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
Sat area 2 Average 13.2 14.4 N/A 109
Sat area 3 Average 10.8 10.6 N/A 98
NorthSea
Sat area 4 Average 8.5 8.6 N/A 101
Sat area 5 Average 8.0 9.7 N/A 121
Sat area 6 Average 14.4 15.4 N/A 107
Sat area 7 Average 12.3 14.7 N/A 119OtherUK
Waters
Sat area 12 Average 15.4 16.1 N/A 104
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 8 Average 17.1 17.7 N/A 100
Sat area 9 Average 18.3 17.9 N/A 98
Sat area 10 Average 19.3 18.3 N/A 95AtlanticOcean
Sat area 11 Average 19.7 17.9 N/A 91
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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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)
GRIDDED, ADJUSTED NEXTRA Hs100/ VERIFICATION
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)
GRIDDED, ADJUSTED NEXTRA Hs100/ VERIFICATION
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
Verification Hs100(m)
GridHs100(
m)
GRIDDED, ADJUSTED NEXTRA Hs100/ VERIFICATION
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
Verification Hs100(m)
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
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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.