Application of Weibull model for redefined significant wave height distributions

Global atlas of extreme significant wave heights and relative risk ratios

Recent studies reveal important trends in mean values, high percentiles and extreme events of significant wave height (SWH) in the northeast (NE) Pacific using buoy measurements. However, the spatial variability of these trends has not been well addressed since the sparse and uneven coverage of wave buoys makes it difficult to assess spatial patterns. In this work, we analyze the long-term variability of extreme significant wave height along the northeast Pacific using two time-dependent extreme value models and three different datasets from buoys, satellite missions and hindcast databases. Significant long-term trends of extreme SWH have been detected reinforcing the previous studies. We also demonstrate an impact of El Nino on extreme wave heights in the NE Pacific as well as important correlations with mid-latitudinal climate patterns (e.g. PNA index).

The significant wave height and peak period as derived from the spectral analysis of 171 measured wave records taken in the ocean off Western Head, Nova Scotia are compared to the more classical parameters derived from individual wave heights and by the Tucker method. The highest surface elevation and the maximum wave height occurring in the records are compared to values predicted by Cartwright and Longuet-Higgins (1956), Goda (1970), and Longuet-Higgins (1952).

The core properties of the wave climate and its changes in the Caspian Sea are established in terms of the annual mean significant wave height and its regional changes in 2002–2013 based on the outcome of the satellite altimetry mission JASON-1. Remotely estimated wave heights are validated against properties of the empirical distribution of instrumentally measured wave heights in the southern Caspian Sea and monthly averages of visually observed wave heights at three locations. A correction for systematic differences leads to very good correspondence between monthly averaged in situ and satellite data with a typical root mean square difference of 0.06 m. The average significant wave height in the Caspian Sea is 0.5–0.7 m in the northern basin of the sea, around 1.2 m in large parts of the central and southern basins and reaches up to 1.8 m in the northern segment of the central basin. The basin-wide average wave intensity varied insignificantly in the range of 1.02–1.14 m in 2002–2013. These estimates overestimate the wave heights by about 30% because low wave conditions are ignored. Substantial and statistically significant changes in the wave height occurred in certain areas. The wave height decreased by 0.019 ± 0.007 m/yr in the eastern segment of the central basin and by 0.04 ± 0.04 m/yr in the western segment of the southern basin. These changes can be explained by an increase in the frequency of westerly winds at the expence of southerly winds. Both basin-wide and regional extreme wave heights exhibit large interannual variations but do not show any significant trend. The patterns of changes in mean and extreme wave height are different. The average wave height has increased while the extreme wave height has decreased in the eastern segment of the southern basin.

Results from recent climate investigations indicate that significant climatic variations occur over periods of time which may be small compared to the design life of a structure. A procedure is developed for quantifying the effects such variations produce in the expected distribution of extreme wave heights. Wave height distribution from hindcasts indicate that this modification to the conventional treatment of extremes can lead to significantly different estimates for wave heights associated with a given recurrence interval. INTRODUCTION Prior to 1970, there was only minimal interest in the United States focused on climatic variability. Normal values of precipitation, temperature, wind, and other weather elements were based on a 20-yr record that was assumed, to represent the long-term mean climate. The time-scale of climate change was popularly believed to be on the order of 10,000's of years and related to advances and retreats of major ice sheets in the Pleistocene. However, during the last 20 years or so researchers investigating different aspects of climate change have begun to amass a large set of evidence which indicates that climatic variability can occur on time scales which significantly affect the activities of man. Since 1970, frequently occurrences of what might once .have been termed "abnormal" weather has led to a much more widespread acceptance of the importance of short-term climatic variability. Droughts in Africa, North America, and Europe, widespread flooding in the Mississippi Valley, the dearth of landfall Atlantic hurricanes, and the extreme cold of the winter of 1976-1977 in the eastern United States are but a few facets of the shifting patterns of world-wide weather in the 1970's. In spite of the general acceptance of the existence of short-term climate fluctuations, practically all planning and design for offshore and onshore structures is done with no direct allowance for this variability, Indirectly, of course, it is expected that, by accumulating a sufficient record length, one can approximate the statistical population of wave heights and water levels, since various past climate states will be included in the sample. However, extrapolations based on data from mixed populations can lead to significant problems in the estimation of extremes (Borgman and Resio, 1977; Resio, 1975). Consequently, it is desirable to examine interrelationships between climate and wave extremes and to base long-term wave height estimates on some combined physical statistical model, if possible. This is complicated by uncertainty of climate forecasts and the increased complexity of the statistical analyses in such an approach. An alternative suggested by Goldman (1977) is to rely more heavily on deterministic estimates of wave heights from dynamical models; but this approach cannot be incorporated into an analysis of risk in a straight forward manner. It is therefore advantageous to follow through an analysis of tile relationship between extreme wave heights and climate fluctuations in spite of increased complexity and uncertainty.

