Wave energy assessment based on trivariate distribution of significant wave height,mean period and direction

Based on the Vine copula theory, a trivariate statistical model of significant wave height, characterized wave period and mean wave direction was constructed. To maintain the properties of the different types of variables, a special copula function was derived from the model developed by Johnson and Wehrly based on the maximum entropy principle. It was then combined with the Archimedean copulas to construct the proposed model. An effective algorithm for generating corresponding joint pseudo-random numbers was also developed. Statistical analysis of hindcast data for the significant wave height, mean wave period, and direction, which were collected from an observation point in the North Atlantic every three hours from 1997 to 2001, was performed. The marginal distributions of the significant wave height and mean wave period were fitted by a modified maximum entropy distribution, and the mean wave direction was fitted by a mixture of von Mises distributions. It was shown that the proposed model is a good fit for the data. The seasonal wave energy resources in the target area were assessed using the model estimates. Histograms of the directional wave energy, wave energy roses, and scatter and energy diagrams were presented.     

Predicting significant wave height off the northeast coast of the United States

To develop a simple method to predict the significant wave height, we analyze 18 years of hourly observations from 12 different buoys that are off the northeast coast of the United States. Water depths ranged from 19 to 4427 m for these moored buoys. We find that, on average, all of these buoys exhibit a region of constant wave height for 10-m wind speeds between 0 and 4 m s⁻¹. That wave height does, however, depend on water depth. For wind speeds above 4 m s^–1, the wave height increases as the square of the wind speed; but the multiplicative factor is again a function of water depth. We synthesize these results in a prediction scheme that yields the significant wave height from simple functions of water depth and 10-m wind speed for wind speeds up to 25 m s^–1.     

Adaptive estimation of wave parameters by Geno-Kalman filtering

Prediction of wave parameters is very important for planning, designing and operation of ocean structures. Accurate estimation of these parameters provides engineers to construct more economical and reliable ocean structures such as harbors, breakwaters, oil production platforms and ocean wave energy converters. For this reason, optimum operation of these plants has become a must. Various methods have been introduced to determine the relation among wind speed previous and current wave parameters. Method proposed in this paper consists of genetic algorithms and Kalman filters which is called as Geno-Kalman filtering. It is based on adaptive calculation to reach the solution. Also a comparison has been made between perceptron Kalman filtering and Geno-Kalman filtering techniques. The application of Geno-Kalman filtering was performed for station 46002 which located in the Coos Bay at Oregon, USA. It is observed that the Geno-Kalman filtering methodology has smaller absolute, mean-square and relative errors than perceptron Kalman filtering. Also coefficient of efficiency value which was used to evaluate results between observed and estimated is higher at Geno-Kalman filtering than perceptron Kalman filtering.     

Seasonality and duration in extreme value distributions of significant wave height

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.     

Modelling the long-term time series of significant wave height with non-linear threshold models

Linear autoregressive models and non-linear threshold autoregressive (TAR) models are used in the present work to describe the time series of the significant wave height of sea-states at Figueira da Foz, located in the Portuguese coast. The seasonal components of this series are identified and a TAR model with two regimes is proposed. A simulation study was carried out with the purpose of verifying if both the non-linear and linear models are suited to describe the probabilistic structure of the process. It is shown that both methods are adequate to describe the lower statistical moments of the original data, but the non-linear model represents better the skewness and the kurtosis of the data.     

南麂站定常波风浪波高与风速的经验关系

本文以南麂海洋站１９８３～１９９０年风、浪的实测资料为依据，建立了南麂海城春、夏、秋、冬季定常波风浪波高与风速的经验关系式。检验结果表明，曲线回归显著，计算值与实测值吻合良好。文中还对偏ＮＮＥ向和偏ＳＳＷ向计算波高随风速增大的快慢，同一方向在同一风速作用下计算波高的季节变化及其机理作了初浅的讨论。     

Significant wave height forecasting using wavelet fuzzy logic approach

Wave heights and periods are the significant inputs for coastal and ocean engineering applications. These applications may require to obtain information about the sea conditions in advance. This study aims to propose a forecasting scheme that enables to make forecasts up to 48 h lead time. The combination of wavelet and fuzzy logic approaches was employed as a forecasting methodology. Wavelet technique was used to separate time series into its spectral bands. Subsequently, these spectral bands were estimated individually by fuzzy logic approach. This combination of techniques is called wavelet fuzzy logic (WFL) approach. In addition to WFL method, fuzzy logic (FL), artificial neural networks (ANN), and autoregressive moving average (ARMA) methods were employed to the same data set for comparison purposes. It is seen that WFL outperforms those methods in all cases. The superiority of the WFL in model performances becomes very clear especially in higher lead times such as 48 h. Significant wave height and average wave period series obtained from buoys located off west coast of US were used to train and test the proposed models.     

