Extreme Wave Heights Research Articles

A comparison of extreme wave analysis methods with 1994–2010 offshore Perth dataset

This study took the hourly wave height records collected 10km southwest of Rottnest Island, offshore of Perth, Western Australia, from 1994 to 2010 as a testing ground and compared the results obtained by the Goda method commonly used in costal engineering community, the generalised extreme value (GEV) and generalised Pareto distribution (GPD) methods which are currently the standard practice in mainstream extreme statistics. The results highlight the merits and limitations associated with those methods and formulas. It is recommended that the coastal engineering community should embrace the GPD distribution as one of the credible candidates due to its merits in the threshold selection techniques and the nature of the distribution. The conventional distributions recommended by Goda could be the other candidates provided a properly selected threshold value. The final selection of the distributions should be made based on the goodness-of-fit test demonstrated in this study. Finally the extreme wave heights for offshore Perth are recommended based on 1994 to 2010 dataset.

Reply to Discussion by Z.J. You of "A multi-distribution approach to POT methods for determining extreme wave heights" by Mazas and Hamm

Reply to Discussion by Z.J. You of "A multi-distribution approach to POT methods for determining extreme wave heights" by Mazas and Hamm

Investigation of trends in extreme value wave height and wind speed

Global altimeter data spanning a period of more than 20 years is analyzed to determine whether there are measurable trends in extreme value return period estimates of wind speed and wave height. The data is subdivided into sections of 4 years duration and extreme value analysis applied to each section. The trends in values across these sections indicate that there appears to be a positive trend in 100 year return period values of wind speed but no consistent trends for 100 year return period wave height. However, the statistical uncertainty associated with estimates of the extreme value wind speed and wave heights is such that the quantitative values of trend are not reliable. Reliable values will require a longer‐duration data set.

Present Wave Climate in the Bay of Biscay: Spatiotemporal Variability and Trends from 1958 to 2001

AbstractClimate change impacts on wave conditions can increase the risk of offshore and coastal hazards. The present paper investigates wave climate multidecadal trends and interannual variability in the Bay of Biscay during the past decades (1958–2001). Wave fields are computed with a wave modeling system based on the WAVEWATCH III code and forced by 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) wind fields. It provides both an extended spatiotemporal domain and a refined spatial resolution over the Bay of Biscay. The validation of the wave model is based on 11 buoys, allowing for the use of computed wave fields in the analysis of mean and extreme wave height trends and variability. Wave height, period, and direction are examined for a large array of wave conditions (by seasons, high percentiles of wave heights, different periods). Several trends for recent periods are identified, notably an increase of summer significant wave height, a southerly shift of autumn extreme wave direction, and a northerly shift of spring extreme wave direction. Wave fields exhibit high interannual variability, with a normalized standard deviation of seasonal wave height greater than 15% in wintertime. The relationship with Northern Hemisphere teleconnection patterns is investigated at regional scale, especially along the coast. It highlights a strong correlation between local wave conditions and the North Atlantic Oscillation and the east Atlantic pattern indices. This relationship is further investigated at the local scale with a new method based on bivariate diagrams, allowing the identification of the type of waves (swell, storm, intermediate waves) impacted. These results are discussed in terms of comparison with previous studies and coastal risk implications.

A maximum-entropy compound distribution model for extreme wave heights of typhoon-affected sea areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.

Evolution of marine storminess in the Belgian part of the North Sea

Abstract. Severe storms have affected European coast lines in the past but knowledge on changes in storminess for the last decades is still sparse. Climate change is assumed to be a main driving factor with the potential to induce changes on the intensity, duration and frequency of powerful marine storms, including a long-term influence on peak wind speeds, surges and waves. It is, therefore, important to investigate whether in the last decades changes in the magnitude of storms, their duration and frequency could be observed. Understanding trends in storminess in the last decades will help to better prepare coastal managers for future events, taking into account potential changes on storm occurrence and magnitude to improve planning of mitigation and adaptation strategies. The purpose of this study was to focus on the evolution of extreme wind conditions, wave height and storm surge levels in the North Sea Region, especially in the Belgian part of the North Sea (BPNS). Based on the analysis performed it is concluded that no clear trend can be observed for the occurrence of significant increasing extreme wind speeds over the BPNS. Furthermore, one can conclude that not enough scientific evidence is available to support scenarios with increased wave height or storminess.

