The effect of directionality on extreme wave design criteria

Sea state design criteria for offshore facilities are frequently provided by direction. For example, it is typical for return-period values of the significant wave height to be specified for each of eight 45° sectors in addition to the omni-directional case. However, it is important that these criteria be consistent so that the probability of exceedance of a given wave height from any direction derived from the directional values is the same as for the omni-directional value. As recently demonstrated by Forristall it is not sufficient simply to scale the directional values so that the value of the wave height from the most severe sector is the same as the omni-directional value.We develop an approach for establishing appropriate directional criteria and an associated omni-directional criterion for a specific location. The inherent directionality of sea states is used to develop a model for the directional dependence of distributions of storm maxima. The directional model is applied to the GOMOS data, and the distributional properties of the 100-year significant wave height are estimated and the implications for design discussed. An objective risk-cost approach is proposed for optimising directional criteria, while preserving overall reliability. Simulation studies are performed, using realistic extreme value assumptions, to quantify the uncertainties.     

On the use of discrete seasonal and directional models for the estimation of extreme wave conditions

Extreme value theory is commonly used in offshore engineering to estimate extreme significant wave height. To justify the use of extreme value models it is of critical importance either to verify that the assumptions made by the models are satisfied by the data or to examine the effect violating model assumptions. An important assumption made in the derivation of extreme value models is that the data come from a stationary distribution. The distribution of significant wave height varies with both the direction of origin of a storm and the season it occurs in, violating the assumption of a stationary distribution. Extreme value models can be applied to analyse the data in discrete seasons or directional sectors over which the distribution can be considered approximately stationary. Previous studies have suggested that models which ignore seasonality or directionality are less accurate and will underestimate extremes. This study shows that in fact the opposite is true. Using realistic case studies, it is shown that estimates of extremes from non-seasonal models have a lower bias and variance than estimates from discrete seasonal models and that estimates from discrete seasonal models tend to be biased high. The results are also applicable to discrete directional models.     

Estimating extreme water level probabilities: A comparison of the direct methods and recommendations for best practise

Over the past five decades, several approaches for estimating probabilities of extreme still water levels have been developed. Currently, different methods are applied not only on transnational, but also on national scales, resulting in a heterogeneous level of protection. Applying different statistical methods can yield significantly different estimates of return water levels, but even the use of the same technique can produce large discrepancies, because there is subjective parameter choice at several steps in the model setup. In this paper, we compare probabilities of extreme still water levels estimated using the main direct methods (i.e. the block maxima method and the peaks over threshold method) considering a wide range of strategies to create extreme value dataset and a range of different model setups. We primarily use tide gauge records from the German Bight but also consider data from sites around the UK and Australia for comparison. The focus is on testing the influence of the following three main factors, which can affect the estimates of extreme value statistics: (1) detrending the original data sets; (2) building samples of extreme values from the original data sets; and (3) the record lengths of the original data sets. We find that using different detrending techniques biases the results from extreme value statistics. Hence, we recommend using a 1-year moving average of high waters (or hourly records if these are available) to correct the original data sets for seasonal and long-term sea level changes. Our results highlight that the peaks over threshold method yields more reliable and more stable (i.e. using short records leads to the same results as when using long records) estimates of probabilities of extreme still water levels than the block maxima method. In analysing a variety of threshold selection methods we find that using the 99.7th percentile water level leads to the most stable return water level estimates along the German Bight. This is also valid for the international stations considered. Finally, to provide guidance for coastal engineers and operators, we recommend the peaks over threshold method and define an objective approach for setting up the model. If this is applied routinely around a country, it will help overcome the problem of heterogeneous levels of protection resulting from different methods and varying model setups.     

Physical Investigation of Directional Wave Focusing and Breaking Waves in Wave Basin

An experimental scheme for the generation of directional focusing waves in a wave basin is established in this paper. The effects of the directional range, frequency width and center frequency on the wave focusing are studied. The distrihution of maximum amplitude and the evolution of time series and spectra during wave packet propagation and the variation of water surface parameters are extensively investigated. The results reveal that the characteristics of focusing waves are significantly influenced hy wave directionality and that that breaking criteria for directional waves are distinctly different from those for unidirectional waves.     

