Average Wave Period Research Articles

Projections of the Adriatic wave conditions under climate changes

Assessing the impact of climate change on wave conditions, including average and extreme waves, is vital for numerous marine-related activities, industries, coastal vulnerability, and marine habitats. Previous research, primarily on a large scale, has investigated this topic, but its relevance for marginal basins like the Adriatic Sea is limited due to the low resolution of the wave models used and atmospheric forcing. To contribute to filling in the gap, here we implemented a high-resolution model (about 2 km) for the period 1992–2050. The future wave climate is simulated for the RCP8.5 emission scenario. This model, developed within the AdriaClim project, comprises, among others, a high-resolution atmospheric downscaling, a circulation Limited Area Model and a spectral wave model. A comparison of our simulation's results with Copernicus Marine Service wave reanalysis on the historical baseline, confirms its accuracy in reproducing both average wave parameters and 95th percentile values, as well as the seasonal cycle, showing the AdriaClim model's suitability as a source to predict future wave climates in the Adriatic Sea. The projected changes suggest a slight increase in average significant wave height and mean wave period, and a more significant decrease at the 95th percentile, with a relevant variability by location and season, partially aligning with previous studies. This study highlights the potential effect of local climate change in coastal areas and the importance of developing long-term simulation with a downscaled modeling system for regional areas.

Forecasting Ocean Waves off the U.S. East Coast Using an Ensemble Learning Approach

Abstract This study introduces an ensemble learning model for the prediction of significant wave height and average wave period in stations along the U.S. Atlantic coast. The model utilizes the stacking method, combining three base learner models—least absolute shrinkage and selection operator (LASSO) regression, support vector machine, and multilayer perceptron—to achieve more precise and robust predictions. To train and evaluate the models, a 20-yr dataset comprising meteorological and wave data was used, enabling forecasts for significant wave height and average wave period at 1-, 3-, 6-, and 12-h intervals. The data collection involved two NOAA buoy stations situated on the U.S. Atlantic coast. The findings demonstrate that the ensemble learning model constructed through the stacking method yields significantly higher accuracy in predicting significant wave height within the specified time intervals. Moreover, the study investigates the influence of swell waves on forecasting significant wave height and average wave period. Notably, the inclusion of swell waves improves the accuracy of the 12-h forecast. Consequently, the developed ensemble model effectively estimates both significant wave height and average wave period. The ensemble model outperforms the individual models in forecasting significant wave height and average wave period. This ensemble learning model serves as a viable alternative to conventional coastal models for predicting wave parameters.

Analysis of intrinsic factors in accurate wave height prediction based on model interpretability

This study addresses the ‘black box issue’ in machine learning by utilizing interpretable model mechanisms for wave forecasting. The Shapley Additive Explanation (SHAP) method is integrated into various deep learning models to evaluate the contributions of different physical features to wave height prediction. By categorizing these features based on their importance levels, the primary factors influencing wave forecasting are thoroughly investigated. The results indicate that variations in feature contribution scores are linked to physical correlations, temporal correlations, model characteristics, and data quality. Remarkably, features directly related to fundamental physical processes, such as significant wave height and average wave period, are essential for accurate predictions. Different models display varying sensitivities to specific features over time, impacting prediction accuracy. This comprehensive analysis leads to an optimized prediction approach, significantly enhancing prediction efficiency and providing a solution for training deep learning models with limited training data.

Study on the energy capture spectrum of a two-body hinged-raft wave energy converter

Wave energy converters (WECs) of the hinged-raft type offer flexible arrangements and can be further applied in arrays. This study employs a numerical model to investigate the energy capture spectrum (ECS) of a two-body hinged-raft WEC under random waves utilizing the open-source simulation software WEC-Sim. The model explores in detail the combined effects of random wave parameters and WEC parameters, including the power take-off (PTO) damping coefficient, PTO stiffness coefficient, and horizontal hinge position, on the ECS. The findings revealed that the hinged-raft WEC is highly sensitive to the average wave period and adaptable to varying wave heights. Optimal energy capture under conditions of varying wave heights can be achieved by adjusting a specific PTO coefficient. These findings underscore the complex response of the two-body hinged-raft WEC to wave parameters and emphasize the importance of understanding these sensitivities and adaptabilities to optimize the WEC system, enhance efficiency, and promote its application in arrays.