Discussion of “a Multi-distribution Approach to POT Methods for Determining Extreme Wave Heights” by Mazas and Hamm, [Coastal Engineering, 58:385–394

The authors proposed a double-threshold method to extract statistically independent storm wave data from historical time-series wave records for extreme wave analysis. The maximum likelihood estimator (MLE) was preferred for estimation of the distribution parameters of the Weibull, Pearson-III and GPD. This discussion is to comment on if the use of the double-threshold method and the MLE will actually improve the accuracy of extreme wave heights estimated. The storm wave datasets used in this discussion are from a 23-year time-series wave record collected off the coast of Sydney in the Tasman Sea and the second storm wave dataset of Mazas and Hamm (2011) who kindly provided the dataset to the discusser. For consistency, the notations used in this discussion will be the same as those defined by the authors.

Historical variation and trends in storminess along the Portuguese South Coast

Abstract. This work investigates historical variation and trends in storm climate for the South Portugal region, using data from wave buoy measurements and from modelling, for the period 1952 to 2009. Several storm parameters (annual number of storms; annual number of days with storms; annual maximum and mean individual storm duration and annual 99.8th percentile of significant wave height) were used to analyse: (1) historical storminess trends; (2) storm parameter variability and relationships; and (3) historical storminess and its relationship to the North Atlantic Oscillation (NAO). No statistically significant linear increase or decrease was found in any of the storm parameters over the period of interest. The main pattern of storm characteristics and extreme wave heights is an oscillatory variability with intensity peaks every 7–8 yr, and the magnitude of recent variations is comparable with that of variations observed in the earlier parts of the record. In addition, the results reveal that the NAO index is able to explain only a small percentage of the variation in storm wave height, suggesting that more local factors may be of importance in controlling storminess in this region.

Long-term response analysis of FPSO mooring systems

The design of mooring systems for floating production units usually considers extreme environmental conditions as a primary design parameter. However, in the case of FPSO (Floating, Production, Storage and Offloading) units, the worst response for the mooring system may be associated with other sea state conditions due to the fact that its extreme response may be associated with a resonant period instead of an extreme wave height. The best way to deal with this problem is by performing long-term analysis in order to obtain extreme response estimates. This procedure is computationally very demanding, since many short-term environmental conditions, and their associated stochastic nonlinear time domain numerical simulations of the mooring lines, are required to obtain such estimates. A simplified approach for the long-term analysis is the environmental contour-line design approach. In this paper a Monte Carlo-based integration procedure combined with an interpolation scheme to obtain the parameters of the short-term response distribution is employed to hasten the long-term analysis. Numerical simulations are carried out for an FPSO at three different locations considering a North Sea joint probability distribution for the environmental parameters. The long-term analysis results are compared against those obtained using extreme environmental conditions and environmental contour-line methodology. These results represent the characteristic load effect for the design of mooring systems of floating units using the reliability analysis for mooring line. The results show that the long-term results are usually more critical than those obtained with the other approaches and even different mooring lines can be identified as the critical ones.

A new approach to estimating the T-year return-period wave height

The paper introduces a new approach to estimating the T-year return-period wave height (TRPW), i.e. the wave height expected to occur in T-year, from two sets of observed extreme data and on the basis of the maximum entropy principle. The main points of the approach are as follows. 1) A maximum entropy probability density function (PDF) for the extreme wave height H is derived from a Euler equation subject to some necessary and rational constraints. 2) The parameters in the function are expressed in terms of the mth moment of H. 3) This PDF is convenient to theoretical and practical applications as it is simple and its four parameters are easy to be determined from observed extreme data. An example is given for estimating the TRPW in 50 and 100 years by the present approach and by some currently used methods using observed data at two hydrographic stations. The comparison of the estimated results shows that the present approach is quite similar to the Pearson-III and Gumbel methods.