Satellite observations of the ocean surface provide a powerful method for acquiring global data on wind speed and wave height. Radar altimeters have now been in operation for more than 25 years, providing a reasonably long term data set with global coverage. This paper presents data from a fully calibrated and validated altimeter dataset. The dataset provides the basis for obtaining a global perspective of a number of parameters critical to ocean engineering design, ship operations and global climate change. Analysis of the data provides ocean climatology of mean monthly values of wind speed and wave height useful for ship operations. The data set is also sufficiently long to provide extreme value (i.e. 100-year return period) estimates of wind speed and wave height. The paper presents such values and describes the approaches most appropriate to obtain statistically significant extreme value estimates from such satellite data. With a data set of this length, it is possible to investigate whether there have been statistically significant changes in the wind and wave climates over the period. Careful trend analysis of the extensive data set shows that there has been a statistically significant increasing trend in mean wind speed over the period. The corresponding increase in wave height is less clear. There is also evidence to suggest that extreme wind speeds and wave heights are increasing and the data set is analysed to investigate these trends. The paper clearly shows the value of this dataset and its application to a range of engineering problems.

Information on possible changes in extreme wave heights is needed to determine the future effectiveness and safety of coastal and flood protection structures. In this study, an assessment of possible changes in the extreme wave heights at selected locations along the German Baltic Sea coast has been carried out on the basis of numerical simulations of waves in the western Baltic Sea and regional climate model data for the past and the future (1961-2100). The future climate change signal of significant wave heights with a return period of 200 years mainly depends on: (i) the location, (ii) the climate change scenario run, (iii) the time period of the comparison, and (iv) the approach adopted to calculate the wave climate. The results show increases of up to +0.5 m and decreases of up to -0.5 m of the extreme wave heights. The increases might have considerable effect on the constructional design of coastal and flood protection structures-such as breakwaters, sea dykes, and vertical walls-because the extreme wave heights are used as input parameters for the design of the structures.

Accurately estimating the return values of significant wave height is essential for marine and coastal infrastructure, particularly as climate change intensifies the frequency and intensity of extreme wave events. Traditional models, which assume stationarity in wave data, often underestimate future risks by neglecting the impacts of climate change on wave dynamics. Combining time series decomposition and recurrence analysis, the research develops a nonstationary framework to predict significant wave height. The stochastic component is modelled using a stationary probability distribution, while the deterministic component is predicted based on sea surface temperature projections from CMIP6 climate scenarios. The model evaluation demonstrates strong predictive capability for both stochastic and deterministic components. Application of the model to China’s coastal waters reveals significant discrepancies between stationary and nonstationary return value estimates. Compared to conventional distribution models, the nonstationary model predicts substantial increases in extreme wave heights. These findings underscore the importance of adopting nonstationary models to more accurately assess future risks posed by extreme wave events in a changing climate.

The spatial and temporal variability of the high individual wave heights, which pose a hazard in India’s shelf seas, has not been investigated. In this study, the spatial and temporal variation of hourly maximum individual wave height (Hmax) in the Indian shelf seas is examined based on 40 years ERA5 Re-Analysis data from European Centre for Medium-Range Weather Forecasts. Waverider buoy data from five locations are used to assess ERA5 Hmax. The variability of Hmax in different temporal scales; daily, monthly and interannual and their linkages with major ocean-atmosphere coupled interaction in the Pacific and the Indian Ocean are presented. Wave climatology throughout India’s western shelf seas shows average Hmax exceeding 2 m during most of the year. Maximum Hmax in the western shelf seas is during May–July, whereas in the southern tip and the eastern shelf seas are during the tropical cyclones and are either in October–December or May. Maximum Hmax is 17.94 m, and it occurred at the northern Bay of Bengal on 25 May 2009 during the passage of tropical cyclone Aila. Spatial variations in Hmax between locations spaced at 1.5° latitude are less than 10% in the northwestern and southeastern shelf seas, but large variations (~ 28%) are in the southwestern and northeastern shelf seas. Annual mean Hmax shows contrasting trends when data for 1979 to 2018 and 1992 to 2018 is considered. Indian Ocean Dipole influence on the Hmax suggests negative correlations in the western shelf seas and positive correlations in the eastern shelf seas. The correlation with climate indices is similar for both significant wave height and Hmax.