Short-term prediction of the significant wave height and average wave period based on the variational mode decomposition–temporal convolutional network–long short-term memory (VMD–TCN–LSTM) algorithm

Abstract. The present work proposes a prediction model of significant wave height (SWH) and average wave period (APD) based on variational mode decomposition (VMD), temporal convolutional networks (TCNs), and long short-term memory (LSTM) networks. The wave sequence features were obtained using VMD technology based on the wave data from the National Data Buoy Center. Then the SWH and APD prediction models were established using TCNs, LSTM, and Bayesian hyperparameter optimization. The VMD–TCN–LSTM model was compared with the VMD–LSTM (without TCN cells) and LSTM (without VMD and TCN cells) models. The VMD–TCN–LSTM model has significant superiority and shows robustness and generality in different buoy prediction experiments. In the 3 h wave forecasts, VMD primarily improved the model performance, while the TCN had less of an influence. In the 12, 24, and 48 h wave forecasts, both VMD and TCNs improved the model performance. The contribution of the TCN to the improvement of the prediction result determination coefficient gradually increased as the forecasting length increased. In the 48 h SWH forecasts, the VMD and TCN improved the determination coefficient by 132.5 % and 36.8 %, respectively. In the 48 h APD forecasts, the VMD and TCN improved the determination coefficient by 119.7 % and 40.9 %, respectively.

Groupiness effect on irregular wave train propagation and impact on cylinder

A wave flume based on solving the Reynolds-averaged Navier-Stokes equation is modelled to simulate the irregular wave group interacting with a cylinder. The irregular wave groups are generated based on the wave envelope spectrum and the improved JONSWAP spectrum. The wave-making boundary and the momentum source term for wave-making and wave dissipation are developed based on the irregular wave theory. To suppress excessive growth of turbulent viscosity, a modified formula for turbulent viscosity is implemented in the shear stress transport turbulence model. Several sets of irregular waves with different groupiness factors are simulated. The effects of groupiness on the wave parameters, wave run-up height and wave force on the cylinder are investigated. The results show that the wave parameters increase as the groupiness increase. The group height factor has a larger influence on the significant wave height than the group length factor. The group length factor mainly influences the average wave period and average wavelength. When the average wavelength is larger than the diameter of the cylinder, the increase in wave group length results in a decrease in wave run-up height and wave force on the cylinder.

Study of Wave Parameters in the West side of Java Sea using Wave Spectral Analysis and Zero Up-Crossing Methods

Waves in the sea have a random shape, where the height, length, and direction of the waves change during the observation time. Due to the unpredictable nature of the waves with certain patterns, a statistical and probability approach is needed in analyzing waves. Before carrying out statistical and probability analysis, it is necessary to extract the wave parameters from the random wave data. There are two methods commonly used to extract wave parameters: the first is the individual wave analysis method, using a zero up/down-crossing technique. The second method is the wave spectral analysis method. In this study, both methods will be applied to observation data from the Pabelokan station [1] in the West Java Sea for a six-day. From this study, it was found that the significant wave height parameter generated by the spectral analysis technique and the zero up-crossing technique showed a positive correlation, which the correlation coefficient is 0.9891. In the study of the wave period investigation, both of method have a positive correlation, but the value of the wave period is very likely to be different. The correlation coefficient values for the average wave period are 0.5848 for Tm01 and 0.5757 for Tm02 .

