Understanding extreme ocean environments and their interaction with fixed and floating structures is critical for offshore and coastal design. Design contours are useful to describe the joint behavior of environmental, structural loading, and response variables. We compare different forms of design contours, using theory and simulation, and present a new method for joint estimation of contours of constant exceedance probability for a general set of variables. The method is based on a conditional extremes model from the statistics literature, motivated by asymptotic considerations. We simulate under the conditional extremes model to estimate contours of constant exceedance probability. We also use the estimated conditional extremes model to estimate other forms of design contours, including those based on the first-order reliability method (FORM), without needing to specify the functional forms of conditional dependence between variables. We demonstrate the application of new method in estimation of contours of constant exceedance probability using measured and hindcast data from the Northern North Sea, the Gulf of Mexico, and the North West Shelf of Australia, and quantify their uncertainties using a bootstrap analysis.

References

References
1.
Madsen
,
H. O.
,
Krenk
,
S.
, and
Lind
,
N. C.
,
1986
,
Methods of Structural Safety
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
2.
Winterstein
,
S. R.
,
Ude
,
T. C.
,
Cornell
,
C. A.
,
Bjerager
,
P.
, and
Haver
,
S.
,
1993
, “
Environmental Parameters for Extreme Response: Inverse Form With Omission Factors
,”
6th International Conference on Structural Safety and Reliability
, Innsbruck, Austria, August 9–13, pp. 551–557.
3.
Winterstein
,
S.
, and
Engebretsen
,
K.
,
1998
, “
Reliability-Based Prediction of Design Loads and Responses for Floating Ocean Structures
,”
27th International Conference on Offshore Mechanics and Arctic Engineering
, Lisbon, Portugal.
4.
Winterstein
,
S. R.
,
Jha
,
A. K.
, and
Kumar
,
S.
,
1999
, “
Reliability of Floating Structures: Extreme Response and Load Factor Design
,”
J. Waterw., Port, Coastal, Ocean Eng.
,
125
, pp.
163
169
.10.1061/(ASCE)0733-950X(1999)125:4(163)
5.
Nerzic
,
R.
,
Frelin
,
C.
,
Prevosto
,
M.
, and
Quiniou-Ramus
,
V.
,
2007
, “
Joint Distributions of Wind/Waves/Current in West Africa and Derivation of Multivariate Extreme I-FORM Contours
,”
16th International Offshore and Polar Engineering Conference
, Lisbon, Portugal.
6.
Jonathan
,
P.
,
Flynn
,
J.
, and
Ewans
,
K. C.
,
2010
, “
Joint Modeling of Wave Spectral Parameters for Extreme Sea States
,”
Ocean Eng.
,
37
, pp.
1070
1080
.10.1016/j.oceaneng.2010.04.004
7.
Heffernan
,
J. E.
, and
Tawn
,
J. A.
,
2004
, “
A Conditional Approach for Multivariate Extreme Values
,”
J. R. Stat. Soc. B
,
66
, pp.
497
546
.10.1111/j.1467-9868.2004.02050.x
8.
Haver
,
S.
, and
Nyhus
,
K.
,
1986
, “
A Wave Climate Description for Long Term Response Calculations
,”
5th International OMAE Symposium
, Tokyo, Vol.
4
, pp.
27
34
.
9.
Jonathan
,
P.
,
Ewans
,
K. C.
, and
Flynn
,
J.
,
2012
, “
Joint Modeling of Vertical Profiles of Large Ocean Currents
,”
Ocean Eng.
,
42
, pp.
195
204
.10.1016/j.oceaneng.2011.12.010
10.
Adhikari
,
S
.,
2005
, “
Asymptotic Distribution Method for Structural Reliability Analysis in High Dimensions
,”
Proc. R. Soc. A
,
461
, pp.
3141
3158
.10.1098/rspa.2005.1504
11.
Adhikari
,
S.
, and
Langley
,
R. S.
,
2002
, “
Reduction of Random Variables in Structural Reliability Analysis
,” 3rd International Conference on Mathematical Methods in Reliability Methodology and Practice, Trondheim, Norway, June 17–20.
12.
Nelsen
,
R. B.
,
1998
, “
An Introduction to Copulas (Lecture Notes in Statistics)
,”
Springer
, New York, p. 236.
13.
Feld
,
G.
,
Randell
,
D.
,
Wu
,
Y.
,
Ewans
,
K.
, and
Jonathan
,
P.
,
2014
, “
Estimation of Storm Peak and Intra-Storm Directional-Seasonal Design Conditions in the North Sea
,”
33rd International Conference on Ocean, Offshore, and Arctic Engineering
, San Francisco, CA, June 8–13.
14.
Tromans
,
P. S.
, and
Vanderschuren
,
L.
,
1995
, “
Risk Based Design Conditions in the North Sea: Application of a New Method
,”
Offshore Technology Conference
, (OTC 7683), Houston, TX.
15.
Ewans
,
K. C.
, and
Jonathan
,
P.
,
2014
, “
Evaluating Environmental Joint Extremes for the Offshore Industry
,”
J. Mar. Syst.
,
130
, pp.
124
130
.10.1016/j.jmarsys.2013.03.007
16.
Jonathan
,
P.
,
Ewans
,
K. C.
, and
Randell
,
D.
,
2013
, “
Joint Modeling of Environmental Parameters for Extreme Sea States Incorporating Covariate Effects
,”
Coastal Eng.
,
79
, pp.
22
31
.10.1016/j.coastaleng.2013.04.005
17.
Jonathan
,
P.
,
Ewans
,
K. C.
, and
Randell
,
D.
,
2014
, “
Non-Stationary Conditional Extremes of Northern North Sea Storm Characteristics
,”
Environmetrics
,
25
, pp.
172
188
.10.1002/env.2262
18.
Keef
,
C.
,
Papastathopoulos
,
I.
, and
Tawn
,
J. A.
,
2013
, “
Estimation of the Conditional Distribution of a Vector Variable Given That One of its Components is Large: Additional Constraints for the Heffernan and Tawn Model
,”
J. Multivar. Anal.
,
115
, pp.
396
404
.10.1016/j.jmva.2012.10.012
19.
Gilleland
,
E.
,
Brown
,
B. G.
, and
Ammann
,
C. M.
,
2013
, “
Spatial Extreme Value Analysis to Project Extremes of Large-Scale Indicators for Severe Weather
,”
Environmetrics
,
24
, pp.
418
432
.
20.
Cheng
,
L.
,
Gilleland
,
E.
,
Heaton
,
M. J.
, and
AghaKouchak
,
A.
,
2013
, “
Empirical Bayes Estimation for the Conditional Extreme Value Model
,” http://www.rap.ucar.edu/staff/ericg/ChengEtAl2014.pdf
You do not currently have access to this content.