As the consumption of traditional energy sources intensifies and their adverse environmental impacts become more pronounced, wave energy stands out as a highly promising member of the renewable energy family due to its high energy density, stability, widespread distribution, and environmental friendliness. The key to its development lies in the precise prediction of Significant Wave Height (WVHT). However, wave energy signals exhibit strong nonlinearity, abrupt changes, multi-scale periodicity, data sparsity, and high-frequency noise interference; additionally, physical models for wave energy prediction incur extremely high computational costs. To address these challenges, this study proposes a hybrid model combining STL-FFT-STFT-TCN-LSTM. This model exploits the Seasonal-Trend Decomposition Procedure based on Loess (STL), Fast Fourier Transform (FFT), Short-Time Fourier Transform (STFT), Temporal Convolutional Network (TCN), and Long Short-Term Memory (LSTM) technologies. The model aims to optimize multi-scale feature fusion, capture extreme wave heights, and address issues related to high-frequency noise and periodic signals, thereby achieving efficient and accurate prediction of significant wave height. Experiments were conducted using hourly data from NOAA Station 41008 and 41047 spanning 2019 to 2022. The results showed that compared with other single models and hybrid models, the STL-FFT-STFT-TCN-LSTM model achieved significantly higher prediction accuracy in capturing extreme wave heights and suppressing high-frequency noise, with MAE reduced by 15.8\%-40.5\%, SMAPE reduced by 8.3\%-20.3\%, and R increased by 1.31\%-2.9\%; in ablation experiments, the model also demonstrated the indispensability of each component step, validating its superiority in multi-scale feature fusion.

Institute of Mathematics and Statistics, Federal University of Rio Grande do Sul (UFRGS), Av. Center for Coastal and Oceanic Geology Studies (CECO), Federal University of Rio Grande do Sul (UFRGS), Av. Abstract The forecast of wave variables are important for several applications that depend on a better description of the ocean state. Due to the chaotic behaviour of the differential equations which model this problem, a well know strategy to overcome the difficulties is basically to run several simulations, by for instance, varying the initial condition, and averaging the result of each of these, creating an ensemble. Moreover, in the last few years, considering the amount of available data and the computational power increase, machine learning algorithms have been applied as surrogate to traditional numerical models, yielding comparative or better results. In this work, we present a methodology to create an ensemble of different artificial neural networks architectures, namely, MLP, RNN, LSTM, CNN and a hybrid CNN-LSTM, which aims to predict significant wave height on six different locations in the Brazilian coast. The networks are trained using NOAA's numerical reforecast data and target the residual between observational data and the numerical model output. A new strategy to create the training and target datasets is demonstrated. Introduction Numerical simulations of both weather and ocean parameters rely on the evolution of nonlinear dynamical systems that have a high sensitivity on initial conditions. Considering that errors in the observations and analysis are present, and therefore in the initial conditions, the concept of a unique deterministic solution of the governing equations becomes fragile [1, 2].

Precise forecasting of significant wave height (Hs) is essential for the development and utilization of wave energy. The challenges in predicting Hs arise from its non-linear and non-stationary characteristics. The combination of decomposition preprocessing and machine learning models have demonstrated significant effectiveness in Hs prediction by extracting data features. However, decomposing the unknown data in the test set can lead to data leakage issues. To simultaneously achieve data feature extraction and prevent data leakage, a novel Adaptive Feature Extraction Time-Frequency Network (AFE-TFNet) is proposed to improve prediction accuracy and stability. It is encoder-decoder rolling framework. The encoder consists of two stages: feature extraction and feature fusion. In the feature extraction stage, global and local frequency domain features are extracted by combining Wavelet Transform (WT) and Fourier Transform (FT), and multi-scale frequency analysis is performed using Inception blocks. In the feature fusion stage, time-domain and frequency-domain features are integrated through dominant harmonic sequence energy weighting (DHSEW). The decoder employed an advanced long short-term memory (LSTM) model. Hourly measured wind speed (Ws), dominant wave period (DPD), average wave period (APD) and Hs from three stations are used as the dataset, and the four metrics are employed to evaluate the forecasting performance. Results show that AFE-TFNet significantly outperforms benchmark methods in terms of prediction accuracy. Feature extraction can significantly improve the prediction accuracy. DHSEW has substantially increased the accuracy of medium-term to long-term forecasting. The prediction accuracy of AFE-TFNet does not demonstrate significant variability with changes of rolling time window size. Overall, AFE-TFNet shows strong potential for handling complex signal forecasting.