Estimation of a five-parameter JONSWAP spectra with an improved particle swarm optimization

An improved particle swarm optimization (PSO) algorithm is presented to estimate a five-parameter JONSWAP spectrum for modeling of certain wave states, including normal events and extreme events at deep-water and shallow-water stations, respectively. The choices of spectral parameters (energy scale coefficient α, peak enhancement coefficient γ, and shape parameter σ) through vast amounts of in situ observations and spectral nonlinear factors are of significant importance for safety of marine structures and activities. Several experiments are carried out for five JONSWAP spectral parameters (α, γa, γb, σa, and σb) using relatively unimpaired and long series significant wave height, dominant wave period, average wave period, maximal spectral value, and ratio of dominant period and average period. And the choices of γ from γa and γb, as well as σ from σa and σb depend on the relationships between current frequency and the peak frequency. Two improvements of PSO algorithm are made, one is the fitness function, another is that the population average replacing particle’s individual optimum in the updating step. Well fitted spectra and statistic results show that the improved PSO model is more suitable to be applied to estimate the wave spectrum at a given record time. This heuristic model can be used without restrictions of water depth and sea state with its intuitive background, easy-programming and portable feature.

Wave energy potential analysis in the Kenitra-Atlantic coastal area (Morocco): First results

Waves generated by winds can transport a large amount of energy across the oceans with little loss. This paper explores the satellite-based data to assess the wave energy potential of Kenitra-Atlantic coastal area (Morocco), with an overall purpose of supporting the plans for developing and using wave energy, and provide guidance about the appropriate applications of wave energy of the Kenitra coastal area. Kenitra is important harbour and industrial city in Morocco. Various indexes, including the temporal distributions of wave parameters and wave energy fluxes, the occurrence of the effective significant wave height and wave energy flux, the variability and frequency of the wave status, were calculated from satellite measured weekly wave data, covering about 3 years (June 2019-November 2022) period. Results indicated that the area is characterized by moderate energy compared to South Africa, the most energetic site in the continent, with average wave significant wave of 1.6 ± 0.7, average wave period of 8.4 ± 2.4 s, average wave energy flux of 11.7 ± 14.0 kW m−1 and with the rate of variability of 28–45%. High energy above the threshold (> 10 kW m−1) for viable electricity production, applying turbines directly powered by waves, occurs only during the northern hemisphere winter (December–March). Hence, for off shore Kenitra, the study recommends other applications for wave energy other than electricity production through wave powered turbines, such as, reverse osmosis membrane-based electricity production technology, desalination, irrigation and water pumping for marine culture, mini-hydro and recreational. Subsequently, future studies may focus on the socio-economic viability of these wave energy applications and on developing other low energy demanding applications.

An Empirical Model of Shape Parameter of Sea Clutter Based on X-Band Island-Based Radar Database

Sea clutter modelling and parameter estimation/prediction are important basis of system design, performance assessment, and target detection of maritime radars. Besides parameter estimation from measured data, parameter prediction from radar parameters, sea state, and the viewing geometry of the radar is an alternative way. In this letter, a dual-polarimetric full-recorded sea clutter database measured by an island-based X-band experimental radar on the Yellow sea of China is introduced. On this database, the model selection reveals that the compound-Gaussian model with inverse Gaussian (CGIG) texture is suited for HH high-resolution sea clutter data, the generalized Pareto (GP) intensity distributions are for HH moderate-resolution data, and the K amplitude distributions are for high and moderate-resolution VV polarized data. Further, three five-parametric empirical formulae are constructed to predict the shape parameter of the CGIG, GP, and K distributions of sea clutter from the area of spatial resolution cell, the grazing angle, the significant wave height, the average wave period, and the wave direction relative to the sight line of radar. The new empirical formulae attain more accurate prediction than existing empirical formula on the database.

Pore-water pressure response of a silty seabed to random wave action: Importance of low-frequency waves

Wave-induced pore pressure in the seabed may cause seabed liquefaction and lead to geohazards such as submarine landslides. Under natural conditions, waves generally consist of different components with various frequencies, and the seabed response to each wave component can vary considerably. However, little is known concerning these differences. In this study, a series of flume experiments were conducted to investigate the pore pressure responses in a silty seabed to various components of random waves. According to the experimental results, the short wave (SW) component had high energies, but the SW-generated high-frequency hydrodynamic pressure (HF p0 ) decayed rapidly in the seabed. The long wave (LW) component had low energies, but the LW-generated low-frequency hydrodynamic pressure (LF p0 ) was effectively propagated in the seabed. The transmittance coefficient of the low-frequency pore pressures (LF p ) was two times that of the high-frequency pore pressures (HF p ). The energy ratio of LF p /HF p was enhanced with increasing soil depth, and the energy of LF p was greater than that of HF p at soil depths ≥15 cm, indicating that the contribution of LWs to the cumulative pore pressure is enhanced with an increase in soil depth. An important implication of our findings is that the use of statistical wave parameters (e.g., significant wave height and average wave period) to determine pore pressure responses of the seabed can underestimate liquefaction risk, and in turn, lead to unsafe engineering designs. • Long wave component generates significantly stronger pore pressure. • High-frequency pore pressures propagated poorly in the seabed. • Low-frequency pore pressures readily propagated within the seabed. • Long wave component had significantly larger contribution to deep soil pore pressure.

