Mean Significant Wave Height Research Articles

Hybrid intelligent models for predicting weekly mean significant wave heights

Accurate predictions of significant wave heights are crucial in the field of marine and ocean engineering. This paper presents two hybrid intelligent models, EN-1 and EN-2, that combine random forest (RF) and extreme learning machine (ELM) methods through direct linear weighting and gene expression programming-based nonlinear weighting methods, respectively, for the prediction of weekly mean significant wave heights. The performances of the EN-1 and EN-2 models were compared with those of 11 reference models. The results showed that the coefficient of determination (R2), mean absolute error (MAE), root mean squared error (RMSE) and mean absolute percentage error (MAPE) of the EN-1 and EN-2 models were 0.9850, 0.0567, 0.0736 and 3.7107%, 0.9940, 0.0335, 0.0487 and 2.2373%, respectively, for the training datasets and 0.9802, 0.0627, 0.0847 and 4.1461%, 0.9754, 0.0707, 0.0966 and 4.2614%, respectively, for the testing datasets, indicating that the EN-1 and EN-2 models have good predictive performance and can be effectively used for the prediction of weekly mean significant wave heights. In addition, a sensitivity analysis was conducted to investigate the influence of the input variables on the model performance.

Uncertainty in Sea State Observations from Satellite Altimeters and Buoys during the Jason-3/Sentinel-6 MF Tandem Experiment

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.

Spatial trend analysis of significant wave heights in the Kara Sea

Over the past decades, the extent of sea ice in the Arctic, including the Kara Sea, has been diminishing. This phenomenon has a direct impact on wind waves as the increased expansion of ice-free water influences wave height. Furthermore, alterations in the ice cover also lead to modifications in atmospheric circulation, necessitating a concurrent analysis of wind and waves to refine the understanding of their interrelationships. In this study, wave modeling data were employed using the WAVEWATCH III model and NCEP/CFSR/CFSv2 reanalyzes. Calculations were performed on a non-structural computational grid. The grid covers the Barents and Kara Seas, as well as the entire northern part of the Atlantic Ocean. The spatial resolution varies from ~ 700 m for the coastal zone of the Kara Sea, to ~ 20 km in the open part of the Kara Sea, covering the period from January 1, 1979 to December 31, 2021. Subsequently, average significant wave heights (SWH), maximum SWH, and the 95th percentile of SWH were computed for each grid node on both monthly and yearly basis. The annual values were analyzed for trends and their significance. Calculations were conducted for both the entire period and ice-free period. Positive trends in annual mean values were observed throughout the sea, with the maximum trend occurring near the boundary with the Barents Sea, barely exceeding 0.2 m/10 years. The northern and northeastern parts of the sea were characterized by significant positive trends of the maximum SWH values. Maximum trend values for the 95th percentile of SWH were also evident in the northern part of the Kara Sea. For the ice-free period, maximum trend values were notable for both the annual mean and the 95th percentile of SWH in the northern part of the sea (maximum trend values are approximately 0.25 m/10 years and 0.5 m/10 years, respectively). Significant positive trends in the annual mean SWH were characteristic of the southern part of the sea, while the largest and significant trends for maximum wave heights were observed in the northeast. The assessment of the contribution of wind and ice regimes to the variability of wind waves remains a subject of discussion.

Machine Learning‐Based Wave Model With High Spatial Resolution in Chesapeake Bay

AbstractA high‐resolution wave model is crucial for accurate modeling of sediment and organic material transports, but its computational costs hinder direct coupling to an ecosystem model. We developed a machine learning model using long short‐term memory to simulate large‐scale, high‐resolution waves. Trained with numerical wave model (NWM) outputs and wind data from nine locations, our model successfully replicates NWM results for daily mean significant wave height and period in Chesapeake Bay with identical spatial resolution. Compared to the NWM, the data‐driven model has root‐mean‐square errors below 6 cm for daily mean significant wave height and 1 s for the wave period in the bay. It demonstrates excellent model skills and can accurately forecast daily mean significant wave height and period at NOAA wave stations comparable to NWMs. Using minimal wind data and having a short runtime, our data‐driven model shows promise as an alternative for wave forecasting and coupling with sediment and ecological models.

