Distribution Of Significant Wave Height Research Articles

Wave energy distribution along the Portuguese continental coast based on a thirty three years hindcast

Abstract An assessment of wave power resource for Portugal continental coast is presented, using thirty three years (1979–2012) of wave hindcast. The hindcast system is based in two spectral wave models, WWIII (WAVEWATCHIII) for the wave generation and SWAN (Simulating WAves Nearshore) for wave transformation in coastal areas. To improve the SWAN model performance, six high resolution areas (Agucadoura, Figueira da Foz, Sao Pedro de Moel, Peniche, Cascais and Sines) were nested into one large area (Iberian coast). The assessment of wave power potential was done by studying the spatial and temporal behaviour using average for different time scales (monthly, seasonal, inter-annual and total time). Moreover, the wave climate variability was determined through the calculation of the coefficient of variation, seasonal variability index and monthly variability index. The results have shown that in Portugal the wave energy is higher in the northwest, that the wave climate variability has more impact in the south and that the month with the highest energy is January. A bivariate distribution of significant wave height and energy period was also determined, showing that the sea states where more wave power can be extracted are different than the ones that occur more frequently.

Wave energy assessement for Northern Spain from a 33-year hindcast

Abstract The wave energy resource along the Northern Spanish coast is determined, for a period of 33 years (1979–2012) based on hindcast results of WAVEWATCH III for the Atlantic ocean area, coupled with the SWAN model for the coastal areas, and using surface winds from ECMWF's ERA- Interim data base. Results are validated with buoy data, in order to evaluate the model's accuracy. Statistical analysis of the wave parameters and wave power results are presented. The analysis was carried out for a coarse grid, on the North of Spain, and for three local areas with a finer mesh: Northwest Galicia, the area between Cape San Adrian and Cape Ortegal and Santander. The case studies include a more realistic perspective of the amount of energy that can be extracted with a wave energy converter, by adopting examples of a large and a small device. A seasonal variability evaluation is done for the nested areas through the analyzes of the seasonal average wave power resource for the different locations, throughout the 33 year hindcast, and the joint distributions of significant wave height and peak period for the number of occurrences and wave power.

Joint description of waves and currents applied in a simplified load case

In order to perform a more accurate analysis of marine structures, joint probability distributions of different metocean parameters have received an increasing interest during the last decade, facilitated by improved availability of reliable joint metocean data. There seems to be no general consensus with regard to the approach of estimating joint probability distributions of metocean parameters and a general overview of recent studies exploring different joint models for metocean parameters is presented. The main objective of this article is twofold: first to establish a joint distribution of significant wave height and current speed and then to assess the possible conservatism in the Norwegian design standard by applying this joint distribution in a simplified load case. Based on NORA10 wave data and simulated current data, a joint model for significant wave height and current speed at one location in the northern North Sea is presented. Since episodes of wind-generated inertial oscillations are governing the current conditions at this location, a joint conditional model with current speed conditional on significant wave height is suggested. A peak-over-threshold approach is selected. The significant wave height is found to be very well modelled by a 2-parameter Weibull distribution for significant wave height exceeding 8 m, while a log-normal distribution describes the current speed well. This model is used to Monte-Carlo simulate joint significant wave heights and current speeds for periods corresponding to the ultimate and accidental limit states (ULS and ALS), i.e. 100 and 10 000 years. The possible conservatism in the Norwegian design standard is assessed by a simplified case study. The results give a clear indication that the Norwegian design standard in not necessarily conservative, neither at ULS nor ALS level.

Some probabilistic properties of deep water wave steepness

Summary This paper provides some probabilistic properties of the deep water wave steepness and the spectral wave steepness by using distributions based on data from the Norwegian continental shelf. Here the average statistical properties represented by the mean value and the standard deviation of the two steepness parameters are considered. Examples of results for the wave steepness are given for a Phillips spectrum and a family of JONSWAP spectra for wind sea, and for sea states described by a joint frequency table of significant wave height and mean zero-crossing wave period for combined wind sea and swell. The results for the spectral wave steepness are obtained by using a joint distribution of significant wave height and spectral wave steepness, and the average statistical features are given for joint frequency tables of significant wave height and mean zero-crossing wave period from three locations on the Norwegian continental shelf.

