Sea State Parameters Research Articles

On the distribution of wave height in shallow water

The statistical distribution of the height of sea waves in deep water has been modelled using the Rayleigh (Longuet-Higgins, 1952) and Weibull distributions (Forristall, 1978). Depth-induced wave breaking leading to restriction on the ratio of wave height to water depth requires new parameterisations of these or other distributional forms for shallow water. Glukhovskiy (1966) proposed a Weibull parameterisation accommodating depth-limited breaking, modified by van Vledder (1991). Battjes and Groenendijk (2000) suggested a two-part Weibull–Weibull distribution. Here we propose a two-part Weibull-generalised Pareto model for wave height in shallow water, parameterised empirically in terms of sea state parameters (significant wave height, HS, local wave-number, kL, and water depth, d), using data from both laboratory and field measurements from 4 offshore locations. We are particularly concerned that the model can be applied usefully in a straightforward manner; given three pre-specified universal parameters, the model further requires values for sea state significant wave height and wave number, and water depth so that it can be applied. The model has continuous probability density, smooth cumulative distribution function, incorporates the Miche upper limit for wave heights (Miche, 1944) and adopts HS as the transition wave height from Weibull body to generalised Pareto tail forms. Accordingly, the model is effectively a new form for the breaking wave height distribution. The estimated model provides good predictive performance on laboratory and field data.

Prediction of seaward slope recession in berm breakwaters using M5' machine learning approach

In the design process of berm breakwaters, their front slope recession has an inevitable rule in large number of model tests, and this parameter being studied. This research draws its data from Moghim’s and Shekari’s experiment results. These experiments consist of two different 2D model tests in two wave flumes, in which the berm recession to different sea state and structural parameters have been studied. Irregular waves with a JONSWAP spectrum were used in both test series. A total of 412 test results were used to cover the impact of sea state conditions such as wave height, wave period, storm duration and water depth at the toe of the structure, and structural parameters such as berm elevation from still water level, berm width and stone diameter on berm recession parameters. In this paper, a new set of equations for berm recession is derived using the M5' model tree as a machine learning approach. A comparison is made between the estimations by the new formula and the formulae recently given by other researchers to show the preference of new M5' approach.

Application of X-Band Wave Radar for Coastal Dynamic Analysis: Case Test of Bagnara Calabra (South Tyrrhenian Sea, Italy)

Sea state knowledge has a key role in evaluation of coastal erosion, the assessment of vulnerability and potential in coastal zone utilization, and development of numerical models to predict its evolution. X-band radar measurements were conducted to observe the spatial and temporal variation of the sea-state parameters along a 3 km long sandy-gravelly pocket beaches forming a littoral cell on Bagnara Calabra. We produced a sequence of 1000 images of the sea state extending offshore up to 1 mile. The survey has allowed monitoring the coastline, the directional wave spectra, the sea surface current fields, and the significant wave heights and detecting strong rip currents which cause scours around the open inlets and affect the stability of the submerged reef-type breakwaters. The possibility to validate the data acquired with other datasets (e.g., LaMMA Consortium) demonstrates the potential of the X-band radar technology as a monitoring tool to advance the understanding of the linkages between sea conditions, nearshore sediment dynamics, and coastal change. This work proves the possibility to obtain relevant information (e.g., wave number, period, and direction) for evaluation of local erosion phenomena and of morphological changes in the nearshore and surf zone.

Amplitude and Dilation Compensation of the SAR Altimeter Backscattered Power

A new method of forming the synthetic aperture radar altimeter multilook backscattered power waveform is proposed for application over water. The method compensates the waveform for both variations in amplitude and dilation in range, which are caused by the geometry of the observation and the signal processing chain of the instrument. Using Cryosat data collected over the Pacific Ocean and over the Black Sea, the method is used to retrack the geophysical parameters of sea surface height and significant wave height, and the noise level of these retracked parameters is compared with the noise levels of conventionally retracked parameters. It is found that applying amplitude compensation and dilation compensation leads to a reduction in the noise level by up to a factor of 4.0 for sea surface height and 2.5 for significant wave height. The reduction in noise is largest for small significant wave heights. In addition, the waveform is accurately modeled by a single argument function, needing only a scaling and offset to fit the multilook waveform, greatly improving the theoretical description of the waveform dependence on the sea state and instrument parameters.

