Significant Wave Height Prediction Research Articles

Long time series of ocean wave prediction based on PatchTST model

In recent years, AI (artificial intelligence) algorithms based on big data have gradually emerged and been applied to short time predictions of ocean waves (e.g. 1 h, 3 h, …, 48 h). However, limited by the lack of a better method and time-consuming computation, long time (e.g. 720 h) predictions have not been investigated yet. Based on the problems with study of long time series wave prediction, by using the hourly wave reanalysis data near Bering Sea from 2016 to 2020, this study establishes a long time series AI prediction model for waves with a forecast length of one month (720 h) based on PatchTST model. The time series prediction results of significant wave height evolution in 2021 show that compared with Informer, LSTM (Long Short Term Memory) and NeuralProphet, PatchTST's is significantly superior with COR (Correlation) averages at 0.90, RMSE (Root Mean Square Error) averages at 0.65 and MAE (Mean Absolute Error) averages at 0.56 on 12 months of 2021, which can be effectively applied to long time significant wave height prediction.

Development of pyramid neural networks for prediction of significant wave height for renewable energy farms

Significant wave height (Hs) is a critical parameter in the design, operation, and maintenance of nearshore and offshore wind and wave farms. In this study, the original pyramid neural network (PNN) was introduced and applied to predict Hs for North Sea renewable energy farms. The performance of PNN was compared with state-of-the-art algorithms. The results show that the machine learning (ML) models trained by the network datasets can accurately predict Hs at any point of nearshore or offshore energy farms, significantly reducing wave monitoring costs. The PNN models predict Hs with high accuracy. The results predicted by PNN, with SRMSE of 0.256 and R2 of 0.873, are more accurate than the corresponding results obtained by the deep neural network (DNN) model, which show that PNNs with their far simpler structures and lower number of parameters are attractive alternatives for complex and time-consuming DNN models. The ensemble of regular models, with SRMSE of 0.247, is ranked as the most accurate method. The results also show that the applied state-of-the-art algorithms including MLR, SNN, DNN, ANFIS, and SVR models predict non-physical negative values of Hs. The PNNs developed in this study predict Hs with positive values. Moreover, the analysis shows that the scatter of the results obtained by the derived nonlinear models is less pronounced than the scatter of corresponding results obtained by other methods. The results also show that to evaluate the performance of nonlinear ML methods for large datasets, the analysis of standard statistical indices is not sufficient. For large datasets standard statistical indices provide inadequate or insufficient information and additional calculations, and statistical analysis are required.

Disentangled Seasonal-Trend representation of improved CEEMD-GRU joint model with entropy-driven reconstruction to forecast significant wave height

In recent years, wave energy has gained popularity among marine researchers for its sustainability, cleanliness, high energy density and wide distribution. As one of the most important parameters of wave energy, Significant Wave Height (SWH) is difficult to predict accurately due to complex sea conditions and the ubiquitous chaotic phenomena in nature. The efficient use of wave energy cannot be achieved without accurate analysis and prediction of SWH. In this study, a novel DST-CEEMD-SampEn-GRU joint model is proposed, which combines Disentangled Seasonal-Trend (DST) to reduce the computational time of the Complementary Ensemble Empirical Mode Decomposition (CEEMD). This is combined with SampEn-based reconstruction to avoid the tremendous computational effort associated with IMF components of CEEMD. The final prediction is made using the Gate Recurrent Unit (GRU). In this paper, we demonstrate the effectiveness of CEEMD, SampEn and DST in improving accuracy through forward ablation experiments respectively. Finally, the proposed model is validated with multi-single machine learning models for muti-hour ahead SWH forecasting. The experimental results demonstrate that DST-CEEMD-SampEn-GRU is statistically superior to all the other methods.