Joint modelling of extreme ocean environments incorporating covariate effects

Characterising the joint distribution of extremes of ocean environmental variables such as significant wave height (H_S) and spectral peak period (T_P) is important for understanding extreme ocean environments and in the design and assessment of marine and coastal structures. Many applications of multivariate extreme value analysis adopt models that assume a particular form of extremal dependence between variables without justification. Models are also typically restricted to joint regions in which all variables are extreme, but regions where only a subset of variables is extreme can be equally important for design. The conditional extremes model of Heffernan and Tawn (2004) provides one approach to overcoming these difficulties.Here, we extend the conditional extremes model to incorporate covariate effects in all of threshold selection, marginal and dependence modelling. Quantile regression is used to select appropriate covariate-dependent extreme value thresholds. Marginal and dependence modelling of extremes is performed within a penalised likelihood framework, using a Fourier parameterisation of marginal and dependence model parameters, with cross-validation to estimate suitable model parameter roughness, and bootstrapping to estimate parameter uncertainty with respect to covariate.We illustrate the approach in application to joint modelling of storm peak H_S and T_P at a Northern North Sea location with storm direction as covariate. We evaluate the impact of incorporating directional effects on estimates for return values, including those of a structure variable, similar to the structural response of a floating structure. We believe the approach offers the ocean engineer a straightforward procedure, based on sound statistics, to incorporate covariate effects in estimation of joint extreme environmental conditions.     

Wave crest and trough distributions in a broad-banded directional wave field

It is well established that the modulational instability enhances the probability of occurrence for extreme events in long crested wave fields. Recent studies, however, have shown that the coexistence of directional wave components can reduce the effects related to the modulational instability. Here, numerical simulations of the Euler equations are used to investigate whether the modulational instability may produce significant deviations from second-order statistical properties of surface gravity waves when short crestness (i.e., directionality) is accounted for. The case of a broad-banded directional wave field (i.e. wind sea) is investigated. The analysis is concentrated on the wave crest and trough distribution. For completeness a comparison with a unidirectional wave field is presented also. Results will show that the distributions based on second-order theory provide a good estimate for the simulated crest and trough height also at low probability levels.     

Disaster prevention design criteria for the estuarine cities:New Orleans and Shanghai The lesson from Hurricane Katrina

1Introduction IntheendofAugust2005,HurricaneKatrina assaultedAtlanticcoastandcoastofGulfofMexico coastswithamaximumwindspeedof175m/h,a bout1200peoplewerekilledinthecatastrophic storm,NewOrleanswasseriouslydamagedbythe turbulenthurricanewindandtheassociate…     

Disaster prevention design criteria for the estuarine cities: New Orleans and Shanghai The lesson from Hurricane Katrina

The accurate prediction of the typhoon （hurricane） induced extreme sea environments is very important for the coastal structure design in areas influenced by typhoon （hurricane）. In 2005 Hurricane Katrina brought a severe catastrophe in New Orleans by combined effects of hurricane induced extreme sea environments and upper flood of the Mississippi River. Like the New Orleans City, Shanghai is located at the estuarine area of the Changjiang River and the combined effect of typhoon induced extreme sea en- vironments, flood peak runoff from the Changjiang River coupled with the spring tide is the dominate factor for disaster prevention design criteria. The Poisson-nested logistic trivariate compound extreme value distribution （PNLTCEYD） is a new type of joint probability model which is proposed by compounding a discrete distribution （typhoon occurring frequency） into a continuous multivariate joint distribution （ typhoon induced extreme events）. The new model gives more reasonable predicted results for New Orleans and Shanghai disaster prevention design criteria.     

Model of Shipping Noise in the Deep Water: Directional Density and Spatial Coherence Functions

The shipping noise properties in the deep ocean are studied. Shipping noise exhibits the strong dual-horned directionality features in the flat-seabed ocean, and its directional density can be modeled by a Von Mises distribution. With the explicit expression for the directional density function, the spatial coherence functions of shipping noise are also derived, and the relative features are studied. The research result shows that the properties of shipping noise are different from the ambient noise of other sources, and it can be used for the sonar array design. The model is well matched with the experimental result, and it can be extended to the situations when the ambient noise exhibits the dual-horned structure.     

Estimation of genetic parameters and breeding values in shrimp Fenneropenaeus chinensis using the REML/BLUP procedure

An analysis of a selection experiment was used to assess the impact of various animal model structures on REML estimates of variance components.The analyses were carried out based on 162 d body mass (BM) of 1 287 animals from 21 paternal half-sib groups of Fenneropenaeus chinensis.Estimated breeding values (EBV) of BM of all individuals were estimated using eight statistical models (A,AB,ABC,ABDC,ABMFC,ABMDC,ABFDC and ABMFDC) and BLUP (best linear unbiased prediction).These models were designed involving factors such as sex,spawn date as fixed effects,maternal genetic effects,full-sib family effects as random effects,mean BM of families at tagging and age at recording (covariate).The results demonstrate the importance of correct interpretation of effects in the data set,particularly those that can influence resemblance between relatives.The data structure and the particular model that was applied markedly influenced the magnitude of variance component estimates.Models based on few effects obtained upward biased estimates of additive genetic variance.The accuracy of genetic parameters and breeding value estimated by ABFDC model was higher than other models.The results imply that additive genetic direct value,full-sib family effects,and covariance effects besides sex and spawn date as fixed effects were very important for estimating genetic parameters and breeding value of body mass.This model had a heritability estimate of 162 d BM of 0.44.The comparison of the efficiency of selection based on breeding values or phenotypic value revealed great difference:average breeding value of the best 24 families selected by the 162 d BM breeding value and phenotype were 0.577 g and 0.366 g,respectively,representing a 36.57% higher efficiency in the former.In conclusion,selection based on breeding value was more effective than selection based on phenotypic value.Our results indicate that effects influencing the magnitude of estimates should be taken into account when estimating heritability and breeding values for BM.     

