Extreme Wave Heights Research Articles

A general framework to obtain seamless seasonal–directional extreme individual wave heights—Showcase Ekofisk

Extreme wave climate provides the basis for safe design of offshore structures and is crucial for planning and executing offshore operations. Covariate modeling of extremes significantly enriches and improves estimates of return levels and exceedance probabilities of extreme sea states. Based on novel observational and hindcast datasets, we formulate a seasonal–directional extreme value model for individual wave heights and present exceedance probabilities for the Ekofisk oil and gas field, a location in the Central North Sea. Subsequently, we elucidate how to downscale estimates of monthly exceedance probabilities and return levels to daily maxima and illustrate how to retrieve consistent results on seamless directional sectors and different seasons, or for the entire covariate space. We conclude with a versatile statistical framework to obtain seasonal–directional extreme waves and reveal a strong seasonal and directional dependence of extreme individual waves at Ekofisk with the highest waves coming from northwest during winter. Moreover, we apply our approach to normalized wave heights and show noticeable variability depending on season and direction with implications for offshore design.

A Wave Directionality and a Within-Year Wave Climate Variability Effects on the Long-Term Extreme Significant Wave Heights Prediction in the Adriatic Sea

The extreme significant wave height predictions often neglect within-year wave climate variability and wave directionality. Depending on a geographical region, local wind patterns and year climate variability could have an influence on the long-term prediction of waves. The Adriatic Sea having two dominant wind patterns of different characteristics, Bura and Jugo, is a great example for the case study. The 23-year hindcast wave data used in the presented study is extracted from the WorldWaves database. Based on wind and wave data, annual extreme significant wave heights generated by different wind patterns and for different months are fitted by Gumbel distribution using maximum likelihood estimation. Combined long-term extremes are then predicted by calculating system probability. It was found that considering the wave directionality, and especially the seasonality of wave climate, leads to a larger prediction of extreme significant wave heights. The extreme value prediction considering wave directionality on average yields 4% larger significant wave heights, while considering within-year climate variability leads to, on average, 8% larger extremes compared to the predictions when both effects are neglected.

Global ocean wave fields show consistent regional trends between 1980 and 2014 in a multi-product ensemble

Historical trends in the direction and magnitude of ocean surface wave height, period, or direction are debated due to diverse data, time-periods, or methodologies. Using a consistent community-driven ensemble of global wave products, we quantify and establish regions with robust trends in global multivariate wave fields between 1980 and 2014. We find that about 30–40% of the global ocean experienced robust seasonal trends in mean and extreme wave height, period, and direction. Most of the Southern Hemisphere exhibited strong upward-trending wave heights (1–2 cm per year) and periods during winter and summer. Ocean basins with robust positive trends are far larger than those with negative trends. Historical trends calculated over shorter periods generally agree with satellite records but vary from product to product, with some showing a consistently negative bias. Variability in trends across products and time-periods highlights the importance of considering multiple sources when seeking robust change analyses.

The projected changes in extreme wave height indices over the Indian Ocean using COWCLIP2.0 datasets

The projected changes in extreme wave height indices over the Indian Ocean using COWCLIP2.0 datasets

Modelling and simulation of extreme wave heights around agatti island of lakshadweep, west coast of India

Small islands experience variation in wave energy regime along shorter shoreline due to refraction, diffraction and variability in direction of wave travel. Nearshore wave climate around these islands is quite complex due to wave transformation associated with configuration of islands, and high steepness in the bathymetry. Understanding wave energy will help in identifying suitable locations for coastal structures, wave energy devices and sediment budgeting. Assessment of extreme wave climate around the islands play a crucial role in the design and survival of coastal infrastructure for any developmental activities in islands. This study investigates the extreme wave climate around the Agatti island of Union Territory of Lakshadweep located in west coast of India. The spatial variability of wave power distribution around the Agatti island is analyzed based on 10 years of wave hindcast data from spectral wave modelling for the period between 2011 and 2020 using spectral wave model. In this study, third-generation spectral wave model was used to simulate the wave climate over the Arabian Sea. Regional model was established using ECMWF model winds and the offshore wave parameters were validated with deep water ocean observations AD07 and AD09 deployed in the Arabian Sea. To understand the nearshore wave transformation along the Agatti island, local wave model of fine resolution was established using high resolution bathymetry and is validated using the coastal buoy (CB02) deployed near Agatti. Nearshore wave parameters such as Significant wave height, Peak wave period (Tp) and Mean wave direction (θm) were analyzed. The wave power distribution around the island was quantified and demarcated for siting of offshore structures for developmental activities. The study reveals that the south zone of the island is more energetic with annual mean wave power of 8–12 kW/m and during monsoon, wave power more than 28 kW/m is observed. The extreme value theory based on Generalized Extreme Value distribution is applied to the extreme wave height estimate based on modelled wave data around the Agatti island. The extreme wave heights for different return periods were estimated around the Agatti island for design and analysis of coastal infrastructure.

