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The retrieval of global significant wave height (SWH) data is crucial for maritime navigation, aquaculture safety, and oceanographic research. Leveraging the high temporal resolution and spatial coverage of Cyclone Global Navigation Satellite System (CYGNSS) data, machine learning models have shown promise in SWH retrieval. However, existing models struggle with accuracy under high-SWH conditions and discard a significant number of such observations due to low quality, which limits their effectiveness in global SWH retrieval, particularly for monitoring tropical cyclone (TC) events. To address this, this study proposes a daily global SWH retrieval framework through the enhanced eXtreme Gradient Boosting model (XGBoost-SC), which incorporates Cumulative Distribution Function (CDF) matching to introduce prior distribution information and reduce errors for SWH values exceeding 3 m. An enhanced loss function is employed to improve accuracy and mitigate the distribution bias in low-SWH retrieval induced by CDF matching. The results were tested over one million sample points and validated against the European Centre for Medium-Range Weather Forecasts (ECMWF) SWH product. With the help of CDF matching, XGBoost-SC outperformed all models, significantly reducing RMSE and bias while improving the retrieval capability for high SWHs. For SWH values between 3–6 m, the RMSE and bias were 0.94 m and −0.44 m, and for values above 6 m, they were 2.79 m and −2.0 m. The enhanced performance of XGBoost-SC for large SWHs was further confirmed in TC conditions over the Western North Pacific and in the Western Atlantic Ocean. This study provides a reference for large-scale SWH retrieval, particularly under TC conditions. [ABSTRACT FROM AUTHOR]

The aim of this study is to introduce and evaluate a dual filter that combines Radial Basis Function neural networks and Kalman filters to enhance the accuracy of numerical wave prediction models. Unlike the existing methods, which focus solely on systematic errors, the proposed framework concurrently targets both systematic and non-systematic parts of forecast errors, significantly reducing the bias and variability in significant wave height predictions. The produced filter is self-adaptive, identifying optimal Radial Basis Function network configurations through an automated process involving various network parameters tuning. The produced computational system is assessed using a time-window procedure applied across divergent time periods and regions in the Aegean Sea and the Pacific Ocean. The results reveal a consistent performance, outperforming classic Kalman filters with an average reduction of 53% in bias and 28% in RMSE, underlining the dual filter's potential as a robust post-processing tool for environmental simulations. [ABSTRACT FROM AUTHOR]

Wave prediction is crucial for ensuring the safety and disaster mitigation of coastal areas, helping to support marine economic activities. Currently, many deep learning models, such as the temporal convolutional network (TCN), have been applied to wave prediction. In this study, a prediction model based on improved TCN-Attention (ITCN-A) is proposed. This model incorporates improvements in two aspects. Firstly, to address the difficulty of calibrating hyperparameters in traditional TCN models, a whale optimization algorithm (WOA) has been introduced to achieve global optimization of hyperparameters. Secondly, we integrate dynamic ReLU to implement an adaptive activation function. The improved TCN is then combined with the attention mechanism to further enhance the extraction of long-term features of wave height. We conducted experiments using data from three buoy stations with varying water depths and geographical locations, covering prediction lead times ranging from 1 h to 24 h. The results demonstrate that the proposed integrated model reduces the R M S E of prediction by 12.1% and M A E by an 18.6% compared with the long short-term memory (LSTM) model. Consequently, this model effectively improves the accuracy of wave height predictions at different stations, verifying its effectiveness and general applicability. [ABSTRACT FROM AUTHOR]

This study aimed to propose an Artificial neural network (ANN) model to fill missing wave data using Bayesian optimization of hyperparameters. Ocean environmental data obtained by ocean buoys have been missed due to the malfunction or maintenance of monitoring system or extremely harsh weather condition during a storm. It is important of the continuity of measured data to analyze ocean environmental condition for the engineering purpose such as the design condition for offshore structure and the assessment of wave condition for a long term return period using the extreme analysis. Five ANN models were applied to estimate three wave parameters of significant wave height, peak wave period, and wave direction using of measurement data at Geomundo ocean buoy for eight years (2010–2017). The wind data of European Centre for Medium-Range Weather Forecasts were employed to estimate the wave parameters with ANN models to fill missing wave data at Geomundo ocean buoy. By comparison of each ANN model result, it could be suggested Bidirectional gated recurrent unit network, Gated recurrent unit network, Feed-forward neural network for the best model to fill the significant wave height, peak wave period and wave direction, respectively. These three ANN models could be applied to fill a long-term missing wave data at ocean buoys.

Understanding spatial variation in ocean waves is critical for erosion planning and infrastructure projects. The study is aimed at (1) performing a cluster analysis to categorize the wave statistics over space and (2) determining the important drivers affecting spatial variations of wave statistics in a low energy, fetch limited environment. In this study, 29 wave gauges were deployed in Back Bay Biloxi, Mississippi. Raw pressure and processed wave height were clustered using two algorithms: Euclidian and Dynamic Time Warping. The Euclidean algorithm was applied to raw and processed data. However, due to the computationally expensive nature of Dynamic Time Warping, this algorithm could not be used on raw pressure data and was only applied to processed wave data. Therefore, three combinations of distance algorithms and data were compared: (1) Euclidean algorithm on raw pressure data, (2) Euclidean algorithm on processed wave height data, and (3) Dynamic Time Warping algorithm on processed wave height data. The results showed similar clustering for Euclidean and Dynamic Time Warping on processed data, with most gauges falling into one cluster. Results from this study reveal that the dendrogram trees of the Euclidean and Dynamic Time Warping algorithms on processed data are similar, where most of the wave gauges fall in one cluster. Conversely, the Euclidian algorithm on the raw pressure data distributed the wave gauges more evenly between the clusters. Additionally, the Euclidean algorithm on the raw pressure data showed that water depth significantly affects wave clustering. [ABSTRACT FROM AUTHOR]