Plotting-Position Estimator for the L-Moment Method and Quantile Confidence Interval for the GEV, GPA, and Weibull Distributions Applied for Extreme Wave Analysis

A Monte Carlo simulation study has been carried out on the reliability of the parameter and quantile estimation of the Generalized Extreme-Value (GEV), Generalized Pareto (GPA), and Weibull distributions by means of the L-moment method. The three population distributions are assigned with five to six values of the shape parameter each, and the scale and location parameters are so specified as to yield the ratio of the 50- to 10-year wave heights at the value of 1.1, 1.2, and 1.3. Samples of extreme wave heights are generated from 16 populations at the size varying from 10 to 1000, and 50,000 samples for respective conditions are analyzed for statistical characteristics. The unbiased plotting position recommended by Hosking and Wallis [1997] is confirmed to yield minimal biases on the parameter estimates, but it yields small biases on quantile estimates. A new plotting position estimator is proposed, which yields minimal quantile bias. A set of empirical formulas are derived for estimation of the coefficient of variations of the L-moment ratios and the quantile of the three distributions.

Dynamical and statistical explanations of observed occurrence rates of rogue waves

Abstract. Extreme surface waves occur in the tail of the probability distribution. Their occurrence rate can be displayed effectively by plotting ln(–ln P), where P is the probability of the wave or crest height exceeding a particular value, against the logarithm of that value. A Weibull distribution of the exceedance probability, as proposed in a standard model, then becomes a straight line. Earlier North Sea data from an oil platform suggest a curved plot, with a higher occurrence rate of extreme wave and crest heights than predicted by the standard model. The curvature is not accounted for by second order corrections, non-stationarity, or Benjamin-Feir instability, though all of these do lead to an increase in the exceedance probability. Simulations for deep water waves suggest that, if the waves are steep, the curvature may be explained by including up to fourth order Stokes corrections. Finally, the use of extreme value theory in fitting exceedance probabilities is shown to be inappropriate, as its application requires that not just N, but also lnN, be large, where N is the number of waves in a data block. This is unlikely to be adequately satisfied.

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.

Future wave climate over the west-European shelf seas

In this paper, we investigate changes in the wave climate of the west-European shelf seas under global warming scenarios. In particular, climate change wind fields corresponding to the present (control) time-slice 1961–2000 and the future (scenario) time-slice 2061–2100 are used to drive a wave generation model to produce equivalent control and scenario wave climate. Yearly and seasonal statistics of the scenario wave climates are compared individually to the corresponding control wave climate to identify relative changes of statistical significance between present and future extreme and prevailing wave heights. Using global, regional and linked global–regional wind forcing over a set of nested computational domains, this paper further demonstrates the sensitivity of the results to the resolution and coverage of the forcing. It suggests that the use of combined forcing from linked global and regional climate models of typical resolution and coverage is a good option for the investigation of relative wave changes in the region of interest of this study. Coarse resolution global forcing alone leads to very similar results over regions that are highly exposed to the Atlantic Ocean. In contrast, fine resolution regional forcing alone is shown to be insufficient for exploring wave climate changes over the western European waters because of its limited coverage. Results obtained with the combined global–regional wind forcing showed some consistency between scenarios. In general, it was shown that mean and extreme wave heights will increase in the future only in winter and only in the southwest of UK and west of France, north of about 44–45° N. Otherwise, wave heights are projected to decrease, especially in summer. Nevertheless, this decrease is dominated by local wind waves whilst swell is found to increase. Only in spring do both swell and local wind waves decrease in average height.

The Second Order Statistics of High Waves in Wind Sea and Swell

The statistics of extreme wave crest elevation and wave height have been calculated for realistic, directionally spread sea and swell using a probabilistic method tested and described previously. The nonlinearity of steep waves is modeled to the second order using Sharma and Dean kinematics, and a response surface (reliability type) method is used to deduce the crest elevation or wave height corresponding to a given probability of exceedance. The effects of various combinations of sea and swell are evaluated. As expected, in all cases, nonlinearity makes extreme crests higher than the corresponding linear ones. The nonlinear effects on the wave height are relatively small.

