Extrapolation of Historical Storm Data for Estimating Design-Wave Heights

1971 ◽  
Vol 11 (01) ◽  
pp. 23-37 ◽  
Author(s):  
C. Petrauskas ◽  
P.M. Aagaard
Keyword(s):  
Wave Height ◽  
Distribution Functions ◽  
Extreme Value Statistics ◽  
Return Periods ◽  
Improved Method ◽  
Design Wave Height ◽  
Straight Line ◽  
Wave Heights ◽  
Computerized Procedures ◽  
Selection Of

Abstract An improved method is presented for selecting offshore structure design waves by extrapolating historical storm data to obtain extreme value statistics. The method permits flexibility in choice of distribution functions through use of computerized procedures, estimates extrapolated wave-height procedures, estimates extrapolated wave-height uncertainty due to small sample size, and includes criteria for judging whether or not given wave-height values can be represented by one or more of the distributions implemented in the method. The relevance of uncertainty to selection of design-wave heights is discussed and illustrated. Introduction The problem of selecting design-wave heights for offshore platforms has many facets, ranging from the development of oceanographic data to the selection of the prudent level of engineering risk for a particular installation. This paper deals only with part of the problem; it describes an improved method for using the small available amount of wave-height information to estimate the extreme value statistics and associated uncertainties for the large storm waves that have a very low probability of occurrence. probability of occurrence. Hindcast wave-height information for design-wave studies usually covers a period of historical record that is shorter than the return period selected for acceptable engineering risk. Return periods commonly used for selection design waves are 100 years or more, but good meteorological data, on Which the calculated wave heights are based, can rarely be obtained for periods covering more than 50 to 60 years. As a consequence, extrapolations to longer return periods are necessary. Present methods for making the extrapolation employ probablistic models through the use of special probability graph papers on which a family of distribution functions plot as straight lines. The wave heights are plotted vs their "plotting-position" return period, and a straight line fitted to the plotted data is extended beyond the data to estimate extreme wave heights for return periods of interest. The methods are described in periods of interest. The methods are described in numerous technical papers and books; Refs. 1 through 5 are examples. The shortcomings of the present commonly used methods are:the straight line drawn through the data is in most cases visually fit to the data, thus is subject to error; andno information is available on the uncertainty of the resulting extrapolation. These shortcomings have been discussed by many authors and many of their concepts influenced this study. The improved method presented in this paper offers:greater flexibility in the choice of distributions through computerized procedures,guidelines for picking the "best" distribution from several implemented in the method, andprocedures for estimating the uncertainty of procedures for estimating the uncertainty of extrapolated wave heights. CONDENSED CONCLUSIONS Procedures described in this paper for extrapolating hindcast storm-wave heights and estimating uncertainty intervals to the extrapolated values are recommended as aids in selecting the design-wave height. The results of the extrapolating procedure and related uncertainty considerations procedure and related uncertainty considerations are only aids to help the engineer assess the risks associated with his design. The actual selection of the design-wave height is a matter of engineering judgment. The choice is subjective and will vary according to the risk chosen for the design. Further consideration of ways to decrease the span of be uncertainty intervals is warranted. Increasing the number of years represented in the sample along with the number of storms is a direct way to decrease the span. In the areas of the world having poor weather records the sample size will be marginal for many years to come. SPEJ P. 23

An Application of Oceanographic Data in Offshore Structural Design

1967 ◽  
Vol 7 (03) ◽  
pp. 273-282
Author(s):  
N.F. Leblanc
Keyword(s):  
Gulf Of Mexico ◽  
Wave Height ◽  
Wind Waves ◽  
Geographical Area ◽  
Recurrence Interval ◽  
Design Wave Height ◽  
Hurricane Wind ◽  
Wave Heights ◽  
Oceanographic Data ◽  
Selection Of