Climate hazards can cause major disasters when they occur simultaneously as compound hazards. To understand the distribution of climate risk and inform adaptation policies, scientists need to simulate a large number of physically realistic and spatially coherent events. Current methods are limited by computational constraints and the probabilistic spatial distribution of compound events is not given sufficient attention. The bottleneck in current approaches lies in modelling the dependence structure between variables, as inference on parametric models suffers from the curse of dimensionality. Generative adversarial networks (GANs) are well-suited to such a problem due to their ability to implicitly learn the distribution of data in high-dimensional settings. We employ a GAN to model the dependence structure for daily maximum wind speed, significant wave height, and total precipitation over the Bay of Bengal, combining this with traditional extreme value theory for controlled extrapolation of the tails. Once trained, the model can be used to efficiently generate thousands of realistic compound hazard events, which can inform climate risk assessments for climate adaptation and disaster preparedness. The method developed is flexible and transferable to other multivariate and spatial climate datasets.

Significant wave height forecasting is a key problem in ocean data analytics. Predicting the significant wave height is crucial for estimating the energy production from waves. Moreover, the timely prediction of large waves is important to ensure the safety of maritime operations, e.g. passage of vessels. We frame the task of predicting extreme values of significant wave height as an exceedance probability forecasting problem. Accordingly, we aim at estimating the probability that the significant wave height will exceed a predefined threshold. This task is usually solved using a probabilistic binary classification model. Instead, we propose a novel approach based on a forecasting model. The method leverages the forecasts for the upcoming observations to estimate the exceedance probability according to the cumulative distribution function. We carried out experiments using data from a buoy placed in the coast of Halifax, Canada. The results suggest that the proposed methodology is better than state-of-the-art approaches for exceedance probability forecasting.

The use of the `ship as a wave buoy analogy' (SAWB) provides a novel means to estimate sea states, where relationships are established between causal wave properties and vessel motion response information. This study focuses on a model-free machine learning approach to SAWB-based sea state estimation (SSE), using neural networks (NNs) to map vessel response spectral data to statistical wave properties for a small uninhabited surface vessel. Results showed a strong correlation between heave responses and significant wave height estimates, whilst the accuracy of mean wave period and wave heading predictions were observed to improve considerably when data from multiple vessel degrees of freedom (DOFs) was utilized. Overall, 3-DOF (heave, pitch and roll) NNs for SSE were shown to perform well when compared to existing SSE approaches that use similar simulation setups. One advantage of using small vessels for SAWB was shown as SSE accuracy was reasonable even when motion responses were low (in high-frequency, low wave height sea states). Given the information-dense statistical representation of vessel motion responses in spectral form, as well as the ability of NNs to effectively model complex relationships between variables, the designed SSE method shows promise for future adaptation to mobile SSE systems using the SAWB approach.

Computational intelligence-based ocean characteristics forecasting applications, such as Significant Wave Height (SWH) prediction, are crucial for avoiding social and economic loss in coastal cities. Compared to the traditional empirical-based or numerical-based forecasting models, "soft computing" approaches, including machine learning and deep learning models, have shown numerous success in recent years. In this paper, we focus on enabling the deep learning model to learn both short-term and long-term spatial-temporal dependencies for SWH prediction. A Wavelet Graph Neural Network (WGNN) approach is proposed to integrate the advantages of wavelet transform and graph neural network. Several parallel graph neural networks are separately trained on wavelet decomposed data, and the reconstruction of each model's prediction forms the final SWH prediction. Experimental results show that the proposed WGNN approach outperforms other models, including the numerical models, the machine learning models, and several deep learning models.

This article explores the concepts of ocean wave multivariate multistep forecasting, reconstruction and feature selection. We introduce recurrent neural network frameworks, integrated with Bayesian hyperparameter optimization and Elastic Net methods. We consider both short- and long-term forecasts and reconstruction, for significant wave height and output power of the ocean waves. Sequence-to-sequence neural networks are being developed for the first time to reconstruct the missing characteristics of ocean waves based on information from nearby wave sensors. Our results indicate that the Adam and AMSGrad optimization algorithms are the most robust ones to optimize the sequence-to-sequence network. For the case of significant wave height reconstruction, we compare the proposed methods with alternatives on a well-studied dataset. We show the superiority of the proposed methods considering several error metrics. We design a new case study based on measurement stations along the east coast of the United States and investigate the feature selection concept. Comparisons substantiate the benefit of utilizing Elastic Net. Moreover, case study results indicate that when the number of features is considerable, having deeper structures improves the performance.