Prediction of significant wave height in hurricane area of the Atlantic Ocean using the Bi-LSTM with attention model

The Bi-LSTM with attention (BLA) model is proposed to predict wave height in the hurricane area of the Atlantic Ocean. Four data features (wave height, wind speed, wind direction, and wave direction) collected at five buoy stations are selected as model inputs, while future wave height is specified as model output. Predictions are obtained for 1-h, 3-h, 6-h, and 12-h lead times. Two evaluation metrics are introduced to evaluate the accuracy and stability of the model. Influencing factors such as input–output ratio and input feature combination are studied. For the input–output ratio, it is found that the shorter lead time requires a larger ratio, with a ratio of 9:1 required for 1-h lead time prediction, with 3:1 for 3-h prediction, 2:1 for 6-h prediction, and 1:1 for 12-h prediction. For the input feature combination, the combination of the wave height, the wind speed, and the coupling of the wind direction and wave direction via the cosine function holds the best prediction performance in 1-h and 3-h lead time prediction. And for 6-h and 12-h forecasts, a combination of wave height and wind speed is best. By comparing overall evaluation metrics and extreme wave height prediction results of the BLA model with those of the Bi-LSTM, LSTM, and LSTM with attention models, we notice that the BLA model has the best and most stable prediction performance.

Spatial-temporal wave height forecast using deep learning and public reanalysis dataset

A novel data-driven model is proposed for efficient spatial–temporal significant wave height forecast in West Pacific using deep learning. A multivariate 3-layer LSTM-based architecture following a matrix-to-matrix mapping fashion is applied to establish the underlying spatial–temporal relationship between wind components and significant wave height field for long-term and ocean-scale forecasts. A parallel modeling strategy is employed to reduce the computational expense in which the forecasting domain is flexibly partitioned into finite windows and trained independently as a sub-model. A 30-year hindcast wave dataset released by EMC (Environmental Modeling Center) Operational Wave Models associated with NCEP Climate Forecast System Reanalysis and Reforecast (CFSRR) wind data is used to drive and test the model. A rectangle sea region covering over 9.33 × 106 km2 in West Pacific is regarded as a modeling domain. The data-driven model is validated against a 12-year period historical hindcast data, and global errors are carefully discussed. The forecasting performance of the established model on tropical cyclone wave events is investigated in terms of both spatial pattern and temporal variance of significant wave height. The extreme significant wave height, rough sea occurrence, as well as seasonal and annual characteristics of significant wave height in the West Pacific are carried out using the proposed model and compared with the original hindcast results. The data-driven model shows promising potential to accurately capture the ambiguous patterns and features that are variant in both spatial and temporal dimensions and has obvious superiority over numerical wave modeling in terms of computational efficiency.

Evaluation of regional climate models and future wave characteristics in an enclosed sea: A case study of the Black Sea

The main objective of this study is to evaluate a possible climate change impact on wave climate in an enclosed sea (Black Sea) until the end of the 21st century. To achieve the goal, the wave data are generated from a third-generation wave model forced with the widely used reanalysis data (Climate Forecast System Reanalysis), and the hindcast wind fields simulated by a Regional Climate Model, namely Rossby Centre regional atmospheric model (version RCA4). The pattern of change in the wave climate is discussed by comparing the historical (1970–2005) with the future for periods 2021–2060 and 2061–2100 under two climate scenarios. The projected changes in the mean wave characteristics are characterized by an increase in the near future for both RCP scenarios that is more prominent under RCP8.5 scenario in the eastern basin. The middle future under RCP8.5 scenario suggests more significant changes in annual mean values than those obtained under RCP4.5 scenario. In the context of climate change, the possible effects are more prominent on extreme wave heights. For example, the increases in the wave heights for the 100-year return period reach the value of 5% and 25% in the western and eastern Black Sea, respectively.

