The parameterisation and prediction of wave height and wind speed persistence statistics for oil industry operational planning purposes

This study sets out to define the basic forms in which wind speed and wave height persistence statistics may be defined for offshore engineering applications, and describes the development of a mathematical persistence model.The model incorporates some of the principles laid down by other workers, but it is fundamentally based on a new concept for parameterising persistence statistics, linking wind speed and sea state percentage probability of exceedance with the persistence average duration.North Sea measured wind and wave data have been used to calibrate and test the model. During the course of these test runs it proved necessary to fine tune the basic Weibull equation of the model, but following these adjustments the model runs were found to correlate well with the measured data.It is concluded that the model may be used to predict wind speed and wave height persistence statistics with acceptable accuracy for preliminary stage oil industry planning purposes and that the calibrated model has particular application for those areas where little measured data are currently available.     

Modified Rayleigh distribution of wave heights in transitional water depths

This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The proposed new method has been applied for calculating the wave height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform. It is demonstrated in this case that the proposed new method can offer better predictions than those by using the conventional Rayleigh wave height distribution model. The proposed new method has been further applied for calculating the total horizontal loads on a generic jacket, and its accuracy has once again been substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh model can be utilized as a promising alternative to the well-established nonlinear wave height distribution models.     

Modified Rayleigh Distribution of Wave Heights in Transitional Water Depths

This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The proposed new method has been applied for calculating the wave height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform. It is demonstrated in this case that the proposed new method can offer better predictions than those by using the conventional Rayleigh wave height distribution model. The proposed new method has been further applied for calculating the total horizontal loads on a generic jacket, and its accuracy has once again been substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh model can be utilized as a promising alternative to the well-established nonlinear wave height distribution models.     

Winds and Waves in the Yellow and East China Seas: A Comparison of Spaceborne Altimeter Measurements and Model Results

Wind speed and wave height measured by satellite altimeters represent a good data source to the study of global and regional wind and wave conditions. In this paper, the TOPEX altimeter wind and wave measurements in the Yellow and East China Seas are analyzed. The results provide a glimpse on the statistical properties and the spatial distributions of the regional wind and wave conditions. These data are excellent for use in the validation and verification of numerical simulations on global and regional scales. The altimeter measurements are compared with model output of temporal statistics and spatial distributions. The results show that the model simulations are in good agreement with TOPEX measurements in terms of the local mean and standard deviation of the variables (wave height and wind speed). For the comparison of spatial distributions, the quality of agreement between numerical simulations and altimeter measurements varies significantly from cycle to cycle of altimeter passes. In many cases, trends in the spatial distributions of wave heights and wind speeds between simulations and measurements are opposite. The statistics of biases, rms differences, linear regression coefficients and correlation coefficients are presented. A rather large percentage (∼50%) of cases show poor agreement based on a combination of low correlation, large rms difference or bias, and poor regression coefficient. There are indications that wave age is a factor affecting the performance of wave modeling skills. Generally speaking, the error statistics in the wave field is correlated to the corresponding error statistics in the wind field under the condition of active wind-wave generation. The error statistics between the wave field and the wind field become less correlated for large wave ages. This revised version was published online in August 2006 with corrections to the Cover Date.     

Statistical modelling of the barrier height fronting a coastal lagoon and the impact of sea-level rise

A temporal stochastic modelling method for predicting exceedance probabilities of the beach barrier elevations fronting intermittently closed and open coastal lagoons is developed. The method incorporates synthetic tides generated from measured tidal harmonics, and randomly sampled values relating to rainfall, beach face slope, lake opening period, and wave height, direction and period. Samples are derived from distributions of each of these parameters formed from standard long term data records. The method is applied to Tabourie Lake, on the south coast of New South Wales. This entrance is sheltered from the dominant wave climate by an island close to shore, the impact of which is separately assessed by phase averaged wave modelling. The barrier elevation is determined from the 2% run-up level arising from constructive waves. The sensitivity of results to a variety of assumptions is tested. The methodology is applied to determine the probabilistic distribution of barrier heights for both stationary and non-stationary (i.e. sea level rise (SLR)) scenarios. Such probabilities can be adopted in a risk based assessment of catchment flooding behind an enclosing barrier for present conditions, or provide management guidelines for future climate scenario, i.e. changes in rainfall, wave climate, sea level. The model can also be used to investigate different management strategies and how these alter the barrier elevation for given probabilities of exceedance.     