Typhoon waves possess significant destructive potential, and their numerical simulation relies on accurate sea surface wind fields. An evaluation of different combinations of the radial air pressure distribution coefficient B and the radius of maximum wind speed (R max) in the Holland wind field (HWF) model was conducted to determine the optimal configuration. The HWF and the ERA5 wind field (EWF) were used as input wind fields to drive the typhoon wave model for China's coastal waters. Validation results indicated that neither wind field accurately reflected real conditions; therefore, a hybrid wind field (HBWF) was created by combining HWF and EWF using weighting coefficients that vary with the radius of wind speed to enhance accuracy. Simulation results showed that the HBWF improved the accuracy of significant wave heights (SWHs), with a mean relative error of 25.29%, compared to 32.48% for HWF and 27.94% for EWF. Additionally, HBWF also demonstrated the best performance in terms of root mean square error (RMSE) and consistency index. Overall, the HBWF enhances the simulation accuracy of typhoon waves in China's coastal waters. [ABSTRACT FROM AUTHOR]

The receptive field (RF) plays a crucial role in convolutional neural networks (CNNs) because it determines the amount of input information that each neuron in a CNN can perceive, which directly affects the feature extraction ability. As the number of convolutional layers in CNNs increases, there is a decay of the RF according to the two-dimensional Gaussian distribution. Thus, an effective receptive field (ERF) can be used to characterize the available part of the RF. The ERF is calculated by the kernel size and layer number within the neural network architecture. Currently, ERF calculation methods are typically applied to single-channel input data that are both independent and identically distributed. However, such methods may result in a loss of effective information if they are applied to more general (i.e., multi-channel) datasets. Therefore, we proposed a multi-channel ERF calculation method. By conducting a series of numerical experiments, we determined the relationship between the ERF and the convolutional kernel size in conjunction with the layer number. To validate the new method, we used the recently published global wave surrogate model for climate simulation (GWSM4C) and its accompanying dataset. According to the newly established relationship, we refined the kernel size and layer number in each neural network of the GWSM4C to produce the same ERF but lower RF attenuation rates than those of the original version. By visualizing the gradient map at several points in West African and East Pacific areas, the high gradient value regions confirmed the known swell sources, which indicated effective feature extraction in these areas. Furthermore, the new version of the GWSM4C yielded better prediction accuracy for significant wave height in global swell pools. The root mean square errors in the West African and East Pacific regions reduced from approximately 0.3 m, in the original model to about 0.15 m, in the new model. Moreover, these improvements were attributed to the higher efficiency of the newly modified neural network structure that allows the inclusion of more historical winds while maintaining acceptable computational consumption. [ABSTRACT FROM AUTHOR]

Significant wave height (SWH) is an important parameter to reflect wave state, which is of great significance in ocean engineering. However, the current wave observation methods have limitations in capturing wave field data with high spatial resolution. In this study, to generate the SWHs field over the Northeast Pacific and Northwest Atlantic, multi-source satellite altimeter data (CRYOSAT-2, SARAL, JASON-3, SENTINEL-3A, SENTINEL-3B, HY-2B and CFOSAT) are fused with a spatial resolution of 0.125° x 0.125° and a temporal resolution of 1 day. We employ the Inverse Distance Weighting (IDW) method and the IDW-based spatiotemporal (IDW-ST) method for data fusion. The fusion results exhibit a consistent spatial distribution characteristic, but the results of the IDW method display the visible trajectory. Moreover, the IDW-ST method, which incorporates time factors, shows great agreement between the fused SWH and buoy data. However, when the water depth change near the grid point has a great influence on the fusion, the complexity of bathymetric topography makes the traditional two-dimensional spatial fusion methods inadequate. Therefore, an improved method is proposed based on the IDW-ST fusion method, which introduces the water depth factor and significantly enhances fusion accuracy in regions where bathymetric variations greatly affect fusion results. The proposed method can be used to generate reliable SWH fields, especially in complex bathymetric topography conditions, and provide significant support for marine infrastructure design, ocean energy utilization and marine disaster protection. [ABSTRACT FROM AUTHOR]

X-band marine radar captures the signal reflected from the sea surface. Theoretical studies indicate that the initial unfiltered signal contains meaningful information about wind wave parameters. Traditional methods of significant wave height (SWH) estimation rely on physical laws describing signal reflection from rough surfaces. However, recent studies suggest the feasibility of employing artificial neural networks (ANNs) for SWH approximation. Both classical and ANN based approaches necessitate costly in situ data. In this study, as a viable alternative, we propose generating synthetic radar images with specified wave parameters using Fourier-based approach and Pierson- Moskowitz wave spectrum. We generate synthetic images and use them for unsupervised learning approach to train a convolutional component of the reconstruction ANN. After that, we train the regression ANN based on the previous convolutional part to obtain SWH back from the synthetic images. Then, we apply preliminary trained weights for the regression model to train SWH approximation on the dataset of real sea clutter images. In this study, we demonstrate the increase in SWH estimation accuracy from radar images with preliminary training on synthetic data. [ABSTRACT FROM AUTHOR]

Accurate observation of nearshore waves is crucial for coastal safety. In this study, the feasibility of extracting wave information from wave video images captured by shore-based cameras using deep learning methods was explored, focusing on inverting nearshore significant wave height (SWH) from instantaneous wave video images. The accuracy of deep learning models in classifying wind wave and swell wave images was investigated, providing reliable classification results for SWH inversion research. A classification network named ResNet-SW for wave types with improved ResNet was proposed. On this basis, the impact of instantaneous wave images, meteorological factors, and oceanographic factors on SWH inversion was evaluated, and an inversion network named Inversion-Net for SWH that integrates multiple factors was proposed. The inversion performance was significantly enhanced by the specialized models for wind wave and swell. Additionally, the inversion accuracy and stability were further enhanced by improving the loss function of Inversion-Net. Ultimately, time series inversion results were synthesized from the outputs of multiple models; the final inversion results yielded a mean absolute error of 0.04 m and a mean absolute percentage error of 8.52%. Despite certain limitations, this method can still serve as a useful alternative for wave observation. [ABSTRACT FROM AUTHOR]

