Analysis of Short-Term and Long-Term Wave Statistics by Time Domain Simulations Statistics

2017 ◽  
Author(s):  
Øistein Hagen ◽  
Ida Håøy Grue ◽  
Jørn Birknes-Berg ◽  
Gunnar Lian ◽  
Kjersti Bruserud
Keyword(s):  
Wave Height ◽  
Time Domain ◽  
Statistical Distributions ◽  
Short Term ◽  
Sea State ◽  
Wave Statistics ◽  
Individual Wave ◽  
Wave Heights ◽  
Crest Height

In the design of new structures and assessment of existing structures, short- and long term statistical distributions of wave height, crest height and wave periods, as well as joint distributions, are important for structural integrity assessment. It is important to model the statistical distributions accurately to calculate wave design criteria and to assess fatigue life. A detailed study of the wave statistics for an offshore location at the Norwegian Continental Shelf field is carried out. Extensive time domain simulations for the complete scatter diagram of possible sea states are carried out by a second order wave model. Time series of the surface elevation are generated for JONSWAP and Torsethaugen wave spectra, and for several wave spreading models. Statistics for individual wave heights, crest heights and wave periods are established. The simulated results for the short-term statistics are compared with existing short term models that are commonly used, viz. the Forristal, Næss and Rayleigh wave height distributions, and the Forristall 2nd order crest height distribution. Also, parameterized distributions for wave height and for crest height are fitted to the simulated data. The long-term distributions F(H) and F(C) of all simulated individual wave heights H and crest heights C are determined by weighting the simulations with the long-term probability of occurrence of the sea state. Likewise, the long-term distributions F(Hmax) and F(Cmax) of the maximum simulated individual wave heights Hmax and crest heights Cmax in the sea states are determined. The design criteria for return periods R = 1, 10, 100 and 10 000 years are determined from the appropriate quantile levels. The effect of statistical uncertainty is investigated by comparing the confidence intervals for the estimated extreme values results as function of the number N of 3-hour time domain simulations per sea state for 10<N<500.

Wave Distributions and Sampling Variability

2007 ◽  
Author(s):  
O̸istein Hagen
Keyword(s):  
Wave Height ◽  
Extreme Values ◽  
Height Distribution ◽  
Short Term ◽  
Sea State ◽  
Sampling Variability ◽  
Wave Statistics ◽  
Individual Wave ◽  
Wave Heights ◽  
Crest Height

The paper describes the effect of sampling variability on the predicted extreme individual wave height and the predicted extreme individual crests height for long return periods, such as for the 100-year maximum wave height and 100-year maximum crest height. We show that the effect of sampling variability is different for individual crest or wave height as compared to for significant wave height. The short term wave statistics is modeled by the Forristall crest height distribution and the Forristall wave height distribution [3,4]. Samples from the 3-hour Weibull distribution are simulated for 100.000 years period, and the 100-year extreme values for wave heights and crest heights determined for respectively 20 minute and 3 hour sea states. The simulations are compared to results obtained by probabilistic analysis. The paper shows that state of the art analysis approaches using the Forristall distributions give about unbiased estimates for extreme individual crest or wave height if implemented appropriately. Direct application of the Forristall distributions for 3-hour sea state parameters give long term extremes that are biased low, and it is shown how the short term distributions can be modified such that consistent results for 20 minute and 3 hour sea states are obtained. These modified distributions are expected applicable for predictions based on hindcast sea state statistics and for the environmental contour approach.

