Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering
OMAE2011
June 19-24, 2011, Rotterdam, The Netherlands
OMAE2011-49
SQUALL RESPONSE BASED DESIGN OF FLOATING UNITS IN WEST AFRICA
Juan Alvarez
Bureau Veritas
Neuilly Sur Seine, France
Pierre Orsero
UTC
Compiegne, France
Valerie Quiniou-Ramus
TOTAL
Paris, France
Michel François
Formerly Bureau Veritas
Neuilly Sur Seine, France
Anne-Gaëlle Moysan
TOTAL
Paris, France
Didier l’Hostis
TOTAL
Paris, France
ABSTRACT
Squalls are one of the main issues for the design of
West Africa floating units mooring systems. At the present time
and due to the lack of more relevant information and models,
squalls are represented by on site time series of time varying
wind speed and relative heading. The first FPSO units were
designed on the basis of a reduced Squall database. Nowadays,
the number of squall records has been significantly increased
and a response based analysis can be carried out.
The present paper is focused on the Gulf of Guinea
environment. The area has been divided into two zones: North
(Nigeria…) and South (Congo, Angola…). This approach
enabled us to deal with 90 Squall events for North zone and 115
Squall events for South zone.
Two different mooring systems, with quite different natural
periods, have been investigated in order to cover the range of
already installed spread moored FPSO’s. For every Squall of
the database, time domain and modal simulations have been
carried out in order to obtain the maximum values of the axial
tension in mooring lines and of the offset of a standard spread
moored unit. Then a statistical procedure is applied a) to
estimate 100-year return period values for these parameters and
b) to assess overall trends besides the differences between
results from both zones and both mooring systems.
Alain Ledoux
TOTAL
Paris, France
classical design procedures in order to evaluate the potential
design margins for extreme responses. Finally, areas needing
further investigation are identified.
INTRODUCTION
In West African waters, squalls cause strong and
sudden winds. Although major progress has been made in the
past few years for describing squall winds, there are still many
uncertainties in calculating their effects on the mooring system
of floating structures, and the lack of design guidelines leads to
time consuming and costly engineering work without a clear
understanding of safety level reached.
The present study was initiated with the objective to define
“Response-Based Design” (RBD) methodologies for the
analysis of mooring systems under squall conditions that could
be applicable to different types of systems, such as spread and
turret moored FPSO’s, or buoy moored tankers. The final
objectives of the project are:
a) To provide the designers with methodologies to design
mooring systems for squall winds, that are suitable for both
early design stages (quick and conservative approach) and
detailed design (accurate assessment of system response)
b) To understand the level of conservatism behind each
methodology.
A comparative study has also been carried out to relate the 100year return period extrapolations with the values derived from
1
Copyright © 2011 by ASME
BACKGROUND
Analysis of wind measurements offshore West Africa
clearly highlights the presence of two wind velocity
populations, differing in intensity, direction stability and
frequency. The normal wind regime is dominated by persistent
southerly trade winds, driven by large-scale atmospheric
pressure systems, and blowing predominately from the southsouthwest.
Extreme winds are caused by squall events. Squalls are
associated with the leading edge of multi-cell thunderstorms,
generated on land, which tend to form along lines separating air
masses and which usually travel westward over the sea. The
squall seasonality is linked to passages of the inter-tropical
convergence zone (ITCZ) on the way north in northern
hemisphere spring then again on the way south in the northern
hemisphere autumn.
Squalls trigger a sudden and large increase of wind speeds (a
squall event usually lasts less than an hour at one given
location), with often (but not always) large variations even a
full reversal, of wind direction.
In-situ wind measurements were analysed during Phase 1 of the
West Africa Gust Joint Industry Project (WAG JIP, [1]), using
more than four years of blended wind records at various fields
operated by Oil Companies (Chevron, ExxonMobil, Shell,
Statoil, Total, Woodside). This work gave very useful insight to
a number of aspects, such as :
• Physics of phenomenon,
• Criteria for squall event identification from records,
• Geographical, seasonal and diurnal variability,
• Directional distribution,
• Extreme values,
• Gust Factors.
WAG Phase 1 was extremely beneficial to JIP participants, who
could significantly improve the reliability of their met-ocean
design criteria.