A Vine-Copula Model for Time Series of Significant Wave Heights and Mean Zero-Crossing Periods in the North Sea

Stochastic descriptions and simulations of oceanographic variables are essential for coastal and marine engineering applications. In the past decade, copula-based approaches have become increasingly popular for estimating the multivariate distribution of some variables at the peak of a storm along with its duration. The modeling of the storm shape, which contributes to its impact, is often simplified. This article proposes a vine-copula approach to characterize hourly significant wave heights and corresponding mean zero-crossing periods as a random process in time. The model is applied to a data set in the North Sea, and time series with the duration of an oceanographic winter are simulated. The synthetic wave scenarios emulate storms as well as daily conditions. The results are useful, for example, as input for coastal risk analyses and for planning offshore operations. Nonetheless, selecting a vine structure, finding appropriate copula families, and estimating parameters is not straightforward. The validity of the model, as well as the conclusions that can be drawn from it, are sensitive to these choices. A valuable byproduct of the proposed vine-copula approach is the bivariate distribution of significant wave heights and corresponding mean zero-crossing periods at the given location. Its dependence structure is approximated by the flexible skew-t copula family and preserves the limiting wave steepness condition.

Application of wave runup and wave rundown formulae based on long-term variation of wave conditions

The purpose of this note is to demonstrate that it is possible to use the proposed formulae in Blenkinsopp et al. [1] to estimate runup and rundown based on long-term variation of wave conditions by using the Myrhaug and Fouques [5] joint distribution of significant wave height and Iribarren number for a sea state. Examples of application are given for typical field conditions including a procedure of determining the 100-years return period values for the runup and rundown and the corresponding values of significant wave height and Iribarren number.

Joint statistical models for significant wave height and wave period in a changing climate

In many marine and coastal engineering applications, the simultaneous distribution of several met-ocean variables is required for risk assessment and load and response calculations. For example, a joint probabilistic description is needed to construct environmental contours for probabilistic structural reliability analyses. Typically, the joint distribution of significant wave height and wave period is needed as a minimum, but other environmental parameters such as wind, current, surges and tides might also be relevant.This paper presents a study on various joint models for the simultaneous distribution of significant wave height and zero-crossing wave period. The alternative models that have been investigated are a conditional model, a bivariate parametric model and several models based on parametric families of copulas. Each of the models is fitted to data generated from a numerical wave model for the current climate and for two future climates consistent with alternative climate scenarios. Additionally, the potential effect of climate change on the simultaneous distribution will be investigated.Initial investigation reveals that straightforward application of some of the most commonly used copulas will not give reasonable joint models. The reason for this is that they are symmetric whereas the empirical copulas display asymmetric behaviour. However, asymmetric copulas can be constructed based on these families of copula, and this significantly improves the fit. Analyses of the extremal dependence in the data indicate that the variables are asymptotically independent. Furthermore, the results suggest that extreme significant wave height and zero-crossing wave period tend to be more correlated in a future climate compared to the current climate.

Statistics of extreme ocean environments: Non-stationary inference for directionality and other covariate effects

Numerous approaches are proposed in the literature for non-stationarity marginal extreme value inference, including different model parameterisations with respect to covariate, and different inference schemes. The objective of this paper is to compare some of these procedures critically. We generate sample realisations from generalised Pareto distributions, the parameters of which are smooth functions of a single smooth periodic covariate, specified to reflect the characteristics of actual samples from the tail of the distribution of significant wave height with direction, considered in the literature in the recent past. We estimate extreme values models (a) using Constant, Fourier, B-spline and Gaussian Process parameterisations for the functional forms of generalised Pareto shape and (adjusted) scale with respect to covariate and (b) maximum likelihood and Bayesian inference procedures. We evaluate the relative quality of inferences by estimating return value distributions for the response corresponding to a time period of 10× the (assumed) period of the original sample, and compare estimated return values distributions with the truth using Kullback–Leibler, Cramer–von Mises and Kolmogorov–Smirnov statistics. We find that Spline and Gaussian Process parameterisations, estimated by Markov chain Monte Carlo inference using the mMALA algorithm, perform equally well in terms of quality of inference and computational efficiency, and generally perform better than alternatives in those respects.

Regression quantile models for estimating trends in extreme significant wave heights

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.

Tides and waves in the Central Mediterranean Sea

ABSTRACTMeteo-marine data are necessary and useful for all tasks and scientific activities of national interest involving the protection, enhancement and improvement of the marine environment. The Institute for Environmental Protection and Research (ISPRA) maintains and manages two monitoring networks in order to gather all physical parameters needed in defining the state of Central Mediterranean Sea: the Sea Level Measurement Network (Rete Mareografica Nazionale, RMN) and the Sea Waves Measurement Network (Rete Ondametrica Nazionale, RON). The RMN includes 36 coastal measurement stations; real-time series of sea-level and meteorological parameters are collected every minute. Tide gauges mainly collect sea level, air and water temperatures, wind speed and direction and relative humidity. The RON consists of 15 real-time directional buoys uniformly distributed along the Italian coastline. They collect the main physical parameters such as significant and maximum wave height, peak and mean wave period, wave direction, sea surface temperature (SST), air temperature, wind speed and direction, atmospheric pressure and relative humidity. In this paper attention is focused on statistical analysis in order to describe wave climates, extreme events, tsunami, sea storms and storm surges and related meteorological information. The statistics taken into consideration are mainly the joint frequency distribution of significant wave heights with respect to direction and peak and mean wave periods. Extreme-event analysis is made through the peak over threshold (POT) method and the generalised Pareto distribution (GPD). Finally, sea-level time series analyses are used to highlight examples of meteorological events (such as tsunami) through harmonic and residual analysis.