Analysis of Factors Influencing Wave Overtopping Discharge from Breakwater Based on an MIV-BP Estimation Model

Aiming at the problem of calculating the overtopping of single-slope breakwaters, a mean impact value-backpropagation (MIV-BP) estimation model for predicting overtopping was established. Experimental data from the Tianjin Research Institute of Water Transport Engineering (TIWTE) were utilized to further enrich the dataset of the CLASH project for single-slope wave overtopping discharge. This paper established a comprehensive prediction model based on an ensemble learning average method combination strategy. There are 10 input parameters in the model, including the offshore effective wave height, average wave period, offshore water depth, toe submergence, toe width, slope tangent, armor rock surface roughness factor, crest height with respect to the static water level, wall height with respect to the static water level, and crest width; the output parameter is the mean overtopping discharge. Subsequently, a comparative analysis was conducted between this estimation model, the Chinese standard formula calculation model, and the European Van der Meer formula calculation model. Compared with the two formulas mentioned above, this estimation model’s coefficient of correlation increased by 0.23 and 0.26, respectively. Finally, a weight evaluation analysis of the 10 main factors affecting overtopping was carried out based on a MIV-BP neural network model. In the analysis, a positive correlation was found for factors, such as the wave height, average wave period, and water depth at the structure toe; a negative correlation was found for factors, such as the slope, crest height with respect to the static water level, wall height with respect to the static water level, and crest width. Overall, the results provide a significant basis and reference for optimizing the design of the wave overtopping control.

Feasibility study of CETO wave energy converter in Iranian coastal areas to meet electrical demands (a case study)

Using wave energy to supply the electrical demand of the coastal population is an exciting idea. In recent years, many wave energy converters (WEC) have been invented, researched, and used in different parts of the world. These WECs can be used alone or in a hybrid system with other renewable resources. Also, they can be used stand-alone or grid-connected to generate electricity. Iran has access to the sea from the north and south. Using wave energy to provide power can be a good solution for energy production. This study investigates the application of a point absorber WEC named CETO to supply electricity for a 300 population on the Coasts of the Caspian Sea, Persian Gulf, and Oman sea. Waves scatter diagram for three locations calculated based on the data collected by the Iranian National Center of Ocean Data. According to these diagrams, the average wave height and period on the Konarak coast in the Oman Sea were 69 cm and 5.4 s, respectively, and Konarak had the best wave condition between the desired location in terms of wave energy potential. Also, the Cost of Energy (COE) and Net Present Cost (NPC) for three areas calculated, and the lowest amount of COE and NPC occurred in Konarak. The COE range at Konarak was between 0.523 and 0.991 $/kWh for different WEC numbers. The best performance in terms of power generation and emissions reduction also occurred in Konarak; and the output power of each CETO unit was 23.01 kW, and emissions and related penalties reduced by about 24 %. Also, the effect of load change and grid extension cost on financial results sensitively analyzed, and the results presented. The obtained financial results compared with the results of some similar WECs and it was found that the obtained results differed very little from the results of other research, and were within their range.