Accurately estimating the return values of significant wave height is essential for marine and coastal infrastructure, particularly as climate change intensifies the frequency and intensity of extreme wave events. Traditional models, which assume stationarity in wave data, often underestimate future risks by neglecting the impacts of climate change on wave dynamics. Combining time series decomposition and recurrence analysis, the research develops a nonstationary framework to predict significant wave height. The stochastic component is modelled using a stationary probability distribution, while the deterministic component is predicted based on sea surface temperature projections from CMIP6 climate scenarios. The model evaluation demonstrates strong predictive capability for both stochastic and deterministic components. Application of the model to China's coastal waters reveals significant discrepancies between stationary and nonstationary return value estimates. Compared to conventional distribution models, the nonstationary model predicts substantial increases in extreme wave heights. These findings underscore the importance of adopting nonstationary models to more accurately assess future risks posed by extreme wave events in a changing climate. [ABSTRACT FROM AUTHOR]

Statistical descriptions of extreme met-ocean conditions are essential for the safe and reliable design and operation of structures in marine environments. The significant wave height ( H S ) is one of the most essential wave parameters for coastal and offshore structural design. Recent studies have reported that a time-varying component exists globally in the H S . Therefore, the non-stationary behavior of an annual maximum series of H S is important for various ocean engineering applications. This study aims to analyze the frequency of H S over the northern Indian Ocean by modeling the non-stationarity in the H S series using a non-stationary Generalized Extreme Value (GEV) distribution. The hourly maximum H S data (with a spatial resolution of 0.5° longitude × 0.5° latitude) collected from the global atmospheric reanalysis dataset of the European Centre for Medium-Range Weather Forecasts (ECMWF) is used for the study. To model the annual maximum series of H S using a non-stationary GEV distribution, two physical covariates (El-Ni n ~ o Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD)) and time covariates are introduced into the location and scale parameters of the GEV distribution. The return levels of various frequencies of H S are estimated under non-stationary conditions. From the results, average increases of 13.46%, 13.66%, 13.85%, and 14.02% are observed over the study area for the 25-year, 50-year, 100-year, and 200-year return periods, respectively. A maximum percentage decrease of 33.3% and a percentage increase of 167% are observed in the return levels of various return periods. The changes in the non-stationary return levels over time highlight the importance of modeling the non-stationarity in H S . [ABSTRACT FROM AUTHOR]

Significant Wave Height (SWH) is a crucial parameter in oceanographic research, essential for understanding various marine and atmospheric processes. Traditional methods for obtaining SWH, such as ship-based and buoy measurements, face limitations like limited spatial coverage and high operational costs. With the advancement of Global Navigation Satellite Systems reflectometry (GNSS-R) technology, a new method for retrieving SWH has emerged, demonstrating promising results. This study utilizes Radio occultation sounder (GNOS) data from the FY-3E satellite and incorporates the latest Vision Transformer (ViT) technology to investigate GNSS-R-based SWH retrieval. We designed and evaluated various deep learning models, including ANN-Wave, CNN-Wave, Hybrid-Wave, Trans-Wave, and ViT-Wave. Through comparative training using ERA5 data, the ViT-Wave model was identified as the optimal retrieval model. The ViT-Wave model achieved a Root Mean Square Error (RMSE) accuracy of 0.4052 m and Mean Absolute Error (MAE) accuracy of 0.2700 m, significantly outperforming both traditional methods and newer deep learning approaches utilizing Cyclone Global Navigation Satellite Systems (CYGNSS) data. These results underscore the potential of integrating GNSS-R technology with advanced deep-learning models to enhance SWH retrieval accuracy and reliability in oceanographic research. [ABSTRACT FROM AUTHOR]

This paper is dedicated to correcting the WAM/ICON numerical wave model predictions by reducing the residue between the model's predictions and the actual buoy observations. The two parameters used in this paper are significant wave height and wind speed. The paper proposes two machine learning models to solve this task. Both models are multioutput models and correct the significant wave height and wind speed simultaneously. The first machine learning model is based on gradient boosted trees, which is trained to predict the residue between the model's forecasts and the actual buoy observations using the other parameters predicted by the numerical model as inputs. This paper demonstrates that this model can significantly reduce errors for all used geographical locations. This paper also uses SHapley Additive exPlanation values to investigate the influence that the numerically predicted wave parameters have when the machine learning model predicts the residue. To design the second model, it is assumed that the residue can be modelled as noise added to the actual values. Therefore, this paper proposes to use the denoising autoencoder to remove this noise from the numerical model's prediction. The results demonstrate that denoising autoencoders can remove the noise for the wind speed parameter, but their performance is poor for the significant wave height. This paper provides some explanations as to why this may happen. [ABSTRACT FROM AUTHOR]

Wave information retrieval from videos captured by a single camera has been increasingly applied in marine observation. However, when the camera observes ocean waves at low grazing angles, the accurate extraction of wave information from videos will be affected by the interference of the fine ripples on the sea surface. To solve this problem, this study develops a method for estimating peak wave periods from videos captured at low grazing angles. The method extracts the motion of the sea surface texture from the video and obtains the peak wave period via the spectral analysis. The calculation results captured from real-world videos are compared with those obtained from X-band radar inversion and tracking buoy movement, with maximum deviations of 8% and 14%, respectively. The analysis of the results shows that the peak wave period of the method has good stability. In addition, this paper uses a pinhole camera model to convert the displacement of the texture from pixel height to actual height and performs moving average filtering on the displacement of the texture, thus conducting a preliminary exploration of the inversion of significant wave height. This study helps to extend the application of sea surface videos. [ABSTRACT FROM AUTHOR]