A hybrid CEEMDAN-VMD-TimesNet model for significant wave height prediction in the South Sea of China

Accurate prediction of significant wave height is of great reference value for wave energy generation. However, due to the non-linearity and non-stationarity of significant wave height, traditional algorithms face difficulties in achieving satisfactory prediction results. In this study, a hybrid CEEMDAN-VMD-TimesNet model is proposed for non-stationary significant wave height prediction. Based on the significant wave height in the South Sea of China, the performance of the SVM model, the GRU model, the LSTM model, the TimesNet model, the CEEMDAN-TimesNet model and the CEEMDAN-VMD-TimesNet model are compared in terms of multi-step prediction. It is found that the prediction accuracy of the TimesNet model is higher than that of the SVM model, the GRU model and the LSTM model. The non-stationarity of significant wave height is reduced by CEEMDAN decomposition. Thus, the CEEMDAN-TimesNet model performs better than the TimesNet model in predicting significant wave height. The prediction accuracy of the CEEMDAN-VMD-TimesNet model is further improved by employing VMD for the secondary decomposition of components with high and moderate complexity. Additionally, the CEEMDAN-VMD-TimesNet model can accurately predict trends and extreme values of significant wave height with minimal phase shifts even during typhoon periods. The results demonstrate that the CEEMDAN-VMD-TimesNet model exhibits superiority in predicting significant wave height.

Assessment and prediction of significant wave height using hybrid CNN-BiLSTM deep learning model for sustainable wave energy in Australia

Wave energy is regarded as one of the powerful renewable energy sources and depends on the assessment of significant wave height (Hs) for feasibility. Hence, this study explores the potential of wave energy by assessing and predicting Hs for two study sites in Queensland (Emu Park and Townsville), Australia. Assessment and prediction of Hs is extremely important for reliable planning, cost management and implementation of wave energy projects. The study utilized oceanic datasets based on wave measurements obtained from buoys along coastal regions of Queensland that are transmitted to nearby receiver stations. The parameters of the datasets include maximum wave height, zero up crossing wave period, peak energy wave period and sea surface temperature to accurately predict Hs. A new hybrid Convolutional Neural Network (CNN) and Bidirectional Long Short Term (BiLSTM) deep learning model with Multivariate Variational Mode Decomposition (MVMD) is developed which is benchmarked by Multi-Layer Perceptron (MLP), Random Forest (RF) and Categorical Boosting (CatBoost) to compare the performance. All models attain relatively high-performance results. The MVMD-CNN-BiLSTM attains slightly better performance values for both study sites among all developed models with highest correlation values of 0.9957 and 0.9986 for Emu Park and Townsville, respectively. Other performance evaluation metrics were also higher for MVMD-CNN-BiLSTM with lowest error values in comparison to the benchmark models. The annual mean of Hs is also computed to compare and obtain an insight with a linear projection. There is a greater ocean wave energy potential for Emu Park for a 10-year period with a projected mean Hs of 0.865 m in comparison to Townsville where the projected mean was of 0.665 m.

STGWN: Enhanced spatiotemporal wave forecasting using multiscale features

This paper addresses the challenge of low accuracy in wave height prediction due to inadequate consideration of irregular topological structures and spatio-temporal dependencies of wave measurement points. We propose a novel spatio-temporal wave prediction method, named the Spatio-Temporal Graph Wave Network (STGWN). This model employs graph convolution instead of conventional 2D convolution, enabling spatial domain modeling of wave fields on a graph structure. Simultaneously, it utilizes LSTM for temporal modeling, effectively enhancing the representation of complex dynamic spatio-temporal correlations among wave nodes. Additionally, a dynamic wave position-aware mechanism is constructed to better identify feature variations among different wave nodes. Furthermore, a multi-scale feature fusion mechanism is designed within the model to prevent the risk of crucial temporal feature disappearance during the extraction of spatial dimension features. The proposed spatio-temporal method for Significant Wave Height (SWH) prediction is validated on a wave dataset comprising four different node distribution characteristics within the study area. Results demonstrate that the STGWN model outperforms comparative models in terms of prediction accuracy and stability across multiple evaluation metrics in the four experimental setups.