Comparing wavelengths simulated by the coastal wave model CWAM and TerraSAR-X satellite data

The accuracy of the high resolution coastal wave forecast model CWAM is validated on the basis of sea state information from satellite images of TerraSAR-X (TS-X). At the same time, the performance of the satellite retrieval of sea state parameters is demonstrated. Employing 2-dimensional spatial Fourier Transformation, image spectra are derived from TS-X and locally varying patterns of the peak wavelength are provided using state-of-the-art satellite retrieval. Subsequently, wavelength comparisons are performed between a typical set of TS-X scenes acquired in December 2013 over the German Bight and the model hindcasts. The results are mostly in reasonable agreement. Potential shortcomings of the wave model are discussed as well.

Global sensitivity of parabolic equation radar wave propagation simulation to sea state and atmospheric refractivity structure

AbstractInadequate representation of the environment is a limitation for prediction of radar system performance as well as for validation of propagation codes. To improve understanding of how different environmental effects/parameters compete and compare, this study examines the sensitivity of radar wave propagation to a suite of environmental parameters for low grazing angle near‐surface radar systems at 3–15 GHz at horizontal and vertical polarizations. A global sensitivity analysis method is used, which accounts for parameter interactions, and propagation is modeled using the parabolic equation method. Environmental parameters examined include eight sea state parameters and eight parameters characterizing the vertical structure and character of range‐independent refractivity profiles. The relative importance of parameters varies more with frequency than polarization, and parameter interactions are found to be significant. Atmospheric mixed layer parameters are found to be the most sensitive, particularly the thickness of the mixed layer. The most significant ocean surface parameter is swell period, although sea directionality is important at 3 GHz and sea surface roughness and salinity are important at 9 and 15 GHz. Because of the spatial variability of sensitivity throughout the domain, regional analysis is performed to determine the most important parameters in different regions of the domain (1000 m in altitude and 60 km in range). These regional sensitivity results, along with those for the whole domain, provide guidance on prioritization of environmental characterization in numerical weather prediction and inversion studies (e.g., refractivity from clutter studies), which are two common methods currently used to address environmental effects on propagation.

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

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 HS. For a single location, this analysis is complicated by the serial dependence of HS 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 , 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 are estimated by simulation under the threshold ensemble model. Return values for HS are then estimated by simulating intra‐storm trajectories of HS 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 HS and other sea state parameters. Model validation is performed by comparing confidence intervals for cumulative distribution functions of and HS for the period of the data with empirical sample‐based estimates. Copyright © 2015 John Wiley & Sons, Ltd.

Significant wave height estimation using SVR algorithms and shadowing information from simulated and real measured X-band radar images of the sea surface

In this paper we propose to apply the Support Vector Regression (SVR) methodology to significant wave height estimation using the shadowing effect, that is visible on the X-band marine radar images of the sea surface due to the presence of high waves. One of the main problems of using sea clutter images is that, for a given sea state conditions, the shadowing effect depends on the radar antenna installation features, such as the angle of incidence. On the other hand, for a given radar antenna location, the shadowing properties depend on the different sea state parameters, like wave periods, and wave lengths. Thus, in this paper we show that SVR can be successfully trained from simulation-based data. We propose a simulation process for X-band marine radar images derived from simulated wave elevation fields using the stochastic wave theory. We show the performance of the SVR in simulation data and how SVR outperforms alternative algorithms such as neural networks. Finally, we show that the simulation process is reliable by applying the SVR methodology trained in the simulation-based data to real measured data, obtaining good prediction results in wave height, which indicates the goodness of our proposal.