Quantifying thresholds for significant dune erosion along the Sefton Coast, Northwest England

Field and model hindcast data are used to establish a critical dune erosion threshold for the Sefton Coast (NW England). Events are classified as causing significant erosion if they result in: (a) a mean dune retreat along the entire study area of >2m; (b) a dune retreat of ≥5m along a coastal segment ≥2km in length; and (c) an eroded area ≥20,000m2. For the period 1996 to 2008, individual storms were characterised using hindcast results from a POLCOMS-WAM model and measured data from the Liverpool Bay Coastal Observatory. Results show that combined extreme surge levels (>1.5m) and wave heights (>4m), or tidal water levels above 9.0m Chart Datum (CD), do not always result in significant dune erosion. Evidence suggests that erosion is more likely to occur when wave heights are >2.6m, peak water level is >10.2m CD at Liverpool and when consecutive tidal cycles provide 10h or more of water levels above 9.4m CD. However, lower water levels and wave heights, and shorter events of sustained water levels, can cause significant erosion in the summer. While the return period for events giving rise to the most severe erosion in the winter is >50years, significant erosion in the summer can be caused by events with return periods <1year. It is suggested that this may be attributable to a known reduction in the mean dune toe elevation c. 30cm. Although the study shows it might be possible to characterise objectively storm events based on oceanographic conditions, the resultant morphological change at the coast is demonstrated to depend on the time and duration of events, and on other variables which are not so easy to quantify. Further investigation is needed to understand the influence of alongshore and seasonal variability in beach/dune morphology in determining the response to the hydrodynamic and meteorological conditions causing significant erosion. Improved monitoring pre- and post-storm of changes in beach/dune morphology is required to develop reliable proxies that can be used to establish early warning systems to mitigate the impacts of erosion and flooding in the future.

Long-term spatial variations in the Baltic Sea wave fields

Abstract. This study focuses on spatial patterns in linear trends of numerically reconstructed basic wave properties (average and extreme wave heights, wave periods) in the Baltic Sea under the assumption of no ice cover. Numerical simulations of wave conditions for 1970–2007, using the WAM wave model and adjusted geostrophic winds, revealed extensive spatial variations in long-term changes in both average and extreme wave heights in the Baltic Sea but almost no changes in the basinwide wave activity and wave periods. There has been a statistically significant decrease in the annual mean significant wave height by more than 10% between the islands of Öland and Gotland and in the southward sea area, and a substantial increase to the south-west of Bornholm, near the coast of Latvia, between the Åland Archipelago and the Swedish mainland, and between the Bothnian Sea and the Bothnian Bay. Variations in extreme wave heights (defined as the threshold for 1% of the highest waves each year) show similar patterns of changes. In several areas the trends in average and extreme wave heights are different. Such a complicated pattern of changes indicates that (i) different regions of the Baltic Sea basin have experienced widespread but essentially different changes in wind properties and (ii) many seemingly controversial trends and variations established in wave properties at different sites in the recent past may reflect the natural spatial variability in the Baltic Sea wave fields.

