RR621 - Wave Mapping in UK Waters

8/13/2019 RR621 - Wave Mapping in UK Waters

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Executive

Health and Safety

Wave mapping in UK watersSupporting document

Martin O Williams

Metocean Advisor PhysE Limited

The Old Customs House

The QuayYarmouth

Isle of Wight

PO41 0PG

This work updates the contour map of 50-year extreme significant wave height that is provided in OT 2001/010 (previously

Section 11 of the Guidance Notes). The updated map, now presented for the 100 year return period, presents extreme

significant wave height in UK waters derived from 373 data sets from the NEXTRA hindcast, calibrated against measured

wave data and verified against established criteria.

This report and the work it describes were funded by the Health and Safety Executive (HSE). Its contents, including anyopinions and/or conclusions expressed, are those of the authors alone and do not necessarily reflect HSE policy.

HSE Books


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Crown copyright 2008

First published 2008

All rights reserved. No part of this publication may be

reproduced, stored in a retrieval system, or transmitted

in any form or by any means (electronic, mechanical,

photocopying, recording or otherwise) without the prior

written permission of the copyright owner.

Applications for reproduction should be made in writing to:

Licensing Division, Her Majestys Stationery Office,

St Clements House, 2-16 Colegate, Norwich NR3 1BQ

or by e-mail to [email protected]

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ACKNOWLEDGEMENTSThe author and editor gratefully acknowledge the valuable contribution

made to this study by the following industry representatives:

Dr Colin K Grant

Metocean Specialist /Deepwater Facilities

BP Exploration

Mr Ian M Leggett

Discipline Head - Metocean Engineering

Shell EP Europe

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TABLE OF CONTENTS

EXECUTIVE SUMMARY ............................................................................................VII1. INTRODUCTION.................................................................................................. 1

1.1 BACKGROUND..................................................................................................................... 12. DATA SOURCES ................................................................................................ 2

2.1 THE NESS, NEXT AND NEXTRA WAVE HINDCASTS .................................................... 22.2 VERIFICATION DATA .......................................................................................................... 52.3 ESTABLISHED CRITERIA ................................................................................................... 8

3. THE MAPPING PROCESS................................................................................ 103.1 DERIVATION OF EXTREME VALUES ............................................................................. 103.2 GRIDDING AND MAPPING ............................................................................................... 10

4. ASSESSMENT OF NEXTRA PERFORMANCE ................................................ 14

4.1 COMPARISON WITH MEASUREMENTS ........................................................................ 144.2 CONTOURS OF NEXTRA WAVE HEIGHTS.................................................................... 154.3 SELECTION OF OPTIMUM GRIDDING METHOD.......................................................... 17

5. CALIBRATION OF NEXTRA HS100 ................................................................... 185.1 CALIBRATION METHOD ................................................................................................... 185.2 CALIBRATION OPTIONS................................................................................................... 185.3 RESULTS OF THE CALIBRATION EXERCISE ............................................................... 20

6. THE FINAL MAP OF 100 YEAR HS..................................................................28

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FIGURES

Figure 1: 100 year extreme significant wave height (m) ......................................................viii Figure 2: The NEXTRA archive grid.............................................................................. 4Figure 3: NEXTRA grid points selected for analysis...................................................... 5

: Locations of verification data sets .................................................................. 6Figure 4: Locations of established criteria ..................................................................... 8Figure 5

Figure 6: Contours of Hs100 from the software gridding options ................................... 12Figure 7: Hs100 (m) measured verification data vs. closest unadjusted NEXTRA...... 14Figure 8: Contours of unadjusted NEXTRA Hs100 (m) from Kriging gridding................ 16Figure 9: Contours of unadjusted NEXTRA Hs100 (m) from Local Polynomial gridding 16Figure 10: Tested calibrations for adjusting NEXTRA Hs100 ........................................ 20Figure 11: Comparison of the potential NEXTRA Hs100 calibrations ............................ 20Figure 12: Grid values of NEXTRA Hs

100(m) adjusted with the four calibrations......... 22

Figure 13: Contours of adjusted NEXTRA Hs100 (m) ................................................... 23Figure 14: Adjusted NEXTRA Hs100 compared to established 100yr design criteria .... 24Figure 15: Relationship between NEXTRA Hs50 and Hs100 (m) ................................... 24Figure 16: Comparison of NEXTRA Hs50 contours (m) and those from OT 2001/010.. 25Figure 17: Comparison of OT 2001/010 and NEXTRA Hs50 grid values (m)................ 26Figure 18: Hs100 (m) the final contour map ............................................................... 28

TABLES

Table 1: NEXTRA metadata.......................................................................................... 3Table 2: Verification data .............................................................................................. 7Table 3: Established criteria.......................................................................................... 9Table 4: Data gridding options .................................................................................... 11Table 5: Hs100 (m) measured data vs. closest unadjusted NEXTRA......................... 14Table 6: Verification and unadjusted NEXTRA Hs100 (m) ............................................ 19Table 7: Adjustment of wave heights by application of the four calibrations ................ 21Table 8: Tabulated comparison from Figure 17........................................................... 26

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EXECUTIVE SUMMARYA contour map of 100 year extreme significant wave heights in UK waters has been produced

by processing, interpolating and contouring 373 data sets from the NEXTRA model hindcast.

The work updates the contour map of 50 year extreme significant wave height that was provided

in:

Department of Energy: Offshore installations: Guidance on design, construction andcertification (4th Edition, 1990).

HMSO Consolidated Edition 1993 (plus Amendment No. 3, 1995).Following withdrawal in 1998, this document was republished as Offshore Technology Report

OT2001/010, with the 50 year map reproduced therein.