Current interaction in large-scale wave models with an application to Ireland

A nested large-scale wave model that covers most of the Atlantic Ocean and focuses on generating accurate swell conditions for Ireland is presented and validated over the two years 2016−2017. A sensitivity analysis for the βmax parameter appearing in the wind input formulation is carried out, optimising the extreme significant wave heights from the model against altimetry data in the North-East Atlantic region around Ireland. An optimal value of 1.75 is found using the ERA5 reanalysis corrected beforehand for a well-known negative bias for the high wind speed values. The impact of currents is studied using the surface currents from the GLORYS12 product. Currents slightly reduce by 1% the root-mean-square and bias errors for significant wave height compared to altimetry data. However, they explain most of the wave energy at scales less than 50m. The variability induced by currents is found to be more noticeable when looking at the satellite tracks. Track following observations indicate that wave refraction and advection induced by mesoscale eddies are correctly captured by the model, inducing a spatial variability reaching up to 0.5m. However, this modulation is of the same order as a shorter-scale variability appearing in the altimetry data. An averaging operator is used to smooth the data and remove those high-frequency variations. The main finding is that a spatial shift seems to appear between the model and the observations, attributed to the relatively poor resolution of the current product used for the scales observed.

Tilt Error in NDBC Ocean Wave Height Records

Abstract We identify and characterize an error in the National Data Buoy Center (NDBC) wave records due to the sustained tilt of a buoy under high winds. We use a standard, operational 3-m aluminum discus buoy from NDBC with two wave systems, one gimballed, and the other strapped down but uncorrected. By comparing the two, we find that the most extreme significant wave heights are systematically overestimated. The overestimation is shown to be confined to a region around the peak frequency in the spectra: 0.05–0.15 Hz. Wave direction and directional spread are unaffected. A bias due to tilt error can be observed starting at winds of 10 m s−1 or wave heights of 4 m. The bias increases as a function of wind speed and wave height, i.e., the bias is +10% when winds are 20 m s−1. Very high waves and winds are relatively rare, so while the tilt error does not affect overall statistics and basic analyses it could potentially affect analysis sensitive to the extremes. A correction is derived for significant wave height, which is a quadratic function of wind speed. The correction is shown to reduce wave heights in uncorrected records, but is found inadequate for general use. There is evidence of tilt error at other NDBC stations, but the full extent of prevalence in the record is not known at this time.

Bias in estimates of extreme significant wave heights for the design of ship structures caused by neglecting within-year wave climate variability

ABSTRACT The effect of within-year wave climate variability on the predicted extreme significant wave heights for the design of ship structures is examined. The significant wave height data is taken from ERA 5 database along frequent shipping routes. Monthly and annual extreme significant wave heights are extracted, and Gumbel distributions are fitted, respectively, using Maximum Likelihood Estimation. Monthly extreme wave heights are then combined, using the method proposed by Carter and Challenor [(1981). Estimating return values of environmental parameters. Q J R Metereol Soc. 107(451):259–266], to account for the effect of intra-annual climate variability. Long-term extreme values by two methods are compared for individual locations and shipping routes. Consequences on the extreme wave bending moments are explored, comparing the results to IACS rules. It was found that neglecting within-year wave climate variability leads to the underestimation of extreme significant wave heights and wave bending moments by up to 10 %. .

Characteristics of Ocean Waves in the Southern Ocean and Seasonal Prediction of Difficulty for the Vessels Crossing the Westerlies