Verification of significant wave representation method

The significant wave representation method is the simplest method for computing the transformation of significant wave height across-shore. However, many engineers are reluctant to use this method because many researchers have pointed out that the method possibly contains a large estimation error. Nevertheless, Rattanapitikon et al. [Rattanapitikon, W., Karunchintadit, R., Shibayama, T., 2003. Irregular wave height transformation using representative wave approach. Coastal Engineering Journal, JSCE 45(3), 489–510.] showed that the wave representation method could be used to compute the transformation of root mean square wave heights. It may also be possible to use it for computing the significant wave height transformation. Therefore, this study was carried out to examine the possibility of simulating significant wave height transformation across-shore by using the significant wave representation method. Laboratory data from small- and large-scale wave flumes were used to calibrate and examine the models. Six regular wave models were applied directly to irregular waves by using the significant wave height and spectral peak period. The examination showed that three regular wave models (with new coefficients) could be used to compute the significant wave height transformation with very good accuracy. On the strength of both accuracy and simplicity of the three models, a suitable model is recommended for computing the significant wave height transformation. The suitable model was also modified for better predictions. The modified model (with different coefficients) can be used to compute either regular wave height or significant wave height transformation across-shore.     

Modelling the long-term distribution of significant wave height with the Beta and Gamma models

The paper suggests modelling the long-term distribution of significant wave height with the Gamma, Beta of the first and second kind models. The three models are interrelated, flexible and cover the three different tail types of Extreme Value Theory. They can be used simultaneously as a means of assessing the uncertainty effects that result from choosing equally plausible models with different tail types. This procedure is intended for those applications that require the long-term distribution of significant wave height as input rather than the prediction of extreme values. The models are fitted to some significant wave data as an illustration. Details about maximum likelihood estimation are given in A.     

中国海域有效波高、海表风速长期变化趋势的季节特征

Long-term variations in a sea surface wind speed(WS) and a significant wave height(SWH) are associated with the global climate change, the prevention and mitigation of natural disasters, and an ocean resource exploitation,and other activities. The seasonal characteristics of the long-term trends in China's seas WS and SWH are determined based on 24 a(1988–2011) cross-calibrated, multi-platform(CCMP) wind data and 24 a hindcast wave data obtained with the WAVEWATCH-III(WW3) wave model forced by CCMP wind data. The results show the following.(1) For the past 24 a, the China's WS and SWH exhibit a significant increasing trend as a whole, of3.38 cm/(s·a) in the WS, 1.3 cm/a in the SWH.(2) As a whole, the increasing trend of the China's seas WS and SWH is strongest in March-April-May(MAM) and December-January-February(DJF), followed by June-July-August(JJA), and smallest in September-October-November(SON).(3) The areal extent of significant increases in the WS was largest in MAM, while the area decreased in JJA and DJF; the smallest area was apparent in SON. In contrast to the WS, almost all of China's seas exhibited a significant increase in SWH in MAM and DJF; the range was slightly smaller in JJA and SON. The WS and SWH in the Bohai Sea, the Yellow Sea, East China Sea, the Tsushima Strait, the Taiwan Strait, the northern South China Sea, the Beibu Gulf, and the Gulf of Thailand exhibited a significant increase in all seasons.(4) The variations in China's seas SWH and WS depended on the season. The areas with a strong increase usually appeared in DJF.     

Derivation of coastal wind and wave parameters from offshore measurements of TOPEX satellite using ANN

The paper discusses an artificial neural network (ANN) approach to project information on wind speed and waves collected by the TOPEX satellite at deeper locations to a specified coastal site. The observations of significant wave heights, average wave period and wind speed at a number of locations over a satellite track parallel to a coastline are used to estimate corresponding values of these three parameters at the coastal site of interest. A combined network involving an input and output of all the three parameters, viz., wave height, period and wind speed instead of separate networks for each one of these variables was found to be necessary in order to train the network with sufficient flexibility. It was also found that network training based on statistical homogeneity of data sets is essential to obtain accurate results. The problem of modeling wind speeds that are always associated with very high variations in their magnitudes was tackled in this study by imparting training in an innovated manner.     

Prediction of wave parameters by using fuzzy logic approach

The purpose of this study is to investigate the relationship between wind speed, previous and current wave characteristics. It is expected that such a non-linear relationship includes some uncertainties. A fuzzy inference system employing fuzzy IF–THEN rules has an ability to deal with ill-defined and uncertain systems. Compared with traditional approaches, fuzzy logic is more efficient in linking the multiple inputs to a single output in a non-linear domain. In this paper, a sophisticated intelligent model, based on Takagi–Sugeno (TS) fuzzy modeling principles, was developed to predict the changes in wave characteristics such as significant wave height and zero up-crossing period due to the wind speed. Past measurements of significant wave height values and wind speed variables are used for training the adaptive model and it is then employed to predict the significant wave height amounts for future time intervals such as 1, 3, 6 and 12 h. The verification of the proposed model is achieved through the wave characteristics time series plots and various numerical error criterias. Also the model results were compared with classical Auto Regressive Moving Average with exogenous input (ARMAX) models. For the application of the proposed approach the offshore station located in the Pacific Ocean was used.     

