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The Bohai Sea off the coast of northern China plays important economic and ecological roles. No studies have been conducted on wave characteristics in the Bohai Sea nearshore area using ocean station data in the past. Observational data (1998–2022) from eight ocean-stations in the Bohai Sea were used in the present study. Overall, wave height (Hs) was small; winter seasons had higher Hs than summer seasons, and the maximum Hs occurred in the Bohai Strait. Joint distribution analysis indicated that waves with Hs ranging from 0.2 to 0.4 m, and mean wave periods (Tm) ranging from 3 to 3.5 s, were most common. Hs in the Bohai Sea nearshore area showed a weak response to climate variability and was moderately correlated with the Ocean Niño Index (ONI) and the North Pacific Index (NPI) in winter, and with the Arctic Oscillation (AO) in summer. Under extreme conditions, Hs was best described by a Generalized Pareto distribution, Tm was best described by a GEV distribution, and wave directions mainly followed a t location-scale distribution. The maximum wave height (Hmax)/ Hs was 1.51, and the ratio varied with location. Machine learning methods were used to calculate Hmax more precisely, and they yielded better results than statistical methods. • Long-term wave climate and variability characteristics are studied. • Climate response analysis of large-scale climate patterns is examined. • Wave parameters PDF distributions under extreme conditions are presented. • Extreme wave parameters in the Bohai Sea are calculated. • Correlation of maximum wave height and Hs is proposed by machine learning method. [ABSTRACT FROM AUTHOR]

A single-degree-of-freedom oscillator with a nonlinear restoring force and stochastic external forcing is studied with the goal of understanding the distributions of certain response rates. Motivated by applications to ship motions, the response rates concern the minimum response rate leading to capsizing (the critical response rate) and a measurement comparing an observed response rate to the critical response rate (the split-time metric), whose distributions are investigated both analytically and numerically. Three nonlinear restoring forces are considered: piecewise linear (experiencing linearly softening stiffness above a "knuckle" point), doubly piecewise linear (experiencing piecewise linearly softening stiffness above a "knuckle" point), and the cubic softening restoring force of the Duffing oscillator. In the first two cases, an efficient numerical simulation of the critical response rate and split-time metric is proposed from a derived distribution; in the latter case, the density of the critical response rate is approximated assuming white noise excitation. A key interest is in the nature of the right tail of the split-time metric, specifically as it relates to its extrapolation through extreme value analysis in estimating the probability of capsizing. The distribution is found to have a "light" tail, which motivates the use of exponential rather than the generalized Pareto distribution for exceedances above threshold in extreme value analysis. Finally, threshold selection through a prediction error criterion for the exponential distribution is examined, and the Weibull distribution tail is suggested as a useful means for a more refined examination of the distribution tail. • First analytic treatment of a split-time method for capsizing in nonlinear oscillators. • Distributions of critical response rate and split-time metric for capsizing are studied. • The main finding is the exponential character of the distribution tails of interest. • Connections to extreme value theory and peaks-over-threshold analysis are made. • This complements similar earlier work on the response in nonlinear oscillators. [ABSTRACT FROM AUTHOR]

The development and application of the Envelope Peak-over-Threshold (EPOT) method is summarized for the roll motion of a ship in irregular waves. The method is based on the conventional Peak-over-Threshold (POT) method, but uses an envelope of the peaks for declustering the data. As suggested by a reduced-order model, a power-law tail should be applicable for the peaks of roll motions, which allows the introduction of physical considerations into the statistical model. A data-driven Generalized Pareto distribution (GPD) is applied to study the behavior of the shape parameter on large-volume samples in order to confirm the theoretical prediction of the tail structure. The physics-informed statistical model approximates data above a suitable threshold with a Pareto distribution, while the threshold is determined with a prediction error criterion. An example is included, where extrapolations with GPD are compared to the physics-informed model. • Application of Peak-over-Threshold method is considered where a time history envelope is used for declustering the data. • The study of behavior of distribution tails of roll motion peaks. • A physics-informed model with power-law, Pareto tail was formulated and applied to amplitudes of roll motions. [ABSTRACT FROM AUTHOR]

