Significant Wave Height Prediction Research Articles

Determination of the wave climate for the southern Brazilian shelf

The main objective of this study is the characterization of the wave climate in the Southern Brazilian Shelf (SBS) based on a thorough review of existing field data and on numerical modeling experiments. A quantitative knowledge about the wave climate of this area is important to understand the mechanisms driving episodic mud bank attachments to the sandy shore, and the interaction of these banks with the flow and waves. The statistical analysis of existent data on the wave climate throughout the SBS indicates that the predominant wave directions are 100° and 160° (E–SE), with wave heights varying between 1 and 1.50 m. The wave period varies between 6 and 14 s, with predominance of mean wave period of 8 s (sea conditions) and 12 s (swell conditions). The spectral wave model SWAN version 40.41 [Booij, N., Haagsma, I.J.G., Holthuijsen, L.H., Kieftenburg, A.T.M.M., Ris, R.C., van der Westhuysen, A.J., Zijlema, M., 2004. SWAN Cycle III Version 40.41 Users Manual, Delft University of Technology, Delft, The Netherlands, p. 118, http://fluidmechanics.tudelft.nl/swan/index.htm] is used to simulate the wave climate for the region. Special attention is given to Cassino Beach, describing the wave climate observed during the Cassino Experiment, carried out in 2005. The verification of the standard SWAN model was carried out based on the comparison between numerical modeling results and available data of significant wave height, peak period, mean wave direction and energy density for the period relative to February of 1998. Results showed satisfactory model predictions of significant wave height and reasonably accurate predictions of peak spectral wave period and direction. The model performance is also considered satisfactory in the representation of the wave climate of the region when the wave spectrum has only one spectral peak, but presents limitations for bimodal wave spectrum. When two spectral peaks are observed, the SWAN model agrees with the spectral level observed in the low frequency, but underestimates the spectral level in the high-frequency band. When considering the presence of mud deposits in the area, model results predict that although the presence of mud attenuates most of the wave energy on the low frequency peak, it has a smaller effect in attenuating the wave energy on the high frequency peak. The comparison between significant wave heights calculated by the SWAN model (with and without mud) and measured with an Nortek acoustic doppler profiler (NDP) for the NDP localization point, and with data from a waverider relative to the 2005 survey for the studied period showed that all the time series have a similar pattern. Observed and calculated results without mud are in agreement, following the expected behavior. By considering the presence of mud in the whole domain, the model with mud shows a clear decrease of the significant wave height in relation to the NDP localization point. Furthermore, the significant wave height is underestimated due to the consideration of a constant mud thickness, extent, density and viscosity in the whole domain.

Improvement in predictability of waves over the Indian Ocean

Accurate prediction of ocean surface waves is a challenging task with many associated difficulties. Availability of good quality wind and wave information from satellite platforms inspired the scientific community to assimilate such data in various spectral wave models for enhancing the accuracy of prediction. Over the Indian Ocean, which is the region of interest for the present study, wave heights in extreme situation can go up to 12–14 m, thereby increasing the probability of coastal hazards. This region is further governed by the southern ocean swells that propagate thousands of kilometers. These are, in general, not well captured by the spectral wave models. Therefore, assimilation of altimeter data in open ocean wave model WAM has been attempted with the aim of enhancing the quality of prediction of significant wave height. Further, simulated wave spectra have been assimilated in a coastal wave model SWAN. This assimilation has been found to significantly improve the prediction of the height of wind waves as well as swell waves.

The estimation of monthly mean significant wave heights by using artificial neural network and regression methods

This paper focuses on the prediction of monthly mean significant wave heights from meteorological data by using both artificial neural network (ANN) and regression methods. Waves and meteorological data used in the study were collected by three different buoys located offshore in the Atlantic. Seven different ANN models comprising of various input combinations of monthly mean wind speeds, sea level pressures and air temperature ratios based on hourly observations were performed to evaluate wave height prediction performance of each meteorological parameter for each buoy. The results indicated that the ANN model, having all parameters in the input layer, gave the best prediction performance. In order to obtain wave heights, some empirical formulas were also suggested through the regression analysis in which wave and meteorological parameters were expressed as two dimensionless groups by using π theorem. The results of these suggested formulas were compared with those of the ANN models. From these comparisons, good performances of proposed formulas were verified by the ANN model results under waves and meteorological conditions of the studied buoys.

