Extreme Significant Wave Height Research Articles

Prediction of extreme significant wave heights using maximum entropy

This paper presents maximum entropy (MaxEnt) as a powerful tool for the prediction of extreme significant wave heights comparing it with models within the extreme value theory (EVT) framework, i.e. the Generalized Pareto distribution (GPD) and the Generalized Extreme Value distribution (GEV). The MaxEnt method produces the least biased probability density function by maximizing the Shannon's form of entropy, which is applied to samples generated using the peak over threshold approach. The aforementioned methods have been tested on a data set from the northern North Sea. The results showed that return levels associated to high return periods obtained with MaxEnt are very stable through the whole threshold range, implying that MaxEnt is more robust to the variation of threshold, i.e. sample size than the GPD, leading to the conclusion that MaxEnt is the more suitable model than the GPD model, for this particular data set.

Projection of Global Wave Climate Change toward the End of the Twenty-First Century

Abstract Wind-generated waves at the sea surface are of outstanding importance for both their practical relevance in many aspects, such as coastal erosion, protection, or safety of navigation, and for their scientific relevance in modifying fluxes at the air–sea interface. So far, long-term changes in ocean wave climate have been studied mostly from a regional perspective with global dynamical studies emerging only recently. Here a global wave climate study is presented, in which a global wave model [Wave Ocean Model (WAM)] is driven by atmospheric forcing from a global climate model (ECHAM5) for present-day and potential future climate conditions represented by the Intergovernmental Panel for Climate Change (IPCC) A1B emission scenario. It is found that changes in mean and extreme wave climate toward the end of the twenty-first century are small to moderate, with the largest signals being a poleward shift in the annual mean and extreme significant wave heights in the midlatitudes of both hemispheres, more pronounced in the Southern Hemisphere and most likely associated with a corresponding shift in midlatitude storm tracks. These changes are broadly consistent with results from the few studies available so far. The projected changes in the mean wave periods, associated with the changes in the wave climate in the middle to high latitudes, are also shown, revealing a moderate increase in the equatorial eastern side of the ocean basins. This study presents a step forward toward a larger ensemble of global wave climate projections required to better assess robustness and uncertainty of potential future wave climate change.

Uncertainty due to choice of measurement scale in extreme value modelling of North Sea storm severity

Modelling extreme storm severity is critical to design and reliable operation of marine structures. Extreme hindcast storm peak significant wave heights (HS) for 816 locations throughout the North Sea are modelled, using the four parameter Poisson point process model of Wadsworth et al. (2010), incorporating measurement scale variability via a Box–Cox transformation. The model allows estimation of the posterior distribution for measurement scale parameter and point process parameters within a Bayesian framework. The effect of measurement scale on return values of significant wave height (HS) is quantified by comparison with a three parameter Poisson point process model ignoring measurement scale uncertainty. It is found that the median value (over all locations) of the median posterior Box–Cox parameter (per location) is approximately 0.7, suggesting that the appropriate measurement scale for extreme value analysis is HS0.7. The value of the median Box–Cox parameter (per location) varies considerably between locations, with a 90% uncertainty band of approximately (0.2, 2.2) and quartiles of 0.4 and 1.2; the value of Box–Cox parameter is also influenced by threshold choice for extreme value analysis in particular. The ratio (over all locations) of the (posterior median) return value from the four parameter model to the return value from the three parameter model (and a return period of 100 times the period of the hindcast) has a median value of 0.92, suggesting that median return values may be reduced for this data set by better modelling of measurement scale effects. The ratio of return values has a 90% uncertainty band of approximately (0.72, 1.37), illustrating the extra variability in return values that incorporation of measurement scale uncertainty introduces.