Damage equivalent wind–wave correlations on basis of damage contour lines for the fatigue design of offshore wind turbines

An adequate representation of the site-specific wind–wave joint distribution is essential for cost-efficient and reliable designs of offshore wind turbines. Therefore, the wind and wave climates are subjected to a correlation of wind and wave parameters for design purposes. These correlations are often based on a lumping of the directional wave climate and subsequent association of the lumped wave climate to the directional wind climate. Preservation of the hydrodynamic fatigue distribution from the full wave climate is an important aspect in the wind-wave correlation process which requires an adequate consideration of the dynamics from the offshore wind turbine. However, only a few wind-wave correlation methods exist for the fatigue design of offshore wind turbines and none of them take the dynamics of the full structure adequately into account. In this study a new wind-wave correlation method has been developed and introduced. The new method is based on the establishment of damage contour lines which are used to determine the sea-state parameters that ensure simultaneous compliance with damage equivalency criterions at different locations within the offshore wind turbine. This simultaneous damage equivalency throughout the structure together with the straightforward derivation of the corresponding damage equivalent sea-state parameters constitutes the novelty of the presented wind-wave correlation method.

Long-term performance assessment and design of offshore structures

The design of an offshore structure is highly dependent on the operating environmental parameters, where a realistic statistical model of the latter is essential to produce a representative estimate of the performance and failure probability. Establishing an accurate model of the offshore environment can be a challenging task. The use of simple probabilistic models may lead to biased results in the stochastic structural analysis since the environmental impact to an existing offshore structure is associated with a wide range of inter-dependent factors. In this paper, the specification of long-term design loads for offshore structures considering multiple environmental factors is investigated where the dependency between several commonly used sea state parameters are instituted through a copula-based multivariate probabilistic model. Several copula functions, capable of modeling both linear and non-linear dependence structures, are considered. The developed multivariate model based on copula concept is compared with the available approaches in the literature using actual environmental data. The modeled sea state parameters are then utilized to characterize the sea load for the reliability analysis of a real jacket structure where the prediction of the long term load is derived in a discretized form. The applicability of this approach in a high dimensional multivariate problem is also discussed.

Beyond significant wave height: A new approach for validating spectral wave models

Wave data are required in many engineering applications. At locations where measured records are not available or are too short for design purposes, estimates of wave properties from numerical wave models are often used to characterise the expected wave climate. Typically, model predictions are validated against observations of the sea-state parameters, such as significant wave height, peak wave period, mean wave period and mean wave direction. However, while agreement between observed and predicted sea-state parameters can be good, in some cases the measured and predicted wave spectra can diverge significantly. In these circumstances, simple sea state parameters alone are not sufficient to describe the range of wave conditions that could arise at a given site. In this paper we present a new, alternative approach for assessing wave model performance by applying new parameterisation to the frequency wave spectrum. Seven parameters (significant wave height, peak frequency, peak energy density, squared Euclidean distance, skewness, kurtosis and mean width deviation) are used to better define the characteristics of unimodal wave spectra. Sensitivity tests are undertaken to analyse the performance and sensitivity of these parameters in identifying differences between observed and predicted wave spectra, using a range of idealised JONSWAP wave spectra. We demonstrate that comparing multiple parameters is a better method to distinguish differences between spectra than the results obtained using individual parameters in isolation. As such, application of two-dimensional validation matrices are proposed to provide a better, qualitative overview of the goodness of fit between observed and predicted wave spectra. The advantages of the new approach are demonstrated through validation of a hindcast spectral wave model at Hastings, southeast England. We believe that we have achieved our purpose here to start a discussion on alternative validation techniques that could be enhanced in the future.

SAR Altimeter Backscattered Waveform Model

The backscatters power single-look waveform recorded by a synthetic aperture radar altimeter is approximated in a closed-form model. The model, being expressed in terms of parameterless functions, allows for efficient computation of the waveform and a clear understanding of how the various sea state and instrument parameters affect the waveform.

