Wave Forecasting Research Articles

Improving global weather and ocean wave forecast with large artificial intelligence models

Improving global weather and ocean wave forecast with large artificial intelligence models

Wind and Wave Hindcast and Observations During the Black Sea Storms in November 2023

Wind and Wave Hindcast and Observations During the Black Sea Storms in November 2023

Exploring Technological Innovation in Wave Forecasting Using Machine Learning: A Literature Analysis

In the face of rapid technological advancements, innovations in wave forecasting are increasingly essential for effectively addressing the complex impacts of climate change. This study aims to explore technological developments in wave forecasting that can manage the complexities related to climate change and enhance the accuracy and efficiency of predictions in dynamic marine environments. Employing a qualitative approach through a Systematic Literature Review (SLR) methodology, the research focuses on literature from databases such as Scopus, DOAJ, and Google Scholar, specifically targeting publications from 2014 to 2024. Recent findings reveal that advancements in machine learning technologies, including deep learning, ensemble learning, transfer learning, and data augmentation, have significantly improved the precision and efficiency of wave forecasting models. Techniques like Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) have been particularly effective in capturing complex, non-linear patterns within wave data, enhancing the overall prediction accuracy. Ensemble learning methods have further contributed by increasing the stability and robustness of forecasts. Moreover, transfer learning and data augmentation play vital roles in adapting these models to rapidly changing environmental conditions, making them highly relevant in the context of climate change. These approaches are crucial for models to remain adaptable and responsive to dynamic oceanic conditions influenced by climate variability. The insights derived from this study are expected to provide valuable direction for the future development of machine learning-based wave forecasting models, emphasizing the need for innovative techniques that can accommodate the complexities and uncertainties brought about by climate change.

A 45-year updating wind and wave hindcast over the Oman Sea and the Arabian Sea

This study focuses on developing a comprehensive and reliable wind and wave hindcast for the Oman Sea and Arabian Sea, spanning a significant 45-year period (1979–2024). The objective is to capture the intricate wind and wave climate of the region, characterized by distinct monsoon cycles and occasional tropical cyclones. The availability of extensive wave data over four decades would be an irreplaceable tool for researchers and engineers, enabling improved accuracy in extreme value analysis, sediment transport studies, and wave-induced current simulations. Despite limited field observations, all available measured data within the region were collected, analyzed for configuration of the models and utilized for model calibration and validation. The hindcast data was generated using the Weather Research and Forecasting (WRF) model for winds and WAVEWATCH III (WW3) model for waves, and evaluated against observational and measured wind and wave parameters. A comprehensive statistical analysis of the hindcast model's performance reveals adequate agreement with measured data, as evidenced by root mean square errors (RMSEs) of 1.23 m/s for wind speeds and 0.37 m for significant wave heights in average. These results underscore the model's reliability for research and engineering applications, particularly in the Arabian Sea, with a focus on the northern coastlines of the Oman Sea. The specific model configuration employed in this study holds significant potential for future investigations in the northern Indian Ocean, offering a valuable tool for understanding and predicting climatical conditions in this region.

Accuracy verification of the 2D spectral AIS method by the hull monitoring data

Accuracy validation of the 2D spectral AIS method (AIS method using two-dimensional wave spectrum; 2D-AIS method) using hull monitoring data of a large ore carrier is discussed. The AIS method predicts the response of actual ships using AIS-based ship position data, hindcast wave data, and response characteristics data. The conventional AIS method uses representative parameters(H, T, θ) from wave spectrum modeling. The modeling involves many uncertainties. By using the 2D wave spectrum as it is, the effect of uncertainties associated with wave spectrum modeling is investigated. Compared to the analysis of the monitoring data conducted in this study, it was found that the 2D-AIS method improves the accuracy to about 15 %, while the conventional AIS method shows an error of up to about 35 % compared to the actual measurements in the long-term maximum expected values. This enhancement is attributed to the inability of the modeled wave spectrum to accurately represent the two-peak wave spectrum observed in extreme sea states, leading to a deficiency in reproducing wave frequency components corresponding to peak frequencies of the response. The findings underscore the effectiveness of the 2D-AIS method in refining long-term hull stress estimations, thus offering valuable insights for enhancing the safety and performance of hull structures.