A novel approach to estimation of extreme value ocean significant wave height is investigated, in which data from adjacent regions are pooled to form a spatial ensemble. The equivalent duration of this ensemble region is the sum of the durations of the data pooled to form the ensemble. To create such a spatial ensemble, data from regions to be pooled must be independent and identically distributed. ERA-Interim reanalysis data are used to investigate the requirement of independent and identically distributed data on a global basis. As a result, typical spatial ensembles are defined for a number of regions of the world and the 100-yr return period significant wave height is calculated for these regions. It is shown that the method can result in a reduction in the confidence interval for such extreme value estimates of between 30% and 60%. The method is demonstrated both with ERA-Interim data and altimeter data.

The inherent uncertainties in estimation of extreme wave heights in hurricane-dominated regions are explored using data from the GOMOS Gulf of Mexico hindcast for the period 1900–2005. In particular, the effect of combining correlated values from a neighbourhood of 72 grid locations on extreme wave height estimation is quantified. We show that, based on small data samples, extreme wave heights can be underestimated and that site averaging usually improves estimates. We present a bootstrapping approach to evaluate the uncertainty in extreme wave height estimates. We also argue in favour of modelling supplementary indicators for extreme wave characteristics, such as a high percentile (95%) of the distribution of 100-year significant wave height, in addition to its most probable value, especially for environments where the distribution of 100-year significant wave height may be skewed.

Inherent uncertainties in estimation of extreme wave heights in hurricane-dominated regions are explored using data from the GOMOS Gulf of Mexico hindcast for 1900–2005. In particular, the effect of combining correlated values from a neighborhood of 72 grid locations on extreme wave height estimation is quantified. We show that, based on small data samples, extreme wave heights are underestimated and site averaging usually improves estimates. We present a bootstrapping approach to evaluate uncertainty in extreme wave height estimates. We also argue in favor of modeling supplementary indicators for extreme wave characteristics, such as a high percentile (95%) of the distribution of 100-year significant wave height, in addition to its most probable value, especially for environments where the distribution of 100-year significant wave height is strongly skewed.

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

The spatial and temporal variability of extreme wave climate along the Central- South American continent is analyzed. The study evaluates changes in the intensity of extreme significant wave height (SWH) throughout the year over the 1980-2008 period, using a calibrated long-term wave reanalysis database forced with NCEP/NCAR reanalysis. A non-stationary extreme value model, based on monthly maxima with a new approach for long-term trends, has been applied. Results show a common positive trend in the Pacific basin throughout all seasons and a significant decreasing trend pattern in the area of Surinam and north of Brazil, on the Atlantic border (up to �1.5 cm/year in March-April-May). A higher increase of the extreme wave heights is found in the austral summer (December- January-February) at Tierra de Fuego and the Falkland Islands, reaching 6.5 cm/year (which means 1.82 m for the 28 years studied). Furthermore, the complete reanalysis period (1948- 2008) is analyzed in order to compare results with the assimilation data period (1980-2008), resulting in some discrepancies, especially in the Atlantic basin.

Ocean surface waves can be major hazards in coastal and offshore activities. However, there exists very limited information on ocean wave behavior in response to climate change, because such information is not simulated in current global climate models. This study made statistical projections of changes in ocean wave heights using sea level pressure (SLP) information from 20 CMIP5 (Coupled Model Intercomparison Project Phase 5) global climate models for the 21st century. The results show significant wave height increases in the tropics (especially in the eastern tropical Pacific) and in Southern Hemisphere high latitudes (south of 45°S). Under the projected 2070–2099 climate condition of the rising high concentration pathway—the RCP8.5 scenario, the occurrence frequency of the present‐day one in 10 year extreme wave heights is likely to double or triple in several coastal regions around the world. These wave height increases are primarily driven by increased SLP gradients and hence increased surface wind energy.