A weather-type statistical downscaling framework for ocean wave climate

Wave climate characterization at different time scales (long-term historical periods, seasonal prediction, and future projections) is required for a broad number of marine activities. Wave reanalysis databases have become a valuable source of information covering time periods of decades. A weather-type approach is proposed to statistically downscale multivariate wave climate over different time scales from the reanalysis long-term period. The model calibration is performed using historical data of predictor (sea level pressure) and predictand (sea-state parameters) from reanalysis databases. The storm activity responsible for the predominant swell composition of the local wave climate is included in the predictor definition. N-days sea level pressure fields are used as predictor. K-means algorithm with a postorganization in a bidimensional lattice is used to obtain weather patterns. Multivariate hourly sea states are associated with each pattern. The model is applied at two locations on the east coast of the North Atlantic Ocean. The validation proves the model skill to reproduce the seasonal and interannual variability of monthly sea-state parameters. Moreover, the projection of wave climate onto weather types provides a multivariate wave climate characterization with a physically interpretable linkage with atmospheric forcings. The statistical model is applied to reconstruct wave climate in the last twentieth century, to hindcast the last winter, and to project wave climate under climate change scenarios. The statistical approach has been demonstrated to be a useful tool to analyze wave climate at different time scales.

Field Measurements of Rogue Water Waves

AbstractThis paper concerns the collation, quality control, and analysis of single-point field measurements from fixed sensors mounted on offshore platforms. In total, the quality-controlled database contains 122 million individual waves, of which 3649 are rogue waves. Geographically, the majority of the field measurements were recorded in the North Sea, with supplementary data from the Gulf of Mexico, the South China Sea, and the North West shelf of Australia. The significant wave height ranged from 0.12 to 15.4 m, the peak period ranged from 1 to 24.7 s, the maximum crest height was 18.5 m, and the maximum recorded wave height was 25.5 m. This paper will describe the offshore installations, instrumentation, and the strict quality control procedure employed to ensure a reliable dataset. An examination of sea state parameters, environmental conditions, and local characteristics is performed to gain an insight into the behavior of rogue waves. Evidence is provided to demonstrate that rogue waves are not governed by sea state parameters. Rather, the results are consistent with rogue waves being merely extraordinary and rare events of the normal population caused by dispersive focusing.

Wave energy and hot spots in Anzali port

Providing energy without unfavorable impacts on the environment is an important issue for many countries. Wave energy is one of the renewable resources with high potential and low impact on the environment, especially in coastal regions. The estimation of the wave characteristics is essential for selection of the appropriate location for wave energy exploitation. In this study, SWAN (Simulating WAves Nearshore) was used for modeling of the wave characteristics and to describe the existence and variability of wave energy in the southern part of the Caspian Sea. The model results were calibrated and verified using in-situ buoy measurements. Wave parameters were simulated and the annual wave energy was estimated in the study area. Then, high-energy spots were determined and the monthly average wave energy and seasonal variations of wave energy in the selected site were investigated. Furthermore, wave energy resource was characterized in terms of sea state parameters i.e. significant wave heights, wave periods and mean directions for selecting the most appropriate wave energy converters in the selected site. It was found that January and February, i.e. winter months, are the most energetic months and the main wave directions with the highest frequencies are northeast and northern-northeast in this site.

Remocean System for the Detection of the Reflected Waves from the Costa Concordia Ship Wreck

This paper presents the validation of the Remocean X-band wave radar as a tool for sea state monitoring in coastal zones, by processing the data collected and processed by the radar platform installed at the port of Giglio Island. In particular, the effectiveness of the sea wave height reconstruction has been tested during the storm on November 27, 2012, by focusing on the analysis of the spectral slope and the statistical properties of the ocean waves. A further proof of the effectiveness of the system has been shown by comparing both the estimated sea state parameters and 2-D directional spectrum with the benchmark forecasting models WaveWatchIII (WW3) and Simulating Wave Nearshore (SWAN).