欧洲北海海域波高区间分布概率研究

为了研究欧洲北海海域的波高全区域概率分布情况,从而为海洋平台等海洋浮式结构物的选址和结构设计提供依据。首先基于Global Waves Statistics(GWS)提供的实测数据,确定典型计算工况的发生概率;同时考虑实测数据中极端波浪环境下的数据缺失导致大波高分布概率偏小的问题,利用三参数Weibull分布确定不同重现期下的极值风速,作为典型计算工况的补充。以不同风速、风向的定常风场为输入项,利用第三代海浪数值模型SWAN模型,对北海全区域波高进行数值模拟。将数值模拟的稳态形式依照各工况的发生概率进行归一化累加处理,认为其结果可以表征全区域的波高概率分布情况。以波高概率分布的计算结果为依据,分析北海海域波浪环境的统计学特征,发现有效波高为7 m以上的大波高频发区在北海北部区域有大范围分布;有效波高4～5 m为北海东北区域的多发海况,极端海况下的有效波高主要分布于7～14 m区间,在地形突变区域的波高发生显著变化。     

Estimation of Design Wave Height for the Waters around the Korean Peninsula

Long term wave climate of both extreme wave and operational wave height is essential for planning and designing coastal structures. Since the field wave data for the waters around Korean peninsula is not enough to provide reliable wave statistics, the wave climate information has been generated by means of long-term wave hindcasting using available meteorological data. Basic data base of hindcasted wave parameters such as significant wave height, peak period and direction has been established continuously for the period of 25 years starting from 1979 and for major 106 typhoons for the past 53 years since 1951 for each grid point of the North East Asia Regional Seas with grid size of 18 km. Wind field reanalyzed by European Center for Midrange Weather Forecasts (ECMWF) was used for the simulation of waves for the extratropical storms, while wind field calculated by typhoon wind model with typhoon parameters carefully analyzed using most of the available data was used for the simulation of typhoon waves. Design wave heights for the return period of 10, 20, 30, 50 and 100 years for 16 directions at each grid point have been estimated by means of extreme wave analysis using the wave simulation data. As in conventional methodsi of design criteria estimation, it is assumed that the climate is stationary and the statistics and extreme analysis using the long-term hindcasting data are used in the statistical prediction for the future. The method of extreme statistical analysis in handling the extreme events like typhoon Maemi in 2003 was evaluated for more stable results of design wave height estimation for the return periods of 30–50 years for the cost effective construction of coastal structures.     

Calculating nonlinear wave crest exceedance probabilities using a Transformed Rayleigh method

This paper concerns the calculation of the wave crest height exceedance probabilities in fully nonlinear mixed sea states. The exceedance probabilities have been calculated by incorporating a fully nonlinear wave model into a Transformed Rayleigh method. This is an efficient approach to the calculation of wave crest exceedance probabilities and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The nonlinear mixed sea states studied include a swell dominated sea state, two wind sea dominated sea states, and two states of mixed wind sea and swell with comparable energy. The wave steepness influence and the finite water depth effects are also considered in the study. The accuracy and efficiency of the Transformed Rayleigh method are validated by comparing the results predicted using the method with those predicted by using the Monte Carlo simulation method, the theoretical Rayleigh method and some empirical formulas.     

Assessment of wind-forcing impact on a global wind-wave model using the TOPEX altimeter

The study presents assessment of an operational wave model (Wavewatch III), focusing upon the model sensitivity to wind-forcing products. Four wind fields are used to drive the model, including the NCEP/NCAR reanalysis and three other products that assimilate various satellite wind measurements having high spatial resolution, including the QuikSCAT scatterometer. Three wave field statistics: significant wave height, mean zero-crossing wave period, and mean square slope are compared with collocated TOPEX altimeter derivatives to gauge the relative skill of differing wind-forced model runs, as well as to demonstrate an extended use of the altimeter beyond simply supplying wave height for wave model validation and assimilation. Results suggest that model output is critically sensitive to choice of the wind field product. Higher spatial resolution in the wind fields does lead to improved agreement for the higher-order wave statistics.     