Variations in the Baltic Sea wave fields

The surface waves in the Baltic Sea are hindcast with the spectral wave model HYPAS during a 12-month period. The model results show a strong temporal and spatial variation in the wave field due to the physical dimensions of the different basins and the predominant wind field. The highest waves in the area are found in the outer part of Skagerrak, as well as in the central and southern parts of the Baltic Proper. To get significant waves above 6 m high, strong winds (15–20 m/s) must have been blowing for 6 to 24 h from a favourable direction over a deep area.     

Estimation of wind speed and wave height during cyclones

Wave and wind characteristics based on the cyclones, in the vicinity of the Nagapattinam coastline (east coast of India) were estimated. In all, 11 cyclones have crossed near the study region during 1960–1996. For the four severe cyclones, the isobaric charts were collected at three hourly intervals from the India Meteorological Department. The storm variables such as central pressure, radius of maximum wind, speed of forward motion and direction of storm movement were extracted and the method based on standard Hydromet pressure profile, were used for the hindcast of storm wind fields. For all the cyclones the maximum significant wave height within the storm and its associated spectral peak period was estimated using the Young’s model considering the moving wind field and the results are compared with the hurricane wave prediction techniques provided in the shore protection manual published by the US Army Corps of Engineers in 1984. The study shows that the estimated wind speed and the data reported by ships were comparable. Empirical expressions relating wind speed, wave height and wave period to storm parameters were derived. The design wave height for different return periods was obtained by fitting a two-parameter Weibull distribution to the estimated significant wave heights. The design wave height was 9.39 m for 1 in 100 year return period for a direct hit of cyclone.     

A joint distribution of significant wave height and characteristic surf parameter

The paper provides a joint distribution of significant wave height and characteristic surf parameter. The characteristic surf parameter is given by the ratio between the slope of a beach or a structure and the square root of the characteristic wave steepness in deep water defined in terms of the significant wave height and the spectral peak period. The characteristic surf parameter is used to characterize surf zone processes and is relevant for e.g. wave run-up on beaches and coastal structures. The paper presents statistical properties of the wave parameters as well as an example of results corresponding to typical field conditions.     

预测有效波高的深度学习模型研究

研究基于RNN、LSTM、GRU深度学习模型,针对NOAA浮标数据集中的44013、44014、44017浮标的数据,通过斯皮尔曼相关性分析提高模型预测效果。实验结果表明,在进行相关性分析后,S-RNN、S-LSTM、 S-GRU的预测效果均比原始RNN、LSTM、GRU模型预测效果好。此外,提出一种基于LSTM的LSTM-Attention 波高预测模型,并进行相关实验,量化LSTM-Attention模型的预测效果,实验结果表明LSTM-Attention模型有更好的预测效果。为评估模型的泛化能力,研究还提出了一种采用邻近浮标数据进行学习,预测浮标缺失数据的方 法。实验结果表明,该方法的预测精度可以达到97.93%。本研究为海浪预测提供了新的方法和思路,也为未来深 度学习模型在海浪预测中的应用提供了参考。     

A weakly non-gaussian model of wave height distribution for random wave train

The wave height distribution with Edgeworth’s form of a cumulative expansion of probability density function (PDF) of surface elevation are investigated. The results show that a non-Gaussian model of wave height distribution reasonably agrees with experimental data. It is discussed that the fourth order moment (kurtosis) of water surface elevation corresponds to the first order nonlinear correction of wave heights and is related with wave grouping.     

基于SVM回归模型的SAR图像有效波高估测

A new method for estimating significant wave height(SWH) from advanced synthetic aperture radar(ASAR) wave mode data based on a support vector machine(SVM) regression model is presented. The model is established based on a nonlinear relationship between σ0, the variance of the normalized SAR image, SAR image spectrum spectral decomposition parameters and ocean wave SWH. The feature parameters of the SAR images are the input parameters of the SVM regression model, and the SWH provided by the European Centre for Medium-range Weather Forecasts(ECMWF) is the output parameter. On the basis of ASAR matching data set, a particle swarm optimization(PSO) algorithm is used to optimize the input kernel parameters of the SVM regression model and to establish the SVM model. The SWH estimation results yielded by this model are compared with the ECMWF reanalysis data and the buoy data. The RMSE values of the SWH are 0.34 and 0.48 m, and the correlation coefficient is 0.94 and 0.81, respectively. The results show that the SVM regression model is an effective method for estimating the SWH from the SAR data. The advantage of this model is that SAR data may serve as an independent data source for retrieving the SWH, which can avoid the complicated solution process associated with wave spectra.