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.

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.

scholarly journals WAVE HEIGHT DISTRIBUTION IN CONSTANT AND FINITE DEPTHS

2012 ◽  
Vol 1 (33) ◽  
pp. 15 ◽  
Author(s):  
Sofia Caires ◽  
Marcel R.A. Van Gent
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Wave Breaking ◽  
Rayleigh Distribution ◽  
Height Distribution ◽  
High Wave ◽  
Wave Height Distribution ◽  
Individual Wave ◽  
Wave Heights

Several alternatives to the Rayleigh distribution have been proposed for describing individual wave heights in regions where depth-induced wave breaking occurs. The most widely used of these is the so-called Battjes and Groenendijk distribution. This distribution has been derived and validated in a context of a shallow water foreshore waves propagating over a gently sloping shallow region towards the shore. Its validity for waves propagating in regions with shallow flat bottoms is investigated here. It is concluded that the distribution on average underestimates (outside its range of validity) high wave height measurements in shallow flat bottoms by as much as 15%.

Comparison of Distributions of Wave Heights From Nonlinear Schröedinger Equation Simulations and Laboratory Experiments

2013 ◽  
Author(s):  
Huidong Zhang ◽  
Zhivelina Cherneva ◽  
C. Guedes Soares ◽  
Miguel Onorato
Keyword(s):  
Numerical Simulations ◽  
Wave Height ◽  
Laboratory Experiments ◽  
Height Distribution ◽  
Nls Equation ◽  
Sea State ◽  
Wave Height Distribution ◽  
Wave Basin ◽  
Wave Heights ◽  
Deep Water Wave

Numerical simulations of the nonlinear Schrödinger (NLS) equation are performed by using random initial wave conditions characterized by the JONSWAP spectrum and compared with four different sea states generated in the deep water wave basin of Marintek. The comparisons show that the numerical simulations have a high degree of agreement with the laboratory experiments although a little overestimation can be observed, especially in the severe sea state. Thus the simulations still catch the main characteristics of the extreme waves and provide an important physical insight into their generation. The coefficient of kurtosis λ40 presents a similar spatial evolution trend with the abnormal wave density and the nonlinear Gram-Charlier (GC) model is used to predict the wave height distribution. It is demonstrated again that the theoretical approximation based on the GC expansion can describe the larger wave heights reasonably well in most cases. However, if the sea state is severe, wave breaking can significantly decrease the tail of wave height distribution in reality and the discrepancy occurs comparing with the numerical simulation. Moreover, the number of waves also plays an important role on the prediction of extreme wave height.

Comparison of Distributions of Wave Heights From Nonlinear Schröedinger Equation Simulations and Laboratory Experiments

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Huidong Zhang ◽  
Zhivelina Cherneva ◽  
Carlos Guedes Soares ◽  
Miguel Onorato
Keyword(s):  
Numerical Simulations ◽  
Wave Height ◽  
Laboratory Experiments ◽  
Height Distribution ◽  
Sea State ◽  
Large Wave ◽  
Wave Height Distribution ◽  
Wave Basin ◽  
Free Surface Displacement ◽  
Wave Heights

Numerical simulations of the nonlinear Schrödinger (NLS) equation are performed by imposing randomly synthesized free surface displacement at the wave maker characterized by the Joint North Sea Wave Project (JONSWAP) spectrum and compared with four different sea states generated in the deepwater wave basin of Marintek. The comparisons show that the numerical simulations have a high degree of agreement with the laboratory experiments although a little overestimation can be observed, especially in the severe sea state. Thus, the simulations still catch the main characteristics of extreme waves and provide an important physical insight into their generation. The coefficient of kurtosis λ40 presents a similar spatial evolution trend with the abnormal wave density, and the nonlinear Gram–Charlier (GC) model is used to predict the wave height distribution. It is demonstrated again that the theoretical approximation based on the GC expansion can describe large wave heights reasonably well in most cases. However, if the sea state is severe, wave breaking can significantly decrease the actual tail of wave height distribution, and discrepancy occurs when comparing with the numerical simulation. Moreover, the number of waves also plays an important role on the prediction of extreme wave height.

Various experimental wave statistics emerging from a single energy spectrum

2021 ◽  
Author(s):  
Maxime Canard ◽  
Guillaume Ducrozet ◽  
Benjamin Bouscasse
Keyword(s):  
Energy Spectrum ◽  
Wave Field ◽  
Wave Energy ◽  
Spatial Dynamics ◽  
Height Distribution ◽  
Sea State ◽  
Wave Statistics ◽  
Wave Basin ◽  
Crest Height