Characterizing the seasonal and directional varying properties in a marine environment

With noticing an increasing number of failure events for offshore structures in the present days, it is now realized that modeling the marine environment especially for exceptional environmental conditions is quite important. It is recognized that a possible improvement in the traditional modeling of environmental characteristics, which are the basis for the load models for structural analysis and design, may be needed. In this paper, the seasonal and directional varying properties in modeling the ocean parameter, the wave height, are studied. The peak over threshold (POT) method is selected to model the extreme wave height by utilizing a non-stationary discrete statistical extreme model. The varying parameters are taken into account with a changing pattern to reflect the seasonal and directional dependent behavior. Both the magnitude and the occurrence rate of the extreme values are investigated. Detailed discussion on the continuity of the established model is also given. The importance of the proposed model is demonstrated in reliability analysis for a jacket structure. The sensitivity to the changing marine environment in reliability analyses is investigated.     

Characterizing the Seasonal and Directional Varying Properties in A Marine Environment

With noticing an increasing number of failure events for offshore structures in the present days, it is now realized that modeling the marine environment especially for exceptional environmental conditions is quite important. It is recognized that a possible improvement in the traditional modeling of environmental characteristics, which are the basis for the load models for structural analysis and design, may be needed. In this paper, the seasonal and directional varying properties in modeling the ocean parameter, the wave height, are studied. The peak over threshold (POT) method is selected to model the extreme wave height by utilizing a non-stationary discrete statistical extreme model. The varying parameters are taken into account with a changing pattern to reflect the seasonal and directional dependent behavior. Both the magnitude and the occurrence rate of the extreme values are investigated. Detailed discussion on the continuity of the established model is also given. The importance of the proposed model is demonstrated in reliability analysis for a jacket structure. The sensitivity to the changing marine environment in reliability analyses is investigated.     

An ambient noise model for the northeast Pacific Ocean basin

An ambient noise model for the Northeast Pacific Ocean Basin is presented. This model possesses the capability of synthesizing the noise field, with resolution in the vertical and horizontal finer than 1/spl deg/. Simulation results utilizing the synthesized field are shown to be in excellent agreement with measured horizontal directionality, vertical directionality, and depth dependence data for frequencies from 12.5 to 250 Hz. An important difference between this model and other models is the consideration of the SOFAR channel component, which is the dominant noise at these low frequencies. It is shown that only when this component of the noise is included can the simulation results be expected to agree with measured data.     

Non-stationary extreme value models to account for trends and shifts in the extreme wave climate due to climate change

The extreme values of wave climate data are of great interest in a number of different ocean engineering applications, including the design and operation of ships and offshore structures, marine energy generation, aquaculture and coastal installations. Typically, the return values of certain met-ocean parameters such as significant wave height are of particular importance. There exist many methods for estimating such return values, including the initial distribution approach, the block maxima approach and the peaks-over threshold approach. In a climate change perspective, projections of such return values to a future climate are of great importance for risk management and adaptation purposes. However, many approaches to extreme value modelling assume stationary conditions and it is not straightforward how to include non-stationarity of the extremes due to for example climate change. In this paper, various non-stationary GEV-models for significant wave height are developed that account for trends and shifts in the extreme wave climate due to climate change. These models are fitted to block maxima in a particular set of wave data obtained for a historical control period and two future projections for a future period corresponding to different emission scenarios. These models are used to investigate whether there are trends in the data within each period that influence the extreme value analysis and need to be taken into account. Moreover, it will be investigated whether there are significant inter-period shifts or trends in the extreme wave climate from the historical period to the future periods. The results from this study suggest that the intra-period trends are not statistically significant and that it might be reasonable to ignore these in extreme value analyses within each period. However, when it comes to comparing the different data sets, i.e. the historical period and the future projections, statistical significant inter-period changes are detected. Hence, the accumulated effect of a climatic trend may not be negligible over longer time periods. Interestingly enough, such statistically significant shifts are not detected if stationary extreme value models are fitted to each period separately. Therefore, the non-stationary extreme value models with inter-period shifts in the parameters are proposed as an alternative for extreme value modelling in a climate change perspective, in situations where historical data and future projections are available.     