Sensitivity Study of Calculated Jacket Fatigue Damage due to Long Term Distribution of Wave Heights

2017 ◽  
Author(s):  
Hege Halseth Bang ◽  
Siri Hoel Smedsrud ◽  
Øistein Hagen ◽  
Terje Nybø
Keyword(s):  
Fatigue Damage ◽  
Wave Height ◽  
Time Domain ◽  
Height Distribution ◽  
Scatter Diagram ◽  
Sea State ◽  
Jacket Structures ◽  
Wave Heights ◽  
The Individual

Marine structures like jacket structures are often highly utilized structures operating in an environment dominated by dynamic loading. The fatigue limit state is of main concern and is to a large extent governing the structural dimensions and the amount of resources utilized in inspection and maintenance of members and joints. There is a considerable degree of uncertainty related to the parameters determining the fatigue damage. The models applied, both for describing the fatigue driving mechanisms e.g. the wave-description and load modeling and the deterioration mechanism, are always compromises between the ability to accurately describe the nature and computationally efficiency. The main focus in this paper is to show how sensitive the calculated fatigue damage of a jacket is to different models for the short term variability of wave heights. To obtain consistent basis for comparison a deterministic fatigue analysis is considered and a potential structural dynamic amplification is not included in the comparison study. Sensitivity to selection of wave spectra will not be addressed. In a deterministic approach the long term distribution of individual wave heights is used to calculate the stress ranges occurring in the joints and butt welds. Typically, the long term variability of sea state conditions is given by a scatter diagram of significant wave height (Hs) and the peak period (Tp). When converting the scatter diagram of sea states to the long term distribution of wave heights, it is common to assume that the individual waves in the sea states are Rayleigh distributed. Later developments indicate that a Forristall distribution may be a more accurate assumption. The following cases have been considered: 1. Assuming that the individual waves in each sea state are Rayleigh distributed. 2. Assuming that the individual waves in each sea state follows a Forristall distribution. 3. Calculating the long term wave height distribution from time domain simulations. In the third method, second order wave theory was used to simulate all sea states in the Hs/Tp scatter diagram. I.e. extensive time domain simulations were carried out to cover the complete scatter diagram of possible sea states. The study is performed for an 8-legged jacket. The analyses are performed for a typical North Sea wave environment for water depth about 110 m. The objective of this study is to investigate the robustness in the current design practice for jacket structures where the individual waves in the sea states are Rayleigh distributed. The paper documents the calculated fatigue lives for main joints along the height of the jacket for the three wave height distributions. Further, the paper gives advice on application of wave distribution models for design of new structures and reassessment of existing structures.

Wave Statistics in Nonlinear Sea States

2011 ◽  
Author(s):  
Mohamed Latheef ◽  
Chris Swan
Keyword(s):  
Empirical Distribution ◽  
Nonlinear Effects ◽  
Rayleigh Distribution ◽  
Second Order ◽  
Wave Crest ◽  
Statistical Distributions ◽  
Sea State ◽  
Wave Statistics ◽  
Wave Basin ◽  
Wave Heights

This paper concerns the statistical distribution of both wave crest elevations and wave heights in deep water. A new set of laboratory observations undertaken in a directional wave basin located in the Hydrodynamics laboratory in the Department of Civil and Environmental Engineering at Imperial College London is presented. The resulting data were analysed and compared to a number of commonly applied statistical distributions. In respect of the wave crest elevations the measured data is compared to both linear and second-order order distributions, whilst the wave heights were compared to the Rayleigh distribution, the Forristall (1978) [1] empirical distribution and the modified Glukhovskiy distribution ([2] and [3]). Taken as a whole, the data confirms that the directionality of the sea state is critically important in determining the statistical distributions. For example, in terms of the wave crest statistics effects beyond second-order are most pronounced in uni-directional seas. However, if the sea state is sufficiently steep, nonlinear effects arising at third order and above can also be significant in directionally spread seas. Important departures from Forristall’s empirical distribution for the wave heights are also identified. In particular, the data highlights the limiting effect of wave breaking in the most severe seas suggesting that many of the commonly applied design solutions may be conservative in terms of crest height and wave height predictions corresponding to a small (10−4) probability of exceedance.

How Should We Combine Long and Short Term Wave Height Distributions?