Nearshore significant wave height prediction based on MIC-LSTM model

Nearshore significant wave height prediction based on MIC-LSTM model

An integrated system to significant wave height prediction: Combining feature engineering, multi-criteria decision making, and hybrid kernel density estimation

Accurate prediction of significant wave height is paramount for the effective design, operation, and maintenance of wave energy converters. However, current research falls short in achieving precise and stable point predictions, along with comprehensive uncertainty analysis of significant wave height. To address this gap, this study presents a comprehensive significant wave height combined prediction system. This integrated system encompasses outlier detection utilizing Autoencoders, sophisticated feature engineering, a multi-criteria decision-based model selection methodology, a multi-objective homogeneous nuclear molecular optimization algorithm, and a hybrid kernel density estimation technique. To tackle the critical issue of model selection within ensemble prediction, we introduce a multi-criteria compromise solution ranking algorithm known as VIKOR for the selection of sub-models. Additionally, a novel multi-objective homogeneous nuclear molecular optimization algorithm is proposed, which incorporates joint opposing selection and an elite retention strategy to effectively manage multiple objectives simultaneously, yielding Pareto optimal solutions for combining weights. Furthermore, a hybrid kernel density estimation approach is developed, surpassing previous methods reliant on a single kernel function and fixed bandwidth, thereby achieving a more precise fit to the distribution of wave height data. The effectiveness of the proposed model is rigorously evaluated using wave height datasets from three distinct locations. The experimental results convincingly demonstrate that the significant wave height combined prediction system outperforms existing solutions, excelling in both point and interval predictions of significant wave height.

Significant wave height prediction from X-band marine radar images using deep learning with 3D convolutions.

This research introduces a deep learning method for ocean wave height estimation utilizing a Convolutional Neural Network (CNN) based on the VGGNet. The model is trained on a dataset comprising buoy wave heights and radar images, both critical for marine engineering. The dataset features X-band radar images sourced from Sokcho, Republic of Korea, spanning from June 1, 2021, to August 13, 2021. This collection amounts to 72,180 three-dimensional images, gathered at intervals of approximately 1.43 seconds. The data collected was highly unbalanced in terms of wave heights, with images of lower wave heights being more common. To deal with data imbalances in the wave height datasets, we categorized the data into three groups based on wave heights and applied stratified random sampling at each level. This approach balances the data patches for each training iteration, reducing the risk of overfitting and promoting learning from diverse data. We also implemented a system to protect data in groups with fewer instances, ensuring fair representation across all categories. This study presents a deep learning regression model for predicting wave height values from radar images. The model extracts features from sequences of 64 radar images using three-dimensional convolutions for both temporal and spatial learning. Using three-dimensional convolutions, the model captures temporal features in radar image sequences and provides accurate wave height estimates with an RMSE of 0.3576 m. The study derived results using radar images under different wave height conditions for 74 days to ensure reliability.

A fast, high-precision deep learning model for regional wave prediction

Accurate prediction of regional significant wave height is crucial for safe ship navigation, route planning, and reducing carbon emissions from shipping. Physics-based wave prediction methods involve complex calculations, limiting real-time information provision. Convolutional Neural Networks (CNNs) have gained popularity for wave prediction but suffer from feature loss, positional insensitivity, and poor performance in high sea conditions. This study introduces a Vision Transformer-based regional wave prediction model (VIT-RWP) to address these issues. VIT-RWP utilizes an attention mechanism to extract the wind-wave mapping relationship. It employs convolution and transpose convolution as encoder and decoder, preserving positional information and relative point positions within the region. Evaluation in four sea areas, including comparison with CNN-RWP, demonstrates VIT-RWP's advantages. Pre-training enhances VIT-RWP's predictive accuracy by over 0.5%, surpassing CNN-RWP by over 5%. VIT-RWP maintains accuracy even with wave heights exceeding 5 m. Importantly, it exhibits remarkable robustness when subjected to Gaussian noise in input data. VIT-RWP's consistent performance across diverse seas establishes its efficacy and accuracy as a reliable wave prediction model.

A hybrid model for multistep-ahead significant wave height prediction using an innovative decomposition–reconstruction framework and E-GRU