An alternative approach for the prediction of significant wave heights based on classification and regression trees

In this study, the performances of classification and regression trees for the prediction of significant wave heights were investigated. The data set used in this study is comprised of 5 years of wave and wind data gathered from a deep water location in Lake Michigan. Training and testing data include wind speed and wind direction as the input variables and significant wave heights ( H s ) as the output variable. To build the classification trees, a C5 algorithm was invoked. Then, significant wave heights for the whole data set were grouped into wave height bins of 0.25 m and a class was assigned to each bin. For evaluation of the developed model, the index of each predicted class was compared with that of the observed data. The CART algorithm was employed for building and evaluating regression trees. Results of decision trees were then compared with those of artificial neural networks (ANNs). The error statistics of decision trees and ANNs were nearly similar. Results indicate that the decision tree, as an efficient novel approach with an acceptable range of error, can be used successfully for prediction of H s . It is argued that the advantage of decision trees is that, in contrast to neural networks, they represent rules.

Response to the Reply by Muraleedharan

Nadarajah [Nadarajah, S., 2008. Letter to the Editor. Coastal Engineering 55, 189–190] pointed out several errors in the paper by Muraleedharan et al. [Muraleedharan, G., Rao, A. D., Kurup, P. G., Unnikrishnan Nair, N., Sinha, M., in press. Modified Weibull distribution for maximum and significant wave height simulation and prediction. Coastal Engineering] which suggested a modified Weibull distribution for maximum and significant wave height simulation and prediction. In response to Nadarajah's [Nadarajah, S., 2008. Letter to the Editor. Coastal Engineering 55, 189–190] comments, Muraleedharan [Muraleedharan, G., 2008. Reply to Saralees Nadarajah. Coastal Engineering 55, 191–193] argued that there were no errors in the original paper by Muraleedharan et al. [Muraleedharan, G., Rao, A. D., Kurup, P. G., Unnikrishnan Nair, N., Sinha, M., in press. Modified Weibull distribution for maximum and significant wave height simulation and prediction. Coastal Engineering]. Here, it is pointed out that the response by Muraleedharan [Muraleedharan, G., 2008. Reply to Saralees Nadarajah. Coastal Engineering 55, 191–193] is at least as incorrect as Muraleedharan et al. [Muraleedharan, G., Rao, A. D., Kurup, P. G., Unnikrishnan Nair, N., Sinha, M., in press. Modified Weibull distribution for maximum and significant wave height simulation and prediction. Coastal Engineering].

Modified Weibull distribution for maximum and significant wave height simulation and prediction

Calibration coefficients incorporated in the modified Weibull distribution are more effective for maximum wave height simulation. The parametric relations are derived there from to estimate various wave height statistics including extreme wave heights. The characteristic function of the Weibull distribution is derived. The Weibull distribution is suggested for the newly defined significant wave height simulation by the method of characteristic function. The statistical tools suggested and developed here for predicting the required wave height statistics are validated against the wave data (both deep and shallow) of eastern Arabian Sea comprising rough monsoon conditions also, giving reasonable accuracy.

Bayesian inference for long-term prediction of significant wave height

This paper considers the problem of estimating long-term predictions of significant wave-height. A method which combines Bayesian methodology and extreme value techniques is adopted. Inferences are based on the Metropolis–Hastings algorithm implemented in an appropriate Markov Chain Monte Carlo scheme. The method is applied to obtain return values of extreme values of significant wave height collected on the northern North Sea. The results are compared with those obtained by Guedes Soares and Scotto [Guedes Soares, C. and Scotto, M.G., 2004. Application of the r-order statistics for long-term predictions of significant wave heights. Coastal Engineering, 51, 387–394].

Significant wave height prediction by using a spatial model

Spatial assessment of variables in a considered region saves its significance for engineering applications. Branches in ocean engineering need the results of this assessment like radius of influence of stations that records the wave measurements and various meteorological variables values. Classical approaches like Kriging do not provide radius of influence for the concerned station. On the other hand, prediction of these measurements from other surrounding stations in the region is a basic requirement. In this paper, it is aimed to predict significant wave height records in a specific region by using trigonometric point cumulative semivariogram (TPCSV) concept. The main difference of this approach from the point cumulative semivariogram (PCSV) approach is the determination of influence radius. More accurate results can be obtained by TPCSV. The spatial correlation and weightings are also obtained through the TPCSV where the distance between two sites is known. The proposed method yields the least prediction error compared with other objective methodologies. The implementation of this methodology is presented for a set of offshore locations distributed along the west United States coastline.