Global extreme wave height variability based on satellite data

[1] The spatial and temporal variability of the extreme significant wave height (SWH) in the ocean is presented. The study has been performed using a highly reliable dataset from several satellite altimeter missions, which provide a good worldwide coverage for the period 1992 onwards. A non-stationary extreme value analysis, which models seasonality and interannual variations, has been applied to characterize the extreme SWH. The interannual variability is explained through variations in the atmosphere and ocean systems, represented by different climate indices, allowing a quantitative contribution of the climate-related patterns. Results demonstrate the strong relationship between the interannual variability of extreme SWH and different ocean and atmosphere variations. A contribution of the AO and NAO indices in the North Atlantic ocean (e.g., every positive unit of the AO explains up to 70 cm of extreme wave height south of Iceland), the NINO3 in the Pacific (every negative unit of NINO3 explains up to 60 cm of extreme wave height in the Drake Passage), the SAM in the Southern ocean and the DMI in the Indian ocean reveal these climate patterns as the most relevant in the interannual extreme wave climate.

EXTREME WAVES IN THE MARGINAL RUSSIAN SEAS: UNCERTAINTY OF ESTIMATION AND CLIMATE VARIABILITY

An analysis of extreme characteristics of surface wind waves in the three marginal Russian seas (Barents, Black and the Sea of Okhotsk) was performed using visual wave observations. Estimates of extreme seas, swell and significant wave heights were computed using the initial value distribution method and the peak over threshold method. Due to the use of large samples compiled for the entire seas the differences between the two methods are considerably smaller than those that would be expected for grid-cell estimates. This implies a relatively high reliability of the results. In the Barents Sea both methods demonstrate growing tendencies for the extreme wind waves, while mean values do not exhibit any significant trends. This hints at a considerable modification of the statistical distribution of wind wave heights rather than on general growth of wind seas. Some further perspectives of the analysis of regional wind wave extremes are discussed.

Long-term time-dependent stochastic modelling of extreme waves

This paper presents a literature survey on time-dependent statistical modelling of extreme waves and sea states. The focus is twofold: on statistical modelling of extreme waves and space- and time-dependent statistical modelling. The first part will consist of a literature review of statistical modelling of extreme waves and wave parameters, most notably on the modelling of extreme significant wave height. The second part will focus on statistical modelling of time- and space-dependent variables in a more general sense, and will focus on the methodology and models used also in other relevant application areas. It was found that limited effort has been put on developing statistical models for waves incorporating spatial and long-term temporal variability and it is suggested that model improvements could be achieved by adopting approaches from other application areas. In particular, Bayesian hierarchical space–time models were identified as promising tools for spatio-temporal modelling of extreme waves. Finally, a review of projections of future extreme wave climate is presented.

On the use of discrete seasonal and directional models for the estimation of extreme wave conditions

Extreme value theory is commonly used in offshore engineering to estimate extreme significant wave height. To justify the use of extreme value models it is of critical importance either to verify that the assumptions made by the models are satisfied by the data or to examine the effect violating model assumptions. An important assumption made in the derivation of extreme value models is that the data come from a stationary distribution. The distribution of significant wave height varies with both the direction of origin of a storm and the season it occurs in, violating the assumption of a stationary distribution. Extreme value models can be applied to analyse the data in discrete seasons or directional sectors over which the distribution can be considered approximately stationary. Previous studies have suggested that models which ignore seasonality or directionality are less accurate and will underestimate extremes. This study shows that in fact the opposite is true. Using realistic case studies, it is shown that estimates of extremes from non-seasonal models have a lower bias and variance than estimates from discrete seasonal models and that estimates from discrete seasonal models tend to be biased high. The results are also applicable to discrete directional models.