The values of 100 year extreme significant wave height (Hs 100) obtained directly from theNEXTRA data were found to be at variance with current industry criteria and with extreme

values based on measured verification data sets. In broad terms, in the North Sea, NEXTRA

was found to produce approximately the same value as the verification data when 100 year

significant wave height was of the order of 14 metres. Below 14m NEXTRA tended to produce

higher values, and above 14m NEXTRA tended to produce lower values.

A precautionary approach was therefore adopted; a calibration was derived through the

assessment of the NEXTRA Hs100 values against equivalent values from measured data. The

resulting algorithm was applied to adjust the NEXTRA results to a level consistent with those

indicated by the measured data, and it is from these adjusted values from that the contour map

has been derived.

The validity of extrapolating the calibration curve beyond the range for which verification data

are available is questionable, and therefore the region of the map in which Hs100 is shown to be

over 18 metres has been blanked off.

The resulting contour map is presented below as Figure 1.

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Figure 1: 100 year extreme significant wave height (m)

Important note: the information displayed on this map is intended to provide guidance and should not be treated as a

substitute for site specific study.

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1. INTRODUCTION

1.1 BACKGROUND

The UK Department of Energy provided guidance on design, construction and certification ofoffshore structures between 1974 and June 1998. This guidance was first published to support

the Offshore Installations (Construction and Survey) Regulations 1974 (SI 1974/289) by

providing a consistent basis for the certification of offshore installations by government-

appointed certifying authorities. The guidance was regularly updated to keep up with evolving

technical knowledge and the fourth and final edition was published in 1990. The document, in

its final format, was entitled:

Department of Energy: Offshore installations: Guidance on design, construction andcertification (4th Edition, 1990).

HMSO Consolidated Edition 1993 (plus Amendment No. 3, 1995).The document was generally referred to as Guidance or The Guidance Notes; sometimes asThe Fourth Edition. Section 11 of that document was entitled Environmental Considerations

and included maps of indicative values of environmental parameters with a 50-year return

period; this return period being selected in accordance with the requirements of SI 1974/289.

Section 11 of the Guidance remained unchanged since initial publication in 1974.

HSE withdrew the Fourth Edition from publication in June 1998 at the end of the certification

regime. However, withdrawal was not a reflection on the soundness of the technical

information it contained. Section 11 that addressed Environmental Considerations was

republished as Offshore Technology Report 2001/010. On re-publication additional text was

added to OT 2001/010 in the form of a warning as follows:

It should be noted that the technical content of the Guidance has not been updated as part ofthe re-formatting of the OTO publication The usermust therefore assess the

appropriateness and currency of the technical information for any specific application.

It remained a concern that, through OT 2001/010, Section 11 of the 4th Edition remained in

everyday use, principally by individuals and organisations that do not have the facilities or data

that would enable them to assess the appropriateness and currency of the technical information

therein. Indeed, substantial advances have been made since Section 11 was prepared,

principally with respect to the hindcasting of wave data. The use of grid-mapped hindcast data,

in combination with appropriate validation against measurements, provides a new and

substantially more robust method for the derivation of contour maps of metocean parameters.

This work therefore updates the contour map of 50-year extreme significant wave height that is

provided in OT 2001/010. The updated map, now presented for the 100 year return period,

presents extreme significant wave height in UK waters derived from 373 data sets from the

NEXTRA hindcast.

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2. DATA SOURCES

2.1 THE NESS, NEXT AND NEXTRA WAVE HINDCASTS

2.1.1 NESS

The North European Storm Study (NESS) was initiated with the intention of producing a high

quality hindcast database of winds, waves, currents and water levels for the North European

continental shelf. The wave model consisted of a coarse (150 km) grid for the North Atlantic

and a fine (30 km) grid for the North European shelf. Wind fields were specified by the UK

Meteorological Office (Met Office) and the Norwegian Meteorological Institute. Wave

modelling for NESS was performed by GKSS Forschungszentrum using a version of their

spectral wave model. HYPAS.

The Hydrodynamic model, used to determine tide and surge parameters was System 21

developed by the Danish Hydraulic Institute. This model operated using the 150 km coarse

grid, within which was nested a 10 km grid covering the Southern North Sea where thebathymetry is more variable.

The NESS model was run for the period October 1964 to March 1989, although output was not

continuous:

! October 1964 to March 1989 Winter data only hindcast: (October to March), except! October 1976 to March 1980 The hindcast included the summers of 1977, 78 and 79.! A number of significant summer storms considered worthy of inclusion were also hindcast.

2.1.2 NEXTFollowing criticism that the NESS hindcast was providing only a poor representation of wind

and wave conditions, the model was re-run using a third generation wave model of the WAM

type (WAMDI Group, 1998). Additional wind fields were generated by Oceanweather Inc

using pressure fields supplied by the USA National Oceanic and Atmospheric Administration

(NOAA) to cover the period 4/1989 to 3/1995, although the earlier wind fields (1964 to 1989)

remained unchanged. The hydrodynamic model was also extended to 1995.

The NEXT model therefore spanned the following periods:

! October 1964 to March 1989 Winter data only hindcast: (October to March), except! A number of significant summer storms in the period 1964 to 1989 were also hindcast.! October 1976 to March 1980 The hindcast included the summers of 1977, 78 and 79.! April 1989 to March 1995 Continuous hindcast, including both summer and winter data.

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2.1.3 NEXTRA

Unfortunately the questionable performance of NESS was not resolved by NEXT and doubts

persisted with respect to both wind and wave criteria, which did not compare favourably with

measurements from the North Sea. The problems were attributed to inconsistencies in the wind

field which comprised a mix of wind fields prepared by:

! The Met Office! The Norwegian Meteorological Institute! Oceanweather Inc.The model was therefore re-run again, this time using a homogenous wind field prepared

entirely by Oceanweather Inc. The period of the hindcast was further extended to 1998,

although on this occasion the hydrodynamic model was not extended. As summarised in Table

1, the period covered by the NEXTRA hindcast is:

!October 1964 to March 1989 Winter data only hindcast: (October to March), except

! A number of significant summer storms in the period 1964 to 1989 were also hindcast.! October 1976 to March 1980 The hindcast included the summers of 1977, 78 and 79.! April 1989 to March 1998 Continuous hindcast, including both summer and winter data.! Hydrodynamic model ends in March 1995.The NEXTRA hindcast is restricted to use by members of the NESS User Group (NUG of

which HSE is a member) and contractors working on their behalf. The data are supplied by

Oceanweather Inc. on 4 DVDs and a CD-ROM.