The Surface Waves Investigation and Monitoring instrument (SWIM) provides the directional wave spectrum within the wavelength range of 23–500 m, corresponding to a frequency range of 0.056–0.26 Hz in deep water. This frequency range is narrower than the 0.02–0.485 Hz frequency range of buoys used to validate the SWIM nadir Significant Wave Height (SWH). The modulation transfer function used in the current version of the SWIM data product normalizes the energy of the wave spectrum using the nadir SWH. A discrepancy in the cut-off frequency/wavelength ranges between the nadir and off-nadir beams can lead to an overestimation of off-nadir cut-off SWHs and, consequently, the spectral densities of SWIM wave spectra. This study investigates such errors in SWHs due to the wavelength cut-off effect using buoy data. Results show that this wavelength cut-off error of SWH is small in general thanks to the high-frequency extension of the resolved frequency range. The corresponding high-frequency cut-off errors are systematic errors amenable to statistical correction, and the low-frequency cut-off error can be significant under swell-dominated conditions. By leveraging the properties of these errors, we successfully corrected the high-frequency cut-off SWH error using an artificial neural network and mitigated the low-frequency cut-off SWH error with the help of a numerical wave hindcast. These corrections significantly reduced the error in the estimated cut-off SWH, improving the bias, root-mean-square error, and correlation coefficient from 0.086 m, 0.111 m, and 0.9976 to 0 m, 0.039 m, and 0.9994, respectively. [ABSTRACT FROM AUTHOR]

Predicting nearshore significant wave heights (SWHs) with high accuracy is of great importance for coastal engineering activities, marine and coastal resource studies, and related operations. In recent years, the prediction of SWHs in twodimensional fields based on deep learning has been gradually emerging. However, predictions for nearshore areas still suffer from insufficient resolution and poor accuracy. This paper develops a NS (NearShore) model based on the GWSM4C model (Global Wave Surrogate Model for Climate simulations). In the training area, the GWSM4C -NS model achieved a correlation coefficient (CC) of 0.977, with a spatial Root Mean Square Error (RMSE), annual mean spatial relative error (MAPE), and annual mean spatial absolute error (MAE) of 0.128 m, 10.7%, and 0.103 m, respectively. Compared to the GWSM4C model's predictions, the RMSE and MAE decreased by 59% and 60% respectively, demonstrating the model's effectiveness in enhancing nearshore SWH predictions. Additionally, applying this model to untrained sea areas to further validate its learning capability in wave energy propagation resulted in a CC of 0.951, with RMSE, MAPE, and MAE of 0.161m, 12.9%, and 0.137m, respectively. The RMSE and MAE were 43% and 39% lower than the GWSM4C model's interpolated predictions. The results shown above suggest that the newly proposed model can effectively improve the performance of GWSM4C in nearshore areas. [ABSTRACT FROM AUTHOR]

This paper describes a calibration procedure for a non-optimally configured High Frequency Radar (HFR) for the period 1 April 2021, to 31 March 2022, to assess sea waves characteristics. The HFR system, a 16.5 MHz WEllen RAdar (WERA), is part of an innovative network for monitoring the state of the sea. The system is installed in the western part of Sicily (Italy) where a wave buoy is positioned. HFR data underestimate the spectral significant wave heights (Hm0), in particular for Hm0 > 2 m, highlighting the need for calibration of the HFR system to ensure its optimal performance for operational purposes. The calibration was performed with both in-situ and modelled data provided by the Copernicus Marine Service. The best results were obtained when the buoy data were used as reference. Encouraging results were achieved as demonstrated by the improvement of the quantitative metrics after the calibration. Indeed, the RMSE decreased from 0.60 to 0.36 m; the correlation R increased slightly from 0.86 to 0.88, the slope from 0.48 to 0.8; whereas intercept from 0.11 to 0.31 m. Moreover, waves higher than > 2 m are well reproduced by the calibrated HFR time series with the RMSE decreasing from 1.3 to 0.53 m. [ABSTRACT FROM AUTHOR]

Significant wave height (SWH) prediction is crucial for marine safety and navigation. A slow failure particle swarm optimization for long short-term memory (SFPSO-LSTM) is proposed to enhance SWH prediction accuracy. This study utilizes data from four locations within the EAR5 dataset, covering 1 January to 31 May 2023, including variables like wind components, dewpoint temperature, sea level pressure, and sea surface temperature. These variables predict SWH at 1-h, 3-h, 6-h, and 12-h intervals. SFPSO optimizes the LSTM training process. Evaluated with R2, MAE, RMSE, and MAPE, SFPSO-LSTM outperformed the control group in 13 out of 16 experiments. Specifically, the model achieved an optimal RMSE of 0.059, a reduction of 0.009, an R2 increase to 0.991, an MAE of 0.045, and an MAPE of 0.032. Our results demonstrate that SFPSO-LSTM provides reliable and accurate SWH predictions, underscoring its potential for practical applications in marine and atmospheric sciences. [ABSTRACT FROM AUTHOR]

The Copernicus Sentinel-6 Michael Freilich (S6-MF) and Jason-3 (J3) Tandem Experiment (S6-JTEX) provided over 12 months of closely collocated altimeter sea state measurements, acquired in "low-resolution" (LR) and synthetic aperture radar "high-resolution" (HR) modes onboard S6-MF. The consistency and uncertainties associated with these measurements of sea state are examined in a region of the eastern North Pacific. Discrepancies in mean significant wave height (Hs, 0.01 m) and root-mean-square deviation (0.06 m) between J3 and S6-MF LR are found to be small compared to differences with buoy data (0.04, 0.29 m). S6-MF HR data are found to be highly correlated with LR data (0.999) but affected by a nonlinear sea state-dependent bias. However, the bias can be explained robustly through regression modelling based on Hs. Subsequent triple collocation analysis (TCA) shows very little difference in measurement error (0.18 ± 0.03 m) for the three altimetry datasets, when analysed with buoy data (0.22 ± 0.02 m) and ERA5 reanalysis (0.27 ± 0.02 m), although statistical precision, limited by total collocations (N = 535), both obscures interpretation and motivates the use of a larger dataset. However, we identify uncertainties in the collocation methodology, with important consequences for methods such as TCA. Firstly, data from some commonly used buoys are found to be statistically questionable, possibly linked to erroneous buoy operation. Secondly, we develop a methodology based on altimetry data to show how statistically outlying data also arise due to sampling over local sea state gradients. This methodology paves the way for accurate collocation closer to the coast, bringing larger collocation sample sizes and greater statistical robustness. [ABSTRACT FROM AUTHOR]

