6.0,6.5] (6.5,7.0] (7.0,7.5] (7.5,8.0] (8.0,8.5] (8.5,9.0] (9.0,9.5] (9.5,10.0] (10.0,10.5] (10.5,11.0] (11.0,11.5] (11.5,12.0] (12.0,12.5] (12.5,13.0] (13.0,13.5] (13.5,14.0] TOTAL

(0,0.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 3

(0.5,1.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 4

(1.0,1.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 4 2 2 1 0 0 0 1 1 16

(1.5,2.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 6 1 2 1 0 2 0 0 0 0 0 0 0 17

(2.0,2.5] 0 0 0 0 0 0 0 0 0 0 0 0 2 4 3 0 0 7 7 5 1 3 2 0 0 0 0 0 34

(2.5,3.0] 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 7 0 2 13 17 13 8 2 0 0 0 0 0 68

(3.0,3.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 7 6 8 22 29 25 8 4 0 0 0 0 0 112

(3.5,4.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3 5 14 23 9 8 5 3 0 0 0 0 74

(4.0,4.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 10 8 3 3 8 2 1 0 0 0 41

(4.5,5.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 7 5 4 5 3 2 0 0 0 29

(5.0,5.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 3 1 3 3 0 0 0 0 16

(5.5,6.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 5 2 0 1 0 0 0 0 11

(6.0,6.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 0 0 0 0 0 6

(6.5,7.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(7.0,7.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(7.5,8.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(8.0,8.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(8.5,9.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(9.0,9.5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

(9.5,10.0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

TOTAL 0 0 0 0 0 0 0 0 0 0 0 0 4 10 14 25 15 29 75 98 69 42 33 12 3 0 1 1 431



Rev. 01, 31-Mar-2015

Page 32 of 39

Figure 13 Scatter diagram of significant wave height and energy period


Rev. 01, 31-Mar-2015

Page 33 of 39

Figure 14 Wave energy matrix showing kWh/m by significant wave height and energy period


Rev. 01, 31-Mar-2015

Page 34 of 39

Figure 15 Normalised wave energy matrix in parts per thousand (1 ppt = 25.963 kWh/m) by significant wave height and energy period


Rev. 01, 31-Mar-2015

Page 35 of 39

Figures 16 to 18 show the richness of content in the spectral data files, respectively plotting the spectral energy, the

spectral direction (where S(f)>1m2/Hz) and the spectral direction spread (where S(f)>1m2/Hz) at each frequency for

all 30 minute records throughout the month. This data in Figure 16 is used to construct the filter applied to Figure

17 and Figure 18.

Figure 16 Time series of wave spectra (m2/Hz)

Figure 17 Direction of the wave spectral components where S(f) > 1m2/Hz

Record number in sequence of 30 minute records in October 2014

Fre

qu

en

cy (

Hz)

200 400 600 800 1000 1200 1400

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Spectral energy density

(m2/Hz)

10

20

30

40

50

60

70

80

90

100

110


Fre

qu

en

cy (

Hz)

200 400 600 800 1000 1200 1400

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Direction(degrees)

0

50

100

150

200

250

300

350


Rev. 01, 31-Mar-2015

Page 36 of 39

Figure 18 Directional spread by frequency and time where S(f) > 1m2/Hz

Figure 19 provides a simple means of comparison of Mean Wave Direction [MDIR], Peak Direction [Dp] and Best

Direction for each 30 minute record during the month.

Figure 19 Comparison of mean wave direction (green), peak direction (pink) and best direction (blue)


Fre

qu

en

cy (

Hz)

200 400 600 800 1000 1200 1400

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Direction(degrees)

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

Record number in sequence of 30min records

Dir

ecti

on

(d

eg

rees)


Rev. 01, 31-Mar-2015

Page 37 of 39

5 CONCLUSIONS AND RECOMMENDATIONS

This report intends to provide an up-to-date contribution to the definition of a set of standards to be applied in the

handling of wave data, based on the experience and expertise of MaRINET’s consortium and ensemble of world-class

wave test facilities. It covered a brief review of the standardization efforts carried out to date, the description of the

sort of wave data commonly considered for wave energy purposes, wave measurement and data analysis common

and suggested practices, as well as data archival and presentation approaches to be followed.

The definition of standards is a dynamic process that follows closely the development of technology, in a constant

interchange of information. In other words, standards adapt to technology evolution which, in turn, seeks the

orientations provided by protocols and guidelines to trace its shortest path towards the market. In the light of this,

the pre-commercial stage of wave energy technology is a clear obstacle in the definition of a stable and unanimous

set of standards. Nevertheless, there is a considerable amount of information on guidelines and standards from

other sectors that the wave energy industry could use as reference and template for the sharing of wave data.

The present work uses the MaRINET experience to provide its contribution towards wave data standardization. It has

been seen before (MaRINET (2012a) and MaRINET (2014)) that, despite the variety of test facilities across MaRINET,

there is a surprisingly large basis of common ground on which to build consensual and unified approaches and

practices. Binned tables are unmistakably a powerful tool to present wave data. This is, in fact, a preferable means

for technology developers to create the necessary interface between technology performance and available

resource. In this sense, the information contained in occurrence tables and scatter diagrams is essential for the

developer to report efficiency and performance of his device through the commonly used power matrix. Occurrence

tables and scatter diagrams should be presented in terms of wave height and period. For wave height, significant

wave height is unanimously the parameter to choose. As regards period, some developers seem to prefer peak

period, others mean energy period. Preferably, a consensus on this matter should be achieved. While this is not the

case, it is important to archive wave data both in (Hs,Tp) and (Hs,Te) binned formats.

A number of the tabular and graphical outputs presented in this report involved the creation of contingency tables

(the term “Occurrence Table” has been preferred for titles of tables, and “Scatter Diagram” for the Figure). In

generating binned ranges for these the following protocols have been adopted by EMEC:

• The notation of (a,b] has been preferred over all other alternatives such as “>a to <=b”, and “>a to ≤b”. The

use of (a,b] means “greater than a and less than or equal to b” within any range of values. Conversely [a,b)

means “equal to or greater than a and less than b”. This notation is growing in popularity, is clear and more

elegant than the alternatives.

• As a general rule the right break is preferred, ie (a,b]. However, as it is useful to be able to identify and

include certain zero conditions for example of no wind (to include calm days) left breaks are occasionally

used to ensure that the total number of records appearing in a table corresponds to the sum of all records

tabulated. In all tabular representations the break method employed should be clear from the row and

column headings and this is identical to the method for any corresponding figure. The break protocol

adopted can be readily changed for any of these if required.

• There is a trade-off between the number of breaks in a range used for bins and the size of tabular output

generated. For this reason the 2 way contingency tables included in the report contain only those columns

and rows where data is present, i.e. empty columns and rows are excluded. Similarly for the series of 3 way

contingency tables only those tables where data are present are included.

• To supplement these, however for the 2 way contingency tables, a number of graphical plots are presented

which are based on a much greater number of bins, and which show explicitly the entire data range.


Rev. 01, 31-Mar-2015

Page 38 of 39

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