The consistency of the upper tail of the extreme response distribution plays an important role in the accuracy of the extreme response prediction. Although the peaks-over-threshold method has a high data utilization of the response time series, the consistency of the upper tail of the extreme response distribution was not thoroughly investigated, especially for the inherent randomness of the short-term sea state. This study aims to estimate the upper tail of the short-term extreme tension distribution of the mooring line considering the short-term variability by the peaks-over-threshold method. The consistency of the extreme tension distribution tail is quantified by a relative error compared with the global maximum method, and the theoretical optimal threshold is defined by minimizing the largest relative error among the tail quantiles for different thresholds. Results from a case study for the mooring line of the fish cage indicate that the effect of the random seed is significant for consistency in the prediction of the distribution tail of the short-term extreme tension. And the generalized Pareto distribution model combined with the L-moments method is recommended for the theoretical optimal threshold. These findings provide some useful suggestions for the preliminary design of the mooring line for offshore structures. • Consistency of the upper tail of the extreme response distribution by the peaks-over-threshold method is investigated. • Effect of the random seed on the consistency of the short-term extreme response distribution tail is analyzed. • Performance of different peaks extraction methods and peak distribution parameter estimation methods is discussed. [ABSTRACT FROM AUTHOR]

In the design of floating breakwaters, assessment of the extreme wave-induced loads on the connections, their weakest element, is required to ensure structure survival. This case study provides guidelines for estimating the extreme wave-induced forces on the connections of a floating breakwater. A Boundary Element Method (BEM) solver was applied to obtain the time-domain response of an array of five pontoons anchored to the sea bottom with elastic mooring lines. The hydrodynamic behaviour of the structure was assessed for short-duration sea states with different wave peak periods and oblique wave directions. Two peak selection criteria were applied to obtain force distributions, and several different probability density functions (PDF) were fitted to the resulting data. The extreme wave-induced forces on every connection and sea state were estimated for two different exceedance levels during a typical 3-h sea state. Based on the results, combination of the Peaks Over Threshold (POT) method and generalized Pareto distribution results is proposed for estimating the wave-induced design forces on the connections of floating pontoon breakwaters. • Extreme tensile forces on the connections of a floating breakwater are estimated. • The interaction of the structure with irregular waves is solved in the time domain. • Short-term distributions of tensile forces on the connections are analysed. • 2 peak selection criteria and 7 PDF are used to fit the force data of 9 sea-states. • Combining the POT method with the Generalized Pareto distribution is recommended. [ABSTRACT FROM AUTHOR]

A thirty-seven year wave hindcast (1979–2015) in Chesapeake bay using NCEP's Climate Forecast System Reanalysis (CFSR) wind is presented. The long-term significant wave heights are generated by the third-generation nearshore wave model SWAN, which is validated using the wave height measurements at buoy stations in the bay. The simulated wave heights are analyzed to characterize their temporal and spatial variabilities as well as long-term changing trends by using an Empirical Orthogonal Function (EOF) analysis and an empirical cumulative distribution function approach. Seasonal variability as well as extreme storm effects on significant wave heights are revealed in the first mode of principle component. Then, an extreme value analysis based on generalized extreme value and generalized Pareto distribution functions is applied to evaluate design wave heights with different return periods. The effects of key parameters including threshold value, time span and data length on the design wave heights are extensively studied. Through the comparisons of different distribution functions evaluated by Bayesian Information Criterion and Akaike Information Criterion, it is found that Gamma distribution function and generalized extreme value analysis provide the best fit for annual and monthly data, while generalized Pareto distribution function gives the best fit when peak-over-threshold analysis is conducted. [ABSTRACT FROM AUTHOR]