INCORPORATION OF WEIBULL DISTRIBUTION IN L-MOMENTS METHOD FOR

The L-moments of the Weibull distribution are derived and incorporated in the regional frequency analysis of peaksover-threshold significant wave heights at eleven stations along the eastern coast of Japan Sea. The effective duration of wave measurements varies from 18.0 to 37.2 years with the mean rate of 10.4 to 15.1 events per year. The eleven stations are divided into three regions to assure homogeneity of the data. Both the Weibull and Generalized Pareto (GPA) distributions fit well to the observed data. The 100-year wave height varied from 8.2 to 11.2 m by the Weibull and 7.6 to 10.3 m by the GPA. The GPA distribution is not recommended for determination of design waves for these stations because it has an inherent upper limit and a tendency of under-prediction.&#x0D; &#x0D; &#x0D; References&#x0D; &#x0D; Coles, S. 2001. An Introduction to Statistical Modeling of Extreme Values, Springer, 208p.&#x0D; &#x0D; Goda, Y., Konagaya, O., Takeshita, N., Hitomi, H., and T. Nagai. 2000. Population distribution of extreme wave heights estimated through regional analysis, Coastal Engineering 2000 (Proc. 26th ICCE, Sydney), ASCE, Sydney, 1078-1091.&#x0D; &#x0D; Greenwood, J A., J. M. Landwehr, N. C. Matalas, and J. R. Wallis. 1978. Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form, Water Resources Res., Vol. 15, No. 5, pp. 1049-1064.&#x0D; http://dx.doi.org/10.1029/WR015i005p01049&#x0D; &#x0D; Hosking, J. R. M. 1990. L-moments: Analysis and estimation of distributions using linear combinations of order statistics, J. Roy. Statistical Soc., Series B, 52, pp. 105-24.&#x0D; &#x0D; Hosking, J. R. M. and J. R. Wallis. 1997. Regional Frequency Analysis, Cambridge Univ. Press, 224p.&#x0D; http://dx.doi.org/10.1017/CBO9780511529443&#x0D; &#x0D; Ma, Q.-S., Li, Y.-B., and J. Li .2006. Regional frequency analysis of siginicant wave heights based on L-moments, China Ocean Engineering, 20(1), pp. 85-98.&#x0D; &#x0D; Petruaskas, C. and P. M. Aagaard. 1971. Extrapolation of historical storm data for estimating design wave heights, J. Soc. Petroleum Engrg., 11, pp. 23-27.&#x0D; &#x0D; van Gelder, P. H. A. J. M. 2000. Statistical Methods for the Risk-Based Design of Civil Structures, Ph.D. thesis Delft University of Technology, 249p.&#x0D; &#x0D; van Gelder, P. H. A. J. M., J. De Ronde, N. W. Neykov, and P. Neytchev. 2000. Regional frequency analysis of extreme wave heights: trading space for time, Coastal Engineering 2000

A multi-distribution approach to POT methods for determining extreme wave heights

Determination of extreme wave heights using a Peaks-Over-Threshold (POT) approach is revisited. Firstly, the GPD-Poisson model is recalled. A double threshold is presented and justified, with objective tools for determining the high threshold. This model is then extended to other statistical distributions, namely the Weibull and Gamma distributions. Objective criteria (BIC and AIC) based upon likelihood are used to select the best-fitting distribution. This method is tested on two locations: the historical IAHR Haltenbanken dataset and a location at the entry of the Strait of Gibraltar. Finally, sensitivity analyses are carried out with respect to the high threshold and to the duration of the dataset to estimate the robustness of the approach presented.

Extrapolation of historical coastal storm wave data with best-fit distribution function

Extreme or design wave heights are often extrapolated from historical storm wave data with an assigned “best-fit” probability distribution function. However, there is no detailed selection criterion on how to select a best-fit distribution from a pool of candidate distributions. This study is to develop this criterion. The 19-year wave data collected off the coast of Sydney in the Tasman Sea is used and analysed to obtain a large sample of peak storm wave heights with the peaks-of-threshold method. With the least-squares method, eight commonly-used candidate distributions, the lognormal, Weibull, FT-I, II and III from the generalised extreme value distribution, and GPD-I, II and III from the generalised Pareto distribution, are all fitted to the storm wave height data to determine the best-fit distribution. An extended least-squares method is also presented to estimate the shape parameter for the three-parameter distributions. It is found that the FT-III and GPD-III with the upper bounded end intend to underestimate extreme wave heights. The observed large storm wave heights are shown to be underestimated by the lognormal, but overestimated by the GPD-I or exponential. Both the FT-I and the Weibull are found to give an equally good fit to the storm wave data. Based on the findings of this study, the general selection criterion is then developed to be unboundedness, goodness of fit, simplicity and confidence level. According to this new criterion, the FT-I distribution of the eight candidates can be uniquely determined to be the best-fit distribution for extrapolation of the historical storm wave data. This general criterion can also be used to select a best-fit distribution for extrapolation of historical wave data collected at the other NSW coastal locations or at any other coasts.