An Empirical Model for Skillful Rogue Wave Forecasts

Abstract One of the leading goals of rogue wave research is to develop a robust rogue wave warning system to mitigate the danger they pose. One such system has been developed by the European Centre for Medium-Range Weather Forecasts (ECMWF), called the freak wave warning system (FWWS), based on nonlinear wave effects. The FWWS predicts maximum expected wave envelope height as a risk parameter for forecasts. Recently, a data-driven alternative has been proposed by Häfner et al., which was distilled from a neural network using wave buoy observations. However, it has yet to be evaluated by a spectral wave model for application to operational wave forecasting. The data-driven, learned model emphasizes bandwidth-controlled linear superposition as the predominant mechanism in crest-to-trough rogue wave generation, while nonlinear effects are a secondary term. The present work evaluates the performance of the empirical model using output from an ECMWF global wave hindcast. We find that the prediction models based on bandwidth effects have the highest log likelihood scores, with the empirical model outperforming all other tested models. In contrast, the expected maximum envelope wave height from the FWWS does not predict the occurrence of rogue waves. These results indicate that the empirical model with wave model input is a skillful predictor and should be considered for operational implementation to improve rogue wave forecasting. Significance Statement Rogue waves are unexpectedly large and unpredictable waves. Encounters with rogue waves can result in damage to marine vessels and offshore infrastructures. Research is devoted to developing systems to predict the risk of rogue wave events. A novel predictive model has been shown to perform well in predicting rogue wave occurrences based on wave buoy observations. This model is a symbolic expression distilled from an artificial neural network that incorporates known rogue wave dynamics and that can be evaluated alongside traditional risk estimates with minor adjustments to operational forecasting systems. This study evaluates the newly proposed empirical model in a forecasting setting. Our work demonstrates the efficacy of the empirical model for operational forecasting purposes.

Random Forests’ Postprocessing Capability of Enhancing Predictive Skill on Subseasonal Time Scales—A Flow-Dependent View on Central European Winter Weather

Abstract Weather predictions 2–4 weeks in advance, called the subseasonal time scale, are highly relevant for socioeconomic decision-makers. Unfortunately, the skill of numerical weather prediction models at this time scale is generally low. Here, we use probabilistic random forest (RF)-based machine learning models to postprocess the subseasonal to seasonal (S2S) reforecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF). We show that these models are able to improve the forecasts slightly in a 20-winter mean at lead times of 14, 21, and 28 days for wintertime central European mean 2-m temperatures compared to the lead-time-dependent mean bias-corrected ECMWF’s S2S reforecasts and RF-based models using only reanalysis data as input. Predictions of the occurrence of cold wave days are improved at lead times of 21 and 28 days. Thereby, forecasts of continuous temperatures show a better skill than forecasts of binary occurrences of cold wave days. Furthermore, we analyze if the skill depends on the large-scale flow configuration of the atmosphere at initialization, as represented by weather regimes (WRs). We find that the WR at the start of the forecast influences the skill and its evolution across lead times. These results can be used to assess the conditional improvement of forecasts initialized during one WR in comparison to forecasts initialized during another WR. Significance Statement Forecasts of winter temperatures and cold waves 2–4 weeks in advance done by numerical weather prediction (NWP) models are often unsatisfactory due to the chaotic characteristics of the atmosphere and limited predictive skill at this time range. Here, we use statistical methods, belonging to the so-called machine learning (ML) models, to improve forecast quality by postprocessing predictions of a state-of-the-art NWP model. We compare the forecasts of the NWP and ML models considering different weather regimes (WRs), which represent the large-scale atmospheric circulation such as the typical westerly winds in Europe. We find that the ML models generally yield better temperature forecasts for 14, 21, and 28 days in advance and better forecasts of cold wave days 21 and 28 days in advance. The quality of forecasts depends on the WR present at the forecast start. This information can be used to assess the conditional improvement of forecasts.