Alternative Environmental Contours for Marine Structural Design—A Comparison Study1

A new approach to estimate environmental contours in the original physical space by direct Monte Carlo simulations rather than applying the Rosenblatt transformation has recently been proposed. In this paper, the new and the traditional approach to estimating the contours are presented and the assumptions on which they are based are discussed. The different results given by these two methods are then compared in a number of case studies. Simultaneous probability density functions are fitted to the joint distribution of significant wave height and wave period for selected ocean locations and environmental contours are estimated for both methods. Thus, the practical consequences of the choice of approach are assessed. Particular attention is given to mixed sea systems. In these situations, the two approaches to environmental contours may be very different while for other wave conditions the contours are similar.

Bivariate distributions of significant wave height and mean wave period of combined sea states

This work presents the results of the fit of three bivariate models to twelve years of significant wave height and mean zero-crossing period data of swell, wind sea components, and combined sea states from Australia. The Conditional Modelling Approach defines the joint distribution from a marginal distribution of significant wave height and a set of distributions of mean zero-crossing period conditional on significant wave height. The second model fits the Plackett model to the data, and the last one applies the Box–Cox transformations to the data with the aim of making it approximately normal to fit a bivariate normal distribution to the transformed data. The conditional model with a lognormal distribution for the significant wave height and lognormal distributions for the zero-crossing period gave the best fit for the total sea states and for the wind component. In case of the swell component the conditional model with a Weibull distribution to the significant wave height and a lognormal distribution to the mean zero-crossing period gave a relatively close fit to the data.

On the distribution of significant wave height and associated peak periods

This study uses 21years (1958–1978) significant wave height and associated peak periods off Azores in the North Atlantic Ocean, extracted from 44years HIPOCAS database. Empirical average conditional exceedances of peak periods are executed. Plausibility of judging the distribution of the peak periods by modelling average conditional exceedance of peak periods by Erlang, generalized Pareto and three-parameter Weibull models is investigated and we also assessed certain peak period statistics predicted by the models. 50year gamma peak period quantiles are reasonably accurate when compared with 44year peak period quantiles (HIPOCAS). Erlang and generalized Pareto estimate of mean peak period are reasonable; whereas all the three models fairly evaluate the average of the one-third the highest peak periods. Weibull model derived parametric relation gauged the average of the one-tenth the highest peak periods. A general statistical formula is suggested for estimation of significant wave period. Average of one-third the highest peak period estimates by the parametric relation derived from generalized Pareto distribution using the general formula for significant wave period, provides reliably precise results. Significant wave period to mean wave period observational ratio of 1.2 is appropriately interpreted for both computed and estimated ratios of mean peak period of one-third the highest significant wave heights to mean peak periods.

Wave spectra partitioning and long term statistical distribution

A new method is presented for a physically based statistical description of wind wave climatology. The method applies spectral partitioning to identify individual wave systems (partitions) in time series of 2D-wave spectra, followed by computing the probability of occurrence of their (peak) position in frequency–direction space. This distribution can be considered as a spectral density function to which another round of partitioning is applied to obtain spectral domains, each representing a typical wave system or population in a statistical sense. This two-step partitioning procedure allows identifying aggregate wave systems without the need to discuss specific characteristics as wind sea and swell systems. We suggest that each of these aggregate wave systems (populations) is linked to a specific generation pattern opening the way to dedicated analyses.Each population (of partitions) can be subjected to further analyses to add dimension carrying information based on integrated wave parameters of each partition, such as significant wave height, wave age, mean wave period and direction, among others. The new method is illustrated by analysing model spectra from a numerical wave prediction model and measured spectra from a directional wave buoy located in the Southern North Sea. It is shown that these two sources of information yield consistent results. Examples are given of computing the statistical distribution of significant wave height, spectral energy distribution and the spatial variation of wind wave characteristics along a north–south transect in the North Sea. Wind or wave age information can be included as an extra attribute of the members of a population to label them as wind sea or swell systems. Finally, suggestions are given for further applications of this new method.