At the time of writing work is proposed with a view to further improving the model.

Oceanweather Inc. has recently acknowledged that the wind parameter output in NEXTRA is

an intermediate value in the calculation of the wave height, and should not be taken as directlyrepresentative of the wind speed. For this reason a contour map the extreme wind speed has not

been attempted as part of the current work. It is anticipated that any additional studies, if

approved, will resolve the wind issues and further improve the quality of the hindcast.

Table 1: NEXTRA metadata

Domain

Resolution

Duration

Data

availability

Relevant

Products

45.4N-72.4N, 21.2W-36.6E

30 km

1st March 1964 to 30th September 1998

(i) Winters only 1964 to 1977

(ii) Continuous 1977-79, 1985-1998

(iii) 40+ selected summer storms

Significant wave height archived at 3 hour intervals;

The NEXTRA grid spans the Northwest European Continental Shelf and the Northeast Atlantic.

There are more than 3000 grid points in total and the model domain is illustrated in Figure 2.

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Figure 2: The NEXTRA archive grid

It was, however, neither practicable nor necessary to process all 3000 points. Therefore the 373representative grid points were manually selected to provide appropriate detail over the region

of interest. The selected grid points are illustrated in Figure 3. Note the increased density of

selected points in shallow regions (e.g. the Southern North Sea) where conditions were

anticipated to change rapidly with location.

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Figure 3: NEXTRA grid points selected for analysis

2.2 VERIFICATION DATA

2.2.1 Platform and Buoy Measurements

The measured verification data were obtained from either oil platform-mounted sensors or wave

buoys including, in the Atlantic west of the UK, Met Office K-buoys. Except at Magnus the

extreme values from the platform measurements were extracted from relevant design or data

reports. Where possible, to ensure consistency with the NEXTRA analyses undertaken for this

project, only the extreme results from fitting a 3-parameter Weibull distribution to the upper

95% of the data were used. In a very small number of cases these were not presented, in which

case values derived from a fit to the uppermost 10% of the available data were selected. At

Magnus, measured 3-hourly wave heights between April 1985 and July 2004 were extrapolated

by fitting a 3-parameter Weibull distribution to upper 95% of the data.

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The same procedure was carried out on frequency distributions compiled from the K-buoy

measurements, which were collected intermittently between 1984 and 2004. The locations of

the measurements are illustrated in Figure 4 and the verification data are summarised in Table 2.

Figure 4: Locations of verification data sets

2.2.2 Satellite Observations

Observations of wave height made by satellite altimeter were downloaded in frequency

distribution format from an internet database1, for the areas shown in Figure 4. Each area

covers 200 x 200 km2, except area 7 at 100 x 100 km

2, chosen to ensure sufficient observations

were included in the extreme value analysis. An extreme value of Hs in each area was derived

by extrapolation of a 3-parameter Weibull distribution fitted to the upper 95% of the

observations. The satellite areas are shown in Figure 4 and the extreme values given in Table 2.

1www.waveclimate.com

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Table 2: Verification data

Group Name Individual I.D. Lat Long Period50 yr Hs 100 yr Hs

(m) (m)K2 (62081) 51.0N 13.3W 91 to04 18.0 18.7

Atlantic K-K4 (62185) 54.5N 12.4W 92 to 04 18.4 19.2

Buoys

K5 (64045) 59.1N 11.4W 84 to 94 17.8 18.5

Magnus 61.6N 1.3E 85 to 04 16.8 17.5

North Cormorant 61.2N 1.2E 83 to 98 16.2 16.8

Buchan 57.9N 0.04E 81 to 95 12.8 13.2

Forties 57.8N 0.9E 74 to 95 12.7 13.2

Auk 56.4N 2.1E 76 to 98 12.4 12.9

West Sole 53.7N 1.15E 72 to 90 8.4 8.7

K13 53.2N 3.2E 80 to 98 8.7 9.0

Leman 53.1N 2.2E 72 to 97 7.1 7.4

Sat Area 1 57.8N 1.0E 85 to 02 11.7 11.4

Sat Area 2 59.5N 3.0E 85 to 02 12.7 14.4

Sat Area 3 55.0N 0.0E 85 to 02 10.3 10.6

Sat Area 4 52.5N 3.0E 85 to 02 8.2 8.6

Sat Area 5 50.0N 1.0W 85 to 02 7.7 9.7

Sat Area 6 49.0N 6.3W 85 to 02 13.9 15.4

Sat Area 7 51.0N 7.0W 85 to 02 11.8 12.3

Sat Area 8 50.0N 12.0W 85 to 02 17.1 17.7

Sat Area 9 53.5N 13.0W 85 to 02 17.6 18.3

Sat Area 10 57.0N 12.0W 85 to 02 18.6 19.3

Sat Area 11 61.0N 11.0W 85 to 02 19.0 19.7

Sat Area 12 62.0N 1.0W 85 to 02 14.9 15.4

SatelliteObservations

Platform

Measurements

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2.3 ESTABLISHED CRITERIA

Established design criteria were cross referenced against the final map in order to define the

degree of consistency between the two. The locations of these criteria are illustrated in Figure

5, the corresponding data being presented Table 3.