Abstract Described in this paper are oceanographic data which should be considered by an offshore design engineer and methods for developing a design wave height from the oceanographic data. The selection of a design wave is predicated on contemplated waves which might affect the site throughout the life of the structure. Selection of a design wave height may be based onarbitrarily established recurrence frequencies of hurricanes affecting the structure (predicted wave heights are associated with the expected variations of forces resulting from these waves) anda risk-type evaluation wherein all possible storms affecting the area are considered (anticipated wave heights are associated with both investment plus risk costs and expected variations of forces). It is shown how the following oceanographic predictions are integrated into design considerations:a classification of storm intensity which considers all recorded storms which affected the design area,the recurrence interval of storms of a given intensity (this interval is dependent on the extent of the geographical area considered in the design problem) anda forecast of all wave heights which might affect the area (geometry of a structure often necessitates consideration of waves from a multiplicity of directions). The authors believe that the described techniques can result in selecting an adequate and reasonable design wave. Introduction Since the inception of offshore operations in the Gulf of Mexico, engineers engaged in designing structural facilities have been plagued with the problem of selecting an adequate and reasonable design wave. In the development of any offshore structure it is mandatory that the engineer evaluate the ability of the structure to withstand the ocean waves to which it will be subjected. Selecting such design waves quite naturally necessitates a coalition of the oceanographer and the design engineer. The oceanographer must provide a detailed knowledge of scientific principles which govern the behavior of waters in the Gulf of Mexico. He should also have an adequate knowledge of the manner in which design waves are utilized by the engineer. Although the design engineer's primary responsibility is applying the oceanographer's specialized knowledge in the creation of real structures, it is important that he possess some knowledge of related oceanographic principles to reasonably evaluate and apply the recommendations of the oceanographer. In the Gulf of Mexico it is the hurricane wind waves which generally govern the design of an offshore facility. The oceanographer must therefore develop techniques for predicting the heights, periods and frequency of all hurricane waves which might affect a particular structure. From this mass of oceanographic data, the design engineer must select the design waves which will apply to his particular design. Past Studies on Frequency and Amplitude of Hurricane Wind Waves Past oceanographic studies on the frequency of hurricane wave heights in the Gulf of Mexico have been devoted largely to predicting the recurrence interval of hurricanes which will generate maximum significant waves of given heights. The maximum significant wave height is the average height of the highest one third of the waves in that portion of the storm producing maximum wave heights. Since these waves occur over a relatively small portion of the storm (Fig. 1) and since the paths of hurricanes vary considerably (Fig. 2), the recurrence frequency of such heights is largely a function of the extent of the geographical area considered.

scholarly journals An Empirical Method for the Estimation of Towing Resistance of a Life Raft in Various Sea States

2007 ◽  
Author(s):  
Lawrence Mak ◽  
Andrew Kuczora ◽  
Antonio Simo˜es Re´
Keyword(s):  
Wave Height ◽  
Significant Wave Height ◽  
Rayleigh Distribution ◽  
Empirical Method ◽  
Extreme Value Statistics ◽  
Sea Trial ◽  
Significant Wave ◽  
Calm Water ◽  
Wave Heights ◽  
Force Variation

Current IMO regulations require life rafts to be tow tested only in calm water. In real evacuation situations, life rafts are deployed in the prevailing environmental conditions, with wind and waves. Added wave resistance is small at low wave heights but increases nonlinearly with increased wave height. If life rafts are to be towed in moderate seas (up to 4 m significant wave height), tow force estimates based only on calm water tow resistance become less reliable. Tow patches, towline, towing craft etc. also need to be designed to withstand dynamic wave loading in addition to mean load. Therefore, mean tow force, tow force variation and maximum tow force are important. A full-scale 16-person, commercially available, SOLAS approved life raft was towed in the tank, in upwind, head seas with significant wave height of 0.5 m. The measured tow force showed that it could be treated as a linear system with wave amplitude, by demonstrating that tow force is mainly inertial and follows a Rayleigh distribution. Therefore, extreme-value statistics used for waves can be applied to developing equations for predicting tow force. A method is proposed to predict life raft tow force at different tow speeds and in various sea states, with waves and wind. The method involved using tank experiments to obtain tow force response for one sea state. The information can then be used to predict life raft tow force in wind and waves for different sea states. Three equations are proposed to demonstrate that a simple tank experiment could provide valuable information necessary to empirically estimate the mean tow force, tow force variation and maximum tow force for a specific life raft in different sea states. The equations are developed for upwind, head seas. These equations were extensively validated using tow force measured in the tank. They were partially validated with limited sea trial data, by towing the same 16-person life raft and a 42-person life raft in upwind, head seas with significant wave height of 1.3 m. The equations were able to predict maximum tow forces to within 15% of the measured.