The current general consensus is that because of global climate change, coastal infrastructures may be subject to more extreme loads in the future than in the past. There has been an increased recognition that more attention should be paid to incorporating nonstationarity within the design process of coastal structures. In this regard, the present study examines the reliability of a conventional rubble mound breakwater using a variety of probabilistic techniques, incorporating ten nonstationary models to study the impacts of nonstationarity, as well as six copula functions to explore the dependence effects of wave extremes. The Gumbel copula most accurately represents the dependence structure of wave heights and periods in the study area. When the dependence of wave parameters is not correctly modeled, the failure probability of the studied structure is significantly underestimated. Assuming the Gumbel copula for modeling dependence of wave parameters, the results indicate that the maximum failure probability of the structure is underestimated by about 33% when a stationary extreme value distribution is fitted to wave height extremes, compared to a nonstationary Generalized Pareto Distribution (GPD). The insights gained from this study suggest that considering nonstationarity in extreme coastal events has more significant impacts on the reliability of coastal structures when the dependence structure of the marine variables is accurately modeled. • A methodology to study the reliability of coastal structures within a nonstationary framework is provided. • The influence of three dependence structures (Independence, Gaussian, and Gumbel copulas) was analyzed. • The impact of 12 nonstationary extreme value distributions on extreme significant wave height was explored. • Two state-of-the-art automated threshold selection methods for the GPD model were used. • The influence of wind speed as covariate of nonstationary extreme wave height, as well as time, was studied. [ABSTRACT FROM AUTHOR]

Characterising storm surge in extreme sea states is important in offshore design. Here we estimate key surge design characteristics such as the maximum surge observed during a storm event of given extreme storm severity and covariates such as storm direction. Inferences are made using a simple non-stationary implementation of the conditional extremes model of Heffernan and Tawn (2004), comprising a set of coupled piecewise stationary marginal and dependence models defined on a partition of the covariate domain. The approach uses samples consisting of pairs of values for peaks over threshold of a conditioning variate, namely storm peak significant wave height, and the corresponding peaks over threshold of an associated value of a key surge characteristic. Each pair is allocated to a particular storm direction covariate interval, and all pairs within the same interval are assumed to exhibit common stationary marginal and conditional extreme value behaviour. Non-stationary marginal extreme value characteristics for each variate are estimated using maximum roughness-penalised generalised Pareto likelihood estimation over covariate intervals. Extremal dependence between variates on a transformed standard Gumbel scale is then estimated using maximum roughness-penalised likelihood estimation for a conditional extremes model, also piecewise stationary with respect to covariates. Sample and threshold uncertainties are quantified using a bootstrapping scheme. Marginal and conditional return value distributions, estimated using numerical integration, incorporate these uncertainties. From offshore radar-based measurements at locations in the northern, central and southern North Sea, we observe that characteristics of surge and significant wave height vary with wave direction at all locations. Surge is a larger contributor to extreme seas in the southern North Sea than in the northern North Sea in particular. There is evidence that extremal dependence between surge characteristics and significant wave height also varies with storm direction. Hence, the size of surge contribution to return values of total water level also varies with storm direction and location. [ABSTRACT FROM AUTHOR]

A new Polynomial approximation method has been used for the estimation of the extreme significant wave heights and wind speeds from 33 years of hindcast data for six locations along the Indian coast. These return value estimates are compared with the values obtained from the well-known Generalised extreme value distribution and Generalised Pareto distribution methods. Further, the entire data is subdivided into three decadal time blocks to assess the time variability in model outputs of extreme values of significant wave heights and wind speeds. Although the comparison, in general, is found good, a closer examination of the results reveals that the present method based on polynomial approximation could be preferred for practical applications. The detailed analysis of the Polynomial approximation method, salient features and its fulfilment of consistency condition which overcomes the shortcomings of the other standard extreme value estimation methods are presented and discussed in this paper. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper concerns the calculation of the short term extreme structural responses of a Spar-type floating wind turbine by applying the peak-over-threshold (POT) method. A new approach is proposed for finding an optimum threshold value by incorporating a declustering algorithm into the POT method. To select the clusters and check the Poisson character of the number of clusters we use the concept of a dispersion index . Then, the method of maximum product of spacing is utilized to estimate the parameters in the Generalized Pareto distribution of the largest values in all the selected clusters over the optimum threshold value. As examples of calculations, optimum threshold values of the out-of-plane and in-plane blade root bending moments and the tower – Spar interface bending moments of the NREL 5-MW OC3-Hywind floating wind turbine have been obtained by utilizing the new approach. The extreme response probability plot based on an optimum threshold value has been compared with the probability plot based on an empirical threshold value, and the accuracy and efficiency of the new approach have been convincingly validated. Goodness-of-fits plots have also been included in this article for testing the accuracy of the proposed new approach. Finally, in order to make a fair comparison, we have also extrapolated the short-term extreme values using the different POT methods and compared them with the reference values obtained directly from a large number of time-domain simulations. [ABSTRACT FROM AUTHOR]