Trends in the surface wind-wave heights in the North Indian Ocean based on 50-year NCEP/NCAR reanalysis wind-wave data

Analysis of 50 years of hourly significant wave heights of the Indian Ocean between 30°N and 60°S is carried out and linear trends of mean significant wave heights and maximum significant wave heights are obtained on annual, seasonal and decadal scales. The significant wave heights (SWH) are obtained from a third-generation spectral wind-wave model forced with six-hourly NCEP-NCAR winds over the Indian Ocean. These SWHs are validated with measurements available in the north Indian Ocean and the correlation coefficient is more than 0.87. The climatology obtained from the spectral wind wave model matches well with the climatology reported in the literature using other models and satellite-based datasets. The maximum SWH ranged from 0.25 m to 22.5 m with the max-SWH exceeding 7 m South of 30°S, and greater than 13 m between 45°S-55°S and 50°E-95°E. In the Northern Indian Ocean (NIO), max SWH reached 5.5 m in the central Bay of Bengal and over 8 m in the western Arabian Sea. The annual trend of the mean SWH showed an overall positive trend in the Indian Ocean, except in the west BoB, northwest Arabian Sea, and a part of the central Indian Ocean. The maximum SWH also followed an overall similar positive trend as that of mean SWH albeit with a prominent negative trend in the BoB, southeastern and northwestern Arabian Sea. There was a significant difference in the SWH trend between the seasons both spatially and temporally for all other decades. However, the maximum SWH showed highly varying trends for all the seasons and decades. The variation in the mean SWH decadal trend showed greater variation in the lower latitudes compared to the higher latitudes.

Global coastal wave storminess

Coastal wave storms pose a massive threat to over 10% of the world’s population now inhabiting the low elevation coastal zone and to the trillions of $ worth of coastal zone infrastructure and developments therein. Using a ~ 40-year wave hindcast, we here present a world-first assessment of wind-wave storminess along the global coastline. Coastal regions are ranked in terms of the main storm characteristics, showing Northwestern Europe and Southwestern South America to suffer, on average, the most intense storms and the Yellow Sea coast and the South-African and Namibian coasts to be impacted by the most frequent storms. These characteristics are then combined to derive a holistic classification of the global coastlines in terms of their wave environment, showing, for example, that the open coasts of northwestern Europe are impacted by more than 10 storms per year with mean significant wave heights over 6 m. Finally, a novel metric to classify the degree of coastal wave storminess is presented, showing a general latitudinal storminess gradient. Iceland, Ireland, Scotland, Chile and Australia show the highest degree of storminess, whereas Indonesia, Papua-New Guinea, Malaysia, Cambodia and Myanmar show the lowest.

Assessment of coastal vulnerability index (CVI) and its application along the Labuhan Maringgai coast, east Lampung Indonesia

The Coastal Vulnerability Index (CVI) is one of the simplest and commonly used methods to assess coastal vulnerability. In this way, it is a common tool contributing to the decision-making process in long-term coastal planning and management. This study aims to assess the level of coastal vulnerability according to coastal typology of Labuhan Maringgai Coast section. The variable formulation of CVI is divided into hydrodynamic factors (mean significant wave heights, mean tide range, and mean sea level rise) and morpho dynamics factors, i.e. geomorphology, coastal slope, and average width of emerged beach. The morpho dynamics data were obtained through observation, direct measurements in the field by systematic sampling, extraction from aerial photographs and digital surface model (DSM). The results of modelling and predictions by several agencies are derived to obtain the hydrodynamics data. The coast of Labuhan Maringgai was divided into 12 transects and the coastal vulnerability index were classified into three categories such as low, moderate, and high. The results of CVI method showed that the most vulnerable transect is located at Desa Bandar Negeri characterized by mud flats and damaged mangroves.

Weather-type statistical downscaling for ocean wave climate in the Chinese marginal seas

A comprehensive understanding of wave characteristics and their variability, based on reliable long-term wave data, is essential in the design, construction, operation and management in offshore and coastal applications. This study aims to downscale multivariate wave data in the Chinese marginal seas at different time scales by employing two weather-type statistical downscaling models. The calibration of both models involves the usage of historical data from ERA5 reanalysis, with sea level pressure and the squared sea level pressure gradient as the predictors and wave parameters as the predictands. The predictor definition considers the swell components in the local wave data. Both models categorize the atmospheric predictors into different weather types using the K-means algorithm (KMA), with and without regression-guided clustering (referred to as WTD-RG and WTD, respectively). Each weather type is associated with sea state parameters. The downscaled wave data from both models are validated against ERA5 data. The results show that both models can generally reproduce the wave statistics for the significant wave height, mean wave direction, mean wave energy flux, and 95th percentile of the significant wave height. However, the WTD-RG model performs better than the WTD model. Additionally, the ERA5 data reveal increasing trends in the mean significant wave height for most areas of the East China Sea and South China Sea and decreasing trends in the Bohai Sea, Yellow Sea, and Beibu Gulf from 1959 to 2021. These patterns are well captured by the WTD-RG model but not by the WTD model.