Substantial effort has gone into identifying threats to the African oystercatcher Haematopus moquini, a species of seabird native to the mainland coasts and offshore islands of southern Africa. Winter storms represent a possible further threat owing to the potential to exclude an obligate intertidal forager from its feeding areas for periods of days. Using data from the Slangkop wave buoy off the Cape Peninsula of South Africa during surveys of the number of oystercatchers on Robben Island, and arguments based on body-mass records, the tentative conclusion is that winter storms do not currently represent a threat to the African oystercatcher but this may become a factor in the future. [ABSTRACT FROM AUTHOR]

Climate data derived from long-term, multisource altimeter significant wave height (SWH) measurements are more valuable than those obtained from a single altimeter source. Such data facilitate exploration of long-term air–sea momentum transfer and more comprehensive investigation of weather system dynamics processes over the ocean. Despite the deployment of the first satellite in the Chinese Haiyang-2 (HY-2) series more than 12 years ago, validation and integration of SWH data from China's offshore waters, derived using Chinese altimeters, have been limited. This study constructed a high-resolution, long-term, multisource gridded SWH climate dataset using along-track data from the HY-2 series, CFOSAT, Jason-2, Jason-3, and Cryosat-2 altimeters. Validation against observations from 31 buoys covering China's offshore waters indicated that the SWH variances from HY-2A, HY-2B, HY-2C, CFOSAT, and Jason-3 altimeters correlated well with observations, with a temporal correlation coefficient of approximately 0.95 (except HY-2A, correlation: 0.89). These SWH measurements generally showed a robust linear relationship with the buoy data. Additionally, cross-calibration between Jason-3 and the HY-2A, HY-2B, HY-2C, and CFOSAT altimeters also demonstrated a typically linear relationship for SWH > 6.0 m. Using this relationship, the SWH data were linearly corrected and integrated into a 10 d mean, long-term, multisource altimeter gridded SWH dataset. Compared with in situ observations, the merged 10 d mean SWHs are more accurate and closely match the observations, with temporal correlation coefficients improving from 0.87 to 0.90 and bias decreasing from 0.28 to 0.03 m. The merged gridded SWHs effectively represent the local spatial distribution of SWH. This study revealed the importance of observational data in the process of merging and recalibrating long-term multisource altimeter SWH datasets, particularly before their application in specific ocean regions. [ABSTRACT FROM AUTHOR]

Typhoon waves possess significant destructive potential, and their numerical simulation relies on accurate sea surface wind fields. An evaluation of different combinations of the radial air pressure distribution coefficient B and the radius of maximum wind speed (Rmax) in the Holland wind field (HWF) model was conducted to determine the optimal configuration. The HWF and the ERA5 wind field (EWF) were used as input wind fields to drive the typhoon wave model for China’s coastal waters. Validation results indicated that neither wind field accurately reflected real conditions; therefore, a hybrid wind field (HBWF) was created by combining HWF and EWF using weighting coefficients that vary with the radius of wind speed to enhance accuracy. Simulation results showed that the HBWF improved the accuracy of significant wave heights (SWHs), with a mean relative error of 25.29%, compared to 32.48% for HWF and 27.94% for EWF. Additionally, HBWF also demonstrated the best performance in terms of root mean square error (RMSE) and consistency index. Overall, the HBWF enhances the simulation accuracy of typhoon waves in China's coastal waters.

Significant wave height (SWH) is an important parameter to reflect wave state, which is of great significance in ocean engineering. However, the current wave observation methods have limitations in capturing wave field data with high spatial resolution. In this study, to generate the SWHs field over the Northeast Pacific and Northwest Atlantic, multi-source satellite altimeter data (CRYOSAT-2, SARAL, JASON-3, SENTINEL-3A, SENTINEL-3B, HY-2B and CFOSAT) are fused with a spatial resolution of 0.125° x 0.125° and a temporal resolution of 1 day. We employ the Inverse Distance Weighting (IDW) method and the IDW-based spatiotemporal (IDW-ST) method for data fusion. The fusion results exhibit a consistent spatial distribution characteristic, but the results of the IDW method display the visible trajectory. Moreover, the IDW-ST method, which incorporates time factors, shows great agreement between the fused SWH and buoy data. However, when the water depth change near the grid point has a great influence on the fusion, the complexity of bathymetric topography makes the traditional two-dimensional spatial fusion methods inadequate. Therefore, an improved method is proposed based on the IDW-ST fusion method, which introduces the water depth factor and significantly enhances fusion accuracy in regions where bathymetric variations greatly affect fusion results. The proposed method can be used to generate reliable SWH fields, especially in complex bathymetric topography conditions, and provide significant support for marine infrastructure design, ocean energy utilization and marine disaster protection.

The receptive field (RF) plays a crucial role in convolutional neural networks (CNNs) because it determines the amount of input information that each neuron in a CNN can perceive, which directly affects the feature extraction ability. As the number of convolutional layers in CNNs increases, there is a decay of the RF according to the two-dimensional Gaussian distribution. Thus, an effective receptive field (ERF) can be used to characterize the available part of the RF. The ERF is calculated by the kernel size and layer number within the neural network architecture. Currently, ERF calculation methods are typically applied to single-channel input data that are both independent and identically distributed. However, such methods may result in a loss of effective information if they are applied to more general (i.e., multi-channel) datasets. Therefore, we proposed a multi-channel ERF calculation method. By conducting a series of numerical experiments, we determined the relationship between the ERF and the convolutional kernel size in conjunction with the layer number. To validate the new method, we used the recently published global wave surrogate model for climate simulation (GWSM4C) and its accompanying dataset. According to the newly established relationship, we refined the kernel size and layer number in each neural network of the GWSM4C to produce the same ERF but lower RF attenuation rates than those of the original version. By visualizing the gradient map at several points in West African and East Pacific areas, the high gradient value regions confirmed the known swell sources, which indicated effective feature extraction in these areas. Furthermore, the new version of the GWSM4C yielded better prediction accuracy for significant wave height in global swell pools. The root mean square errors in the West African and East Pacific regions reduced from approximately 0.3 m, in the original model to about 0.15 m, in the new model. Moreover, these improvements were attributed to the higher efficiency of the newly modified neural network structure that allows the inclusion of more historical winds while maintaining acceptable computational consumption.