scholarly journals ON THE METHODOLOGY OF SELECTING DESIGN WAVE HEIGHT

1988 ◽  
Vol 1 (21) ◽  
pp. 67 ◽  
Author(s):  
Yoshimi Goda
Keyword(s):  
Data Analysis ◽  
Least Square Method ◽  
Distribution Functions ◽  
Least Square ◽  
Type I ◽  
Extreme Wave ◽  
Empirical Formulas ◽  
Wave Data ◽  
Design Wave Height ◽  
Wave Heights

A statistically-rational method of extreme wave data analysis is presented. A combination of the Fisher-Tippett type I and the four Weibull distributions is proposed as the candidates of distribution functions. The least square method is used for data fitting. The best plotting position formula for each function is determined by the Monte Carlo method with 10,000 simulations per sample size. Confidence intervals of estimated extreme wave heights for given return periods are evaluated by simulations and expressed in the form of empirical formulas, for both the cases when the true distribution is known and unknown. An example of extreme wave data analysis is given.

scholarly journals Extreme Gravity Waves In The Arabian Gulf

2009 ◽  
Vol 6 (1) ◽  
pp. 21 ◽  
Author(s):  
S. Neelamani ◽  
K. Al-Salem ◽  
K. Rakha
Keyword(s):  
Wave Height ◽  
Arabian Gulf ◽  
Wave Period ◽  
Return Periods ◽  
Threshold Method ◽  
Total Period ◽  
Significant Wave ◽  
Wave Heights ◽  
Mean Wave Period ◽  
Significant Wave Heights

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. 

DETERMINATION OF EXTREME VALUES OF WAVES, WINDS CURRENTS, AND TIDES FOR THE DESIGN OF OFFSHORE INSTALLATIONS

1974 ◽  
Vol 14 (1) ◽  
pp. 166
Author(s):  
P. M. Aagaard
Keyword(s):  
Wave Height ◽  
Extreme Values ◽  
Meteorological Data ◽  
Extreme Value Distribution ◽  
Relevant Information ◽  
Extreme Value ◽  
Distribution Functions ◽  
Design Parameters ◽  
Final Design ◽  
Wave Heights

Frequently the only relevant information available to a designer about a propective offshore platform site is its location, the water depth, and whatever can be gleaned from oceanographic atlases. In spite of this lack of data the platform designer is faced with the problem of selecting design parameters such that the proposed platform will not fail during its exposed life. He therefore needs to know what are the greatest wave height, current speed, etc., the platform will experience, and must specify studies that can provide the needed information on extreme values. This paper discusses methods used in such studies and their associated uncertainties.The method for acquiring extreme value data should be chosen on the basis of available oceanographic and meteorological data for the site, reliability requirements, time available before final design, and cost. Wave height is usually the most critical design parameter. Data over a long time span (e.g. greater than ten years) are needed to achieve reliable extreme values. Measured wave data covering such time spans are almost never available for a site of interest, and schedules seldom permit lengthy data-collection periods. Frequently the most reliable extreme wave heights can be obtained by calculating wave heights (i.e. hindcasting) from windfields derived from historical weather charts and fitting certain extreme-value distribution functions to the hindcast results. This preferred approach should include calibration of the wave height calculation method with local measured data. Alternative approaches, usually involving greater uncertainties in predicted extremes, are also appropriate for particular cases. Methods for determining extreme winds, currents, and tides are similar to those used for extreme waves, but some differences result from the nature of the phenomena and the type of data typically available.

scholarly journals DESIGNING BERM BREAKWATERS FOR DIFFERENT WAVE HEIGHTS AND DIFFERENT QUARRY YIELD

2017 ◽  
pp. 33
Author(s):  
Sigurdur Sigurdarson ◽  
Jentsje Van der Meer
Keyword(s):  
Wave Height ◽  
Initial Phase ◽  
Full Range ◽  
Stability Parameter ◽  
Design Rules ◽  
Design Wave Height ◽  
Final Design ◽  
Wave Heights ◽  
The Stability ◽  
Design Options

