TY - JOUR

T1 - Efficient estimation of return value distributions from non-stationary marginal extreme value models using Bayesian inference

AU - Ross, E.

AU - Randell, D.

AU - Ewans, K.

AU - Feld, G.

AU - Jonathan, P.

PY - 2017/9/15

Y1 - 2017/9/15

N2 - Extreme values of an environmental response can be estimated by fitting the generalised Pareto distribution to a sample of exceedances of a high threshold. In oceanographic applications to responses such as ocean storm severity, threshold and model parameters are typically functions of physical covariates. A fundamental difficulty is selection or estimation of an appropriate threshold or interval of thresholds, of particular concern since inferences for return values vary with threshold choice. Historical studies suggest that evidence for threshold selection is weak in typical samples. Hence, following Randell et al. (2016), a piecewise gamma-generalised Pareto model for a sample of storm peak significant wave height, non-stationary with respect to storm directional and seasonal covariates, is estimated here using Bayesian inference. Quantile regression (for a fixed quantile threshold probability) is used to partition the sample prior to independent gamma (body) and generalised Pareto (tail) estimation. An ensemble of independent models, each member of which corresponds to a choice of quantile probability from a wide interval of quantile threshold probabilities, is estimated. Diagnostic tools are then used to select an interval of quantile threshold probabilities corresponding to reasonable model performance, for subsequent inference of extreme quantiles incorporating threshold uncertainty. The estimated posterior predictive return value distribution (for a long return period of the order of 10,000 years) is a particularly useful diagnostic tool for threshold selection, since this return value is a key deliverable in metocean design. Estimating the distribution using Monte Carlo simulation becomes computationally demanding as return period increases. We present an alternative numerical integration scheme, the computation time for which is effectively independent of return period, dramatically improving computational efficiency for longer return periods. The methodology is illustrated in application to storm peak and sea state significant wave height at a South China Sea location, subject to monsoon conditions, showing directional and seasonal variability.

AB - Extreme values of an environmental response can be estimated by fitting the generalised Pareto distribution to a sample of exceedances of a high threshold. In oceanographic applications to responses such as ocean storm severity, threshold and model parameters are typically functions of physical covariates. A fundamental difficulty is selection or estimation of an appropriate threshold or interval of thresholds, of particular concern since inferences for return values vary with threshold choice. Historical studies suggest that evidence for threshold selection is weak in typical samples. Hence, following Randell et al. (2016), a piecewise gamma-generalised Pareto model for a sample of storm peak significant wave height, non-stationary with respect to storm directional and seasonal covariates, is estimated here using Bayesian inference. Quantile regression (for a fixed quantile threshold probability) is used to partition the sample prior to independent gamma (body) and generalised Pareto (tail) estimation. An ensemble of independent models, each member of which corresponds to a choice of quantile probability from a wide interval of quantile threshold probabilities, is estimated. Diagnostic tools are then used to select an interval of quantile threshold probabilities corresponding to reasonable model performance, for subsequent inference of extreme quantiles incorporating threshold uncertainty. The estimated posterior predictive return value distribution (for a long return period of the order of 10,000 years) is a particularly useful diagnostic tool for threshold selection, since this return value is a key deliverable in metocean design. Estimating the distribution using Monte Carlo simulation becomes computationally demanding as return period increases. We present an alternative numerical integration scheme, the computation time for which is effectively independent of return period, dramatically improving computational efficiency for longer return periods. The methodology is illustrated in application to storm peak and sea state significant wave height at a South China Sea location, subject to monsoon conditions, showing directional and seasonal variability.

KW - Bayesian inference

KW - Extreme

KW - Non-stationary

KW - Numerical integration

KW - Return value

KW - Significant wave height

KW - Splines

KW - Aluminum alloys

KW - Bayesian networks

KW - Computational efficiency

KW - Diagnostic products

KW - Inference engines

KW - Integration

KW - Marine applications

KW - Monte Carlo methods

KW - Ocean currents

KW - Pareto principle

KW - Storms

KW - Water waves

KW - Nonstationary

KW - Numerical integrations

KW - Probability

KW - Bayesian analysis

KW - ensemble forecasting

KW - estimation method

KW - numerical model

KW - probability

KW - regression analysis

KW - return period

KW - significant wave height

KW - threshold

KW - Pacific Ocean

KW - South China Sea

U2 - 10.1016/j.oceaneng.2017.06.059

DO - 10.1016/j.oceaneng.2017.06.059

M3 - Journal article

VL - 142

SP - 315

EP - 328

JO - Ocean Engineering

JF - Ocean Engineering

SN - 0029-8018

ER -