Figure 5: Locations of established criteria

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Table 3: Established criteria

Location Lat N Long -W/E Supplier 50yr Hs (m) 100yr Hs (m)

Northern North Sea

Magnus 61.6 1.3 BP 15.7 16.4

Thistle 61.4 1.6 BP 15.3 15.9

N. Corm 61.2 1.2 BP 15.4 16.0

Rhum 60.1 1.8 BP 13.6 14.2

NW Hutton 61.1 1.3 BP 15.0 15.6

Brent A 61.0 1.7 Shell 15.0 15.6

Bruce 59.8 1.7 BP 13.6 14.2

Central North Sea

Harding

Miller

Cyrus

Andrew

Goldeneye

Buchan

N Everest

Fulmar

Kittiwake

Mungo

Monan

Marnock

Lomond

Anasuria

GannetShearwater

Ula

Machar

Curlew

Auk

Southern North Sea

Tyne

Ketch

Cleeton

West Sole

CarrackInde

K13

Sean

Leman

Moray Firth

Beatrice

59.3

58.7

58.2

58.1

58.0

57.9

57.8

57.5

57.5

57.4

57.3

57.3

57.3

57.2

57.257.1

57.2

57.1

56.7

56.4

54.5

54.1

54.1

53.8

53.653.4

53.2

53.2

53.1

58.1

1.5

1.4

1.4

1.4

-0.4

0.0

1.8

2.1

0.5

2.0

1.9

1.7

2.2

0.9

1.01.9

2.9

2.1

1.3

2.1

2.5

2.5

1.3

1.2

2.82.6

3.2

2.9

2.2

-3.1

BP

BP

BP

BP

Shell

BP

BP

Shell

Shell

BP

BP

BP

BP

Shell

ShellShell

BP

BP

Shell

Shell

Shell

Shell

Shell

Shell

ShellShell

Shell

Shell

Shell

Encana

13.4

13.6

13.1

13.0

12.8

12.6

13.0

12.8

12.8

13.0

13.1

12.9

13.4

12.8

12.812.8

13.4

13.1

12.8

12.8

8.8

9.6

9.8

8.6

8.78.0

8.2

8.1

7.5

9.0

14.0

14.2

13.6

13.5

13.3

13.2

13.5

13.3

13.3

13.5

13.6

13.4

14.0

13.3

13.313.3

14.0

13.6

13.3

13.3

9.3

10.1

10.3

9.0

9.28.4

8.6

8.5

7.9

9.3

West of UK

Clair

Foinaven

Morecambe N.

Morecambe S.

60.7

60.3

54.0

53.9

-2.6

-4.3

-3.7

-3.6

BP

BP

HSE

HSE

15.8

17.3

N/A

N/A

16.6

18.0

8.7

7.4

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3. THE MAPPING PROCESS

3.1 DERIVATION OF EXTREME VALUES

3.1.1 NEXTRA

Values of 100 year significant wave height (Hs100) were derived by extrapolation of the 3-

parameter Weibull distribution fitted to the upper 95% of the cumulative frequency distribution.

The analyses were performed using OceanStats2 software (PhysE Limited) that uniquely

provides a batch processing facility, thus facilitating the analysis of the selected 373 NEXTRA

grid points.

3.1.2 Verification Data

Extreme Hs values were extracted from relevant entries in the appropriate criteria reference

documents. Where possible the Hs100 values derived from the 3-parameter Weibull distributionfitted to the upper 95% of available data was extracted, but in some cases this was not presented

and therefore values derived from fits to the upper 10% were used.

One exception was the Magnus Field; because of the importance of the Northern North Sea, and

the fact that new data had recently become available, the Magnus data were re-processed for this

study. Here, 3-hourly measured wave heights between April 1985 and July 2004 were

extrapolated by fitting the 3-parameter Weibull distribution to the upper 95% of the available

data.

3.1.3 Established Criteria

Final values were cross referenced against the established 100 year design values of Hs,extracted from design reports or as supplied by HSE.

3.2 GRIDDING AND MAPPING

3.2.1 Gridding

Golden Software Inc, 2002. Surfer, Version 8, was selected as the preferred application for

gridding and mapping.

Gridding is the process of creating a regularly spaced, rectangular grid of values from

irregularly spaced input data. The grid is the base from which the contour map is created. Caremust be taken in the choice of gridding algorithms as the chosen method can have a significant

impact on the final contour map; different methods can produce very different, and sometimes

inappropriate, results.

The software offers twelve gridding algorithms, as summarised in Table 4.

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Table 4: Data gridding options

No. Gridding Method Comment

1 Inverse Distance to a Power Weighted average interpolator, either exact or smoothing. Produced

noisy contours.

2 Kriging Well-proven v. flexible method, represents irregularly spaced data

well. Expresses trends in data producing accurate grid. Can be

either exact or smoothing interpolator. Default Surfer method as it

generally provides best representation of data.

3 Minimum Curvature Widely used in earth sciences, generates smooth, elastic surface

through each data point with minimum bending. Can introduce

high magnitude artefacts in areas of no data. Here, produced

noisy contours.

4 Modified Shepherds method Similar to inverse power. Produced spurious contours in some

areas.

5 Natural Neighbour Complex polygon interpolator. Good for irregularly spaced data,

but does not generate data in areas of no observations. Here,

produced good representation of data but slightly noisy contours.

6 Nearest Neighbour Assigns value of nearest point to each grid node. Here, produced

unacceptable results.

7 Polynomial Regression Defines large scale trends and patterns in data. Here, produced

unacceptable results.

8 Radial Basis Functions Series of exact interpolation functions. Flexible and produces

similar results to Kriging.

9 Triangulation with Linear

Interpolation

Generates triangular faces between data points. Here, produced

angular contours.

10 Moving Average Assigns values to grid nodes by averaging data within defined

search ellipse. Here produced unacceptable results.

11 Data Metrics Used to provide information about gridded data on a node by node

basis. Here produced unacceptable results.