Knowledge of the squall physical phenomenon was also
developed thanks to Phase 3 of the WAG JIP [3], [4]: in-situ
measurements with a vertical and horizontal array of
anemometers were conducted on Total E&P Congo platform
“Likouala” for two years. This provided information about the
spatial distribution and coherence of squall winds, and thus
gave an insight about how squalls apply on large structures
such as Floating Production Storage and Offloading vessels
(FPSO).
design condition for some deepwater FPSO mooring systems,
although to date no failure has been observed in reality.
Therefore, it is of upmost importance to understand the level of
conservatism behind the current design methodology and
alternatives that are proposed in the present paper.
DATA PRESENTATION
To reach the present objectives, the authors have made
use of in-situ wind records acquired by TOTAL S.A. in the
frame of the WAG JIP, or by TOTAL affiliates, in particular
Total Upstream Nigeria, Total E&P Angola and Total E&P
Congo.
WAG Phase 1
From the WAG1 JIP [1], TOTAL, as the Operator of
fields offshore Nigeria, Congo and Angola, had supplied time
series of wind recorded in these three regions, see Table 1.
Site
Elevation
of sensor
Start
End
Nigeria
84m
03/04/2003
09/03/2004
2s
17
Congo
30m
01/01/1997
31/10/1998
5s
13
Angola
60m
27/05/2002
12/01/2004
1s
4
Sample Intervals
Events
Table 1: WAG1 data sets
WAG Phase 3
From WAG3 [3] [4] , TOTAL as a JIP partner has
access to the global database, see Table 2 .
Site
Elevation of sensor
Start
End
Sample Intervals
Events
Congo
10m->38m
01/12/2006
01/05/2007
3s
41
Congo
10m->38m
01/12/2007
01/05/2008
3s
25
Table 2: WAG3 data sets
TOTAL own database
TOTAL has also access to operational data in order to
build their own database and to improve their understanding of
Squall phenomena. Those continuous operational records were
taken on floating units offshore Congo, Angola and Nigeria, see
Table 3 .
Site
Elevation of sensor
Start
End
Sample Intervals
Events
CONGO
51m
28/05/2008
31/03/2009
120s
12
ANGOLA
60m
01/01/2007
31/03/2009
60s
31
NIGERIA
50m
19/02/2008
21/03/2009
60s
73
Table 3: Total database units
Although major progress has been achieved during the past few
years with describing squall physical properties, there are still
many uncertainties when it comes to calculating their effects on
floating structures. It turns out (see e.g. [2]) that squalls are the
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Copyright © 2011 by ASME
Data preparation
Two subsets have been built from the available data.
One subset called North of Gulf of Guinea was based on
records from offshore Nigeria; the other, called South of Gulf
of Guinea, was based on records from offshore Congo+Angola.
Following further data quality control and preparation, which is
not detailed here but which includes sensor height correction to
a common height of 10 meters, the resulting two subsets
included respectively 90 and 115 squall events for a cumulated
duration of approximately 2 and 6.5 years. An example time
series is given in Figure 1 in which is represented in blue the
one minute mean wind speed (u1MIN), in red the one minute
mean direction (θ1MIN), in dot blue the maximum three second
gust each minute (U3SEC:1MIN).
units, where spread moored FPSO’s used to be aligned with
primary Swell. The mooring pattern is illustrated in Figure 2.
The aim of the present work is to analyze the effect of winds,
thus wind forces coefficients are necessary for the study.
Current force coefficients have also been added in the model in
order to account for damping due to the relative motions
between the floater and water. Wind force coefficients and
current force coefficients have been deduced from those of
installed units. They are shown for illustration in Figure 3 and
Figure 4.
700.0
A1
A16
A2
A15
A3
A14
A4
A13
P7P8
P6
P5
S8
S7
S6
S5
N
C
F16
F15
F14
F13
F1
F2
F3
F4
Point
E
F12
F11
F10
F9
F5
F6
F7
F8
P4
P3
P2
P1
S4
S3
S1S2
A5
A12
A6
A11
A7
A10
A8
A9
Figure 2: Mooring pattern
Wind Force Coefficient [kNs²/m²]
Last but not least, extreme wind speeds were calculated in a
compatible method as in WAG1.
SQUALL RESPONSE BASE APPROACH
For the Gulf of Guinea environment, the response of a
typical FPSO has been analyzed. The following methodology
has been applied:
a) Building of a numerical model to represent the floater
configuration,
b) Computing the response of the model under each squall
event of the data base and then extrapolating the response
to extremes (values at return periods of interest for the
evaluation of the system) ,
c) Comparison between RBD results and other
methodologies.