Performance Evaluation of the Newly Operational NDBC 2.1-m Hull

Abstract The importance of quantifying the accuracy in wave measurements is critical to not only understand the complexities of wind-generated waves, but imperative for the interpretation of implied accuracy of the prediction systems that use these data for verification and validation. As wave measurement systems have unique collection and processing attributes that result in large accuracy ranges, this work quantifies bias that may be introduced into wave models from the newly operational NOAA National Data Buoy Center (NDBC) 2.1-m hull. Data quality consistency between the legacy NDBC 3-m aluminum hulls and the new 2.1-m hull is compared to a relative reference, and provides a standardized methodology and graphical representation template for future intrameasurement evaluations. Statistical analyses and wave spectral comparisons confirm that the wave measurements reported from the NDBC 2.1-m hulls show an increased accuracy from previously collected NDBC 3-m hull wave data for significant wave height and average wave period, while retaining consistent accuracy for directional results, purporting that hull size does not impact NDBC directional data estimates. Spectrally, the NDBC 2.1-m hulls show an improved signal-to-noise ratio, allowing for increase in energy retention in the lower-frequency spectral range, with an improved high-frequency spectral accuracy above 0.25 Hz within the short seas and wind chop wave component regions. These improvements in both NDBC bulk and spectral data accuracy provide confidence for the wave community’s use of NDBC wave data to drive wave model technologies, improvements, and validations.

A Recurrent-Cascade-Neural network- nonlinear autoregressive networks with exogenous inputs (NARX) approach for long-term time-series prediction of wave height based on wave characteristics measurements

To overcome the data limitations of wave and environmental characteristics for estimating the significant wave height (Hs), this study investigates the use of an available dataset for wave characteristics to predict a long-term period of Hs for the Red Sea. A novel soft-computing approach is designed for the time-series prediction of Hs using the time delay of average wave period and Hs measurements. Buoy station of Jeddah, Saudi Arabia, datasets for 2009 and 2010 are used for designing and validating the proposed model. The time-series identification system of nonlinear autoregressive networks with exogenous inputs (NARX) and recurrent neural network (RNN) with cascade input variables based on neural network solutions were integrated through a sequential system to develop the new approach RNNARX. The RNNARX was compared with the conventional RNN, NARX neural network (NNARX), and previous studies’ results to verify its robustness. The proposed model was evaluated to predict hourly and daily Hs. The results showed that the proposed model achieves good performance for long-term prediction of Hs. The sequential system improved the performance of RNN and NNARX models for the time-series prediction of Hs. The comparison results showed that RNNARX performance is suitable for the Hs prediction of the study region. The model performances in terms of coefficient determination and root mean square error were 0.90 and 0.149 m, respectively, with a prediction error of 2.95% for four days lead times.

Estimation of directional wave spectra and hull structural responses based on measured hull data on 14,000 TEU large container ships

To ensure hull structural strength of container ships in association with their increase in size, it is very important to grasp the hull stress histories all over the hull structure in actual sea state. However, ordinary hull stress monitoring systems are insufficient for this purpose because of the small number of stress sensors actually practicable. Therefore, in this paper, we discuss an approach to reproduce the hull stress responses which are not measured based on the estimated wave spectrum from the limited measurement data. To achieve this, we introduce a new model to estimate directional wave spectra based on measured ship stress responses and ship response functions, and further we estimate other ship responses using the model. To model an arbitrarily shaped directional wave distribution, the 360° direction is discretized into 36 directions of 10-degree intervals instead of using a directional distribution function, and in each direction, the wave spectrum is represented using the Ochi (3P) spectrum with three parameters (average wave period, significant wave height, and kurtosis). The authors discuss the evaluation results based on two stress response combinations, and a comparison is made between the sea state estimates made by the proposed method and the ocean wave hindcast database (JWA). Furthermore, by comparing the significant values and the spectra of the measured response of the ship with the estimated response based on both the estimated sea state by the proposed method and the hindcast sea state, the accuracies of the proposed method and the hindcast method are discussed in terms of ship stress estimation at non-instrumented locations.