As waves are exploited as renewable energy, developing new forecasting technologies is essential to accurately predict significant wave height. In this study, a wave height prediction model is proposed that includes a decomposition–reconstruction framework and ensemble gated recurrent unit (E-GRU). First, variational mode decomposition (VMD) decomposes the original wave height series into multiple subsequences to decrease the uncertainty and nonstationarity of the data. Second, the refined composite multiscale fuzzy entropy (RCMFE) is adopted to reconstruct subsequences into several components to reduce the computational complexity. A GRU is then used to predict each component individually to capture more temporal information from historical data. Finally, we predict all the subresults by E-GRU and obtain the final result. We test the proposed hybrid model using wave height data from three buoy stations. The comparative evaluation of prediction accuracy across four models is achieved through the utilization of key performance metrics, namely, the coefficient of determination (R2), Nash–Sutcliffe efficiency coefficient (ENS), Legates and McCabe index (ELM), Willmott's index (WI), root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). Among these metrics, the VMD-RCMFE-E-GRU model distinctly emerges as the superior performer for forecasting hourly wave height across all stations and future temporal intervals, as evidenced by its notably lowest RMSE, MAE, and MAPE values, coupled with the highest R2, ENS, ELM, and WI scores. The case results show that the proposed hybrid model is more effective for wave height prediction.

Significant wave height prediction based on the local-EMD-WaveNet model

This research constructed the innovative Local-EMD-WaveNet, a multi-channel neural network model, specifically designed for the prediction of significant wave height (SWH) at a singular point. It leverages Local Empirical Mode Decomposition (EMD) on significant wave heights in Ghanaian waters, integrating the derived decomposition results with wind speed data. This compiled data is then channeled into the model, which exploits the capabilities of dilated causal convolution to capture and analyze the time-series characteristics integral to future SWH predictions. The model ingeniously embeds EMD within the training process, treating the decomposed sub-waves and wind speed sequences as unique channels along the “depth” dimension. Following the application of dilated causal convolution, these channels are systematically “stacked”. Compared to conventional LSTM and direct data incorporation methods, Local-EMD-WaveNet consistently outperforms, especially in long-term predictions. The model exhibited significant improvements in Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) during 48 and 56 time-step predictions, marking increases of 27.3% and 23.5%, respectively, outshining both WaveNet and LSTM. Particularly in situations with larger wave height variations, Local-EMD-WaveNet accurately captures waveforms' peaks and troughs. These results validate Local-EMD-WaveNet as a reliable wave forecasting tool with considerable potential in ocean engineering and maritime applications.

SIGNIFICANT WAVE HEIGHT PREDICTION USING TRANSFER LEARNING

Wave prediction needed for maritime construction is generally performed by numerical models. This method, however, requires a high-performance computer and a large cost of computational resources. With the development of neural networks, which can compute at a low cost, the use of neural networks in wave prediction has recently been studied. However, because a large amount of training data is required for neural network tasks using scarce datasets, it is difficult to predict wave conditions accurately. Fan et al. (2020) reported that using LSTM model for prediction of significant wave height (Hs) was higher accuracy than conventional neural network model. Additionally, they recommended using at least 2 years of training data for 6h predictions, that is, an excessively small amount of data is not presumed to predict sufficiently Hs. Therefore, we propose a wave prediction method using transition learning. Transfer Learning is the method of transferring trained knowledge from one model to another. In this study, we investigate whether transfer learning can be used to improve the performance of Hs prediction by transferring the knowledge learned at Sakata port, which has a large amount of training data, to the coast of Yamagata, which has a scarce one.

A novel multivariable hybrid model to improve short and long-term significant wave height prediction

Accurate significant wave height (Hs) prediction is crucial for marine renewable energy development. The hybrid models combining multi-resolution analysis techniques such as empirical mode decomposition and wavelet transform with intelligence algorithm have flourished in Hs forecasting. However, these hybrid models cannot fit multivariable input mode well. In this study, a novel multivariable hybrid model is proposed. The improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and recurrence quantification analysis (RQA) were integrated as the deterministic and stochastic components decomposition (DSD) method. Then three machine learning models was integrated with DSD method as hybrid models, respectively. For more sufficient forecasting information, wind speed (Ws), wind direction (Wd) and Hs were adopted as inputs to construct multivariable hybrid models. The forecasting experiment was benchmarked with those from univariate hybrid models, multivariable single models and univariate single models. Three buoy-measured datasets were utilized for validation. Results revealed the positive effect of wind data on long-term prediction and the improvement to prediction by the DSD method. Benefiting from the advantages of both, multivariable hybrid models outperformed other benchmark models. Among them, the multivariable hybrid model based on long short-term memory (LSTM) network, DSD-LSTM-m, achieved the best forecasting performance.