Numerical Model
A typical 2 million barrel spread moored FPSO has
been considered. The mooring system of the unit is composed
of 16 lines (4 bundles of 4 lines). The heading of the vessel has
been set to 22.5° which is a common value for West Africa
Wind Moment Coefficient [kNms²/m²]
Figure 1: Example time series of wind speed and direction
during a squall event
0
30
60
90
120
150
180
Incidence w.r.t FPSO [Degrees]
Longitudinal Force
Transversal Force
Moment
Figure 3: Wind force coefficients
Wind/current force coefficients are commonly derived from
wind tunnel tests. During the wind tunnel tests, the wind loads
on the above-water portion of the FPSO are determined in a
boundary-layer wind profile. Commonly the wind profile is
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Copyright © 2011 by ASME
represented by a logarithmic profile (NPD or API profile), but
from recent results (WAG1 JIP or WAG3 JIP) it has been found
that squall vertical profile does not match with these
representations and is more slab-like.
Wind tunnel facility could generate such profile as they do
when performing test for current loading however to our
knowledge it has not been yet performed and related problems
such as boundary layer thickness and blockage correction
should be addressed.
0
30
60
90
120
150
Current Moment Coefficient [kNms²/m²]
Current Force Coefficient [kNs²/m²]
Another source of possible inaccuracy in the evaluation of wind
loads, which not further investigated in the present study, is the
use of tunnel mean force coefficients to calculate the time
varying load from the instantaneous wind speed.
180
domain simulation under environment, including first and
second order effects. But in the present case, as waves are not
considered, hydrodynamic loads are reduced to added mass.
From the line point of view, the quasi-dynamic analysis takes
into account:
• the displacement of the upper end of the mooring line
due to the floater low frequency and wave frequency
motions,
• the weight and the buoyancy of the mooring line
components,
• the elasticity of the mooring line components.
The quasi dynamic analysis includes all the floater dynamic
effects such as inertia, low frequency wind, except the dynamic
of the line itself.
Response based design (RBD)
For each squall event of the database a time domain
calculation has been carried out to extract the maximum axial
line tension and the maximum offset amidships. Results of
maximum tension in the most loaded line versus maximum
offset are shown in:
• Figure 5 for a water depth of 800m.
• Figure 6 for a water depth of 1300m.
Each cross or circle in Figure 5 and Figure 6 represent the
results of one squall from the data base.
3000
Longitudinal Force
Transversal Force
Maximum axial tension [kN]
Incidence w.r.t FPSO [Degrees]
Moment
Figure 4: Current force coefficients
The 4x4 spread mooring system consists of the following
segments, from anchor to fairlead:
• 600m of 132mm studless chain,
• 102 mm Sheathed spiral strand wire rope (the length
has been adjusted according to the water depth – see
below),
• 100m of 132mm studless chain.
1500
0
Two different water depths have been considered for the
numerical modeling: 1300m and 800m.
Due to that, two systems with quite different natural periods are
obtained:
• Around 400s in surge and sway for the water depth of
1300m
• Around 200s in surge and sway for the water depth of
800m
These natural periods are in accordance with already installed
FPSO’s of similar characteristics.
The response of the squall will be obtained by a quasi-dynamic
time domain calculation. The quasi-dynamic analysis is a time
25
Maximum offset [m]
NORTH ZONE
SOUTH ZONE
Figure 5: Water depth 800m
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Water depth=1300m
3000
Maximum axial tension [kN]
RP
(years)
100
50
25
10
1
Offset
(m)
Water depth=800m
80
Maximum offset [m]
NORTH ZONE
SOUTH ZONE
RP
(years)
Offset
(m)
95% lower
value
(m)
95% upper
value
(m)
100
24
19
28
50
22
17
26
25
20
16
23
10
17
14
20
Figure 6: Water depth 1300m
Then, results from the direct simulation have been extrapolated
to obtain the extreme values at return periods of 100, 50, 25, 10
and 1 year (denoted RP100, RP50, RP25, RP10, and RP1 in
figures below).
1
For the extrapolation of offsets, the following hypotheses have
been made:
• a threshold has been defined at a return period of 0.1
year,
• a fit to a Gumbel function has been carried out.