Validation of the WAMC4 wave model for the Black Sea

The present paper describes the set-up and application of the third-generation wave model — WAM Cycle 4 to the Black Sea. The wind fields are calculated by a regional atmosphere model (REMO), which was driven with the conditions from the global NCEP re-analysis project. These atmospheric data are used to force the state-of-the-art WAM model. The validation is done by comparison of wave model output against directional buoy measurements registered at three deep-water locations and wave gauge data taken at a point in intermediate depth near the Black Sea coast. The results reveal that agreement between modeled and measured data is satisfactory and the quality of the simulations increases under more energetic and severer wind and wave conditions. Following the validation, a 41-year wave hindcast was implemented spanning the period 1958–1998.     

A Bayesian method for the estimation of return values of wave heights

Bayesian statistics offer a novel means of estimating return values of wave heights and hence of establishing design criteria for offshore structures. The Bayesian method has significant advantages over the classical method since it enables all types of uncertainty (physical, parameter, distribution) associated with the design wave prediction to be handled in a consistent manner in the same analysis.The basic principles of the Bayesian method for drawing inferences are outlined step-by-step. It is shown how Bayesian estimators of return values for wave heights are established by taking an expectation over all parameters and contending distributions. When the Bayesian procedure is applied to large data sets, such as wave data sets, computational difficulties could be encountered, making a “remedial” procedure necessary. However, the Bayesian procedure has been used successfully with wave data sets from the northern North Sea. Furthermore, the associated remedial procedure is such that the program can be made suitable for many existing computers, e.g. desk computers.     

Extreme value statistics for wave run-up on a natural beach

Statistics of wave run-up maxima have been calculated for 149 35-minutes data runs from a natural beach. During the experiment incident wave height varied from 0.4 to 4.0 m, incident wave period from 6 to 16 s, and beach face slope from 0.07 to 0.20. Four extreme statistics were calculated; the maximum run-up height during each run, the 2% exceedence level of shoreline elevation, the 2% exceedence height for individual run-up peaks, and the 2% exceedence level for swash height as determined by the zero-upcrossing method. These statistics were best parameterized when normalized by the incident significant wave height and plotted against the Iribarren number, ξ = β/(H/L₀)^1/2. The swash data (with set-up removed) showed less scatter than total run-up (with set-up included). For Iribarren number greater than 1.5 the run-up was dominated by the incident frequencies, for lower Iribarren number longer period motions dominated the swash. A reasonable value of wave steepness for a fully developed storm sea is 0.025 so that a storm Iribarren number can be estimated as 6.3 times the beach slope. Using this and an offshore design wave height, the included graphs may provide guidance in determining a design run-up height.     

A three-frequency scatterometer technique for the measurement ofocean wave spectra

A microwave technique for the measurement of ocean wave spectra has been compared with wave gauge output during extensive field testing. The method is based on the dual-frequency technique for detecting long ocean waves by matching the modulation of short waves with the beat wavelength between two transmitted microwave frequencies. The new method, however, utilizes three microwave frequencies in order to reduce mean backscatter not related to short-wave modulation. Two prototype scatterometers have been built using three frequencies at L-band and at K_u-band. Wave spectra have been measured by both radar systems which, when properly normalized, agree well with simultaneous in situ measurements taken by conventional wave gauges at the pier site. Thirteen sets of spectra have been computed, five of which correspond to a situation in which a local wind sea was generated and then decayed. The present experiment does not demonstrate the directionality of this new technique     

Analysis of SARAL/AltiKa Wind and Wave over Indian Ocean and its Real-time Application in Wave Forecasting System at ISRO

The current study aims to analyze the wind and wave parameters over Indian Ocean region obtained from first Ka –band altimeter AltiKa onboard SARAL, a collaborative mission of Indian Space Research Organization (ISRO) and Centre National d'Etudes Spatiales (CNES), France. It also demonstrates a real time application of SARAL data by assimilating the wave height in a wave model operational at the Space Applications Centre, ISRO. State-of–the art coastal wave model Simulating Wave Near shore (SWAN) is used for this purpose. The well-tested optimal interpolation technique is adopted for assimilation. Before proceeding to the assimilation per se, SARAL/AltiKa Wind and Significant Wave Height (SWH) have been validated using in- situ observations and WAVEWATCH III model. Apart from assessment of wind and wave data quality, this also served the purpose of providing error covariance to be used in assimilation. Supremacy of the assimilation run over parallel control run without assimilation has been judged by comparing the results with buoy observations at Indian National Centre for Ocean Information System (INCOIS). The statistics of validation of the assimilation run has been found to be extremely encouraging and interesting.     