Analysis of the Caribbean wave climate for wave energy harvesting

In this study, the design requirements for a regional wave energy converter are identified from the analysis of 10 years of spectral data provided by nine buoys located across the Caribbean. It indicated that the average significant wave height and wave period in the Caribbean is 1.62 m and 5.91 s, respectively, while the average total theoretical power capable of being absorbed from a wave energy converter is 7.4 kilowatts per meter of surface waves. Devices should be designed to withstand a significant wave height of 19.0 ± 2.8 meters (95% confidence) for a 1 in 100 year return wave. This was determined by performing various extreme wave analyses. Additionally, a design life of 30 years for a device would have a probability of exceedance regarding this return wave as 26%. Using two-dimensional wave spectra analysis for the resource study, the overall spectral width, directionality coefficient and direction of the maximum directionally resolved wave power for the region are determined to be 0.172, 0.74 and 42°, respectively. It is expected that the combination of these information would improve the viability of a wave energy industry in the Caribbean and advance technological development.

Forecasting wind waves in the US Atlantic Coast using an artificial neural network model: Towards an AI-based storm forecast system

This study presents an artificial intelligence (AI) model to forecast time-series wind waves in the US Atlantic Coast. The fundamental technique in the proposed model is the Long Short-term Memory model, which is able to learn patterns from data sequence. The model is trained using historical wind data, wave data, temperature data, and atmospheric pressure data. Then the model is used to forecast significant wave height, average wave period, and mean wave direction. A 2-year meteorological data measured at four NOAA buoy stations in the US Atlantic Coast are used to train and evaluate the model’s forecast skills. The results show the artificial neural network model converges fast and does not have over-fitting nor under-fitting issues. Furthermore, a short-term forecast (e.g., 1 to 6 h) achieves higher accuracy than a long-term forecast (e.g., 24 to 48 h). This study shows that sufficient forecast accuracy can be obtained by using the input hours equal to the forecast lead time. Comparison using rose plots confirms that the artificial neural network model reproduces wave height and wave period statistics very well. The artificial neural network model is used to forecast storm waves induced by Hurricanes Isaias and Eta in the US South Atlantic region, and two winter storms in the US North Atlantic region. The model forecast is compared with NOAA measurement. The results show that the artificial neural network model is able to accurately forecast both significant wave height and average wave period associated with storm events when the forecast lead time is relatively short (e.g., 1 to 6 h). The proposed artificial neural network model can serve as an alternative tool to traditional coastal models for wave prediction and storm forecast.

Research on wave and tidal current law prediction and coupling mechanism applied to ocean energy utilization

The energy efficiency of integrated wave and current turbine is closely related to the velocity and direction of wave force and tidal current force.To study the blade motion of the wave-tidal current integrated variable-pitch turbine, raise the capacity efficiency of the turbine, take Fishing grounds of Changjiang estuary Port as an example,based on the tidal current and wave features data in recent two years,time series prediction model was established to predict the changes of wave and tidal current in the next 24 hours respectively, and the prediction accuracy is up to 93%. The wave theory applicable to Fishing grounds of Changjiang estuary Port was confirmed as the second-order strokes wave theory, the wave-tidal current coupling equivalent velocity vector was deduced, which is related to the tidal current velocity, flow direction, average wave direction, average wave period and significant wave height. The predicted wave-current coupling velocity vector is obtained after the predicted 24 hours wave-current data was substituted into it, which can provide a method and basis for the design of marine energy turbine’s variable angle law in the future, and can be applied to the development of new energy and the prediction of Marine environment.

Rapid deterministic wave prediction using a sparse array of buoys

A long-standing problem in maritime operations and ocean development projects has been the prediction of instantaneous wave energy. Wave measurements collected using an array of freely drifting arrays of Surface Wave Instrument Float with Tracking (SWIFT) buoys are used to test methods for phase-resolved wave prediction in a wide range of observed sea states. Using a linear inverse model in directionally-rich, broadbanded wave fields can improve instantaneous heave predictions by an average of 63% relative to statistical forecasts based on wave spectra. Numerical simulations of a Gaussian sea, seeded with synthetic buoys, were used to supplement observations and characterize the spatiotemporal extent of reconstruction accuracy. Observations and numerical results agree well with theoretical deterministic prediction zones proposed in previous studies and suggest that the phase-resolved forecast horizon is between 1–3 average wave periods for a maximum measurement interval of 10 wave periods for ocean wave fields observed during the experiment. Prediction accuracy is dependent on the geometry and duration of the measurements and is discussed in the context of the nonlinearity and bandwidth of incident wave fields.