Predicting Characteristic Length Scales of Barrier Island Segmentation in Microtidal Environments

AbstractSegmented barrier islands can be found in regions with small tidal ranges. In contrast to tidally dominated barriers, where inlet dynamics are thought to control island length scales, the controls on barrier island length scales in wave‐dominated environments have not been quantified. These microtidal barriers typically have a curved shoreline, suggesting the influence of wave‐driven alongshore sediment transport. Microtidal barriers are also typically hydrodynamically isolated from one another, as weak tidal flows limit interactions between adjoining barriers. To better understand the controls on and scales of barrier segmentation in the relative absence of tides, here we develop a theoretical framework to estimate the alongshore length scales at which a barrier will either breach or heal following a disturbance in the barrier morphology. The non‐dimensional framework compares the timescales of overwash (advective) and alongshore sediment transport (diffusive) processes along barrier island chains. We then apply this framework to modern barrier islands in the microtidal Gulf of Mexico using wave hindcast data and the lengths, widths, heights, and lagoon depths measured from remotely sensed geospatial data and topobathymetric data. We find that most of these barriers are currently longer than their critical length scale, often as a result of coastal restoration efforts. Our critical length scale analysis suggests that most of the Gulf of Mexico barriers are vulnerable to segmentation despite coastal restoration efforts intended to protect fisheries and the mainland coasts.

Event-based wave statistics for the Baltic Sea

Abstract. Typical statistics, such as mean or percentiles, provide an excellent baseline for studying variations and changes in physical variables that have socioeconomic relevance. Nonetheless, they lack information on how often, and for how long, a certain wave height is exceeded, which might be needed for practical applications, such as planning marine operations. Using a 29-year wave hindcast, we determined the individual events where the significant wave height exceeded warning thresholds for Baltic Sea marine traffic (2.5, 4, and 7 m). During the summer months (JJA), the significant wave height exceeded 2.5 m less than twice a month. During the winter months (DJF), a significant wave height of 2.5 m was exceeded on average once a week in the larger Baltic Proper and Bothnian Sea sub-basins. Events with wave heights of over 7 m occurred roughly once every other year in the larger sub-basins. Our case study for fish-farm-related operations compared two sites that are located 10 and 30 km from the coast in the Bothnian Sea, where we determined wave events that could affect operations at the cage – meaning a significant wave height over 1 m. During the growth period of rainbow trout (May–October) there were roughly twice as many possibly disruptive events at the location further offshore than at the location closer to the coast. Even at the less-exposed location half of the wave events lasted more than 12 h, with a few events in September and October lasting around a week.

A machine learning approach to nearshore wave modeling in large lakes using land-based wind observations

This study presents a novel machine learning-based (ML) framework that utilizes the ConvLSTM-1D model to simulate wave heights at a nearshore location in Lake Michigan using a nonuniform land-based array of wind observations from a broad geographic region as an input. This approach was applied to Lake Michigan to perform a 70-year ice-free hindcast of waves near Chicago, IL (USA). Because of annual winter gaps in Great Lakes buoy observations, output from the Wave Information System model (WIS) was used for the training, validation, and testing of the ML model. Models with different numbers of wind stations were tested, showing that a single wind station as an input feature produced a reasonably accurate wave height. However, the wave height model accuracy increased as more wind input data was included from around the lake, largely plateauing beyond the inclusion of four stations that spanned Lake Michigan’s southern basin. The optimized model lookback period was found to be 10 h for all models, suggestive of a fetch-limited temporal coupling between the wind observations and nearshore waves. The extended time series showed a statistically significant increase in the interannual standard deviation of the storm wave height and the storm height over the mean wave height while no correlation was found with the annual water level time series. The ML framework offers a promising avenue for utilizing historical wind records to extend wave height time series for nearshore locations, particularly in enclosed and semi-enclosed basins where waves are strongly linked to local winds.