12 Local Polynomial Assigns values to grid nodes by using weighted least squares fit to

data within defined search ellipse. Here, generated smoothest, most

natural contours.

Contours of Hs100 from each of the methods in Table 4 are reproduced in Figure 4.1, using the

same numbering scheme.

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12

1. Inverse Distance 2. Kriging 3. Min. Curvature

4. Modified Shepherds 5. Natural Neighbour 6. Nearest Neighbour

7. Polynomial Regression 8. Radial Basis Functions 9. Triangulation

10. Moving Average 11. Data Metrics 12. Local Polynomial

Figure 6:Contours of Hs100from the software gridding options

Methods 1, 6, 7, 10 and 11 were rejected at the first pass and from the others method 2 (Kriging)

and method 12 (local polynomial) were selected by experimentation as candidate methods forproducing contours of Hs100:


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1. Kriging interpolation. Well-proven, flexible method, representing irregularly spaced data

well. The algorithm expresses trends in the underlying data producing an accurate grid.

Block Kriging estimates the average value of blocks centred on each grid node, the size and

shape of which are the same as a grid cell. Since it is not estimating a value at a single point

block Kriging is not an exact interpolator, but it was employed here as it does generate a

smoother grid.

2. Local Polynomial interpolation. Assigns values to grid nodes by using a weighted least

squares fit to data within a defined search ellipse. For each grid node, the neighbouring data

are identified by the user-specified sector search, the specification being the width of each

sector the software searches for data. Using only the identified data, a local polynomial is

fitted and the grid node value is set to this value. The polynomial can be order 1, 2 or 3.

3.2.2 The Base Map

The coastline and bathymetry were downloaded from the US National Geophysical Data Centre

web facility

2

.

! The coastline was extracted from the World Vector Shoreline data set at a scale of

1:250000. The mapping software was configured to recognise the coastline as a boundary

to the contouring process, thus blanking regions that represent land.

! The bathymetry was downloaded from the ETOPO2 bathymetric database gridded at two

minute (latitude/longitude) resolution.

Both required conversion to Surfer format. The bathymetry was interpolated on to a 50 x 33

grid using the Kriging method.

3.2.3 Grid Resolution and Blanking

Grid resolution refers to the number of columns and rows of data in the interpolated grid and

hence the number or intersections or nodes. Contour lines are drawn as a series of straight-

line segments between adjacent grid nodes; a finer grid will therefore create smoother contours.

A resolution of x = 50, y = 33 was found by experimentation to provide an appropriate level of

detail for Kriging interpolation and x = 100, y = 66 for Local Polynomial interpolation. In both

cases additional contour smoothing was necessary.

To avoid producing erroneous onshore values the coastline around the UK, Ireland, Europe and

all major islands was digitised and assigned a blanking value that the mapping software

recognised as a boundary to the contouring process.

3.2.4 Filtering and Smoothing

The gridded data were filtered and smoothed prior to final presentation.

! A low pass linear convolution filter was applied to reduce small scale variability in the

interpolated data.

! In addition to filtering the grid, further smoothing was carried out by re-constituting the grid

with 5-point cubic spline interpolation. The original grid node values were preserved in this

process.

2http://www.ngdc.noaa.gov/mgg/mggd.html


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4. ASSESSMENT OF NEXTRA PERFORMANCE

4.1 COMPARISON WITH MEASUREMENTSAn assessment of NEXTRA model performance was carried out by comparing Hs100 from each

verification data set with that obtained from the closest NEXTRA grid point.

The wave height comparisons are plotted in Figure 6 and the corresponding values are given in

Table 4.

NEXTRA/MEASURED VERIFICATION

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

14.0

15.016.0

17.0

18.0

19.0

20.0

Ma

gnus

.Cormoran

t

Bu

chan

Fo

rties

Au

k

West

So

leK13

Le

man

K2(62081)

K4(62185)

K5(64045)

100year

Hs

(m)

60

70

80

90

100

110

120

130

%

Measured

NEXTRA

NEXTRA as % of measured

Figure 7: Hs100(m) measured verification data vs. closest unadjusted NEXTRA

Table 5: Hs100(m) measured data vs. closest unadjusted NEXTRA

Area LocationNEXTRAGP

VerificationHs100(m)

UnadjustedNEXTRAHs100 (m)

Distance fromverification(km)

NEXTRA as% ofverification

Magnus 14158 17.5 16.8 12.3 90

N. Cormorant 14267 16.8 15.4 11.2 91

Buchan 14894 13.2 12.8 13.1 102

Forties 14836 13.2 14.0 4.3 106

Auk 15021 12.9 14.1 9.3 109

West Sole 15570 8.7 9.0 7.7 102

K13 15514 9.0 9.8 7.9 109

UKWaters

Leman 15635 7.4 8.7 17.0 118

K2 buoy 16977 18.7 17.5 1.9 94

K4 16213 19.2 18.2 3.8 95

Atlantic

Ocean

K5 15294 18.5 18.3 13.3 99


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Comparison of the NEXTRA extreme values against the measured verification data reveals a

clear trend:

! In the northern North Sea NEXTRA extreme Hs values are less than the corresponding

verification data in the northern North Sea by 8% to 10%.

! In the central North Sea NEXTRA extreme Hs values are in general greater than the

verification data by 6% to 10% (Buchan is an outlier).

! In the southern North Sea NEXTRA extreme Hs values are greater than the verification

data by up to 3 to 15%.

! In the Atlantic area west of the UK, NEXTRA extreme Hs values are less than the

verification data by up to 6%.

Further inspection of the data reveals that, in general:

! If Hs100> 14m then NEXTRA < Verification Data

! If Hs100!14m then NEXTRA !Verification Data

! If Hs100< 14m then NEXTRA > Verification Data

The degree of spatial variability in the comparisons indicates that:

! NEXTRA model performance is not consistent across the mapping domain.

