TY - JOUR

T1 - Joint modeling of wave spectral parameters for extreme sea states

AU - Jonathan, P.

AU - Flynn, J.

AU - Ewans, K.

PY - 2010

Y1 - 2010

N2 - Characterising the dependence between extremes of wave spectral parameters such as significant wave height (HS) and spectral peak period (TP) is important in understanding extreme ocean environments and in the design and assessment of marine structures. For example, it is known that mean values of wave periods tend to increase with increasing storm intensity. Here we seek to characterise joint dependence in a straightforward manner, accessible to the ocean engineering community, using a statistically sound approach. Many methods of multivariate extreme value analyses are based on models which assume implicitly that in some joint tail region each parameter is either independent of or asymptotically dependent on other parameters; yet in reality the dependence structure in general is neither of these. The underpinning assumption of multivariate regular variation restricts these methods to estimation of joint regions in which all parameters are extreme; but regions where only a subset of parameters are extreme can be equally important for design. The conditional approach of Heffernan and Tawn (2004), similar in spirit to that of Haver (1985) but with better theoretical foundation, overcomes these dificulties. We use the conditional approach to characterise the dependence structure of HS and TP. The key elements of the procedure are: (1) marginal modelling for all parameters, (2) transformation of data to a common standard Gumbel marginal form, (3) modelling dependence between data for extremes of pairs of parameters using a form of regression, (4) simulation of long return periods to estimate joint extremes. We demonstrate the approach in application to measured and hindcast data from the Northern North Sea, the Gulf of Mexico and the North West Shelf of Australia. We also illustrate the use of data re-sampling techniques such as bootstrapping to estimate the uncertainty in marginal and dependence models and accommodate this uncertainty in extreme quantile estimation. We discuss the current approach in the context of other approaches to multivariate extreme value estimation popular in the ocean engineering community. © 2010 Elsevier Ltd. All rights reserved.

AB - Characterising the dependence between extremes of wave spectral parameters such as significant wave height (HS) and spectral peak period (TP) is important in understanding extreme ocean environments and in the design and assessment of marine structures. For example, it is known that mean values of wave periods tend to increase with increasing storm intensity. Here we seek to characterise joint dependence in a straightforward manner, accessible to the ocean engineering community, using a statistically sound approach. Many methods of multivariate extreme value analyses are based on models which assume implicitly that in some joint tail region each parameter is either independent of or asymptotically dependent on other parameters; yet in reality the dependence structure in general is neither of these. The underpinning assumption of multivariate regular variation restricts these methods to estimation of joint regions in which all parameters are extreme; but regions where only a subset of parameters are extreme can be equally important for design. The conditional approach of Heffernan and Tawn (2004), similar in spirit to that of Haver (1985) but with better theoretical foundation, overcomes these dificulties. We use the conditional approach to characterise the dependence structure of HS and TP. The key elements of the procedure are: (1) marginal modelling for all parameters, (2) transformation of data to a common standard Gumbel marginal form, (3) modelling dependence between data for extremes of pairs of parameters using a form of regression, (4) simulation of long return periods to estimate joint extremes. We demonstrate the approach in application to measured and hindcast data from the Northern North Sea, the Gulf of Mexico and the North West Shelf of Australia. We also illustrate the use of data re-sampling techniques such as bootstrapping to estimate the uncertainty in marginal and dependence models and accommodate this uncertainty in extreme quantile estimation. We discuss the current approach in the context of other approaches to multivariate extreme value estimation popular in the ocean engineering community. © 2010 Elsevier Ltd. All rights reserved.

KW - Extreme valueanalysis

KW - Generalised

KW - Joint extremes

KW - Pareto

KW - Hydraulic structures

KW - Metadata

KW - Ocean currents

KW - Ocean engineering

KW - Offshore structures

KW - Uncertainty analysis

KW - Engineering community

KW - North west shelf of australia

KW - Significant wave height

KW - Theoretical foundations

KW - Wave spectral parameters

KW - Structural design

KW - bootstrapping

KW - design

KW - multivariate analysis

KW - offshore structure

KW - regression analysis

KW - sea state

KW - spectral analysis

KW - wave height

KW - wave modeling

KW - wave-structure interaction

KW - Atlantic Ocean

KW - Australia

KW - Gulf of Mexico

KW - North Sea

U2 - 10.1016/j.oceaneng.2010.04.004

DO - 10.1016/j.oceaneng.2010.04.004

M3 - Journal article

VL - 37

SP - 1070

EP - 1080

JO - Ocean Engineering

JF - Ocean Engineering

SN - 0029-8018

IS - 11-12

ER -