In this study, the European Centre for Medium-Range Weather Forecasts reanalysis v5 (ERA5) wave height reanalysis data and sea-level pressure data from two seasonal prediction systems were used to study the wave characteristics of the Southern Ocean and the seasonal prediction of difficulty for the vessels crossing the westerlies. The results show that significant wave height, extreme wave height, and extreme wave processes were all much stronger in austral winter than in austral summer, making it more difficult for vessels to cross the westerlies in winter. Furthermore, the difficulty of crossing the westerlies has increased over the last 40 years, except in areas east of South America. We found that the monthly frequency of crossing the westerlies between 100° E and 75° W could be accurately estimated point by point using the monthly mean sea-level pressure difference between 30° S and 65° S. With a 1-month lead, the multi-model forecasts gave a fairly accurate forecast of such sea-level pressure difference signal between 150° E to 60° W for target months from May to December. Based on these assessments, we could estimate the difficulty of crossing the westerlies in some specific months in advance using a seasonal prediction system. We also found that the seasonal prediction system produced inaccurate predictions of sea-level pressure at high latitudes, which is the main barrier to further accurately estimating the difficulty of crossing the westerlies. These findings may provide support for predicting difficulty for the vessels crossing the westerlies with a 1-month lead and can provide planning for the route and the allocation of material reserves.

Evaluation of the performance of a dynamic wave climate ensemble simulated using with EURO‐CORDEX winds in the Black Sea and Sea of Azov

AbstractThis study evaluates the performance of a dynamic ensemble of wave climate simulations for the Black Sea. The ensemble members (and ensemble means) are evaluated for the historical period (1979–2005). The spectral wave model (simulating waves nearshore [SWAN]) was forced with eight Coupled Model Intercomparison Project Phase 5 (CMIP5) based Regional Climate Models (RCMs) wind fields to obtain each of the eight ensemble members. The RCM‐forcings used belongs to the European branch of the Coordinated Regional Downscaling Experiment (EURO‐CORDEX). The ensemble members' historical wave climate is thoroughly compared against the ERA5 reanalysis, in situ observations, and altimeter measurements. In addition to the individual evaluation of ensemble members, the results for the 8‐member ensemble mean are also examined. The performance of the ensemble members in reproducing the mean and extreme significant wave heights, mean wave periods, and mean wave directions is found to be good, with differences generally between +25 and −15% in comparison to ERA5. Differences between +10% and −30% were found for the comparison with altimeter measurements. We conclude that the ensemble better represents the wave climate of the Black Sea, than its individual members. The 8‐member ensemble provides a more balanced dataset for the Black Sea wave climate and a better representation of the associated uncertainty. Thus, further wave climate projections for the Black Sea should rely on the use of an ensemble.

Extreme Wind Wave Climate off Jeddah Coast, the Red Sea

Climate change can give rise to significant changes in the intensity and frequency of extreme events. In the present study, extreme wave events off the central-eastern coast of the Red Sea, near the city of Jeddah, were investigated using a 39-year wave hindcast generated using WaveWatch III configured at a 3.3 km resolution forced with ERA5 reanalysis winds. The validated model outputs were used to derive the annual and seasonal climatology for the region at a few selected locations off the Jeddah coast. The study revealed robust temporal and spatial variability in the region, considering the influence of both northern and southern Red Sea waves that meet at the convergent zone. Generalized Pareto Distribution (GPD) and Generalized Extreme Value (GEV) were two models used for the estimation of extreme wave analysis in the study region. The extreme significant wave heights were estimated for 10, 25, 50, and 100-year return periods. For offshore locations, the estimated return periods using the GPD method were 3.27, 3.44, and 3.38 m, respectively. GPD with the POT method was the more suitable approach, as it produced reduced bias and RMSE. At all locations, linear trends show an increase during the summer, winter, and pre-summer periods. No significant increase in the Hs trend was observed at the selected locations near and off the coast. However, the decrease in trend observed at all locations during the pre-winter period was noticeable for the 99th percentile Hs.

Long-Term and Seasonal Variability of Wind and Wave Extremes in the Arctic Ocean

Over recent decades, the Arctic Ocean has experienced dramatic variations due to climate change. By retreating at a rate of 13% per decade, sea ice has opened up significant areas of ocean, enabling wind to blow over larger fetches and potentially enhancing wave climate. Considering the intense seasonality and the rapid changes to the Arctic Ocean, a non-stationary approach is applied to time-varying statistical properties to investigate historical trends of extreme values. The analysis is based on a 28-year wave hindcast (from 1991 to 2018) that was simulated using the WAVEWATCH III wave model forced by ERA5 winds. Despite a marginal increase in wind speed (up to about 5%), results demonstrate substantial seasonal differences and robust positive trends in extreme wave height, especially in the Beaufort and East Siberian seas, with increasing rates in areal average of the 100-year return period up to 60%. The reported variations in extreme wave height are directly associated with a more effective wind forcing in emerging open waters that drives waves to build up more energy, thus confirming the positive feedback of sea ice decline on wave climate.