2008 ◽  
Author(s):  
George Z. Forristall
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Ocean Engineering ◽  
Short Term ◽  
Method Of Calculation ◽  
Individual Wave ◽  
Long Time ◽  
Wave Heights ◽  
The Individual

Estimating the maximum wave or crest height that will occur in a long return interval is one of the fundamental problems for ocean engineers. Long time series of individual wave heights are not available. The calculations must start with measured or hindcast time series of significant wave heights. An extreme value distribution is fit to that data. The resulting long term distribution is then combined with a short term distribution for the individual heights. This study is concerned with finding the most accurate methods for that calculation. The basic tool is the Borgman integral, but it has been applied in many different ways. Theoretical derivations do not clearly indicate which method is most accurate, and time series of measurements long enough for accurate tests do not exist. These problems were circumvented in this study by constructing very long simulated time series with known distributions. Both initial value and storm based methods were tested. The correct method of calculation depends on what question is being asked. The distribution of the maximum wave heights in a six hour interval is different than the distribution of the maxima of all of the waves. The distribution of the maxima in a storm is different than the distribution of the maxima in an interval. We believe that the finding the maximum in a storm is the most appropriate question for ocean engineering design. The Tromans and Vanderschuren (1995, Proc. Offshore Tech. Conf., OTC 7683) method accurately matches the results from our storm simulations.

Comparison of Design Wave Approach and Short Term Approach With Increased Wave Height in the Evaluation of Whipping Induced Bending Moment

2012 ◽  
Author(s):  
Quentin Derbanne ◽  
Fabien Bigot ◽  
Guillaume de Hauteclocque
Keyword(s):  
Wave Height ◽  
Return Period ◽  
Significant Wave Height ◽  
Bending Moment ◽  
Short Term ◽  
Sea State ◽  
Significant Wave ◽  
Non Linear ◽  
Term Analysis

The evaluation of extreme bending moment corresponding to a 25 years return period requires very long simulations on a large number of sea states. This long term analysis is easy to do with a linear model of the ship response, but is impractical when using a time consuming model including non linear and slamming loads. In that case some simplified methods need to be applied. These methods are often based on Equivalent Design Waves (EDW) which are calibrated on the extreme linear value. The general practice is to define the EDW as a regular wave. A very simple method is to compute the non linear bending moment applying the pressure correction on the hull without recomputing the ship motions. A better method is to recompute in time domain the non linear ship response on this Design Wave. It is even possible to define a more realistic Design Wave, taking into account the frequency and directional content of the sea states used in the long term analysis: those waves are called Response Conditioned Wave and Directional Response Conditioned Waves. The different methods are applied to an Ultra Large Container Ship (ULCS). Hydro-structure calculations are carried out on a severe design sea state, taking into account Froude-Krylov pressure correction, slamming forces and whipping response. Results of a very long computation are compared to the results of the Design Wave approaches. Another method is proposed to compute very rare events. It is based on an artificial increase of the significant wave height of the sea state, and the assumption of the independence of the non linear effects to the significant wave height. Using this method it is possible, with a simulation of only a few hours, to predict a very rare short term event, corresponding to a very long return period. The results are compared to the Design Wave results and appear to be much more precise.

A Simple and Robust Method for Calculating Return Periods of Ocean Waves

2018 ◽  
Author(s):  
Edward B. L. Mackay ◽  
Lars Johanning
Keyword(s):  
Ocean Waves ◽  
New Method ◽  
Threshold Analysis ◽  
Return Periods ◽  
Peaks Over Threshold ◽  
Short Term ◽  
Sea State ◽  
Individual Wave ◽  
Buoy Measurements

A new method is introduced for combining the long-term distribution of sea states with the short-term distribution of individual wave or crest heights, conditional on sea state. The method uses a Monte Carlo approach to simulate random realisations of the maximum wave or crest height in each sea state. A peaks-over-threshold analysis is conducted on the random maxima in each sea state in order to estimate the long-term distribution of individual wave or crest heights. The new method is significantly simpler than existing methods such as the equivalent storm approach, requires fewer assumptions and has similar computational times. The new method is applied to a 35 year dataset of wave buoy measurements and is shown to produce almost identical estimates of return values of individual crest heights to the equivalent storm method.

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.