! Any adjustment of NEXTRA will not be linear across the range of wave heights within the

database.

4.2 CONTOURS OF NEXTRA WAVE HEIGHTS

Contours of Hs100 derived from NEXTRA data prior to any form of further adjustment are given

as follows:

Figure 8: Kriging gridding of the 373 NEXTRA grid points using a grid size of x = 50, y = 33;

resulting in 1650 interpolated grid points.

Figure 9: Local Polynomial gridding of the 373 NEXTRA grid points. The grid resolution was

x = 100, y = 66 giving a total of 6600 interpolated grid nodes.


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Figure 8:Contours ofunadjusted NEXTRA Hs100(m) from Kriging gridding

Figure 9:Contours of unadjusted NEXTRA Hs100(m) from Local Polynomial gridding


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Cross checking the contours on the maps against the measured verification data shows:

! Values of Hs100 derived from NEXTRA data are low in the exposed Atlantic, Northern

North Sea and Faroe Shetland Channel.

! The contours are in reasonable agreement with the verification data in the central North

Sea.

! Values of Hs100derived from NEXTRA data are high in the southern North Sea.

It was therefore concluded that calibration of the extreme NEXTRA wave heights was required

prior to production of the final map.

4.3 SELECTION OF OPTIMUM GRIDDING METHOD

As evidenced by Figures 8 and 9, interpolation by the Kriging and Local Polynomial gridding

methods gives significantly different results. The Kriging grid (Figure 8) has retained the smallscale variability in the unadjusted NEXTRA extreme values to a greater level than the Local

Polynomial grid (Figure 9). In contrast, the contours from the Local Polynomial grid represent

the smoother spatial transition of wave conditions that may be expected to occur naturally.

Experimentation with Local Polynomial gridding of adjusted NEXTRA extreme values

produced maps of smoothly varying Hs contours, which after some adjustment matched the

verification data to an acceptable degree. However, the process had a number of weaknesses:

! Gridding the adjusted model data by Local Polynomial interpolation produced contours

that in some areas were inconsistent with spot values of adjusted NEXTRA Hs100.

! Optimum contour positioning was only possible by applying two geographically dependentcalibrations. Combining the grids was complex and resulted in a contrived wave map.

! An additional, somewhat arbitrary adjustment of the calibrated wave heights was required

to incorporate a degree of conservatism in the contours.

On the basis of this assessment, the wave height map based on the Local Polynomial gridding

method was rejected in favour of the Kriging technique. The advantages of this approach are:

! A simple, more robust calibration was possible.

! The contours more closely reflected spatial trends in underlying NEXTRA data.

! In relation to the underlying grid of NEXTRA model data, the positioning of the contours

was thus optimal.

Development of the optimised wave map using the Kriging technique is described in the

following sections.


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5. CALIBRATION OF NEXTRA Hs100

5.1 CALIBRATION METHOD

Calibration of the unadjusted NEXTRA extreme wave heights was carried out in the followingsequence:

1. Extract the Hs100from the closest NEXTRA grid point to each verification data location or,for the satellite data, the average of unadjusted NEXTRA extreme values from grid points

lying in each satellite area.

2. Plot these NEXTRA extreme values against the corresponding verification data.

3. Fit a curve to the plotted data, such that the equation of the curve describes the adjustmentto be applied to the NEXTRA extreme values.

4. Apply the equation of the fitted curve to the 373 unadjusted NEXTRA extreme values.

5. Interpolate the adjusted NEXTRA extremes and contour the interpolated grid.

6. Cross-check the contours and underlying grid against the verification data and established

design criteria.

5.2 CALIBRATION OPTIONS

Previous attempts at mapping with Local Polynomial interpolation showed that a number of

potential calibration options were possible. Since the satellite extreme values were based on

data from a relatively wide area, they were expected to be at variance with nearby location

specific measured verification data; the calibration exercise therefore included verification data

sets with and without satellite extreme values. The following potential calibrations were tested:

1. All verification data - North Sea measurements, Atlantic K-Buoy and satellite areas 1-12

2. North Sea measurements and Atlantic K-Buoy measurements

3. North Sea measurements and satellite areas 1-4

4. North Sea measurements only

Table 6 summarises the verification data and the unadjusted NEXTRA values used in the

calibration.


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Table 6: Verification and unadjusted NEXTRA Hs100(m)

Area LocationNEXTRA

GP

Verification

Hs100(m)

Unadjusted

NEXTRA

Hs100(m)

Distance from

Verification

(km)

NEXTRA as

% of

Verification

Magnus 14158 17.5 15.8 12.3 90

N. Cormorant 14267 16.8 15.4 11.2 91

Buchan 14894 13.2 12.8 13.1 102

Forties 14836 13.2 14.0 4.3 106

Auk 15021 12.9 14.1 9.3 109

West Sole 15570 8.7 9.0 7.7 102

K13 15514 9.0 9.8 7.9 109

Leman 15635 7.4 8.7 17.0 118

Sat area 1 Average 12.2 11.4 N/A 93



NorthSea




Sat area 7 Average 12.3 14.7 N/A 119OtherUK

Waters


K2 buoy 16977 18.7 17.5 1.9 94

K4 buoy 16213 19.2 18.2 3.8 95

K5 buoy 15294 18.5 18.3 13.3 99



Sat area 10 Average 19.3 18.3 N/A 95AtlanticOcean


In order to optimise the positioning of the adjusted Hs100 contours in relation to the verification

data andestablished criteria, the calibration requirements were:

1. To amend with a single calibration the unadjusted NEXTRA Hs100 values in areas whereoffshore activities are prevalent.

2. To increase the unadjusted Hs100 values above 15m, to represent conditions in the Faroe-

Shetland Channel and Northern North Sea.