Extreme Gravity Waves In The Arabian Gulf

The extreme significant wave heights and the corresponding mean wave periods were predicted for return periods of 12, 25, 50, 100 and 200 years for 38 different locations in the territorial and offshore locations of countries surrounding the Arabian Gulf. The input wave data for the study is hindcast waves obtained using a WAM model for a total period of 12 years, (1993 to 2004). The peak over threshold method (with 1.0 m as threshold value), is used for selecting the data for the extreme wave analysis. In general, a Weibull distribution is found to fit the data well compared to the Gumbel distribution for all these locations. From the joint probability of wave height and wave period, a simple polynomial relationship (Tmean = C3 (Hs)C4) is used to obtain the relationship between the significant wave height and mean wave period for all the 38 locations. The value of C3 is found to vary from 3.8 to 4.8 and the value of C4 is found to vary from 0.19 to 0.32. The mean wave period was found to be more sensitive to change in locations within the Gulf and it is less sensitive to change in return periods from 12 years to 200 years. The significant wave heights for 100 year return period varied from 3.0 to 4.5 for water depths of 9 to 16 m, whereas in the offshore sites (depths from 30 to 60 m) it varied from 5.0 to 7.0 m. A large number of coastal projects are in progress in the Arabian Gulf and many new projects are being planned in this region for the future. The results of the present study will be highly useful for optimal design of the ocean structures for these projects.

Wind-driven wave heights in the German Bight

Wind speed, friction velocity and significant wave height data from the FINO1 platform in the southern German Bight 45 km off the coast for the years 2004 to 2006 have been evaluated and related to each other. The data show a clear dependence of the hourly mean wave height to the hourly mean friction velocity and wind speed. Wave heights increase with decreasing stratification and increasing fetch. Synoptic weather patterns for the highest wave heights in the southern German Bight are determined. The analysis is made separately for four wind direction sectors. The two strongest storms in the evaluated period, “Britta” and “Erwin”, are analysed in more detail. Finally, the 50-year extreme significant wave height has been estimated to be about 11 m most probably coming from northerly directions.

Variability of extreme wave heights in the northeast Pacific Ocean based on buoy measurements

Recent studies reveal important trends in mean values and high percentiles of significant wave height in the northeast Pacific. However, changes of the extreme wave heights through time have not received much attention. In this work, the long‐term variability of extreme significant wave height along the northeast Pacific is modeled using a time‐dependent extreme value model. Application of the model to significant wave height data sets from 26 buoys over the period 1985–2007 shows significant positive long‐term trends in extreme wave height between 30–45°N near the western coast of the US averaging 2.35 cm/yr. We also demonstrate an impact of El Niño on extreme wave heights (about 25 cm per unit of NINO3.4 index) in the northeast Pacific as well as important correlations with mid‐latitudinal climate patterns (e.g., NP and PNA indices).

Statistical estimation of extreme ocean environments: The requirement for modelling directionality and other covariate effects

With increasing availability of good directional data, provision of directional estimates of extreme significant wave heights, in addition to the omni-directional estimates, is more common. However, interpretation of directional together with omni-directional design criteria is subject to inconsistency, even in design guidelines. In particular, omni-directional criteria are usually estimated ignoring directional effects. In this article, for data which exhibit directional effects, we show that a directional extreme value model generally explains the observed variation significantly better than a model which ignores directionality, and that omni-directional criteria developed from a directional model are different from those generated when directionality is not accounted for. We also show that omni-directional criteria derived from a directional model are more accurate and should be preferred in general over those based on models which ignore directional effects. We recommend use of directional extreme value models for estimation of both directional and omni-directional design criteria in future, when good directional data are available. If effects of other covariates (e.g. time or space) are suspected, we similarly recommend use of extreme value models which adequately capture sources of covariate variability for all design analysis.

The Mediterranean surface wave climate inferred from future scenario simulations

This study is based on 30-year long simulations of the wind-wave field in the Mediterranean Sea carried out with the WAM model. Wave fields have been computed for the 2071–2100 period of the A2, B2 emission scenarios and for the 1961–1990 period of the present climate (REF). The wave model has been forced by the wind field computed by a regional climate model with 50 km resolution. The mean SWH (Significant Wave Height) field over large fraction of the Mediterranean sea is lower for the A2 scenario than for the present climate during winter, spring and autumn. During summer the A2 mean SWH field is also lower everywhere, except for two areas, those between Greece and Northern Africa and between Spain and Algeria, where it is significantly higher. All these changes are similar, though smaller and less significant, in the B2 scenario, except during winter in the north-western Mediterranean Sea, when the B2 mean SWH field is higher than in the REF simulation. Also extreme SWH values are smaller in future scenarios than in the present climate and such SWH change is larger for the A2 than for the B2 scenario. The only exception is the presence of higher SWH extremes in the central Mediterranean during summer for the A2 scenario. In general, changes of SWH, wind speed and atmospheric circulation are consistent, and results show milder marine storms in future scenarios than in the present climate.