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12
Table 5: Extreme values for SOUTH Zone
Water depth=1300m
RP
(years)
Offset
(m)
95% lower
value
(m)
95% upper
value
(m)
100
122
101
138
50
113
94
128
25
105
87
119
10
93
78
106
As the system is highly non linear for the tension parameter
(the non linearity is less evident for offsets), the tension
extrapolations will be deduced from the offset.
Extreme values, and the limits of a 95% confidence (obtained
by bootstrapping), are given in Table 4 to Table 7 for the offset
parameter.
It is observed that the responses (tension and offset) to the
squalls are significantly influenced by the mechanical system:
stiffness and natural periods, thus water depth.
Although it is not obvious to extract a trend for all the systems,
it appears that the NORTH zone is more severe than SOUTH
zone, which is a consistent result with the physics of squalls.
95% upper
value
(m)
71
54
85
66
51
79
61
47
73
54
43
64
38
32
43
Table 4: Extreme values for SOUTH Zone
1500
0
95% lower
value
(m)
1
65
55
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Table 6: Extreme values for NORTH Zone
Water depth=800m
RP
(years)
100
50
25
10
1
5
Offset
(m)
95% lower
value
(m)
95% upper
value
(m)
51
44
55
47
41
51
43
38
46
38
33
41
25
22
27
Table 7: Extreme values for NORTH Zone
Copyright © 2011 by ASME
Comparison between statistical extreme values from RBD
and other approaches
During the design of the first floating units in West
Africa the squalls were not a well documented phenomenon.
The squall events were not discriminated from the normal
wind, and the floating units were designed using a constant
wind or a spectral wind (typically a NPD spectrum).
Nowadays the common practice is to rescale the squalls time
series records so that the maximum wind speed matches the
value at a given return period. The response is then taken as the
maximum response over all the squall time series, or as the
MPM- or the expected value- of the distribution of response.
In the following those approaches will be compared to the
statistical extremes derived from the direct calculations.
Thus, the first step is to rescale each squall of the data base and
to calculate the induced response (tension and offset).
The rescaling has been done with target 1 minute maximum
wind velocity between 15 and 40m/s. An example of the results
obtained from the rescaling is presented in Figure 7 for:
• The axial tension parameter
• A water depth of 1300m
• SOUTH zone
Each line in Figure 7 represents the results for one rescaled
squall.
Thus, the values obtained at a given return period (100 years,
50 years, 25 years and 1 year) by the RBD approach have been
compared to values obtained by:
• rescaling
• constant wind
• spectral wind
for a one minute wind speed with the same return period.
For illustration, the results obtained for the offset parameter at
the NORTH zone in Figure 8 (water depth 800m) and Figure
9 (water depth of 1300m).
Due to the rather limited number of squall events it seemed
advisable, for the RBD results, to consider the upper value of
the 95% confidence interval.
Then, it can be observed that the maximum response obtained
by a rescaling procedure is always on the conservative side (i.e.
higher than the 95% confidence interval), whereas, at least for
the higher return periods in all cases, both the other rescaling
approaches and the sustained wind approaches are on the nonconservative side.
70
60
OFFSET [m]
Maximum axial tensionin most loaded line [kN]
50
40
30
20
10
0
1 minute wind speed at an elevation of 10m [m/s]
RP100
Figure 7: Results rescaling – Tension – Water depth =1300m –
SOUTH ZONE
RP50
RP25
RP10
RP1
MAXIMUM OVER ALL SQUALLS
RBD 95% CONFIDENCE INTERVAL
RBD
SPECTRAL WIND
EXPECTED
MPM
CONSTANT WIND
From the set of results at any given rescaling wind speed, the
following information could be extracted:
• The maximum response over all the database.
• The most probable value (“MPM”)
• The “EXPECTED” value (mean value of the
distribution).
Figure 8: NORTH ZONE - Water depth 800m
In order to complete the comparison the response of the floater
under constant wind and spectral wind has been calculated too.
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(the wind participation factor is defined as the ratio between the
wind force for a unit wind speed and the generalized mass of
the oscillator). Time response for a typical squall and maximum
value are shown on Figure 10.