3. To maintain unadjusted Hs100 values of around 14m, to represent conditions in the CentralNorth Sea.

4. To decrease slightly Hs100values below 13m, to represent conditions in the Southern NorthSea.

An exponential curve was found by experimentation to be the most robust solution to these

requirements. Other types of fit e.g., linear, logarithmic and power law were less successful in

meeting allthe specified requirements and hence were rejected. A quadratic curve fitted to the

data in calibrations 1, 3 and 4 was of similar quality as the exponential fit, although the

placement of the associated contours was sufficiently poor to reject this. It may have been

possible to force a higher order polynomial to fit the data, but this would have resulted in an

excessively complicated calibration and hence a contrived contour map.

The curves from the four tested calibrations are given in Figure 10.


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20

Calibration 1: North Sea measured, K-Buoy & sate llite

verification data vs unadjusted NEXTRA

y = 3.8458e0.0887x

56

7

89

10

11

1213

14

1516

17

1819

20

21

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Unadjusted NEXTRA Hs100(m)

Verificatio

nHs100(m)

Calibration 2: North Sea measured & K-Buoy verification data vs

unadjusted NEXTRA

y = 3.6063e0.0942x

56

7

89

10

111213

1415

16

1718

19

2021

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Unadjusted NEXTRA Hs100(m)

Verificatio

nHs100(m)

Calibration 3: North Sea measured & satellite areas 1-4

verification data v s unadjusted NEXTRA

y = 3.5709e0.0975x

56

7

89

10

11

121314

15

1617

1819

20

21

6 7 8 9 10 11 12 13 14 15 16 17 18 19Unadjusted NEXTRA Hs100(m)

Ve

rificationHs100(m)

Calibration 4: North Sea measured verification data vs

unadjusted NEXTRA

y = 3.1153e0.1073x

56

7

89

10

11

121314

15

1617

1819

20

21

6 7 8 9 10 11 12 13 14 15 16 17 18 19Unadjusted NEXTRA Hs100(m)

Ve

rificationHs100(m)

Figure 10: Tested calibrations for adjusting NEXTRA Hs100Note differing axis scales

5.3 RESULTS OF THE CALIBRATION EXERCISE

5.3.1 Calibration Selection

To assess their individual merits, the four potential calibrations were applied to a range of wave

heights between 5m and 18m, and the calibrated values plotted against their unadjusted

counterparts (Figure 11). The adjusted wave heights are given in Table 7.

COMPARISON OF TESTED NEXTRA Hs100CALIBRATIONS

6

7

8

9

10

11

12

13

14

1516

17

18

19

20

21

22

7 8 9 10 11 12 13 14 15 16 17 18 19

Unadjusted wave height (m)

Adjustedwavehe

ight(m)

Cal 1: North Sea measured, Atlantic K-Buoy & all satellite

Cal 2: North Sea measured & Atlantic K-Buoy

Cal 3: North Sea measured & satellite areas 1-4

Cal 4: North Sea measured only

Figure 11: Comparison of the potential NEXTRA Hs100calibrations


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Table 7:Adjustment of wave heights by application of the four calibrations

Adjusted Wave Height (m)

Calibration 1 Calibration 2 Calibration 3 Calibration 4Unadjusted

Wave

Height (m)

North Sea measured

K-BuoysSatellite areas 1-12

North Sea measured

K Buoys

North Sea measured

Satellite areas 1-4 North Sea measured

8 7.8 7.7 7.8 7.410 9.3 9.3 9.5 9.112 11.1 11.2 11.5 11.314 13.3 13.5 14.0 14.016 15.9 16.3 17.0 17.318 19.0 19.7 20.7 21.5

Examination of Figure 11 and the data in Table 7 shows that:

! Calibrations 1, 2 and 3 gave comparable results up to a wave height of 13m. Wave heights

in the lower classes were adjusted downwards more by calibration 4.

! For wave heights above 12m, calibrations 1 and 2 provided less upwards adjustment than

calibrations 3 and 4.

! Calibrations 3 and 4 maintained the unadjusted 14m wave height requirement.

! Inclusion of the satellite data in the calibration had the effect of narrowing the range of

adjusted wave heights.

To assist the calibration selection, the 373 NEXTRA Hs100 values were adjusted with each of

the calibrations, gridded using the Kriging technique and compared to the verification data

(Figure 12). For the platform measurements the closest gridded Hs100 to each was extractedfrom the grids; for comparison with the satellite extreme values the Hs100of all grid nodes in a

satellite area were averaged to give a single representative extreme wave height for that area.

In Figure 12, data lying above the 1:1 reference line indicates that the calibration and gridding

processes have resulted in adjusted extreme values higher than the verification data, and hence

would incorporate an element of conservatism in the final mapped wave heights.


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GRIDDED, ADJUSTED NEXTRA Hs100/ VERIFICATION

CALIBRATION 1

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Verification Hs100(m)

GridHs100(m)


CALIBRATION 2

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Verification Hs100 (m)

GridHs100(

m)


CALIBRATION 3

6

7

8

9

10

11

12

13

14

1516

17

18

1920

21

22

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22


GridHs100(

m)


CALIBRATION 4

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22


GridHs100(

m)

Figure 12: Grid values of NEXTRA Hs100(m) adjusted with the four calibrations andplotted against corresponding verification extreme values

From Figure 12:

! Calibrations 1 and 2 were rejected on the grounds that there was insufficient margin for

conservatism in the mapped wave heights in the Central North Sea, Northern North Sea

and Atlantic regions.

! Calibration 4 was rejected on the grounds that the mapped wave heights in the Faroe-

Shetland Channel and Atlantic regions were excessively high in relation to the verification

data.

! Calibration 3 (North Sea measurements and satellite areas 1-4) was thus the preferred

option, and the NEXTRA extreme values were accordingly adjusted by:

Adjusted Hs = 3.5709e0.0975[NEXTRA Hs]

Contours of adjusted Hs100 are shown in Figure 13. The individual (adjusted) extreme values

upon which the map is based are also shown.