Contribution of tropical cyclone induced waves to the mean and extreme wave climatology in the Bay of Bengal

This paper examines the contribution of tropical cyclones (TCs) to the mean wave and the extreme wave climatology in the Bay of Bengal (BoB). To assess the impact of TCs on the wave activity in the BoB, we compare 40-years long WAVEWATCH III (WW3) numerical simulation with a twin experiment, where TC signatures are filtered out from the wind forcing dataset. Our experimental strategy of twin simulations, with and without TCs, allow us to separate the TC-induced waves from the background wave activity and therefore allow us to quantify their contribution. The simulation samples more than 200 TCs in the BoB and is extensively validated against the available buoy observations that measure 39 TCs in the BoB. Results show that TCs contribute up to ∼80 % and ∼40 % to the extreme significant wave height (SWH) climatology defined as the maximum SWH and highest 1 % SWH and up to ∼9 % to the mean SWH climatology during the post-monsoon season with slightly lesser contributions during the pre-monsoon season. This contribution is largest in the northern BoB and along the east coast of India during the post-monsoon season and in the eastern BoB and along the Bangladesh and Myanmar coast during the pre-monsoon season.

Coastal Vulnerability Classification of the North Coast of Java using K-Nearest Neighbor

Indonesia has many beaches that attract the attention of tourists, including the north coast of Java. In addition to visual appeal, there are also other potentials such as settlements, agriculture, fisheries, ports, ponds, and other resources. However, there is also a threat to coastal damage caused by, among other things, wave action, tides, abrasion, and tidal flooding. For this reason, in developing coastal areas on the north coast of Java, it is necessary to consider the potential for damage to the coast based on the physical condition of the coast and a system that can classify the vulnerability levels of coastal areas is also needed. The Coastal Vulnerability Index (CVI) can be determined and classified using for example the Gornitz formula, or using data driven model and machine learning based on the coastal parameter data. This study demonstrates how the K-Nearest Neighbor, also known as K-NN algorithm, can be used to classify the level of vulnerability of the coastal areas. This study uses 290 points (locations) along the northern coasts of Java. The parameters that determine the coastal vulnerability are mean sea level (MSL), mean significant wave height (MSWH), mean tidal range (MTR), shoreline changes, landforms and slopes. In this study, the classification of coastal vulnerability levels is classified into 4, namely “low, moderate, high and very high”. The K-NN system uses 80% of the data for training and 20% for testing, with the value of K = 1 to 10. The test results show that the K-NN method is capable of classifying the vulnerability levels of the North Coast of Java. From the test results for values of K = 1 to K = 10, and by randomizing the training data and test data gives an average accuracy rate of 86.21% to 97.13%, with the best K value obtained at K = 2.

Dominant morphodynamic processes of a macrotidal beach of the eastern tropical Pacific and its relationships with climate variability

In this study, the influence of different coastal processes, including ocean-atmospheric processes of regional scale, on the spatiotemporal variability of the morphodynamic from the emerged zone of a beach in the Colombian eastern tropical Pacific, specifically in the macrotidal regime's Playa La Bocana, was analyzed during 2014–2019. The linear dependence of the sediment volume on the tide, rainfall, and winds was quantified using Pearson correlations and with large-scale oceanic and climatic relationships, that could be related to sediment volume anomalies. The highest correlation sediment volume monthly mean values are presented with the tide on an intra-annual scale. On an inter-annual scale, the sea surface temperature and sea level pressure composites were consistent with the El Niño-Southern Oscillation patterns. Thus, a cooling (warming) of the tropical Pacific is associated with a higher (lower) sediment volume onshore at Playa La Bocana. Furthermore, it was found that increase (decrease) on Swell (Mean Wave Period and Significant Wave Height) decreased (increased) the volume of sediments. These results show that the tide is the main modulator of beach sediment volume changes under the macrotidal regime, on the intra-annual scale, and that on the inter-annual scale, sediment volume responds to the combined effect of the tide and changes in swell intensity modulated by ENSO conditions.