Present-day infralittoral prograding wedges (IPWs) in Central-Eastern Tyrrhenian Sea: Critical issues and challenges to their use as geomorphological indicators of sea level

A census of 83 Infralittoral Prograding Wedges (IPWs) was carried out in the Central-Eastern Tyrrhenian Sea, to learn more about their morpho-bathymetric variability and test their reliability as environmental indicators of current sea level. With this aim, a database recording for each wedge the main morphometric indices, the effective fetch and the significant height of the storm waves– here used as proxies for sea state forcing to which they are exposed- and the ground elevation in the backshore - here used as a numerical descriptor of coastal morphology and energy of the relief- was realized (Campania Region IPWs Database).The statistical analysis on the entire IPWs dataset explored the relationship between the environmental and morphometric variables while the Principal Component Analysis grouped the variables into two clusters, governed by sea state forcing and energy of relief in the backshore, respectively. The multi-regression analysis highlighted a significant correlation of IPWs depth with effective fetch and extreme significant wave height and a moderate correlation with the ground elevation in the backshore. The outcomes that emerged from the observational law on present-day IPWs were then applied to relict IPWs, currently lying on the continental shelf and at the shelf margin, with the aim of establishing their original depth of formation. This procedure aims to solve the non-trivial issue, namely that concerning the reliability of paleo-IPWs as proxies for past sea levels. Thus, a simplified equation based only on the use of geographical variables is proposed here to roughly establish the original depth (with errors of few metres) of paleo-IPWs, whose geographical exposure is known and the effective fetch computable. Although the applicability of this method suffers from spatial and temporal restrictions, due to the girth of the original dataset, it provides a first analytical procedure for gauging the original depth of formation of paleo-IPWs which, over the last decade, have been increasingly used as environmental indicators of past sea levels. This study highlights the relationship between the depth of these sedimentary coastal bodies and sea storm wave climate at a regional scale and provides clues for the use of their past counterparts as morphological proxies of past sea level stands. Further developments of this study would use a wider dataset so as to extend the observational law on present-day IPWs to a Mediterranean scale and strengthen the applicability of the method to a spatially broader set of paleo-IPWs.

Regional assessment of extreme significant wave heights in the Bohai Sea and northern Yellow Sea

The regional assessment of extreme significant wave heights (SWHs) is crucial for the design of coastal and offshore structures. In this study, the Bohai Sea and northern Yellow Sea are selected as the study region, and a 40-year (1979-2018) time series hindcast of SWHs is selected as the initial database. To extract the independent and identically distributed sample from this database, an automated method is employed. Since the winter storm dominates the extreme wave and winter storm samples are similar to independent non-tropical cyclone samples, especially for large samples, the extreme sample is extracted from the independent non-tropical cyclone sample. In most of the study region, large independent non-tropical cyclone samples occur evenly every year. The N-largest maxima (NLM) method is used for extraction, and the reasonable N values are determined by analysing the fitting result and extrapolation uncertainty and validated by the reasonable threshold range of the POT method. At a few locations, the large independent non-tropical cyclone sample rarely or never occurs in particular years. The diagnostic NLM method is proposed to exclude the small values. Benefitting from this method, a regional assessment of extreme SWHs is performed.

Modeling waves over the Changjiang River Estuary using a high-resolution unstructured SWAN model