X-band marine radar captures the signal reflected from the sea surface. Theoretical studies indicate that the initial unfiltered signal contains meaningful information about wind wave parameters. Traditional methods of significant wave height (SWH) estimation rely on physical laws describing signal reflection from rough surfaces. However, recent studies suggest the feasibility of employing artificial neural networks (ANNs) for SWH approximation. Both classical and ANN based approaches necessitate costly in situ data. In this study, as a viable alternative, we propose generating synthetic radar images with specified wave parameters using Fourier-based approach and Pierson–Moskowitz wave spectrum. We generate synthetic images and use them for unsupervised learning approach to train a convolutional component of the reconstruction ANN. After that, we train the regression ANN based on the previous convolutional part to obtain SWH back from the synthetic images. Then, we apply preliminary trained weights for the regression model to train SWH approximation on the dataset of real sea clutter images. In this study, we demonstrate the increase in SWH estimation accuracy from radar images with preliminary training on synthetic data.

This study introduces a new machine learning-based algorithm for the retrieving significant wave height (SWH) using synthetic aperture radar (SAR) images. This algorithm is based on the azimuthal cut-off wavelength and was developed in quad-polarized stripmap (QPS) mode in coastal waters. The collected images are collocated with a wave simulation from the numeric model, called WAVEWATCH-III (WW3), and the current speed from the HYbrid Coordinate Ocean Model (HYCOM). The sea surface wind is retrieved from the image at the vertical–vertical polarization channel, using the geophysical model function (GMF) CSARMOD-GF. The results of the algorithm were validated against the measurements obtained from the Haiyang-2B (HY-2B) scatterometer, yielding a root mean squared error (RMSE) of 1.99 m/s with a 0.82 correlation (COR) and 0.27 scatter index of wind speed. It was found that the SWH depends on the wind speed and azimuthal cut-off wavelength. However, the current speed has less of an influence on azimuthal cut-off wavelength. Following this rationale, four widely known machine learning methods were employed that take the SAR-derived azimuthal cut-off wavelength, wind speed, and radar incidence angle as inputs and then output the SWH. The validation result shows that the SAR-derived SWH by eXtreme Gradient Boosting (XGBoost) against the HY-2B altimeter products has a 0.34 m RMSE with a 0.97 COR and a 0.07 bias, which is better than the results obtained using an existing algorithm (i.e., a 1.10 m RMSE with a 0.77 COR and a 0.44 bias) and the other three machine learning methods (i.e., a >0.58 m RMSE with a <0.95 COR), i.e., convolutional neural networks (CNNs), Support Vector Regression (SVR) and the ridge regression model (RR). As a result, XGBoost is a highly efficient approach for GF-3 wave retrieval at the regular sea state. [ABSTRACT FROM AUTHOR]

Using shallow-water buoy observations, reanalysis data, and numerical models, this study analyzes the variations in sea temperature and significant wave height (SWH) caused by two sequential tropical cyclones (TCs) 'Lionrock' and 'Kompasu' in October 2021 in the northeast Beibu Gulf, South China Sea. The results show that the sea surface temperature (SST) cooling of the nearshore waters was larger than the offshore water in the basin of the gulf, with the cooling amplitude and rate decreasing and the cooling time lagging behind wind increasing from coast to offshore. The near-surface temperature at the buoy station had a maximum decrease of 2.8 °C after 'Lionrock', and the decrease increased slightly to 3 °C after the stronger wind of 'Kompasu'. The total decrease of 4.6 °C indicates that the sequential TCs had a superimposed effect on the cooling of the Beibu Gulf. The heat budget analysis revealed that the sea surface heat loss and the Ekman pumping rate in the nearshore waters during 'Kompasu' (−535 W/m2 and 5.8 × 10−4 m/s, respectively) were significantly higher than that (−418 W/m2 and 4 × 10−4 m/s) during 'Lionrock'. On the other hand, the SST cooling (−1.2 °C) during the second TC is smaller than (−1.6 °C) the first weaker TC in the gulf basin, probably due to the deepening of the mixed layer. During the observation period, the waves in the Beibu Gulf were predominantly wind-driven. The maximum SWHs reached 1.58 m and 2.3 m at the bouy station near shore during the two TCs, and the SWH variation was highly correlated to the wind variation with a correlation of 0.95. The SWH increases from the nearshore to offshore waters during the TCs. The SAWN and ARCIRC coupled model results suggest that wave variations in the Beibu Gulf are primarily influenced by water depth, bottom friction, and whitecapping. Two days after the TCs, sea surface cooling and high waves appeared again due to a cold air event. [ABSTRACT FROM AUTHOR]

Studies on the variability in ocean wave climate provide engineers and policy makers with information to plan, develop, and control coastal and offshore activities. Ocean waves bear climatic imprints through which the global climate system can be better understood. Using the recently updated ERA5 dataset, this study evaluated the spatiotemporal distribution and variability in significant wave height (SWH) in the Eastern Tropical Atlantic (ETA). The short-term trends and rates of change were obtained using the Mann–Kendall trend test and the Theil–Sen slope estimator, respectively, and decadal trends were assessed using wavelet transformation. Significant, positive monthly and yearly trends and a prevailing decadal trend were observed across the domain. Observed trends suggest that stronger waves are getting closer to the coast and are modulated by the Southern and Northern Atlantic mid-latitude storm fields. These observations have implications for the increasing coastal erosion rates on the eastern coast of the Tropical Atlantic. [ABSTRACT FROM AUTHOR]