Significant wave height prediction based on dynamic graph neural network with fusion of ocean characteristics

Significant wave height (SWH) is one of the core parameters for wave and accurate prediction of SWH is of great importance for ocean resource assessment. In this paper, we propose a new multi-characteristic and multi-node SWH prediction model(MCMN). The model considers the lead–lag effect among ocean characteristics and utilizes time lag correlation to automatically learn advanced indication information. For the temporal features, temporal correlations are extracted from high-dimensional spatial features efficiently in parallel using Temporal Convolutional Network(TCN). Additionally, the dependencies between nodes are modeled as the joint result of stable long-term patterns and dynamic short-term patterns. To obtain these dependencies, we introduce a novel dynamic graph neural network. Compared to previous SWH predictions focused solely on individual nodes, this model allows us to more fully explore the spatio-temporal dependencies between the nodes by capturing both long-term and short-term spatio-temporal relationship patterns among the nodes. Experiments were conducted with 120 nodes in the South China Sea and East China Sea, respectively. The results show that the model provides reliable predictions. Finally, we compare with five deep learning models, and the results show that our model has better performance in multi-node and multi-step SWH prediction.

Improved Prediction of Local Significant Wave Height by Considering the Memory of Past Winds

AbstractWave and water depth were measured with an instrumented tripod in the Yellow River Delta from 9 December 2014 to 29 April 2015. Concurrent wind data were also collected from a nearby wind station. A high‐precision model for predicting local significant wave height (Hs) with wind speed (vw) is constructed using an improved data‐driven approach. The proposed model realized high accuracy as it solves the problem that the Hs falls too fast during the wind‐decreasing periods. It was tackled by considering the remaining influence of historical vw on the present Hs via incorporating a memory curve of the past wind effect. This innovative approach significantly improves the prediction (R2 from 0.60 to 0.83). The winds in the past 24 hr still left an influence on the waves at the observation site although the influence decreases with time. Physically, it is an implicit but simpler consideration of wind fetch/duration. Further data modeling experiments indicated that the decisive factor for the Hs at the site is the wind speed. Wind directions slightly improve the prediction, indicating that waves are slightly affected by the underwater seabed slope along different wind directions, and northwest winds cause the strongest waves at the site. Adding atmospheric pressure or water depth even reduces the accuracy, which indicated that storm surges and wave deformations under different tide levels have a weak impact on Hs. The proposed local wave model can be easily constructed with available wind and wave data, making it expandable to other regions dominated by wind waves.

Application of Empirical Mode Decomposition and Hodrick Prescot filter for the prediction single step and multistep significant wave height with LSTM

The study discusses the application of the Empirical Model Decomposition (EMD) and Hodrick Prescot (HP) filter for significant wave height prediction. Long Short-Term Memory (LSTM) is applied for sequence predictions in Natural Language Processing (NLP). LSTM can also be modeled to time series forecasting, particularly for cyclic data since LSTM learns from experience to forecast the data. The time series signal is a combination of frequencies or spectra, when the LSTM is applied to the raw signal the prediction is lagged, to reduce the lag in the forecast the noise in the time series signal is filtered. Since, the time series consists of various frequency components, filtering the higher-frequency components is required to reduce the delay in prediction from the LSTM neural network model. The EMD is applied to the original time series wave data to split the signal into several frequencies in time series or Intrinsic Mode Functions (IMFs). Similarly, when the HP filter is applied to the original wave data or time series signal it gives a trend and cycle. The LSTM is applied to the IMFs and HP filter trend time series to predict the EMD-IMFs and Trend respectively. All the predicted IMFs are summed to compare with the original raw time series. The single step and multistep prediction or forecasting is carried out for 1-h interval, 6-h, 12-h, and 24 h interval. With the increase in forecasting interval the error values also increased and changing the lambda parameter of HP filter played a critical step for the multistep prediction. The EMD-LSTM is computationally expensive as it takes higher amount time to predict each IMF compared to HP-LSTM. Finally, the results are compared with between normal LSTM, EMD-LSTM and HP-LSTM.