Sea spray aerosol flux estimation based on long-term variation of wave statistics

Summary This note provides estimates of the mean sea spray aerosol flux based on long-term wave statistics using the whitecap method based on the limiting steepness and threshold vertical acceleration criteria. The aim is to present a procedure demonstrating how global wave statistics can be used to give estimates of the long-term aerosol flux. These estimates are obtained by using bivariate distributions of significant wave height and characteristic wave period, representing open ocean deep water waves in the Northern North Sea and the North Atlantic.

Estimation of wave runup on shorelines based on long-term variation of wave conditions

This article provides a simple analytical method which can be used to give estimates of the wave runup on shorelines based on long-term variation of wave conditions. This is achieved by providing bivariate distribution of significant wave height with the wave runup. This wave runup is defined in terms of significant wave height and spectral peak period in deep water. This article presents the mean value and the standard deviation, that is, more precisely the conditional expected value and the conditional variance of the wave runup for given significant wave height. Examples of results corresponding to typical field conditions are also given. Based on, for example, global wave statistics, the present analytical results can be used to make estimates of the wave runup.

Trivariate maximum entropy distribution of significant wave height, wind speed and relative direction

A trivariate maximum entropy distribution of significant wave height, wind speed and the relative direction is proposed here. In this joint distribution, all the marginal variables follow modified maximum entropy distributions, and they are combined by a correlation coefficient matrix based on the Nataf transformation. The methods of single extreme factors and of conditional probability are presented for the joint design of trivariate random variables. The corresponding sampling data about significant wave heights, wind speeds and the relative directions from a location in the North Atlantic is applied for statistical analysis, and the results show that the trivariate maximum entropy distribution is sufficiently good to fit the data, and method of conditional probability can reduce the design values efficiently.

Wind waves in the Black Sea: results of a hindcast study

Abstract. In this study we describe the wind wave fields in the Black Sea. The general aims of the work were the estimation of statistical wave parameters and the assessment of interannual and seasonal wave parameter variability. The domain of this study was the entire Black Sea. Wave parameters were calculated by means of the SWAN wave model on a 5 × 5 km rectangular grid. Initial conditions (wind speed and direction) for the period between 1949 and 2010 were derived from the NCEP/NCAR reanalysis. According to our calculations the average significant wave height on the Black Sea does not exceed 0.7 m. Areas of most significant heavy sea are the southwestern and the northeastern parts of the sea as expressed in the spatial distribution of significant wave heights, wave lengths and periods. Besides, long-term annual variations of wave parameters were estimated. Thus, linear trends of the annual total duration of storms and of their quantity are nearly stable over the hindcast period. However, an intensification of storm activity is observed in the 1960s–1970s.

Stokes drift estimation based on long-term variation of wave conditions

This article provides a simple analytical method which can be used to give estimates of the Stokes drift based on long-term variation of wave conditions. This is achieved by providing bivariate distributions of significant wave height with surface Stokes drift as well as with volume Stokes transport. These Stokes drift parameters are defined in terms of significant wave height and characteristic wave periods. This article presents the mean value and the standard deviation of these Stokes drift parameters, that is, more precisely the conditional expected values and the conditional variances for given significant wave height, as well as examples of results corresponding to typical field conditions. Based on, for example, global wave statistics, the present analytical results can be used to make estimates of the Stokes drift.

Response to "Discussion of 'Modelling significant wave height distributions with quantile functions for estimation of extreme wave heights' [Ocean Engneering 54 (2012) 119–131]" by Zai-Jin You and David Callaghan

The discussers have commented on the reference paper, discussing would be used and compared as done for example in Guedes various questions that include the method of quantiles, the characteristics of the data sets used in the examples and the conclusion about the choice among the various quantile distributions. The authors agree that whenever there is a distribution that has an analytical expression for its distribution F(x), the quantile function Q(p) can be derived from it and both describe the probabilistic nature of the variable x. In fact, when both can be derived explicitly it is equivalent to use one or the other to extreme value predictions. It is then a matter of taste the choice of one or the other. This is already stated in the original paper, where it is indicated that the purpose of presenting the quantile functions is exactly to suggest an alternative and equivalent method to determine extremes. However in cases inwhich F(x) does not have a closed form, then Q(p) should be used for extreme value analysis as the discussers also state. This would then be an advantage of using the quantile functions because in most cases what is available is a data set from which inferences are made for a F(x). This means that in practice an analytical expression of F(x) is not available, although an analytical expression might be adopted to model the data. The discussers then go on to comment on the case studies used for the demonstration of the application of the method. They specifically comment on the choice of daily maxima, which was done to reduce the size of the data set and the correlation among data. The objective of the paper was to propose the quantile functions and to demonstrate how they could be applied. The objective was not to determine the extreme value significant wave heights at a particular location. If that would have been the case indeed more care would be given to choose a data set with less correlation between the data as discussed for example in Ferreira and Guedes Soares (2000) and also several methods