Wave-Former: Lag removing univariate long time series forecasting transformer for ocean waves

Long-Sequence Time Series Forecasting (LSTSF) of ocean waves using univariate modelling has always been a challenging task in the field of oceanography as it demands a high prediction capacity model capable to capture precise long-range dependency between input and output variables. Inherently, it exhibits the problem of “time lag or phase shift” in predictions which is due to high autocorrelation in between time dependent sequential values. Very few researchers had tried to remove this “phase shift” problem in the univariate modelling including the author of present work wherein preprocessing of time series data was done by different methods. Many failed in gaining high prediction accuracy at longer forecasting intervals. Overcoming these limitations, present work aims for LSTSF of ocean waves ranging from 24 to 144 hours (hrs) at the three locations of Gulf of Mexico using “WaveFormer” architecture based on the Informer. Probabilistic self-attention mechanism has proved to be efficient to remove the “time lag or phase shift” in ocean waves as well as in predicting the waves at large time intervals (144 hrs). Low Root Mean Squared Errors (RMSEs) (0.045–0.100) and high correlation coefficients (0.90–0.99), low values of test loss (0.002–0.012) of all the developed models demonstrated the competency of WaveFormer.

Super-resolution on unstructured coastal wave computations with graph neural networks and polynomial regressions

Accurate high-resolution wave forecasts are essential for coastal communities, but local and even coastal coverage is often still missing due to the heavy computational load of modern state-of-the-art wave models. This study presents a machine learning super-resolution approach that drastically reduces the computational effort, while keeping errors negligible for the majority of forecasting applications. The method consists of first computing a wave forecast on a coarse mesh which is then converted to a forecast of finer resolution with the help of machine learning. To demonstrate the feasibility and the potential for practical applications of this approach, we present a case study of a 44-year hindcast along the French Basque coast over an unstructured mesh. We introduce two machine learning approaches, a graph neural network and a polynomial ridge regression and compare their performances in different sea states and spatial environments. Both models exhibit very small prediction errors for the significant wave heights, with Root Mean Square Errors (RMSEs) ranging from 0.3cm to 2cm, depending on the study region, while being up to 80 times faster than a direct computation of a numerical wave model at the corresponding spatial resolution. To the best of our knowledge, this is the first time that a super-resolution approach is extended to unstructured meshes in the field of coastal sciences.

CanESM5-derived ocean wave projections — Considerations for coarse resolution climate models

This study presents the first set of CanESM5-driven wave projections for two emission scenarios (SSP5-8.5 and SSP2-4.5) and two time periods for mid- and end-century. While coarse resolution climate models, like CanESM5, might be less attractive for development of ocean wave projections, their results are needed to explore the full range of inter-model uncertainty in CMIP6 projections. Considering the coarse resolution limitation, wave simulations were obtained with a proposed computationally efficient 2-step bias-correction approach that consists of (i) calibrating the wind-to-wave energy transfer in the ocean wave model to reduce the underestimation of extremes resulting from coarse resolution, and (ii) bias-correcting the surface winds with a multivariate bias-correction to reduce remaining systematic biases. Results showed overall good performance in comparison with state of the art reanalysis and satellite data. Resulting projections provide increased understanding of future changes in wave conditions, confirming previously reported global-scale changes, such as higher waves in the eastern tropical Pacific and lower waves in the North Atlantic. They also provide more detailed information for areas affected by sea ice conditions in comparison to the latest CMIP5-based wave ensembles, which is critical for the Arctic region, a hotspot for ocean wave changes. Moreover, while the largest changes are typically seen by the end-century under SSP5-8.5, this study reveals that for some variables and areas, such as the mean wave period, larger changes occur for lower warming levels as a result of competing driving factors. Finally, the presented projections can contribute to ongoing efforts to generate a large multi-model ensemble of wave projections based on CMIP6.

Pitching Stabilization Control for Super Large Ships Based on Double Nonlinear Positive Feedback under Rough Sea Conditions