Multi factors-PredRNN based significant wave height prediction in the Bohai, Yellow, and East China Seas

IntroductionCurrently, deep-learning-based prediction of Significant Wave Height (SWH) is mostly performed for a single location in the ocean or simply relies on a single factor (SF). Such approaches have the disadvantage of lacking spatial correlations or dynamic complexity, leading to an inevitable growth of the prediction error with time.MethodsHere, attempting a solution, we develop a Multi-Factor (MF) data-driven 2D SWH prediction model for the Bohai, Yellow, and East China Seas (BYECS). Our model is developed based on a multi-channel PredRNN algorithm that is an improved deep-learning calculation of the ConvLSTM.ResultsIn our model, the MF of historical SWH, 10 m surface winds, ocean surface currents, bathymetries, and open boundaries are used to predict 2D SWH in the next 1-72h. Our modeled SWHs show the correlation coefficients as 0.98, 0.90, and 0.87 for the next 6h, 24h, and 72h, respectively.DiscussionAccording to the ablation experiments, winds are the dominant factor in the MF model and the memory-decoupling module is the key improvement of the PredRNN compared to the ConvLSTM. Furthermore, when the historical SWH is excluded from the input, the correlation coefficients remain around 0.95 in the 1-72h prediction due to the elimination of the error accumulation. It was worse than the MF-PredRNN with the historical SWH before 10h but better than it after 10h. Overall, for the prediction of SWH in the BYECS, our MF-PredRNN-based 2D SWH prediction model significantly improves the accuracy and extends the effective prediction time length.

A novel hybrid model based on grey wolf optimizer and group method of data handling for the prediction of monthly mean significant wave heights

Significant wave height prediction is challenging owing to the nonlinear and nonsmooth attributes of wave heights. This study presents a hybrid model coupling group method of data handling (GMDH) with grey wolf optimizer (GWO) for the prediction of significant wave heights. The datasets were assembled from three different observations, Stations 41001, 41002 and 44004 in the Atlantic; the datasets of Stations 41001 and 41002 were used for training, and those of Station 44004 were used for testing. The performance of the GWO-GMDH model was compared with four artificial intelligence models, the GMDH, gene expression programming (GEP), adaptive neuro-fuzzy inference system (ANFIS) and back propagation (BP) neural network models, and one empirical equation derived by Buckingham π-theorem. Both regression plots and statistical indices (e.g., correlation coefficient (R), root mean squared error (RMSE), mean squared error (MSE) and mean absolute percentage error (MAPE)) were adopted to evaluate the performance of the hybrid GWO-GMDH model. The MSE, RMSE, MAPE and R values were 0.041, 0.202, 7.353% and 0.953, respectively, for the training datasets and 0.031, 0.175, 7.598% and 0.941, respectively, for the testing datasets. Compared with the single GMDH model, the statistical indices of the training datasets of the hybrid GWO-GMDH model were almost the same; however, the MSE, RMSE and MAE values decreased by 24.39%, 13.37% and 7.95%, respectively, and the R value increased by 2.28% in the testing datasets. Compared with the GEP, BP, and ANFIS models and empirical equation models, the GWO-GMDH model also shows high accuracy and robustness, especially compared with empirical formulations. In addition, a graphical user interface (GUI) was developed to facilitate the application of practical engineering use.

A training strategy to improve the generalization capability of deep learning-based significant wave height prediction models in offshore China

Accurate forecasting of significant wave height (SWH) is crucial for ensuring the safety of marine navigation. To achieve good accuracy, deep learning models need to be trained separately using SWH data from all forecast locations. However, improving the generalizability of SWH prediction models is vital for practical engineering purposes. This paper proposes a training strategy that utilizes multi-point data fusion by using wave data obtained from different locations to construct a training dataset. To verify the feasibility of training strategy, the artificial neural network (ANN), long short-term memory (LSTM), and temporal convolutional network (TCN) models are used to test in China offshore. The RMSE and MAPE of different models with 2h advance forecasts are almost 0.05 and 4%, indicating that the models have good forecasting performance. Additionally, the models exhibit consistency with the model trained solely by single position data, which demonstrates that the training strategy applies to various models. In addition, in sea areas without wave training data, two locations are randomly selected and used in the pre-trained model to predict SWH. The various models demonstrate favorable forecasting results, further demonstrating that the training strategy proposed in this study can enhance the generalizability of models.