Numerical Modeling of Nearshore Wave Transformation and Breaking Processes in the Yellow River Delta with FUNWAVE-TVD Wave Model

The presence of wave coherence, which contributes to the inhomogeneity of wave characteristics and significantly affects wave processes over nearshore regions of the Yellow River Delta (YRD), was simulated and analyzed in this study. A phase-resolving Boussinesq-type wave model, FUNWAVE-TVD, was used to simulate waves with desirable coherency effects. Bathymetry and topography data were obtained from the Chinese nautical chart and E.U. Copernicus Marine Service Information. After the model configuration, spatial distributions of the root mean square and significant wave heights, and the maximum cross-shore current velocity and vorticity over the domain with respect to different degrees of wave coherence and energy spectrum discretization were investigated. The results indicate that the complexity of the spatial distribution and magnitude of longshore variations in wave statistics are proportional to the degree of coherence. Waves with higher coherency exhibit more complex variabilities and stronger fluctuations along the longshore direction. The influence of morphological changes on wave height in the YRD was discernible by comparing the results with and without coherency effects. The cross-shore current velocity decreased as the waves moved toward the surf zone, while the vorticity accelerated, indicating a higher shear wave magnitude. The simulated wave dissipates more than 60% (80%) of its energy when it reaches water depths of less than 5 m (2 m) and completely dissipates when it breaks at the shore.

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

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

Development of design typhoon profile for offshore wind turbine foundation design in Southern China

For offshore wind development in Southern China, typhoon represents the extreme environmental loading condition to be considered in the design of the turbine structures. For the geotechnical design of the foundations, it is specified by the design code that the effect of cyclic loading on the soil strength and stiffness must be considered. This necessitates the complete time history of loads on the foundation experienced during a design typhoon. Idealised storm profiles with staged mean wind speeds and significant wave heights are commonly used as input to time-domain simulations to generate the foundation load history. However, no such design typhoon profile is provided in the Chinese design standard which creates considerable difficulty and uncertainty in the design process. In this paper, the methodology and the rationale that were applied to derive the design typhoon profiles for an offshore wind project in Guangdong province are presented. The wind and wave characteristics generated by typhoon are described in detail and the implications for the foundation design are discussed. To demonstrate application of the proposed typhoon profile, a case study for the ULS design of a suction bucket jacket is presented.

Numerical modeling of wave penetration inside a harbor

Wave penetration analysis is typically performed to ensure that the coastal structure at the harbour provides adequate shelter from waves and currents for ship berthing. Generally, wave penetration inside a harbour occurs through the entrance. The type of coastal protection (usually a breakwater) also has an impact on wave agitation within the harbour. In this research, wave penetration analysis has been done, mainly, by using MIKE 3 Wave FM software to model seven different scenarios as individual cases. From the seven different cases, the mean wave disturbance coefficient and mean significant wave height in the berthing area are determined. The model results showed that the wave penetration on the turning circle in the navigation channel is relatively unaffected by the wave disturbance in all seven cases. It is observed that 80 % of the time the significant wave height in the berthing area was less than or equal to 0.1 meters. The wave climate in the berthing area is therefore classified as good. Consequently, it can be concluded that the breakwaters are achieving their goal of reducing the impact of wave action and currents within the harbour.

Influence of Long-Term Wind Variability on the Storm Activity in the Caspian Sea

Wind and wave conditions are limiting factors for economic activity, and it is very important to study the long-term variability of storm activity. The main motivation of this research is to assess the impact of wind variability on the storm activity in the Caspian Sea over the past 42 years. The paper presents the analysis of a number of storms based on the results of wave model WAVEWATCH III and the Peak Over Threshold method. The mean, maximum, and 95th percentile significant wave heights were analyzed by season. The highest waves were in the Middle Caspian Sea in winter. Detailed interannual and seasonal analyses of the number and duration of storm waves were performed for the whole Caspian Sea and its separate regions. Positive significant trends were found in the whole sea. Significant positive trends in the number and duration of storms were found for the North and Middle Caspian. In the South Caspian, the trends were negative and not significant. High correlations were found between the number of storms and events with wind speed > 10–14 m/s and 95th percentile wind speed. Positive trends in the number of storms in the Middle Caspian were caused by positive trends in extreme wind situations.