Application of a POT model to estimate the extreme significant wave height levels around the Balearic Sea (Western Mediterranean)

Application of a POT model to estimate the extreme significant wave height levels around the Balearic Sea (Western Mediterranean)

Extreme waves for Kuwaiti territorial waters

The extreme significant wave heights and the corresponding wave periods were predicted for return periods of 12, 25, 50, 100 and 200 yr for 19 different locations in Kuwaiti territorial waters. Though the total coast length of Kuwait is only about 500 km including all islands and the total area of the Kuwaiti territorial water is about 7611 km 2, the extreme significant wave height vary from 1.86 to 4.02 m for 100 yr return period, among these 19 locations. In general Weibull distribution is found to fit the data well compared to the Gumbel distribution. The input wave data for the present work is obtained by hind casting waves using a WAM model. Wave data is hindcasted for a total period of 12 yr, starting from 1 January 1993 to 31 December 2004. From the joint probability of wave height and wave period, a simple polynomial relationship is obtained between the significant wave height and mean period for all the 19 locations. It is found that the wave period for wave heights of 100 yr return period cannot exceed 6.5 s. A large number of coastal projects are in progress and many new projects are planned for the near future in the Kuwaiti territorial waters. The results of the present study will be highly useful for optimal design of these projects.

Extreme wave predictions around New Zealand from hindcast data

A recently implemented wave hindcast for the New Zealand region was used in conjunction with wave‐buoy data to evaluate extreme significant wave height at multiple sites around New Zealand, for the first time. Hindcast storm wave heights were under‐predicted compared with wave‐buoy measurements at three inshore sites, and a method for scaling the hindcast data to improve the comparison of predicted extreme wave heights was explored. Different statistical methods for predicting extreme wave heights were also compared. Offshore, extreme wave heights displayed a north‐south and an east‐west gradient that is in keeping with the mean wave climate, with larger waves in the south and in the west. However, the variation of extreme wave heights between sites was less than the mean wave climate would suggest, because mid‐latitude depressions generate comparatively large waves on the generally more sheltered northeast coast. At the most energetic site to the southwest of the South Island, a 1 in 100‐year return significant wave height Hs (100) of 19.3 m and maximum wave height H max(100)> of 45 m were predicted. At the least energetic site to the northeast of the North Island, estimates of HS (100) = 13.9m and H max(100) = 33m were obtained.

Estimation of the long‐term variability of extreme significant wave height using a time‐dependent Peak Over Threshold (POT) model

Recent evidence suggests long‐term changes in the intensity and frequency of extreme wave climate around the globe. These changes may be attributable to global warming as well as to the natural climate variability. A statistical model to estimate long‐term trends in the frequency and intensity of severe storm waves is presented in this paper. The model is based on a time‐dependent version of the Peak Over Threshold model and is applied to the Washington NOAA buoy (46005) significant wave height data set. The model allows consideration of the annual cycle, trends, and relationship to atmosphere‐ ocean‐related indices. For the particular data set analyzed the inclusion of seasonal variability substantially improves the correlation between the model and the data. Also, significant correlations with the Pacific–North America pattern, as well as long‐term trend, are detected. Results show that the model is appropriate for a rigorous analysis of long‐term trends and variability of extreme waves and for providing time‐dependent quantiles and confidence intervals.