小型漁船のための東京湾における有義波高の推定

小型漁船のための東京湾における有義波高の推定

Application of the r largest-order statistics for long-term predictions of significant wave height

This paper deals with the extremal properties of time series of significant wave height modelled by means of extreme value techniques. The limiting joint generalized extreme value (GEV) distribution for the r largest-order statistic model is used to estimate return values of significant wave height. A method based on filtering the observations to extract the r largest independent values is adopted. A case study of the northern North Sea data set is presented, and the results are compared with those obtained from the Annual Maxima (AM) method.

Temporal significant wave height estimation from wind speed by perceptron Kalman filtering

Significant wave height estimates are necessary for many applications in coastal and offshore engineering and therefore various estimation models are proposed in the literature for this purpose. Unfortunately, most of these models provide simultaneous wave height estimations from wind speed measurements. However, in practical studies, the prediction of significant wave height is necessary from previous time interval measurements. This paper presents a dynamic significant wave height prediction procedure based on the perceptron Kalman filtering concepts. Past measurements of significant wave height 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 from the wind speed measurements only. The verification of the proposed model is achieved through the dynamic significant wave height and wind speed time series plots, observed versus predicted values scatter diagram and the classical linear significant wave height models. The application of the proposed model is presented for a station in USA.

The SWAN model used to study wave evolution in a flume

The SWAN numerical model is used to model the evolution of JONSWAP wave spectra and hence the significant wave height of waves in a tank. Comparison with experiment has shown that modelling triad interactions in the numerical model leads to too low predictions of spectra and significant wave height and should therefore be excluded. The modelling of the breaking constant was also investigated, by looking at the use of a constant breaking constant, Nelson formula, and Goda formula (added into SWAN for this study). Using a constant value of 0.78 within SWAN gave the best comparison between theory and experiment.

Modelling uncertainty in long-term predictions of significant wave height

This paper deals with the application of different methods to estimate the occurrences of high sea states. A case study of the Norwegian continental shelf is considered. The Annual Maxima Method and the Peak Over Threshold Method are used to obtain return values for 25, 50 and 100 years. Several parametric models are used to fit the long-term distribution of significant wave height and to obtain predictions of extremes values. It is shown that the prediction of these sea states depends very much on the tail behaviour of the fitted distribution.

Wave hindcasting off the coast of Portugal

A study was conducted applying a second-generation wave model to predictions in coastal zones. The model was calibrated with wave measurements conducted off the Portuguese coast, for a period of 6 months. The wind fields used in the calculation were supplied by the European Centre for Medium Range Weather Forecast (ECMRWF). The calibrated model allows good predictions of significant wave height. Satisfactory comparisons have been made with predictions of the WAM model

An evaluation of directional analysis techniques for multidirectional, partially reflected waves Part 2: application to field data

Based on the findings of a numerical investigation, presented in the Part 1 companion paper, two methods of directional analysis, the maximum likelihood method (MLM) and the Bayesian directional method (BDM) are applied to over 80 field data sets. These cover a wide range of environmental conditions, for which multidirectional, partially reflective sea states exist. The results show that trends similar to those found using the numerical simulations are observed in the field estimates of relative predictions of incident significant wave height, average reflection coefficients, main directions and directional spreading. It is concluded that overall the BDM produces the more accurate results when applied to real sea waves.

A parametric wave prediction model based on Time delay concept

Parametric wind-sea relationships for prediction of significant wave height (Hs) and zero-upcrossing period (Tz) for slight to moderate sea states have been presented in this paper based on the analysis of time series wind and wave data collected off west coast of India in March 1986. Wave measurements are made by deploying Data well wave rider buoy from an oceanographic research vessel Gaveshani. Observations revealed a series of growing and decaying phases of sea state with wind speeds ranging from 0 to 11.5 m/s .The characteristic feature of the proposed parametric model is the introduction of 'Time-delay' concept in place of wind duration limit. A time-lag of 6 hr is noticed between wind speed and wave height and same has been incorporated in this model which enables forecasting seas at 6-hourly synoptic time intervals. Model comparison is made and the predicted values of Hs and Tz closely agree with the recorded wave observations. Results show that the present method yields significant wave height prediction with an r.m.s. difference of 0.12 m for the observed Hs ranging from 0. 6 to 2.3m.