&lt;p&gt;As it strongly impacts the design of offshore structures, the accurate control of experimental wave fields is of great interest for the ocean engineering community. A significant majority of sea keeping tests are based on the stochastic approach. Long duration runs of irregular design sea states are generated at model scale in numerical or experimental wavetanks. The run duration is carefully chosen to observe the emergence of extreme events. The quality of the wavefield at the domain area of interest is assessed thanks to i) the wave energy spectrum and ii) the crest height distribution. The accurate reproduction of those two quantities stands a difficult process. Numerous complex phenomena such as wave breaking or Benjamin Feir (modulational) instabilities strongly impact the wave field. The shapes of i) the wave spectrum and ii) the tail of crest height distributions significantly evolve along the tank depending i) the wave steepness, ii) the spectral width, iii) the water depth and iv) the directional spreading (for directional sea states) [1, 2, 3].&lt;/p&gt;&lt;p&gt;The vast majority of the work in this area has focused on reproducing realistic wave energy spectra at the location of interest, assuming the indirect control of wave statistics. The present study intends to question such a characterization of a sea state. We address the problem within the framework of long crested irregular deep water waves generated in an experimental wave tank. In this respect, using the Ecole Centrale de Nantes (ECN) towing tank (140m*5m*3m), a narrow banded sea state has been generated at several locations of a long domain. The shape of the spectrum is accurately controlled thanks to a procedure based on wavemaker motion iterative correction [4]. For such nonlinear wave conditions the statistics along the wave propagation in the tank are known to be enhanced by significant spatial dynamics [1, 3]. As a result, configurations characterized by strictly identical wave spectra lead to the emergence of strongly different crest distributions. The data yielded by the study provide convincing evidence that the characterization of the wave field using the sole energy spectrum is insufficient. Particular attention must be given to the spatial dynamics of the wave field in order to control the wave statistics.&lt;/p&gt;&lt;p&gt;[1] Janssen, P. A. (2003). Nonlinear four-wave interactions and freak waves. &lt;em&gt;Journal of Physical Oceanography&lt;/em&gt;, &lt;em&gt;33&lt;/em&gt;(4), 863-884.&lt;/p&gt;&lt;p&gt;[2] Shemer, L., Sergeeva, A., &amp; Liberzon, D. (2010). Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves. &lt;em&gt;Journal of Geophysical Research: Oceans&lt;/em&gt;, &lt;em&gt;115&lt;/em&gt;(C12).&lt;/p&gt;&lt;p&gt;[3] Onorato, M., Cavaleri, L., Fouques, S., Gramstad, O., Janssen, P. A., Monbaliu, J., ... &amp; Trulsen, K. (2009). Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin.&lt;/p&gt;&lt;p&gt;[4] Canard, M., Ducrozet, G., &amp; Bouscasse, B. (2020, August). Generation of 3-hr Long-Crested Waves of Extreme Sea States With HOS-NWT Solver. In &lt;em&gt;International Conference on Offshore Mechanics and Arctic Engineering&lt;/em&gt; (Vol. 84386, p. V06BT06A064). American Society of Mechanical Engineers.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;

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.

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.

scholarly journals Comprehensive Wind and Wave Statistics and Extreme Values for Design and Analysis of Marine Structures in the Adriatic Sea

2021 ◽  
Vol 9 (5) ◽  
pp. 522
Author(s):  
Marko Katalinić ◽  
Joško Parunov
Keyword(s):  
Adriatic Sea ◽  
Extreme Values ◽  
Wave Climate ◽  
Offshore Structures ◽  
Model Parameters ◽  
Peak Period ◽  
Significant Wave ◽  
Wave Statistics ◽  
Wave Heights ◽  
Almost All

Wind and waves present the main causes of environmental loading on seagoing ships and offshore structures. Thus, its detailed understanding can improve the design and maintenance of these structures. Wind and wave statistical models are developed based on the WorldWaves database for the Adriatic Sea: for the entire Adriatic Sea as a whole, divided into three regions and for 39 uniformly spaced locations across the offshore Adriatic. Model parameters are fitted and presented for each case, following the conditional modelling approach, i.e., the marginal distribution of significant wave height and conditional distribution of peak period and wind speed. Extreme significant wave heights were evaluated for 20-, 50- and 100-year return periods. The presented data provide a consistent and comprehensive description of metocean (wind and wave) climate in the Adriatic Sea that can serve as input for almost all kind of analyses of ships and offshore structures.

scholarly journals On the physical constraints for the exceeding probability of deep water rogue waves

2021 ◽  
Author(s):  
Saulo Mendes ◽  
Alberto Scotti ◽  
Paul Stansell
Keyword(s):  
Sample Size ◽  
Rogue Wave ◽  
Probability Distributions ◽  
Rogue Waves ◽  
Uneven Distribution ◽  
Large Set ◽  
Sea State ◽  
Sampling Variability ◽  
The North ◽  
Wave Heights