The paper demonstrates the use of the geometrical design rules for berm breakwaters in a potential project in Greenland. With practically no information about the sizes of armourstone that could be used for the design, the initial phase of the study looked at the full range of the stability parameter Hs/ΔDn50 of 1.7 to 3.0 for the design wave height of Hs=4.4 m. This corresponds to armourstone classes ranging from 5-15 t down to 1-3 t. Six different design options based on six different options for the largest stone class are compared. The final design then relies on the actual quarry yield, the total volume of material needed for the project and the construction equipment that can be brought to the site.

scholarly journals HYDRAULIC STABILITY AND OVERTOPPING PERFORMANCE OF A NEW TYPE OF REGULAR PLACED ARMOR UNIT

2018 ◽  
pp. 111
Author(s):  
Bas Reedijk ◽  
Tamara Eggeling ◽  
Pieter Bakker ◽  
Robert Jacobs ◽  
Markus Muttray
Keyword(s):  
Wave Height ◽  
Single Layer ◽  
Model Tests ◽  
Roughness Coefficient ◽  
Design Wave Height ◽  
Wave Heights ◽  
New Type ◽  
Adverse Influence ◽  
2D And 3D ◽  
Hydraulic Stability

The XblocPlus is a new type of interlocking single layer armour units that is placed with uniform orientation. This is novel and different from all other single layer, interlocking armouring systems. The hydraulic stability of the XblocPlus breakwater armour unit was tested in 2D and 3D hydraulic model tests. Wave overtopping tests were performed to determine the roughness coefficients of the EurOtop overtopping formula for the XblocPlus. Model tests on a rubble mound breakwater with XblocPlus armour included 2D tests with a 1:30 seabed slope and with 1:2 and 3:4 breakwater slopes and 3D model tests with a flat seabed and with a 3:4 breakwater slope. Wave heights up to 150% of the design wave height were tested in the 2D tests and up to 200% with wave directions 0° to 60° in the 3D tests. No armour unit displacements were observed in 2D tests with 1:2 slope. In the 2D tests with 3:4 slope one armour unit was displaced when the wave height reached 159% of the design wave height. No damage to the XblocPlus armour layer was observed in the 3D tests. A roughness coefficient of 0.45 was deduced from overtopping tests with wave heights of 60% to 100% of the design wave height. The model test results indicate little or no influence of wave steepness on XblocPlus stability and no adverse influence of wave obliquity while the seabed slope in front of the breakwater may have some impact on the XblocPlus armour layer stability.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

scholarly journals Estimation of Significant Wave Heights from ASCAT Scatterometer Data via Deep Learning Network

2021 ◽  
Vol 13 (2) ◽  
pp. 195
Author(s):  
He Wang ◽  
Jingsong Yang ◽  
Jianhua Zhu ◽  
Lin Ren ◽  
Yahao Liu ◽  
...  
Keyword(s):  
Deep Learning ◽  
Wave Height ◽  
Significant Wave Height ◽  
Incidence Angle ◽  
Ocean Waves ◽  
Global Scale ◽  
Learning Technology ◽  
Sea State ◽  
Significant Wave ◽  
Wave Heights

Sea state estimation from wide-swath and frequent-revisit scatterometers, which are providing ocean winds in the routine, is an attractive challenge. In this study, state-of-the-art deep learning technology is successfully adopted to develop an algorithm for deriving significant wave height from Advanced Scatterometer (ASCAT) aboard MetOp-A. By collocating three years (2016–2018) of ASCAT measurements and WaveWatch III sea state hindcasts at a global scale, huge amount data points (>8 million) were employed to train the multi-hidden-layer deep learning model, which has been established to map the inputs of thirteen sea state related ASCAT observables into the wave heights. The ASCAT significant wave height estimates were validated against hindcast dataset independent on training, showing good consistency in terms of root mean square error of 0.5 m under moderate sea condition (1.0–5.0 m). Additionally, reasonable agreement is also found between ASCAT derived wave heights and buoy observations from National Data Buoy Center for the proposed algorithm. Results are further discussed with respect to sea state maturity, radar incidence angle along with the limitations of the model. Our work demonstrates the capability of scatterometers for monitoring sea state, thus would advance the use of scatterometers, which were originally designed for winds, in studies of ocean waves.

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