Climatology, variability and extrema of ocean waves: the Web‐based KNMI/ERA‐40 wave atlas

AbstractThe European Centre for Medium‐Range Weather Forecasts (ECMWF) has recently finished ERA‐40, a reanalysis covering the period September 1957 to August 2002. One of the products of ERA‐40 consists of six‐hourly global fields of wave parameters, like significant wave height and wave period. These data have been generated with the centre's WAM wave model. From these results we have derived climatologies of important wave parameters, including significant wave height, mean wave period, and extreme significant wave heights. Particular emphasis is on the variability of these parameters, both in space and time. Besides being important for scientists studying climate change, these results are also important for engineers who have to design maritime constructions. This paper describes the ERA‐40 data and gives an overview of the results derived. The results are available on a global 1.5° × 1.5° grid. They are accessible from the Web‐based KNMI/ERA‐40 wave atlas at http://www.knmi.nl/waveatlas. Copyright © 2005 Royal Meteorological Society

North Atlantic Ocean Wave Climate Change Scenarios for the Twenty-First Century

Using the observed relationships between sea level pressure (SLP) and significant wave height (SWH) as represented by regression models, climate change scenarios of SWH in the North Atlantic were constructed by means of redundancy analysis (for seasonal means and 90th percentiles of SWH) and nonstationary generalized extreme value analysis (for seasonal extreme SWH). SWH scenarios are constructed using output from a coupled climate model under three different forcing scenarios. Scenarios of future anomaly seasonal statistics of SWH are constructed using climate model projections of anomaly seasonal mean SLP while projections of seasonal extreme SWH are made using projections of seasonal mean SLP and seasonal SLP gradient index. The projected changes in SWH are assessed by means of a trend analysis. The northeast Atlantic is projected to have increases in both winter and fall seasonal means and extremes of SWH in the twenty-first century under all three forcing scenarios. These changes are generally accompanied by decreases in the midlatitudes of the North Atlantic and increases in the southwest North Atlantic. The rate and sign of the projected SWH change is not constant throughout the twenty-first century. In the Norwegian and North Seas, the projected SWH changes are characterized either by faster increases in the late decades than in the early decades, or by decreases in the early decades followed by increases, depending on the forcing scenario and the specific location. Using lower or higher rates of increase in greenhouse gases forcing generally leads to reduced or increased rates of change, respectively, in ocean wave heights. The sign and rate of future wave height changes in the North Sea in particular appear to be quite dependent on the forcing conditions. In general, global warming is associated with more frequent occurrence of the positive phase of the North Atlantic Oscillation (NAO) and strong cyclones, which leads to increases of wave heights in the northeast Atlantic.

On estimating extreme wave heights using combined Geosat, Topex/Poseidon and ERS-1 altimeter data

The estimation of extreme significant wave heights H s using altimeter observations is investigated. Data from the following three satellite missions are used: Geosat, ERS-1 and Topex/Poseidon. Practical methods of estimating extreme H s are described and limitations of their application to altimeter data are highlighted. Extreme H s are estimated using the three-parameter Weibull distribution, with maxima selected via the peaks over threshold method, and the Fisher-Tippet type I distribution, using data selected via the initial distribution method. Altimeter estimates are compared to extreme H s calculated from deep water buoy data. A comparative analysis of global estimates of satellite-derived extreme H s based on standard statistics investigates time-space undersampling and how it affects the reliability of long-term extreme wave estimates made using satellite altimeter data.

Influence Of Wave Steepness On Extreme Ship Hull Vertical WaveBending Moments

Sources of uncertainty in calculation of lifetime vertical wave bending moment are described concisely. Joint probability distribution of significant wave heights and mean zero crossing periods is defined. Wave data from the wave atlas Global Wave Statistics (GWS) for the North Atlantic area are analysed. Extreme significant wave heights for different return periods are calculated. Associated wave steepnesses are estimated by extrapolation procedure. It is shown in the paper that data from GWS lead to considerable overestimation of actual wave steepnesses of extreme sea states. Implications of these overestimates on lifetime vertical wave bending moments are analysed. As a result of this study, the methodology to estimate more realistic extreme vertical wave bending moments is indicated.