Due to the rapid development of a global navigation satellite system and the rapid growth of ships, the traditional control algorithms are not suitable; hence, the longitudinal rocking phenomenon generated by external disturbances is more serious when a ship is sailing. This paper takes a mathematical model of the super large oil tanker “KVLCC2”’s longitudinal motion as the controlled plant, establishing a multi-input multi-output instability control system, using the root trajectory shaping method and a weighting matrix to ensure the stability of its transfer function’s mathematical model. An improved closed-loop gain-shaping algorithm is utilized to design a simple robust controller. And a dual nonlinear positive feedback control algorithm is added to the control system to further improve the controller’s pitching stabilization performance and reduce the controller’s output energy. In order to verify that the controller has a consistently strong robustness, simulation experiments are carried out by adding a level 6, 7 and 8 wind wave model and a perturbation link to the control system, respectively. The results show that when the value of the hysteresis constant is taken as 0.25, the output values of the heave displacement and the pitch angle are greatly reduced, and the longitudinal rocking phenomenon is significantly improved. The dual nonlinear positive feedback control algorithm enhances the ship’s pitching stabilization control capability and further reduces the controller’s output energy, which provides technical support for the smooth and efficient sailing of super large ships under changing sea conditions. Combined with a global navigation satellite system, this algorithm provides a new method for pitching stabilization control of super large ships.

Wave energy assessment and wave converter applicability at the Pacific coast of Central America

Nowadays, numerous governments have instituted diverse regulatory frameworks aimed at fostering the assimilation of sustainable energy sources characterized by reduced environmental footprints. Solar, wind, geothermal, and ocean energies were subject to extensive scrutiny, owing to their ecological merits. However, these sources exhibit pronounced temporal fluctuations. Notably, ocean dynamics offer vast energy reservoirs, with oceanic waves containing significant amounts of energy. In the Central American Pacific context, the exploration of wave energy resources is currently underway. Accurate numerical wave models are required for applied studies such as those focused on the estimation of exploitable wave power; and even more so in Central American region of the Pacific Ocean where existing numerical models simulations have so far relied on coarse resolution and limited validation field data. This work presents a high-resolution unstructured wave hindcast over the Central American Pacific region, implemented using the third-generation spectral wave model WAVEWATCH III over the period between 1979 and 2021. The results of the significant wave height have been bias-corrected on the basis of satellite information spanning 2005 to 2015, and further validation was performed using wave buoy and acoustic Doppler current profiler (ADCP) records located in the nearshore region of the Central America Pacific coast. After correction and validation of the wave hindcast, we employed the dataset for the evaluation and assessment of wave energy and its possible exploitation using different wave energy converters (WECs). This evaluation addressed the need to diverse the energy portfolio within the exclusive economic zones of Guatemala, El Salvador, Honduras, Nicaragua, Costa Rica, Panama, Colombia, and Ecuador in a sustainable manner. Moreover, a comprehensive analysis was carried out on the advantages of harnessing wave energy, juxtaposed with the imperative of regulatory frameworks and the current dearth of economic and environmental guidelines requisite for development within the region.

Assessments of multiple metocean forecasts in the North Atlantic Ocean

Accurate wind and wave forecasts are crucial for a variety of marine operations, including ship design, navigation safety, and engineering. This study evaluates the predictability of wind and wave conditions in the North Atlantic Ocean using both deterministic and ensemble forecast models. A dataset of 29 deep water buoys was used to validate deterministic and ensemble forecasts from the National Centres for Environmental Prediction (NCEP), the Canadian Meteorological Centre (CMC), the European Centre for Medium-Range Weather Forecasts (ECMWF), and the German Weather Service (DWD). A comparison of deterministic and ensemble forecast performance was conducted using eight statistical metrics focusing on the significant wave heights associated with 10-m wind speed. The results indicate that ensemble models exhibit higher correlation coefficients and lower scatter root mean square error especially beyond the 7th forecast day, outperforming deterministic models. The findings suggest that ensemble forecasts offer a more reliable estimation of forecast, enhancing predictability for marine operations.