An Experimental Study of Shallow Water Wave Statistics on Mild Bed Slopes

2011 ◽  
Author(s):  
Vasiliki Katsardi ◽  
Chris Swan
Keyword(s):  
Water Depth ◽  
Measured Data ◽  
Intermediate Water ◽  
Statistical Distributions ◽  
Spectral Bandwidth ◽  
Peak Period ◽  
Wave Statistics ◽  
Wave Heights ◽  
Bed Slope ◽  
Water Depths

This paper describes a new series of laboratory observations, undertaken in a purpose built wave flume, in which a number of scaled simulations of realistic ocean spectra were allowed to evolve over a range of mild bed slopes. The purpose of the study was to examine the distribution of wave heights and its dependence on the local water depth, d, the local bed slope, m, and the nature of the input spectrum; the latter considering variations in the spectral peak period, Tp, the spectral bandwidth and the wave steepness. The results of the study show that for mild bed slopes the statistical distributions of wave heights are effectively independent of both the bed slope and the spectral bandwidth. However, the peak period plays a very significant role in the sense that it alters the effective water depth. Following detailed comparisons with the measured data, the statistical distributions for wave heights in relatively deep water are found to be in reasonable agreement with the Forristall [1] and Glukhovskii [2] distributions. For intermediate water depths, the Battjes & Groenendijk [3] distribution works very well. However, for the shallowest water depths none of the existing distributions provides good agreement with the measured data; all leading to an over-estimate of the largest wave heights.

Strength Performance of Steel Catenary Riser Using Short Term and Long Term Analysis Methodologies

2016 ◽  
Author(s):  
Feng Wang ◽  
Roger Burke ◽  
Anil Sablok ◽  
Kristoffer H. Aronsen ◽  
Oddgeir Dalane
Keyword(s):  
Bending Moment ◽  
Current Profile ◽  
Short Term ◽  
Sea State ◽  
Strength Performance ◽  
Steel Catenary Riser ◽  
Analysis Methodology ◽  
Riser Design ◽  
Term Analysis

Strength performance of a steel catenary riser tied back to a Spar is presented based on long term and short term analysis methodologies. The focus of the study is on response in the riser touch down zone, which is found to be the critical region based on short term analysis results. Short term riser response in design storms is computed based on multiple realizations of computed vessel motions with various return periods. Long term riser response is based on vessel motions for a set of 45,000 sea states, each lasting three hours. The metocean criteria for each sea state is computed based on fifty six years of hindcast wind and wave data. A randomly selected current profile is used in the long term riser analysis for each sea state. Weibull fitting is used to compute the extreme riser response from the response of the 45,000 sea states. Long term analysis results in the touch down zone, including maximum bending moment, minimum effective tension, and maximum utilization using DNV-OS-F201, are compared against those from the short term analysis. The comparison indicates that the short term analysis methodology normally followed in riser design is conservative compared to the more accurate, but computationally more expensive, long term analysis methods. The study also investigates the important role that current plays in the strength performance of the riser in the touch down zone.

Random Waves and Capsize Probability Based on Large Amplitude Motion Analysis

2002 ◽  
Author(s):  
Jan O. de Kat ◽  
Dirk-Jan Pinkster ◽  
Kevin A. McTaggart
Keyword(s):  
Time Domain ◽  
Random Waves ◽  
Extreme Wave ◽  
Small Probability ◽  
Safe Operation ◽  
Short Term ◽  
Physical Behavior ◽  
Wind Climate ◽  
Large Amplitude Motion

The objective of this paper is to apply a methodology aimed at the probabilistic capsize assessment of two naval ships: a frigate and a corvette. Use is made of combined knowledge of the wave and wind climate a ship will be exposed to during its lifetime and of the physical behavior of that ship in the various sea states it is likely to encounter. This includes the behavior in extreme wave conditions that have a small probability of occurrence, but which may be critical to the safe operation of a ship. Time domain simulations provide the basis for deriving short-term and long-term statistics for extreme roll angles. The numerical model is capable of predicting the 6 DOF behavior of a steered vessel in wind and waves, including conditions that may lead to broaching and capsizing.

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