A high resolution unstructured SWAN model has been implemented for the Changjiang River Estuary (CRE). Five different winds are adopted to assess their quality over the CRE, including ERA5, CFSv2, GFS, CCMP-NRT and a newly available high resolution (9 km) wind product from APRCP (Asia-Pacific Regional Coupled Prediction System). The performance of the five winds, together with four wind input source functions is evaluated by comparing with satellite altimeter observations and multiple in-situ observations. Systemic difference is presented in the four input source functions, with the JANSSEN and KOMEN packages outperformingWST in terms of significant wave height (Hs) over the CRE. The default ST6 has comparative skill as JANSSEN during fair weather conditions but tends to predict higher Hs during extreme weather events. All winds have the tendency to underestimate the altimeter observed Hs during fair weather conditions. Part of the negative bias attributes to the overestimation of altimeter observations, while the boundary conditions only play a minor role, given a relatively large model domain extending to about 135° E. The CFSv2/GFS wind has the best performance during fair weather conditions, but overestimates the extreme wave height during typhoon events. The ERA5, on the other hand, underestimates Hs during both fair and extreme weather conditions. In terms of extreme waves, CCMP-NRT generally agrees best with observations. The high resolution APRCP behaves significantly different from other wind forcings and shows poorer performance in wave simulation. But high resolution winds have the advantage in resolving the detail wind structure and show better performance in reproducing the high frequency wave fluctuations adjacent to the CRE. In addition, the deviation due to different wind forcings is more distinct than the different input source functions. Nevertheless, given a certain wind forcing, calibrations would further improve the model performance. This study provides a good start to build a hindcast and forecast system for the CRE region.

Forecasting hurricane-forced significant wave heights using a long short-term memory network in the Caribbean Sea

Abstract. A long short-term memory (LSTM) neural network is proposed to predict hurricane-forced significant wave heights (SWHs) in the Caribbean Sea (CS) based on a dataset of 20 CS, Gulf of Mexico, and western Atlantic hurricane events collected from 10 buoys from 2010–2020. SWH nowcasting and forecasting are initiated using LSTM on 0, 3, 6, 9, and 12 h horizons. Through examining study cases Hurricanes Dorian (2019), Sandy (2012), and Igor (2010), results illustrate that the model is well suited to forecast hurricane-forced wave heights much more rapidly at a significantly cheaper computational cost compared to numerical wave models, with much less required expertise. Forecasts are highly accurate with regards to observations. For example, Hurricane Dorian nowcasts had correlation (R), root mean square error (RMSE), and mean absolute percentage error (MAPE) values of 0.99, 0.16 m, and 2.6 %, respectively. Similarly, on the 3, 6, 9, and 12 h forecasts, results produced R (RMSE; MAPE) values of 0.95 (0.51 m; 7.99 %), 0.92 (0.74 m; 10.83 %), 0.85 (1 m; 13.13 %), and 0.84 (1.24 m; 14.82 %), respectively. In general, the model can provide accurate predictions within 12 h (R≥0.8) and errors can be maintained at under 1 m within 6 h of forecast lead time. However, the model also consistently overpredicted the maximum observed SWHs. From a comparison of LSTM with a third-generation wave model, Simulating Waves Nearshore (SWAN), it was determined that when using Hurricane Dorian as a case example, nowcasts were far more accurate with regards to the observations. This demonstrates that LSTM can be used to supplement, but perhaps not replace, computationally expensive numerical wave models for forecasting extreme wave heights. As such, addressing the fundamental problem of phase shifting and other errors in LSTM or other data-driven forecasting should receive greater scrutiny from Small Island Developing States. To improve models results, additional research should be geared towards improving single-point LSTM neural network training datasets by considering hurricane track and identifying the hurricane quadrant in which buoy observations are made.

Influence of climate variability on wind‐sea and swell wave height extreme over the Indo‐Pacific Ocean

AbstractIn the Indo‐Pacific Ocean (IPO), extreme significant wave heights (SWHs) can substantially induce coastal erosion, flooding, and devastating impacts on coastal livelihoods. This study examines the seasonal influence of the El Niño–Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), Southern Annular Mode (SAM), and Pacific North American (PNA) pattern on extreme wind‐wave parameters. The climatic extremes are calculated utilizing ERA5 reanalysis datasets from 1979 to 2019 and a nonstationary generalized extreme value distribution. Significant increases in extreme wind‐sea (Hmax) and swell SWH (HmaxSw) response to ENSO occur over the northeast North Pacific (NP) during December–February (DJF) and western NP during June–August (JJA). The PNA influence exhibits a similar pattern to ENSO during DJF yet is inactive in JJA. Hmax and HmaxSw responses to the IOD during September–November (SON) include significant increases over the western Pacific, southern Indian Ocean (IO), and southwest tropical IO, yet decreases over the central tropical IO. The HmaxSw response to the SAM is larger than that for Hmax over the southern IPO during DJF, which extends toward the eastern Pacific in March–May (MAM). Overall, extreme wind‐sea and swell parameter responses are found to be associated with sea level pressure (SLP) and SLP gradients.