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Figure 13: Contours of adjusted NEXTRA Hs100(m)

5.3.2 Comparison of Adjusted Hs100with Established Criteria

As evidenced in Figure 14, the adjusted NEXTRA Hs100data agree well with established design

values throughout the region, with the majority of NEXTRA data lying close to or slightly

above the 1:1 reference.

NEXTRA Hs100 adjusted withcalibration 3

Kriging gridding Grid resnx = 50, y =33 Grid low pass filtered andspline

smoothed


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GRIDDED, ADJUSTED NEXTRA Hs 100/ ESTABLISHED CRITERIA -

CALIBRATION 3

6

7

8

9

10

11

12

13

14

1516

17

18

19

20

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Established 100 year criteria (m)

GridHs100(m)

`

Figure 14:Adjusted NEXTRA Hs100(m) compared to

established 100 year design criteria

There is some scatter in the lower wave height classes, which represent the Southern North Sea

and Liverpool Bay areas, but this is to be expected given the complications in the modelling

process afforded by the shallow and variable bathymetry. Notwithstanding the two obvious

outliers the grid values are typically within 10% of the established criteria.

5.3.3 Comparison with OT 2001/010 50 Year Wave Map

Contours of 50 year wave heights from the map published in OT 2001/0103 (see Section 1 for

details) were digitised, such that they could be compared to equivalent contours from NEXTRA.

Examination of the ratios of Hs50 to Hs100 from the 373 unadjusted NEXTRA grid points

showed that the relationship was linear (Figure 15):

NEXTRA Hs 100 /NEXTRA Hs 50

y = 0.96x - 0.04

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

NEXTRA Hs 100(m)

NEXTRA

Hs50(m)

Figure 15: Relationship between NEXTRA Hs50and Hs100(m)

3

BOMEL Limited, 2002. OT 2001/010 Environmental Considerations. Prepared for the Health and Safety Executiveby HSE Books. Published by HMSO. ISBN 0 7176 2379 3


34/38


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26

NEXTRA Hs 50/ OT 2001/010 Hs 50

6

7

8

9

10

11

12

13

14

15

1617

18

19

20

21

50.0N,14.0W

55.0N,11.0W

60.0N,10.0W

61.0N,2.0E

58.0N,1.0E

57.5N,4.0E

56.5N,5.0E

56.0N,4.0E

56.0N,7.0E

55.5N,0.0E

54.5N,1.0E

53.5N,4.0E

51.5N,2.0E

Hs(m)

50

55

60

65

70

75

80

85

90

95

100105

110

115

120

125

%

OT 2001/010

NEXTRA

NEXTRA as % of OT

Figure 17: Comparison of OT 2001/010 and NEXTRA Hs50grid values (m)

Table 8: Tabulated comparison from Figure 17

Area Lat Long50yr Hs

(m)*

NEXTRA

50yr Hs (m)

NEXTRA as

% of OT

50.0N 14.0W 17.4 18.6 107

55.0N 11.0W 17.9 20.2 113Atlantic

60.0N 10.0W 18.9 19.9 105

61.0N 2.0E 16 15.0 94

58.0N 1.0E 14 13.2 95Northern

North Sea57.5N 4.0E 14 14.0 100

56.5N 5.0E 12 13.2 110

56.0N 4.0E 12 12.8 107

56.0N 7.0E 10 12.0 120

Central

North Sea

55.5N 0.0E 12 9.7 81

54.5N 1.0E 10 9.9 99

53.5N 4.0E 10 10.0 100Southern

North Sea51.5N 2.0E 8 6.7 84

* Values extracted from OT 2001/0104and are the only public domain values

4

BOMEL Limited, 2002. OT 2001/010 Environmental Considerations. Prepared for the Health and Safety Executiveby HSE Books. Published by HMSO. ISBN 0 7176 2379 3.


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! The difference in contour positioning between the two maps varies spatially, with the

largest differences occurring in the Central North Sea.

! Differences in the North Sea arise because:

1. The OT 2001/010 contours predict a much steeper wave height gradient on the

western side.

2. The OT 2001/010 contours imply greater energy in the southern and Northern

North Sea areas.


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6. THE FINAL MAP OF 100 YEAR Hs

Adjustment of the NEXTRA extreme values using a calibration based on North Sea data only

has been shown to be the most appropriate approach. However, there remains concern that the

Hs100 contours off the continental shelf west of the UK are inadequately verified, since theadjustment here is based on an extrapolation of the calibration curve beyond the range of the

North Sea data. The large wave heights in this area (shown Figure 13) are a result of adjusting

the NEXTRA data such that conditions in the Faroe-Shetland Channel and Northern North Sea

oil fields are adequately represented.

It is thus considered that the Hs100 contours of more than 18m are unreliable and for the final

wave map they have therefore been replaced by a clearly marked area labelled >18m. The

final 100 year contour map is presented in Figure 18.

Figure 18:Hs100(m) the final contour map

Important note: the information displayed on this map is intended to provide guidance and should not be treated as a

substitute for site specific study.

Published by the Health and Safety Executive 05/08


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Wave mapping in UK watersSupporting document

Health and Safety

Executive

This work updates the contour map of 50-year extreme

significant wave height that is provided in OT 2001/010

(previously Section 11 of the Guidance Notes). The

updated map, now presented for the 100 year return

period, presents extreme significant wave height in UK

waters derived from 373 data sets from the NEXTRA

hindcast, calibrated against measured wave data andverified against established criteria.

This report and the work it describes were funded by the

Health and Safety Executive (HSE). Its contents, includingany opinions and/or conclusions expressed, are those

of the authors alone and do not necessarily reflect HSE

policy.

Documents

RR621 - Wave Mapping in UK Waters