This paper reviews the research and development of the Envelope Peaks over Threshold (EPOT) method that has taken place in the last three years. The EPOT method is intended for the statistical extrapolation of ship motions and accelerations from time-domain numerical simulations, or possibly, from a model test. To model the relationship between probability and time, the large roll angle events must be independent, so Poisson flow can be used. The method uses the envelope of the signal to ensure the independence of large exceedances. The most significant development was application of the generalized Pareto Distribution (GPD) for approximation of the tail, replacing the previously used Weibull distribution. This paper reviews the main aspects of modeling the GPD, including its mathematical justification, fitting the parameters of the distribution, and evaluating the probability of exceedance and its confidence interval. [ABSTRACT FROM AUTHOR]

A series of 1: 50 model tests have been conducted to study the dynamics of a taut mooring system and two hybrid mooring systems attached to a deep-water semi-submersible in the 100-year wave condition of the South China Sea. Three typical environmental conditions were tested, including head sea, beam sea and quartering sea. The mixture Gamma- Generalized Pareto distribution (GPD) model is applied to study short term extreme dynamic mooring tensions based on the measured data, the results are compared with the estimations from mixture Gamma and two-parameter Weibull models. A birth-death Markov chain Monte Carlo (MCMC) sampling procedure is developed to fit the parameters of a mixture Gamma- GPD via Bayesian inference, and an extensive discussion of the de-clustering procedure, parameters of the prior distribution for threshold and MCMC iteration steps on Bayesian inference are carried out. It is found that the Weibull model underestimates the most probable largest dynamic mooring tensions. On the contrary, the mixture Gamma model overestimates the extreme dynamic mooring tension significantly. The mixture Gamma- GPD can present good estimations of extreme dynamic mooring tension, and its performance is robust to the sample definition, MCMC iteration steps and parameters of threshold prior distribution. • Model tests have been conducted to study the dynamics of mooring systems attached to a deepwater semi-submersible. • The mixture Gamma Generalized Pareto distribution model is applied to study short term extreme dynamic mooring tensions. • A birth-death Markov chain Monte Carlo sampling is used to fit the parameters of mixture Gamma- GPD via Bayesian inference. • MGGPD is a powerful model for analysis, which presents accurate estimations of extreme dynamic mooring tension. • MGGPD is very robust and insensitive to sample definition, iteration steps and parameters of threshold prior distribution. [ABSTRACT FROM AUTHOR]

Regression quantile models are proposed to model extreme significant wave height distributions in two Portuguese locations of Figueira da Foz and Azores in the North Atlantic Ocean. A data set from a 44 years hindcast produced in the HIPOCAS project was used in this study. In order to identify trends with time, the data set was divided in 11 samples of 4 year data. Three-parameter Weibull, generalised extreme value and generalised Pareto quantile functions are fitted to data and extrapolated to 50 and 100 year significant wave height return periods. The algorithm of distributional least absolutes is used to estimate the model parameters. The regression quantile models showed the ability to model the historical trends that may subsist in long term data sets, a feature that the traditional fitting of extreme distributions does not account for. [ABSTRACT FROM AUTHOR]