&lt;p&gt;&lt;strong&gt;(manuscript accepted into Applied Ocean Research https://www.researchgate.net/publication/344786014)&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Abstract&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Nearly four decades have elapsed since the first efforts to obtain a realistic narrow-banded model for extreme wave crests and heights were made, resulting in a couple of dozen different exceeding probability distributions. These models reflect results of numerical simulations and storm records measured from oil platforms, buoys, and more recently, satellite data. Nevertheless, no consensus has been achieved in either deterministic or operational approaches. Typically, distributions found in the literature analyze a very large set of waves with large variations in sea-state parameters while neglecting homogeneous smaller samples, such that we lack a suitable definition for the sample size and homogeneity of sea variables, also known as sampling variability (Bitner-Gregersen et al., 2020). Naturally, a possible consequence of such sample size inconsistency is the apparent disagreement between several studies regarding the prediction of rogue wave occurrence, as some studies can report less rogue wave heights while others report more rogue waves or the same statistics predicted by Longuet-Higgins (1952), sometimes a combination of the three in the very same study (Stansell, 2004; Cherneva et al., 2005). In this direction, we have obtained a dimensionless parameter capable of measuring how large the deviations in sea state variables can be so that accuracy in wave statistics is preserved. &amp;#160;In particular, we have defined which samples are too heterogeneous to create an accurate description of the uneven distribution of rogue wave likelihood among different storms (Stansell, 2004). Though the literature is rich in physical bounds for single waves, here we describe empirical physical limits for the ensemble of waves (such as the significant steepness) devised to bound these variables within established and prospective wave distributions. Furthermore, this work supplies a combination of sea state parameters that provide guidance on the influence of sea states influence on rogue wave occurrence. Based on these empirical limits, we conjecture a mathematical model for the dependence of the expected maximum of normalized wave heights and crests on the sea state parameters, thus explaining the uneven distribution of rogue wave likelihood among different storms collected by infrared laser altimeters of the North Alwyn oil platform discussed in Stansell (2004). Finally, we demonstrate that for heights and crests beyond 90% of their thresholds (H&gt;2H&lt;sub&gt;1/3&lt;/sub&gt;&amp;#160;for heights), the exceeding probability becomes stratified, i.e. they resemble layers of probability curves according to each sea state, suggesting the existence of a dynamical definition for rogue waves rather than purely statistical.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Bitner-Gregersen, E. M., Gramstad, O., Magnusson, A., Malila, M., 2020. Challenges in description of nonlinear waves due to sampling variability. J. Mar. Sci. Eng. 8, 279.&lt;/p&gt;&lt;p&gt;Longuet-Higgins, M., 1952. On the statistical distribution of the heights of sea waves. Journal of Marine Research 11, 245&amp;#8211;265.&lt;/p&gt;&lt;p&gt;Stansell, P., 2004. Distribution of freak wave heights measured in the north sea. Appl. Ocean Res. 26, 35&amp;#8211;48.&lt;/p&gt;&lt;p&gt;Cherneva, Z., Petrova, P., Andreeva, N., Guedes Soares, C., 2005. Probability distributions of peaks, troughs and heights of wind waves measured in the black sea coastal zone. Coastal Engineering 52, 599&amp;#8211;615.&lt;/p&gt;

Long-Term Area Statistics for Maximum Crest Height Under a Fixed Platform Deck

2018 ◽  
Author(s):  
Øistein Hagen ◽  
Jørn Birknes-Berg ◽  
Ida Håøy Grue ◽  
Gunnar Lian ◽  
Kjersti Bruserud ◽  
...  
Keyword(s):  
Time Series ◽  
North Sea ◽  
Extreme Values ◽  
Second Order ◽  
Irregular Waves ◽  
Scatter Diagram ◽  
Short Term ◽  
Wave Impact ◽  
Crest Height

As offshore reservoirs are depleted, the seabed may subside. Furthermore, the extreme crests estimates are now commonly higher than obtained previously due to improved understanding of statistics of non-linear irregular waves. Consequently, bottom fixed installations which have previously had sufficient clearance between the deck and the sea surface may be in a situation where wave impact with the deck must be considered at relevant probability levels. In the present paper, we investigate the long-term area statistics for maximum crest height under a fixed platform deck for 2nd order short crested and long crested sea based on numerical simulations as a function of platform deck dimension for jackets. The results are for one location in the northern North Sea, but some key results are also reported and verified for a more benign southern North Sea location. Time domain simulations for long crested and short crested waves over a spatial domain with dimension of a platform deck are performed, and relevant statistics for airgap assessment determined. Second order waves are simulated for the different cells in the (Hs, Tp) scatter diagram for Torsethaugen two-peak wave spectrum for long-crested and short-crested sea. A total of 1000 3-hour sea states are generated per cell, and time series generated for 160 spatial points under a platform deck. Short-term and long-term statistics are established for the maximum crest height as function of platform dimension; inline and transverse to the wave direction, and over the area. Results are given for the linear sea and for the second order time series. The annual q-probability estimates for the maximum crest height over area as a function of platform dimension is determined for a location at the Norwegian Continental Shelf by weighting the short-term statistics for the individual cells in the scatter diagram with the long-term probability of occurrence of the sea state. To reduce the number of numerical second order simulations, the effect of excluding cells that have a negligible effect on the long term extreme crest estimate is discussed. The percentiles in the distribution of maximum crest (over area) in design sea states that corresponds to the extreme values obtained from the long-term analysis are determined for long crested and short crested sea. The increase in the extreme crest over an area compared to the point in space estimate is estimated for both linear and second order surface elevation.

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