Accurate significant wave height (SWH) forecasting is essential for various marine activities. While traditional numerical and mathematical-statistical methods have made progress, there is still room for improvement. This study introduces a novel transformer-based approach called the 2D-Geoformer to enhance SWH forecasting accuracy. The 2D-Geoformer combines the spatial distribution capturing capabilities of SWH numerical models with the ability of mathematical-statistical methods to identify intrinsic relationships among datasets. Using a comprehensive long time series of SWH numerical hindcast datasets as the numerical forecasting database and ERA5 reanalysis SWH datasets as the observational proxies database, with a focus on a 72-hour forecasting window, the 2D-Geoformer is designed. By training the potential connections between SWH numerical forecasting fields and forecasting errors, we can retrieve SWH forecasting errors for each numerical forecasting case. The corrected forecasting results can be obtained by subtracting the retrieved SWH forecasting errors from the original numerical forecasting fields. During longterm validation periods, this method consistently and effectively corrects numerical forecasting errors for almost every case, resulting in a significant reduction in root mean square error compared to the original numerical forecasting fields. Further analysis reveals that this method is particularly effective for numerical forecasting fields with higher errors compared to those with relatively smaller errors. This integrated approach represents a substantial advancement in SWH forecasting, with the potential to improve the accuracy of operational SWH forecasts. The 2D-Geoformer combines the strengths of numerical models and mathematical-statistical methods, enabling better capture of spatial distributions and intrinsic relationships in the data. The method's effectiveness in correcting numerical forecasting errors, particularly for cases with higher errors, highlights its potential for enhancing SWH forecasting accuracy in operational settings. [ABSTRACT FROM AUTHOR]

As an emerging observational method, spaceborne global navigation satellite system-reflectometry (GNSS-R) has been applied recently for significant wave height (SWH) retrieval. However, the complexity of the sea surface and the influence of multiple potential factors have been constraining the accuracy of SWH retrieval. This study verified the effect of sea surface temperature (SST), sea surface salinity (SSS), and seasonal variation on cyclone-GNSS (CYGNSS) observables for the first time. After controlling for the SWH, the CYGNSS observables exhibit a dependence on SST and SSS, where the dependence on SST dominates. The correlation coefficient (R) between SST and CYGNSS observables is the highest in 3.5–4 m, which is 0.53. In addition, the geographical distribution of retrieval bias exhibits seasonality. Therefore, seasonal factors can provide an additional contribution to SWH retrieval. SWH retrieval is based on the multilayer perceptron. The European center for medium-range weather forecast reanalysis 5th Generation SWH data were used as the reference for the computation of retrieval performance metrics. The results show that after considering SST, salinity, and season, the root mean square error (RMSE) of the retrieved SWH decreases from 0.65 to 0.48 m and the R increases from 0.66 to 0.83. The retrievals were compared to the ground truth measurements from the National Data Buoy Center buoys; the RMSE decreased from 0.52–1.07 m to 0.30–0.61 m, and the R increased from 0.44–0.71 to 0.60–0.78. [ABSTRACT FROM AUTHOR]

We utilized data from the numerical wave model WAVEWATCH-III and examined the spatial variability of waves considering 30 nearshore locations in the eastern Arabian Sea. The wave parameters from the model compare well with the buoy data (correlation coefficient ~ 0.98 and bias ~ 0.17 m). During monsoon, wave heights in the central-eastern Arabian Sea are higher than those in the southern and northern parts due to the influence of the Findlater jet and intermediate-period waves are dominating the entire area. The significant wave height is less than 1.5 m in non-monsoon and reaches 5 m in July. Variation in wave height between two nearby locations is highest in the northeastern Arabian Sea along the Gujarat coast. For a distance of 388 km from central Kerala to Karnataka, there is no significant spatial variability in wave height. Eastern Arabian Sea experiences a higher peak period in the non-monsoon due to reduction in the local wind speed. The integral period does not show significant spatial variability similar to wave height. The maximum (minimum) wave heights were found in 2013 (2015) and the variations are linked to the monsoon intensity. [ABSTRACT FROM AUTHOR]

Similar in strength to hurricanes, Extratropical Cyclones (ECs) are responsible for innavigable sea states, coastal inundation and erosion, and subsequent destruction to coastal infrastructure. Across modern operational wave models, there exists a known systematic underestimation of wave heights during these extreme events. Using a global database of EC storm tracks and 36 years of satellite altimeter data, we examine EC structure and assess model performance through storm centered composite analyses of significant wave height (${H_s}$ H s ) and U10 wind speed ($|U10|$ | U 10 | ). Through the collocation of satellite altimeter observations with a state-of-the-art reanalysis product (ERA5), we investigate model performance with respect to $|U10|$ | U 10 | and ${H_s}$ H s within ECs of varying intensities. By rotating our data reference frames, we align all storm directions to account for asymmetry in EC wind fields and subsequent increased wave growth This rotation results in the organization of the strongest wind speed and ${H_s}$ H s , as well as trends in the ERA5 performance. A characteristic EC radii is calculated and used to normalize data coordinates in the storm centered reference frame, which highlights the organization of EC structures. Performance metrics are then compared within different EC quadrants to explore the relationship between wind forcing accuracy and underestimation of ${H_s}$ H s . [ABSTRACT FROM AUTHOR]

The applicability of high-frequency (HF) radar systems for wave measurement in an estuary was explored by extracting the significant wave height (${H_{sr}}$ H sr ) using a traditional Barrick equation from the Doppler spectra observed by three radar systems installed in Ise Bay, Japan. The minimum value of ${H_{sr}}$ H sr estimated around each grid point was relatively consistent with the wave height observed with a wave gauge/buoy, except for a deterioration of wave measurement accuracy caused by a decrease in seawater conductivity from the freshwater inflow after flooding. Furthermore, the relationship between the accuracy and the signal-to-noise ratios for the first- and second-order peaks (SNR1 and SNR2, respectively) highlighted the difficulty in determining the threshold values of SNRs in the bay. Thus, we suggest the use of ${H_{sr}}$ H sr as a criterion for quality control when applying a nonlinear inversion method for estimating ocean wave spectra based on the Bayesian possibility theorem (BIM). Our suggestion is to select the appropriate Doppler spectra and increase the acquisition rates of wave data with low relative error compared to BIMs using SNR1 and SNR2. These results can promote the applicability of the nonlinear inversion in estuary regions. [ABSTRACT FROM AUTHOR]