This study evaluates the extreme waves in the Mediterranean and the Black Sea. Annual Maximum Series (AMS), and Partial Duration Series (PDS) of the significant wave heights (H m0) are used from the ERA5 dataset. Generalized Extreme Value (GEV), Gumbel, Weibull, Lognormal, and Generalized Pareto Distribution (GPD) models are used to predict H m0 for 50, 100, and 500-years of return periods. The statistical models are compared by using Anderson-Darling test statistics and the best-fitting AMS and PDS models at each grid cell is mapped to depict spatial variability within the study area. The uncertainty of the return levels is estimated by using the Monte Carlo simulation technique. The effect of varying width and temporal location of data window on the results is studied. The highest return levels of H m0 are found in the Algerian basin, offshore Libya, the Tyrrhenian Sea, and offshore Crimea. The relative performance of statistical models showed that GEV outperformed other AMS models in the 43% of the study area, followed by Gumbel (29%), Lognormal (24%), Weibull (4%). In case of PDS models, Weibull dominates the region by covering 93% of the study area, with the remaining regions being characterized as GPD. • Extreme Value Analysis of Mediterranean and Black Sea wave heights. • Spatial distributions of 50-, 100-, and 500- year return levels. • 33% of underestimation to 41% of overestimation is found among different models. • An iterative model selection framework based on Anderson-Darling test. • Uncertainty analysis by Monte-Carlo random sampling. [ABSTRACT FROM AUTHOR]

The assessment of global directional extreme significant wave height (SWH) is crucial for the ocean infrastructure, which requires the dominant directional sector to be identified. In this study, 40-year (1979–2018) global SWHs and wave directions obtained from ERA5 are employed as the initial database. To study the extreme wave, storms over the initial threshold are extracted, which show that the non-tropical cyclonic storm is stable with the direction and most directions are within the dominant directional sector. Thus, the directional extrapolation is performed based on the independent non-tropical cyclone sample. To identify the dominant directional sector, an automated method is proposed based on the circular mean sample. Benefiting from this method, global patterns of sector width and representative direction of dominant directional sector can be obtained and classified. To make sufficient use of extreme samples for reasonable extrapolation, the peak over threshold method with the generalized Pareto distribution model is employed to evaluate the global directional extreme SWHs. The spatially comparable patterns accord with the distribution of wind zones and reveal the effect of swells in low latitudes, which can be used to realize design optimization and key protection of ocean infrastructures, especially for infrastructures that are not symmetrical. • The non-tropical cyclonic storm is stable with the direction and presents direction aggregation. • An automated method is proposed for identifying the dominant directional sector and its global patterns are classified. • Global directional extreme wave patterns accord with the distribution of wind zones and reveal the effect of swells. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a statistical model to characterize the long-term extreme value distribution of significant wave height, conditioning to the duration of the storm and accounting for seasonality. A time-dependent version of the peak over threshold (POT) approach is used to build the model, which is then applied to specific reanalysis time series and NOAA buoy records. The model considers the annual and semiannual cycles which are parameterized in terms of harmonic functions. The inclusion of seasonal variabilities substantially reduces the residuals of the fitted model. The information obtained in this study can be useful to design maritime works, because (a) the model improves the understanding of the variability of extreme wave climate along a year and (b) the model accounts for the duration of the storm, which is a key parameter in several formulations for rubble mound breakwater design. [Copyright &y& Elsevier]