Modified Weibull distribution for maximum and significant wave height simulation and prediction

Calibration coefficients incorporated in the modified Weibull distribution are more effective for maximum wave height simulation. The parametric relations are derived there from to estimate various wave height statistics including extreme wave heights. The characteristic function of the Weibull distribution is derived. The Weibull distribution is suggested for the newly defined significant wave height simulation by the method of characteristic function. The statistical tools suggested and developed here for predicting the required wave height statistics are validated against the wave data (both deep and shallow) of eastern Arabian Sea comprising rough monsoon conditions also, giving reasonable accuracy.     

Wave run-up on bermed coastal structures

Reliable estimation of wave run-up is required for the effective and efficient design of coastal structures when flooding or wave overtopping volumes are an important consideration in the design process. In this study, a unified formula for the wave run-up on bermed structures has been developed using collected and existing data. As data on berm breakwaters was highly limited, physical model tests were conducted and the run-up was measured. Conventional governing parameters and influencing factors were then used to predict the dimensionless run-up level with 2% exceedance probability. The developed formula includes the effect of water depth which is required in understanding the influence of sea level rise and consequent changes of wave height to water depth ratio on the future hydraulic performance of the structures. The accuracy measures such as RMSE and Bias indicated that the developed formula is more accurate than the existing formulas. Additionally, the new formula was validated using field measurements and its superiority was observed when compared to the existing prediction formulas. Finally, the new design formula incorporating the partial safety factor was introduced as a design tool for engineers.     

Transformation model of wave height distribution on planar beaches

A new probability density function (pdf) for the transformation of depth-limited wave height distributions is presented. Assuming the bore approach for modeling the energy dissipation in the inner surf zone to be valid, an analytical expression for the transformation of wave height distribution including shoaling and breaking on a planar beach is obtained. The resulting expression for the pdf is formulated with a single function and only one shape parameter, which is calibrated as a function of the local root-mean-square (rms) wave height-to-water depth ratio and the local Iribarren number. The transformed pdf is able to reproduce the shape of field and laboratory measured wave height histograms and the sharp change in the shape of the wave height distribution in depth-limited breaking conditions for low exceedance probability. Results show that the theory is appropriate to represent wave height distribution transformation over shallow foreshores or in the surf zone. Alternatively, a combination of the new model with existing state-of-the-art wave energy propagation models allows the complete definition of the wave height distribution transformation on a planar beach.     

Calibration/Validation of an Altimeter Wave Period Model and Application to TOPEX/Poseidon and Jason-1 Altimeters

The altimeter radar backscatter cross-section is known to be related to the ocean surface wave mean square slope statistics, linked to the mean surface acceleration variance according to the surface wave dispersion relationship. Since altimeter measurements also provide significant wave height estimates, the precedent reasoning was used to derive empirical altimeter wave period models by combining both significant wave height and radar backscatter cross-section measurements. This article follows such attempts to propose new algorithms to derive an altimeter mean wave period parameter using neural networks method. Two versions depending on the required inputs are presented. The first one makes use of Ku-band measurements only as done in previous studies, and the second one exploits the dual-frequency capability of modern altimeters to better account for local environmental conditions. Comparison with in situ measurements show high correlations which give confidence in the derived altimeter wave period parameter. It is further shown that improved mean wave characteristics can be obtained at global and local scales by using an objective interpolation scheme to handle relatively coarse altimeter sampling and that TOPEX/Poseidon and Jason-1 altimeters can be merged to provide altimeter mean wave period fields with a better resolution. Finally, altimeter mean wave period estimates are compared with the WaveWatch-III numerical wave model to illustrate their usefulness for wave models tuning and validation.     

A simplified method of obtaining the response of structures from large data banks of wave power spectral densities

A statistical method using empirical orthonormal functions (EOF's) is presented for efficiently representing large data banks of archived nondirectional wave power spectral densities (PSD's). This reduced data set is used to obtain a displacement output probability density function of an offshore structure in response to a wave field. An example is presented thai utilizes five months of NOAA estimated wave spectra taken at 4-h intervals in the Eastern Pacific Ocean. Structural Applications Software was developed to provide the output probability density function for any frequency band of interest without requiring the many tapes of original data. For nonlinear problems, a method of generating typical random wave data is discussed that will allow for Monte Carlo simulation.