160
140
120
OFFSET [m]
100
80
60
40
20
0
RP100
RP50
RP25
RP10
RP1
MAXIMUM OVER ALL SQUALLS
RBD 95% CONFIDENCE INTERVAL
RBD
SPECTRAL WIND
EXPECTED
MPM
CONSTANT WIND
Figure 9: NORTH ZONE - Water depth 1300m
SQUALL RESPONSE
OSCILLATOR
SPECTRUM
OF
LINEAR
Figure 10: Maximum offset and associated direction (red circle) and
normalized linear X – Y response (green line) for a typical squall and
for given values of the natural period and the damping percentage
(T = 300 s, ξ = 6%)
Squall Response Index
In order to quantify the squall severity and by analogy
with the pseudo-spectral acceleration in use in earthquake
engineering, a Squall Response Index has been defined as the
average value of the pseudo-acceleration associated with the
maximum normalized offset Rk (T , ξ ) over the period and
damping intervals:
In earthquake engineering, the concept of the response
spectrum has been used for many years as an effective way to
deal with random transient loadings induced by earthquakes
and to evaluate maximum seismic responses. By analogy with
the earthquake response spectra and for the Gulf of Guinea
environment, the squall time histories have been transformed
into Squall Response Spectra by a three-step approach:
a) Computation of the maximum offset values and their
associated directions as responses of parametric single
degree of freedom linear oscillators,
b) Evaluation of the squall severity by the Squall Response
Index as average value of the pseudo-acceleration,
c) Determination of the Squall Response Spectra by fitting
extreme-value distributions to the parametric values of
extreme response for a given return period.
Parametric Linear Response
For all squalls, {S k , k
= 1..n}, defined by their speed
2
 2π 
∫ ∫ Rk (T , ξ ). T  dTdξ
For a given squall {S k } , the value of the Squall Response Index
1
SRI k =
∆T .∆ξ
SRI k (see Figure 11) is compared with the maximum
normalized offset response
Rk (T , ξ ) as parametric function
of natural period T and damping percentage ξ.
The frequency content of the squall time signal is clearly
apparent on Figure 11 as it produces greater response of the
parametric linear oscillator.
The Squall Response Index has been computed for all squalls
recorded in the South and North zones of the Gulf of Guinea.
The results for the fifty most important squalls in the North and
South zones, are plotted in Figure 12 by decreasing severity,
showing a great dispersion and a ratio of 1 to 5.
Vk (t ) and direction Dk (t ) time histories and for all natural
periods T and damping percentages ξ defined within given
intervals, Txξ ∈ Tmin , Tmax x ξ min , ξ max , the maximum
[
offset
][
]
Rk (T , ξ ) and the associated direction Dk (T , ξ ) have
been computed as the maxima values of the time response for a
normalized linear oscillator characterized by its natural period
T, its damping percentage ξ and a unit wind participation factor
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Significant differences have been observed for the Squall
Response Spectra for the North and South zones of the Gulf of
Guinea in terms of the 100-year extreme offset for parametric
values of the natural period (see Figure 13 and Figure 14),
particularly within the natural period interval between 200 and
400 s. This observation could possibly be the result of
insufficient squall data for the North zone.
Figure 11: Parametric maximum offset depending upon natural period
T and three different values of the damping percentage ξ (red = 4%,
green = 6%, blue = 8%) and Squall Response Index (horizontal black
line, for a typical squall
Figure 13: NORTH ZONE / 100-year extreme value of the maximum
normalized offset R as function of period T and for three different
values of damping ξ (red = 4%, green = 6%, blue = 8%)
Figure 12: Distribution of the Squall Response Index for the fifty most
important squalls in the North and South zones of the Gulf of Guinea
Squall Response Spectrum
For any given FPSO modal data specified by its natural
period T, its modal damping percentage ξ, its generalized mass
M and wind participation factor w, the Squall Response Spectra
could be defined as the combination of the fitted probability
distributions for the 100-year extreme offset and its associated
direction :
• Extreme Value distribution for the parameterized
maximum offset R (T , ξ ) fitted to the offset values
Rk (T , ξ ) with a 0.1 threshold for the return period,
•
Circular von Mises distribution up to the 4th order for the
parameterized direction D (T , ξ ) fitted to the direction
values
values
Dk (T , ξ ) associated with the maximum offset
Rk (T , ξ )
Figure1 14: SOUTH ZONE / 100-year extreme value of the maximum
normalized offset R as function of period T and for three different
values of damping ξ (red = 4%, green = 6%, blue = 8%)
The offset direction distributions for the North and South zones
of the Gulf of Guinea have also significant differences in terms
of most probable directions for squall responses as exhibited on
Figure 15 and Figure 16 (polar plots of circular direction
distributions in geographic coordinates). However, these
distributions exhibit a greater stability in terms of sensitivity to
natural period and damping coefficient.