We consider the estimation of return values in the presence of uncertain extreme value model parameters, using maximum likelihood and other estimation schemes. Estimators for return value, which yield identical values when parameter uncertainty is ignored, give different values when uncertainty is taken into account. Given uncertain shape ξ and scale parameters of a generalised Pareto (GP) distribution, four sample estimators q for the N -year return value q 0 , popular in the engineering community, are considered. These are: q 1 , the quantile of the distribution of the annual maximum event with non-exceedance probability 1 − 1 / N , estimated using mean model parameters; q 2 , the mean of different quantile estimates of the annual maximum event with non-exceedance probability 1 − 1 / N ; q 3 , the quantile of the predictive distribution of the annual maximum event with non-exceedance probability 1 − 1 / N ; and q 4 , the quantile of the predictive distribution of the N -year maximum event with non-exceedance probability exp [ − 1 ]. Using theoretical arguments, and simulation of samples of GP-distributed peaks over threshold (with ξ ∈ [ − 0.4 , 0.1 ]) and different GP parameter estimation schemes, we show that the rank order of estimators q and true value q 0 can be predicted, and that differences between estimators q and q 0 can be large. Judgements concerning the relative performance of estimators depend on the choice of utility function adopted to assess them. We consider bias in return value, bias in exceedance probability and bias in log exceedance probability. None of the four estimators performs well with respect to all three utilities under maximum likelihood estimation, but the mean quantile q 2 is probably the best overall. The estimation scheme of Zhang (2010) provides low bias for q 1. • Return value (RV) estimation is central to current practice in metocean design • We consider RV estimation with uncertain extreme value (EV) models from fits to data. • Standard approaches to estimating N-year RVs are inconsistent when uncertainty is incorporated. • We quantify bias of estimators using theory and simulation in a metocean context. • The mean over RV estimates from different plausible sets of EV parameters performs relatively well. [ABSTRACT FROM AUTHOR]

Extreme wave analysis is essential for the design and deployment of marine structures. Since extremes in natural phenomena tend to occur in clusters, it is necessary to de-cluster them in order to form a dataset of independent samples. There are several algorithms used to identify independent storms (clusters of significant wave height extremes), most of which have the disadvantage of relying on an arbitrarily selected de-clustering parameter. In this paper, an existing statistical method for systematic cluster size inferencing is used with runs de-clustering, and applied for the first time to extreme wave analysis. The Generalised Pareto Distribution (GPD) is fitted to an extreme wave dataset, and the return periods of significant wave height extremes are calculated using the resulting model function. The methodology proposed in this paper is illustrated using hindcast data for the winter months of two locations: one that is exposed to the long Atlantic swell off the west coast of France, and another in the North Sea that is characterised by short fetch. This work demonstrates how extremal index estimation may be used in conjunction with the well-known runs de-clustering algorithm to predict the return periods of significant wave height extremes. • A novel method is presented for estimating the return periods of Hs extremes. • The method infers an optimal run length for every extreme wave threshold examined. • The method showed higher qualitative GPD parameter stability than existing algorithms. [ABSTRACT FROM AUTHOR]

The study investigates extreme value analysis of wave climate around the Farasan islands' protected coastal zone in the southern Red Sea. It provides an overall idea of the extreme wave conditions in the southern Red Sea, which are influenced by the Indian monsoon and local climates as well as by the effect of complex topography due to the presence of corals and high steepness in the bathymetry. The significant wave height return levels for the select shallow and deep regions around the Farasan islands are estimated using extreme value models; Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD). Both block maxima and annual maxima methods are used in the GEV and GPD established with Peak Over Threshold (POT). The GPD method gives more reliable return level estimates compared to GEV. The trend analysis shows that, the trends of near extremes (90th and 95th percentile Hs) are significant in the offshore regions around the Farasan Islands, but not significant in the nearshore regions. The seasonal analysis indicate that the seasonal estimates of extreme Hs are more reliable than annual estimates considering the differences in the seasonal wave generation mechanisms over the region. • Hindcasting of wind waves in the Red Sea using WW3. • Validation of WW3 outputs with altimeter data. • The climate and linear trends of wave heights around the Farasan islands. • Derivation of wave height return values using Extreme Value Analysis. • Seasonality and directionality of extreme wave heights were analysed. [ABSTRACT FROM AUTHOR]