The lack of automatic wave measurement equipment leads to a decrease in the number of observations. Which, in turn, leads to a decrease in the quality of numerical forecasting. This paper presents an algorithm for obtaining wind wave parameters (significant height, period and direction of the main wave system) using a marine radar. This approach has the potential to significantly expand the coverage and increase the number of observations. The methods utilized in this research involve spectral analysis of time series images of the sea surface. The field measurements of waves in the drift and on the move of the ship obtained during the AI57, AI58 and AI63 sea expeditions conducted between 2021 and 2022 aboard a research vessel AkademikIoffe. The accuracy of the algorithm is confirmed through validation against data acquired from wave buoys, altimetry satellites, and visual observations. [ABSTRACT FROM AUTHOR]

Satellite radar altimeters (SA) have been providing ocean wind and wave measurements for over 35 years. These data have been used for modelling data assimilation, improving wind and wave climatology, and determining long-term trends of the oceanic wave parameters. Fixed observational sites (in situ locations), such as buoys, have provided reliable wave observations since the early 1970s. However, their positioning is inhomogeneous, mainly in the Northern Hemisphere, and only provides point measurements. SA significant wave height (SWH) measurements have been proven as accurate as in situ observations, particularly in the open ocean. Progress in coastal altimetry sensors, upgraded data corrections, and new extraction algorithms have recently improved the quality of SA measurements closer to the coast. This study evaluates the performance of 12 SA missions from 1985 to 2020, particularly in nearshore areas. The SA SWH along-track measurements are compared with observations from 402 in situ locations, distributed worldwide within 25 km of the coastline. Results indicate a slight overestimation from the 12 SA missions, mainly for lower sea states (under 2 m high) and closer to the coast (0 to 10 km). The Sentinel-3 mission showed the highest percentages of valid measurements near the coast and presented 72.66% of collocated in situ data. This SA mission has shown the best overall performance closer to the coast, with biases, correlation coefficient, and root-mean-squared error of 0.23 m, 0.85 m, and 0.50 m, respectively. SA undersampling in coastal areas is present and can lead to underestimation during extreme wave events. The cross-validation of the wave data in two regional analyses conducted during periods of severe wave conditions is evaluated for the new altimeters' generation. [ABSTRACT FROM AUTHOR]

Significant wave height (SWH) is a key parameter for wave energy extraction, ship navigation, oil and gas extraction, coastal structure construction, etc. Direct measurements of SWH using buoys are expensive and accurate over a limited area while numerical models are computationally expensive, inaccurate, with limited generalizability. Thus, this work focuses on developing generalizable machine learning models for predicting SWH from wind parameters (speed, direction, and gust) and atmospheric parameters (temperature and pressure). Two deep learning models (Artificial Neural Network (ANN) and Self Normalizing Neural Network (SNN) and two gradient boosting tree-based models (XGBoost and LightGBM) have been used in this study. Three different data sets were collected from the National Data Buoy Center: Data Set-1 (DS1): 12 years of data from 47 stations; Data Set-2 (DS2): 14 months of additional data from 6 stations randomly selected from DS1; Data Set-3 (DS3): 13 years data from completely 6 new stations. DS1 was split into training, testing, and validation datasets. Training and hyper-parameter tuning was done on the train and validation dataset, while the performance of the models was evaluated on the DS1 test dataset, DS2, and DS3, employing three error metrics: Mean Squared Error (MSE), Mean Absolute Error (MAE), and R-square score (R2). The collected data underwent data cleaning, preprocessing, and exploratory data analysis before modeling. The deep learning models have demonstrated superior fitting capacity to the tree-based models, achieving the lowest MSE (0.047), MAE (0.153), and highest R2 score (0.953) on test data. However, the gradient boosting models demonstrate better generalizing capacity than the deep learning models on DS2 and DS3. This study helps further Sustainable Development Goal 7 (SDG 7) by allowing fast and cheap assessment of wave height for ocean energy site development.

Accurate observation of nearshore waves is crucial for coastal safety. In this study, the feasibility of extracting wave information from wave video images captured by shore-based cameras using deep learning methods was explored, focusing on inverting nearshore significant wave height (SWH) from instantaneous wave video images. The accuracy of deep learning models in classifying wind wave and swell wave images was investigated, providing reliable classification results for SWH inversion research. A classification network named ResNet-SW for wave types with improved ResNet was proposed. On this basis, the impact of instantaneous wave images, meteorological factors, and oceanographic factors on SWH inversion was evaluated, and an inversion network named Inversion-Net for SWH that integrates multiple factors was proposed. The inversion performance was significantly enhanced by the specialized models for wind wave and swell. Additionally, the inversion accuracy and stability were further enhanced by improving the loss function of Inversion-Net. Ultimately, time series inversion results were synthesized from the outputs of multiple models; the final inversion results yielded a mean absolute error of 0.04 m and a mean absolute percentage error of 8.52%. Despite certain limitations, this method can still serve as a useful alternative for wave observation.

This paper is dedicated to correcting the WAM/ICON numerical wave model predictions by reducing the residue between the model’s predictions and the actual buoy observations. The two parameters used in this paper are significant wave height and wind speed. The paper proposes two machine learning models to solve this task. Both models are multioutput models and correct the significant wave height and wind speed simultaneously. The first machine learning model is based on gradient boosted trees, which is trained to predict the residue between the model’s forecasts and the actual buoy observations using the other parameters predicted by the numerical model as inputs. This paper demonstrates that this model can significantly reduce errors for all used geographical locations. This paper also uses SHapley Additive exPlanation values to investigate the influence that the numerically predicted wave parameters have when the machine learning model predicts the residue. To design the second model, it is assumed that the residue can be modelled as noise added to the actual values. Therefore, this paper proposes to use the denoising autoencoder to remove this noise from the numerical model’s prediction. The results demonstrate that denoising autoencoders can remove the noise for the wind speed parameter, but their performance is poor for the significant wave height. This paper provides some explanations as to why this may happen.