An experimental study on the parameterization of reshaped seaward profile of berm breakwaters

Berm breakwaters are rubble mound structures in which the seaward slope of the initial profile may be reshaped to become more stable under severe wave attack. The stones in the seaward slope move from the initial slope to an equilibrium profile. A 2D experimental study has been carried out in a wave flume at a hydraulic laboratory of Tarbiat Modares University to study the effects of sea state and structural parameters on the reshaped profile parameters of such breakwaters. A series of 287 tests have been performed to cover the effect of various sea state conditions such as wave height, wave period, number of waves and water depth at the toe of the structure, and structural parameters such as berm width, berm elevation above still water level and armor stone size. All the tests have been done employing irregular waves with a JONSWAP spectrum. In this paper, first the reshaped profiles are schematized, and then the key parameters of the reshaped seaward profiles such as step height, step length and depth of intersection point of initial and reshaped profile are investigated, using results of this experimental work. Eventually, formulae that include some sea state and structural parameters are derived for estimation of the reshaped profile parameters. To assess the validity of the proposed formulae, comparisons are made between the estimated parameters of reshaped profiles by these formulae and earlier formulae given by other researchers. The comparisons show that the estimation procedure foretells reshaping parameters well and with less scatter according to the present data and also other experimental results within the range of parameters tested.

X-Band Marine Radar System for High-Speed Navigation Purposes: A Test Case on a Cruise Ship

This letter deals with the investigation of the performance of the REMOCEAN wave-radar system for sea state monitoring, with a specific focus to the navigation purposes. In particular, we present the results of the processing of data collected by an X-band wave-radar installed on the Cruise Roma, during the voyage from Civitavecchia (Italy) to Barcelona (Spain) and return, on 9th and 10th March, 2012. The effectiveness of the REMOCEAN data processing is analyzed by comparing the estimated sea state parameters with the expectation provided by the operational forecasting runs of the WaveWatchIII spectral modeling.

Joint distributions of wave height and period in laboratory generated nonlinear sea states

The main goal of the work is to investigate the joint distribution of the wave heights and periods of nonlinear wave time series obtained in laboratory conditions. Three groups of laboratory experiments carried out in Marintek, Norway and in CEHIPAR, Spain are used in the work. Due to different scales of the generated waves only the series that in full scale have the same distance from the wave maker are compared. For different initial steepness of the produced wave time series the spatial variations of the main sea state parameters, the power spectral density, the joint distribution of wave heights and periods, and marginal distributions of the wave heights and the wave periods are studied. The observed results of the joint distributions are also compared with the theoretical model of Longuet-Higgins (1983). It is found that the observed joint distributions of wave heights and periods in the Marintek and in the CEHIPAR basins are similar to each other. However the results show that close to the mode of the joint density there is a deviation with different degrees of intensity from the theoretical ones, especially for large wave steepness.

Identifying trends in the ocean wave climate by time series analyses of significant wave heightdata

Reliable return period estimates of sea state parameters such as the significant wave height are of great importance in marine structural design and ocean engineering. Hence, time series of significant wave height have been extensively studied in recent years. However, with the possibility of an ongoing change in the global climate, this might influence the ocean wave climate as well and it would be of great interest to analyze long time series to see if any long-term trends can be detected. In this paper, long time series of significant wave height stemming from the ERA-40 reanalysis project containing six-hourly data over a period of more than 44 years are investigated with the purpose of identifying long term trends. Different time series analysis methods are employed, i.e. seasonal ARIMA, multiple linear regression, the Theil–Sen estimator and generalized additive models, and the results are discussed. These results are then compared to previous studies; in particular results are compared to a recent study where a spatio-temporal stochastic model was applied to the same ERA-40 data. However, in the current analysis, the spatial dimension has been reduced and time series of the spatial minima, spatial mean and spatial maxima respectively have been analyzed for temporal trends.