Wind Waves Web Atlas of the Russian Seas

The main parameters of wind waves in the World Ocean are connected with global climate change. Renewable energy technologies, intensive shipping, fishery, marine infrastructure, and many different human marine activities in the coastal zone and open sea need knowledge about the wind-wave climate. The main motivation of this research is to share various wind wave parameters with high spatial resolution in the coastal zone via a modern cartographic web atlas. The developed atlas contains information on 13 Russian Seas, including the Azov, Black, Baltic, Caspian, White, Barents, Kara, Laptev, East Siberian, Chukchi, Bering Seas, the Sea of Okhotsk, and the Sea of Japan/East Sea. The analysis of wave climate was based on the results of wave modeling by WAVEWATCH III with input NCEP/CFSR wind and ice data. The web atlas was organized using the classic three-tier architecture, which includes a data storage subsystem (database server), a data analysis and publishing subsystem (GIS server), and a web application subsystem that provides a user interface for interacting with data and map services (webserver). The web atlas provides access to the following parameters: mean and maximum significant wave height, wave length and period, wave energy flux, wind speed, and wind power. The developed atlas allows changing the map scale (zoom) for detailed analysis of wave parameters in the coastal zones where the wave model spatial resolution is 300–1000 m.

A Multidecadal Assessment of Mean and Extreme Wave Climate Observed at Buoys off the U.S. East, Gulf, and West Coasts

The current understanding of wind-generated wave climate from buoy-based measurements is mainly focused on a limited number of locations and has not been updated to include measurements in the past decade. This study quantifies wave climate variability and change during the historical period of 1980–2020 through a comprehensive analysis of wave height measurements at 43 buoys off the U.S. Pacific, Atlantic, and Gulf of Mexico Coasts. Variabilities and trends in the annual and monthly mean and 95th percentile significant wave heights (SWH) and the number of extreme wave events are quantified for the cold and warm seasons. We calculate the SWH long-term and decadal trends, and temporal variabilities using the ordinary least squares regression and coefficient of variation, respectively. Independent extreme wave events are identified using a method based on the peaks-over-threshold and the autocorrelation function, which accounts for the geographical variation in the timespan between independent extreme events. Results show that the warm season’s interannual variabilities in monthly and annual SWH are smaller in the Pacific while larger in the Atlantic and Gulf, with the largest variabilities observed at buoys in the Gulf and lower latitudes of the Atlantic. Strong significant alternating decadal trends in SWH are found in the Pacific and Atlantic regions. Buoys in the Atlantic and Gulf regions have experienced higher numbers of extreme wave events (anomalies) compared to the Pacific region. In general, the long-term trend in the number of extreme events during the cold season is positive at buoys located at higher latitudes but negative at lower latitudes.

Global atlas of extreme significant wave heights and relative risk ratios

Interest in offshore wind, wave, and tidal energy power generation to supply electricity to the grid nearshore or power off-grid applications far offshore has motivated numerous studies of the ocean wave climate, including extreme wave conditions that characterize project risk and wave loads for design. The present study uses the 30′ resolution 31-year Global WAVEWATCH III® model hindcast, the 4′ resolution 31-year coastal US model hindcast, and the US NOAA buoy network to estimate and map the global distribution of the mean, 50-, 5- and 1-year significant wave heights and the relative-risk-ratios computed by non-dimensionalizing these n-year extreme wave heights with their mean values. A two-step linear correction method is applied to correct systematic underbias of model-derived extreme wave heights relative to the observation-derived values, resulting in a 20% or more increase in model-derived values compared to uncorrected ones. The corrected 30’ resolution extreme wave height and relative risk ratio atlas generated herein provides important metrics that support resource characterization and international standards development for the marine energy industry, including resource and site assessment, and the establishment of upper design limits for device type classification and certification to streamline product line development.

Extremes and variability of wind and waves across the oceans until the end of the 21st century

The wave model WAVEWATCHIII is used to produce wave information, until the end of the 21st century, covering all ocean areas. Global wind and ice-cover climate data from a total of 120 years are used as input for the wave model. The period is divided into four 30-year slices, where the first (1980–2009) represents the recent past, the second (2010–2039) the near future, the third (2040–2069) the mid-century and the last one (2070–2099) represents the end of the 21st century. For each period, the mean value, the standard deviation and the 99th percentile are computed for significant wave height of total sea, wave energy and cumulative wave energy, and also for the 10-m wind magnitude field, used to force the wave model. Changes from the recent past to the present and to each of the two future periods are obtained and analyzed. The results show an increase in mean significant wave height of total sea, wave energy and cumulative wave energy in the South Atlantic, and an increase in variability and a decrease of mean significant wave height of total sea in the North Atlantic. Other regions also present changes but are less marked and less consistent through time.