Distributions of return values for ocean wave characteristics in the South China Sea using directional–seasonal extreme value analysis

Abstract

Estimation of ocean environmental return values is critical to the safety and reliability of marine and coastal structures. For ocean waves and storm severity, return values are typically estimated by extreme value analysis of time series of measured or hindcast sea state significant wave height H S . For a single location, this analysis is complicated by the serial dependence of H S in time and its non-stationarity with respect to multiple covariates, particularly direction and season. Here, we report a non-stationary extreme value analysis of storm peak significant wave height H sp S , assumed temporally independent given covariates, incorporating directional and seasonal effects using a spline-based methodology incorporating an ensemble of models for different extreme value thresholds. Quantile regression is used to estimate suitable thresholds. For each threshold, a Poisson process is used to estimate the rate of occurrence of threshold exceedances, and a generalised Pareto model characterises the magnitude of threshold exceedances. Covariate effects are incorporated at each stage using penalised tensor products of B-splines to give smooth model parameter variation as a function of covariates. Optimal smoothing penalties are selected using cross-validation, and uncertainty is quantified using bias-corrected and accelerated bootstrap resampling. We use the model to estimate environmental return values for a location in the Makassar Strait, in the South China Sea. Return values distributions for H sp S are estimated by simulation under the threshold ensemble model. Return values for H S are then estimated by simulating intra-storm trajectories of H S consistent with the characteristics of the simulated storm peak events using a matching procedure. Return values for maximum individual crest elevation C are estimated by marginalisation using a pre-specified conditional distribution for C given H S and other sea state parameters. Model validation is performed by comparing confidence intervals for cumulative distribution functions of H sp S and H S for the period of the data with empirical sample-based estimates.

Bayesian inference for nonstationary marginal extremes

“…These authors have performed a number of recent analyses similar to that reported here using maximum likelihood inference, incorporating cross‐validation to estimate optimal spline roughness penalty coefficients and an all‐encompassing bootstrap scheme to estimate uncertainties in model parameters and return values (e.g., Jonathan et al , ; Feld et al , ). In particular, we have performed a direct comparison of maximum likelihood and Bayesian inference for the South China Sea application (reported in Randell et al , ), obtaining good agreement for model parameter and return value estimates. Moreover, maximum likelihood inferences for the northern North Sea location considered here are provided in the Supporting Information accompanying this work, again showing good agreement between maximum likelihood and Bayesian inferences.…”

“…We demonstrated the utility of the model in application to a directional-seasonal analysis of storm peak significant wave height at a northern North Sea location and estimation of predictive directional-seasonal return value distributions necessary for the design and reliability assessment of marine and coastal structures. These authors have performed a number of recent analyses similar to that reported here using maximum likelihood inference, incorporating cross-validation to esti-mate optimal spline roughness penalty coefficients and an all-encompassing bootstrap scheme to estimate uncertainties in model parameters and return values (e.g., Jonathan et al, 2014;Feld et al, 2015). In particular, we have performed a direct comparison of maximum likelihood and Bayesian inference for the South China Sea application (reported in Randell et al, 2015), obtaining good agreement for model parameter and return value estimates.…”

Consistent Design Criteria for South China Sea With a Large-Scale Extreme Value Model

“…Incorporating seasonal effects could be an another area of potential application though in case of the South China Sea there appears to be a direct correlation between directional and seasonal effects (Randell et al, 2015a). However it would be worthwhile to establish such a model in the spatial context to actually see the full relationship.…”

Spatial and Seasonal Variability of Metocean Design Criteria in the Southern South China Sea From Covariate Extreme Value Analysis

“…Recently, new deductive methods for data extrapolation were developed. These rely on non-stationary extreme value analysis, hereafter referred to as CEVA ("Covariate Extreme Value Analysis") and are described in ( [1], [18], [19], [20]). Briefly, CEVA performs a non-stationary directional-seasonal analysis of storm peak significant wave height using a penalized maximum likelihood approach.…”