This article compares the accuracy of return value estimates from stationary and non-stationary extreme value models when the data exhibits covariate dependence. The non-stationary covariate representation used is a penalised piecewise-constant (PPC) model, in which the data are partitioned into bins defined by covariates and the extreme value distribution is assumed to be homogeneous within each bin. A generalised Pareto model is assumed, where the scale parameter can vary between bins but is penalised for the variance across bins, and the shape parameter is assumed constant over all covariate bins. The number and sizes of covariate bins must be defined by the user based on physical considerations. Numerical simulations are conducted to compare the performance of stationary and non-stationary models for various case studies, in terms of quality of estimation of the T -year return value over the full covariate domain. It is shown that a non-stationary model can give improved estimates of return values, provided that model assumptions are consistent with the data. When the data exhibits non-stationarity in the generalised Pareto tail shape, the use of non-stationary model assuming a constant shape parameter can produce biases in return values. In such cases, a stationary model can give a more accurate estimate of return value over the full covariate domain as only the most extreme observations (regardless of covariate) are used to estimate tail shape. In other cases, the assumption of a stationary model will ignore key features of the data and be less reliable than a non-stationary model. For example, if a relatively benign covariate interval exhibits a long (or heavy) tail, extreme values from this interval may influence the T -year return value for very large T. However the sample of peaks over threshold, with high threshold, used to estimate a stationary model in this case may not include sufficient observations from this interval to estimate the return value adequately. • Effect of non-stationarity in data on shape of tail of distribution quantified. • Monte Carlo simulations used to compare stationary and non-stationary models. • Effects of threshold level, covariate bin placement and bin width investigated. • Penalised piecewise-constant model is more accurate when model assumptions are valid. • Non-stationary model can be less accurate when model assumptions are violated. [ABSTRACT FROM AUTHOR]

This paper concerns the estimation of 3-h short-term dynamic responses of semi-submersible system moored by two hybrid mooring systems. The global maximum method, which is applied by fitting 50 individual maximum observations by Gumbel distributions, is used to obtain extreme surge motion and mooting tensions. The accuracy of the numerical model has been validated by the model tests. The most probable maximum extreme (MPME) values of Gumbel distribution fitted by L-moments are adopted as the benchmarks and used to check the accuracy of the extrapolation methods. The average conditional exceedance rate (ACER) method as well as optimized peaks-over-threshold (POT) method combined with Generalized Pareto distribution (GPD), three parameters Weibull distribution and Generalized Extreme Value distribution (GEV) are applied to study 3-h return levels. The effects of threshold, ensemble size and simulation duration on extreme values are investigated, and suitable empirical thresholds are suggested. A method to predict short-term extreme values by combing 20 individual realizations is given, the effects of parameters estimation method, threshold and duration are discussed. • 3-h short-term dynamic responses of semi-submersible system moored by two hybrid mooring systems are determined. • The accuracy of numerical model has been validated by the model tests. • The most probable maximum extreme (MPME) value of Gumbel distribution fitted by L-moments are adopted as the references. • The average conditional exceedance rate (ACER) method as well as optimized peaks-over-threshold (POT) method are applied. • An optimized POT method is applied to estimate the 3-h maximum measured surge motion and mooring tension. [ABSTRACT FROM AUTHOR]

The performance of the Maximum Entropy method is compared to the one of the Generalized Pareto distribution in extrapolating the extreme wave climate over the northern part of Atlantic Ocean, based on a twenty-year dataset of satellite altimeter measurements of significant wave height. Both methods are employed on peaks over threshold samples, which consist of medians above a given threshold value calculated for each satellite passage, over a grid of points of 1° latitude x 1° longitude. Additionally, the generalized extreme value distribution employed on annual maxima data has been used as a reference model. The results indicate that the Maximum Entropy method is significantly less sensitive to the threshold level than the Generalized Pareto distribution, that is, to the variation of the sample size, when producing extreme values of significant wave height. • The performance of the Maximum Entropy method (MaxEnt) is compared to the one of the Generalized Pareto distribution (GPD). • A 20-year dataset of satellite altimeter measurements of significant wave height of the northern Atlantic Ocean is used. • Both methods are employed on peaks over threshold (POT) samples. • The generalized extreme value distribution (GEV) of annual maxima data has been used as a reference model. • The results indicate that the MaxEnt is significantly less sensitive to the variation of the sample size. [ABSTRACT FROM AUTHOR]