The Wave-Coherent Stress and Turbulent Structure over Swell Waves

Abstract The generation of ocean surface waves by wind has been studied for a century, giving rise to wave forecasting and other crucial applications. However, the reacting force of swell waves on the turbulence in the marine atmospheric boundary layer (ABL) remains unknown partly due to the unclear magnitude and profile of wave-coherent (WC) stress. In this study, the intersection frequency between the energy-containing range and inertial subrange range in the turbulent spectra is identified based on the attached eddy model (AEM), as the intersection modulated by swell wave could help to comprehend the physical process between the ocean surface wave and the marine ABL. Using observations from a fixed platform located in the South China Sea, this study shows that the intersection when the WC stress accounts for a lower proportion of the total wind stress (<10%) follows U/(2πz) given by AEM, where U is the wind speed and z is the height. While the intersection depends on the drag coefficient of WC stress for the case, WC stress accounts for a large part of the total wind stress (>10%). Considering the unclear magnitude and profile of WC stress, this study derives a new function to depict the WC stress. Significance Statement Turbulence located in the energy-containing range of the spectra is the primary source of momentum, heat, and water vapor fluxes between the ocean and marine atmospheric boundary layer (ABL). Thus, a better understanding of the turbulent structure within the wave boundary layer can help us accurately parameterize those fluxes. In addition to absorbing energy from the marine ABL, waves, especially swell waves, influence the turbulent structure. However, until now, the turbulent structure is unclear due to the unclear wave-coherent stress size and profile. In this study, a function that can depict the wave-coherent stress is proposed. We found that the wave-coherent stress can modulate the intersection between the energy-containing range and the inertial subrange range in the turbulent spectra.

Sentiment Analysis of BMKG Weather Information Service Using K-Nearest Neighbor Method

The Meteorology, Climatology, and Geophysics Agency (BMKG) is a government institution that provides information related to air quality, climate, dry days, satellite imagery, wave forecasts, wind forecasts, and fire potential. This information is disseminated not only through BMKG's official website but also via the social media platform X, making it easier for the public to access up-to-date information. This study aims to classify user sentiment towards the weather information services provided by BMKG using the K-Nearest Neighbor (KNN) method. Data was collected through a web crawling technique, resulting in 1,031 data points analyzed in this research. The data processing stages included Pre-Processing and sentiment calculation using Vader's Sentiment and Random Forest. The classification results using the KNN algorithm showed an accuracy rate of 96%, with an average precision of 96%, an average recall of 96%, and an average f-measure of 96%. These findings indicate that the KNN model can effectively classify user sentiment towards BMKG's services.

Analysis and extreme event prediction of waves in the eastern shelf seas of China based on a 44-year hindcast

Analysis and extreme event prediction of regional waves are crucial for the design, spatial layout and protection of ocean engineering structures. In this study, the regional wave characteristic is analysed in the eastern shelf seas of China based on a 44-year wave hindcast. The spatial variation of peak period is smaller than that of significant wave height, which may be affected by swell propagation, and the seasonal distribution differences of these parameters can generally be explained by changes in the East Asian monsoon and are significantly affected by tropical cyclones. Both local wind wave and remotely generated swell should be considered when designing ocean structures. In addition, the joint distribution characteristics of wave period and height reveal a natural regional classification of representative wave states, which can be used to avoid deploying structures near classification boundaries. The extreme wave events are characterized by their number, duration and intensity, highlighting areas susceptible to extreme waves. Meanwhile, the extreme event is predicted, and its return patterns are highly consistent with weather system characteristics such as tropical cyclone tracks. The results can provide a significant basis for the design and protection of ocean engineering structures.

Integrated assessment of offshore wind and wave power resources in mainland Portugal

This study presents a comprehensive analysis of offshore wind and wave energy resources in mainland Portugal, aiming to facilitate sustainable energy exploitation. The study integrates the spatial distribution and temporal variability of those energy resources, as well as the interplay between wind and wave patterns and co-location feasibility. A 44-year dataset (1979–2022), derived from ERA5 reanalysis wind and SWAN wave model across the concession zones designated by the Portuguese government (labelled as P1 to P6) are utilised. The results indicate promising prospects for wind and wave power densities in these zones, emphasising the suitability of the offshore renewable energy extraction. Additionally, analysis revealed fluctuations in wind and wave power variability among the selected locations, with concession zone P3 (Leixões) emerging as a promising candidate due to its relatively lower variability and stable distribution patterns of both resources. The analysis on co-location feasibility demonstrated the potential for efficient energy extraction in location P5 proving to be the most favourable in wind-wave resource integration. Moreover, time lag analysis highlighted opportunities for optimising energy capture efficiency. Overall, this study provides valuable insights into the sustainable exploitation of wind and wave power resources, contributing to deliver informed decision-making for renewable energy investment.