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Copyright © 2011 by ASME
conditions. This methodology seems to be promising for spread
moored units but requires further work. It could facilitate
access to reliable results during early design phase.
Figure 15: NORTH ZONE / von Mises circular distribution of the
offset direction for T=300s and for three different values of damping
ξ (red = 4%, green = 6%, blue = 8%)
For detailed design of spread moored units, the common
practice nowadays is to rescale the squalls and to consider
either the maximum response obtained from the worst squall
events or another value extracted from the set of responses.
It seems that considering for design the MPM or the expected
value of the distribution of response of the rescaled squalls is
not appropriate, as response obtained in such way is most often
lower than the extrapolation from RBD models.
On the other hand, it has been observed that applying the
rescaling methodology is a conservative approach if the
maximum of response is considered. The resulting
conservatism, when compared to the RBD extrapolations, is
acceptable and the results obtained are quite close. Thus it
seems reasonable to continue to design floating units with the
maximum response of the rescaled squalls, although it could be
optimized if required.
The present studies have been made with a spread moored
system in deep water. The case of a weathervaning system or
the case of a coastal unit (shallow water) could lead to different
results.
Additionally, despite the increased number of squall events
with respect to present metocean specification it should be
highlighted that this number is still too low to derive reliable
extreme values. Thus it seems advisable in the present study to
consider the upper bound of the 95% confidence interval of the
extrapolations. For further research an increased database is
needed in order to reduce the uncertainty in selecting the
extrapolation distribution and probably the confidence interval.
Figure 16: SOUTH ZONE / von Mises circular distribution of the
offset direction for T=300s and for three different values of damping
ξ (red = 4%, green = 6%, blue = 8%)
The Squall Response Spectra can then be used to determine an
approximation of the extreme squall response of a FPSO
represented by its surge and sway modes using a quadratic
modal combination technique but the detailed methodology is
not presented here and will be the subject of a future dedicated
paper about the Squall Spectral Response.
CONCLUSIONS
A response-based approach and a spectral approach have been
developed to assess the response of spread moored FPSO’s to
squalls in West Africa.
Using the squall response spectra, the response to squalls is
calculated once for all, independently and quickly – for any
system to obtain an order of magnitude of response to extreme
squalls, and its significance with respect to other design
Last, the way of accounting for the non-linearity of response in
statistical extrapolation and the validity of the wind coefficients
for this kind of application requires further work too.
NOMENCLATURE
RBD: Response-Based Design
RPX: X years return period
MPM: Most Probable Maximum.
ACKNOWLEDGMENTS
The authors wish to thank Bureau Veritas, UTC and
Total for permission to publish this paper. Special thanks are
addressed to Total Upstream Nigeria, Total E&P Angola and
Total E&P Congo for providing access to the in-situ squall
wind records. The views expressed are those of the authors, and
do not necessarily reflect those of Bureau Veritas, UTC and
Total.
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REFERENCES
[1] Fugro GEOS, 2004. West Africa Gust Joint Industry Project.
Phase 1 Final Report. C56110/3219/R1. Confidential.
[2] Legerstee, F., François, M., Morandini, C. and Le Guennec,
S. (2006). Squall: Nightmare for Designers of Deepwater West
African Mooring Systems. Proceedings of the 25th
International Conference on Offshore Mechanics and Arctic
Engineering, Hamburg, Germany, 4-9 June 2006. OMAE200692328
[3] Jeans, G., Redford, S., Bellamy, I. and Mundy, R., (2008).
The WAG Squall Measurement System. Proceedings of the
27th International Conference on Offshore Mechanics and
Arctic Engineering, Estoril, Portugal, 15-20 June 2008.
OMAE2008-57337.
[4] Jeans, G., and Johnson, R., (2011). The WAG platform
structural effects study. Proceedings of the 30th International
Conference on Offshore Mechanics and Arctic Engineering,
Rotterdam, The Netherlands, June 19-24, 2011. OMAE201150138
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