Experimental Study on the Effects of A Breakwater on Wave Field Characteristics

Studies on the possible effects of a detached breakwater on the characteristics of the wavefield are carried out experimentally.A serpentine wave generator is used to generate both uni- andmulti-directional waves.Characteristics of the wave fields analyzed here include the wave fielddirectionality,and the probability distributions of surface elevations and of the wave heights.Owing to thepresence of the breakwater,waves outside the harbour are found to be reflected with,however,concen-trated energy within the harbour entrance.In general,wave heights can be approximated with a Rayleighdistribution,with occasional deviations from the theory.This occurs more frequently for waves with high-er peak frequency values than for those with lower values both for uni-and multi-directional waves.Sur-face elevations can be approximated with the Gaussian model.although the Edgeworth's form of the typeA Gram-Charlier series expansions would yield better fits.Wave directionality is found to have nodiscernible effects on     

Correlation of extreme waves and water levels using a third-generation wave model and a 3D flow model

A procedure to correlate extreme wave heights and extreme water levels in coastal waters using numerical models together with joint probability analysis has been proposed. A third-generation wave model for wave simulation and a three-dimensional flow model for water level simulation are coupled through the surface atmospheric boundary layer. The model has been calibrated and validated against wind, wave and water level data collected in the coastal waters of Hong Kong. The annual maximum wave height and the concomitant water level have been obtained by simulating the annual extreme typhoon event for 50 consecutive years. The results from bivariate extreme value analysis of the simulated data show that the commonly used empirical method may lead to underestimation of the design water level.     

Wave characteristics and extreme parameters in the Bohai Sea

This paper is aimed at the whole Bohai Sea,as the complement and improvement of wave characteristics and extreme parameters.Wave fields were simulated in the Bohai Sea by using wave model SWAN from 1985 to 2004.The input data based on the hindcast of high-resolution wind fields from RAMS and water level fields from POM,which have been tested and verified well.Comparisons of significant wave heights between simulation and station observations show a good agreement in general.By statistical analysis,the wave characteristics such as significant wave heights, dominant wave directions and their seasonal variations are discussed.In addition,main wave extreme parameters and directional extreme values particularly for 100-year return period are investigated.     

A straightforward approach for using single time domain simulations to assess characteristic extreme responses

Short-term wave design approach of marine structures, using nonlinear time domain simulations, is a design procedure that is recognized by various modern standard codes. One of the most challenging points of this approach is the evaluation of the characteristic extreme values for response parameters used in the design check equations. The most straightforward and recommended way to evaluate a response characteristic value is by fitting an extreme value probability distribution to the N-sample of extreme values extracted from N independent time domain simulations with duration equal to the short-term period indicated by the code, which is usually taken as 3 h. However, this procedure would not be practical for some types of marine structures, such as risers and mooring lines, under numerous design load cases and demanding huge finite element models. A more feasible approach would be to assess the response extreme value distribution using only a single short-term time domain simulation with duration shorter than 3 h. But reduced time simulations always introduce some additional statistical uncertainty into the extreme values estimates. This paper discusses a workable way of properly taking into account the statistical uncertainty associated with the simulation length in the assessment of a characteristic short-term extreme response value based on a single time series.     

Characterizing random wave surface elevation data

The definition and subsequent use of dimensional and dimensionless parameters to characterize various nonlinear aspects of ocean surface waves has again become a matter of great interest to the offshore community. The desire to ascertain whether laboratory simulations are adequately representing the surface waves found in the oceans and the concern over the mechanisms behind platform response phenomena, like ringing, has driven this resurgence of interest. This paper presents a depth independent characterization of single design waves, from which improved estimates of localized wave crest front and back slopes follow that are consistent with discrete time series analysis. Characterization of the nature of the entire wave data recorded requires a combination of spectral parameters and probabilistic models in addition to those used in the design wave characterization. A new expression for the direct evaluation of the kurtosis from knowledge of the spectral bandwidth, the relationship between some of the common spectral parameters, and some modified spectral parameters are presented and discussed. Three illustrative examples are presented. The first example provides a detailed examination of wave data measured from a series of random amplitude and random phase tests in a large model basin. The second presents estimates of the various parameters for the Pierson-Moskowitz and Wallops wave spectrum models. The third example investigates the use of the spectral peakedness ratio for comparing data with selected wave spectrum models. The examples illustrate how the formulae can provide a comprehensive local and global parametric characterization of surface wave elevation data.