Observations and Modeling of Linear and Nonlinear Spatio-Temporal Wave Statistics

2010 ◽  
Author(s):  
Leonel Romero ◽  
W. Kendall Melville
Keyword(s):  
Spatial Information ◽  
Second Order ◽  
Stochastic Simulations ◽  
Ocean Engineering ◽  
Engineering Applications ◽  
Large Wave ◽  
Wave Statistics ◽  
Wave Parameters ◽  
Wave Heights ◽  
Spatio Temporal

We present an analysis of airborne wave observations collected in the Gulf of Tehuantepec. The data includes LIDAR measurements of the surface displacement as a function of two horizontal dimensions and time in fetch-limited conditions, with fetches between 50 and 300 km and winds between 10 and 20 m/s. The spatio-temporal data have an advantage over the commonly used single point time-series measurements allowing direct estimates of the wavelength and wave slope, including spatial information such as the lengths of crests exceeding threshold wave heights and slopes. The statistics of these wave parameters are particularly important for risk assessment of off-shore structures and in other ocean engineering applications. We present an analysis of several statistical wind-wave parameters, including the joint probability distribution function (pdf) of wave amplitudes and wavelengths, the pdf of wave heights, wavenumber vectors, and wave slopes, including the statistics of crests lengths exceeding threshold wave heights or slopes. The empirical findings from the LIDAR data are related to the analytical work by Longuet-Higgins (1957) [1] for a linear spectrum, including the average length of contours surrounding large wave heights. The effect of second-order nonlinearities on the distribution of crest lengths is investigated with numerical stochastic simulations from computed directional wavenumber spectra. The results show that second-order nonlinearities can increase the crest length density of large waves by about a factor of two or more. The results are discussed in the context of predicting wave statistics for ocean engineering applications.

Physics-Based Approach to Wave Statistics and Probability

2013 ◽  
Author(s):  
Alexander V. Babanin
Keyword(s):  
Extreme Events ◽  
Modulational Instability ◽  
Probability Distributions ◽  
Rayleigh Distribution ◽  
Order Theory ◽  
Second Order ◽  
Ocean Engineering ◽  
Actual Distribution ◽  
Wave Statistics ◽  
Wave Heights

Design criteria in ocean engineering, whether this is one in 50 years or one in 5000 years event, are hardly ever based on measurements, and rather on statistical distributions of relevant metocean properties. Of utmost interest is the tail of these distributions, that is rare events such as the highest waves with low probability. Engineers have long since realised that the superposition of linear waves with narrow-banded spectrum as depicted by the Rayleigh distribution underestimates the probability of extreme wave crests, and is not adequate for wave heights either, which is a critical shortcoming as far as the engineering design is concerned. Ongoing theoretical and experimental efforts have been under way for decades to address this issue. Here, we will concentrate on short-term statistics, i.e. probability of crests/heights of individual waves. Typical approach is to treat all possible waves in the ocean or at a particular location as a single ensemble for which some comprehensive solution can be found. The oceanographic knowledge, however, now indicates that no single and united comprehensive solution is possible. Probability distributions in different physical circumstances should be different, and by combining them together the inevitable scatter is introduced. The scatter and the accuracy will not improve by increasing the bulk data quality and quantity, and it hides the actual distribution of extreme events. The groups have to be separated and their probability distributions treated individually. The paper offers a review of physical conditions, from simple one-dimensional trains of free waves to realistic two-dimensional wind-forced wave fields, in order to understand where different probability distributions can be expected. If the wave trains/fields in the wave records are stable, distributions for the second-order waves should serve well. If modulational instability is active, rare extreme events not predicted by the second-order theory should become possible. This depends on wave steepness, bandwidth and directionality. Mean steepness also defines the wave breaking and therefore the upper limit for wave heights in this group of conditions. Under hurricane-like circumstances, the instability gives way to direct wind forcing, and yet another statistics is to be expected.

scholarly journals Spatial Statistics of the Sea Surface in Fetch-Limited Conditions

2011 ◽  
Vol 41 (10) ◽  
pp. 1821-1841 ◽  
Author(s):  
Leonel Romero ◽  
W. Kendall Melville
Keyword(s):  
Surface Area ◽  
Spatial Information ◽  
Length Distribution ◽  
Second Order ◽  
Joint Probability Distribution ◽  
Unit Surface Area ◽  
Large Wave ◽  
Analytical Approximations ◽  
Unit Surface ◽  
Wave Heights

Abstract An analysis of airborne wave observations collected in the Gulf of Tehuantepec is presented. The data include lidar measurements of the surface displacement as a function of two horizontal dimensions in fetch-limited conditions, with fetches between 20 and 500 km and winds between 10 and 20 m s−1. The spatial data have an advantage over the commonly used single-point time series measurements, allowing direct estimates of the wavelength and wave slope, including spatial information such as the lengths of crests exceeding various thresholds. This study presents an analysis of several statistical wind wave parameters, including the joint probability distribution function (pdf) of wave amplitudes and wavelengths; the pdf of wave heights, wavenumber vectors, and wave slopes; as well as the statistics of the lengths of crests exceeding threshold wave heights and slopes. The empirical findings from the lidar data are compared against analytical theories in the literature, including some that had not been tested previously with field data such as the work by M. S. Longuet-Higgins describing the length of contours surrounding large wave heights per unit surface area. The effect of second-order nonlinearities on the distribution of crest lengths per unit surface area is investigated with analytical approximations and stochastic numerical simulations from computed directional wavenumber spectra. The results show that second-order nonlinearities can increase the crest-length distribution of large waves by a factor of 2 or more.

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.

scholarly journals Statistics of Extreme Waves in Coastal Waters: Large Scale Experiments and Advanced Numerical Simulations

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 99 ◽  
Author(s):  
Jie Zhang ◽  
Michel Benoit ◽  
Olivier Kimmoun ◽  
Amin Chabchoub ◽  
Hung-Chu Hsu
Keyword(s):  
Large Scale ◽  
Numerical Models ◽  
Low Frequency ◽  
Local Maximum ◽  
Second Order ◽  
Irregular Waves ◽  
Extreme Waves ◽  
Ocean Engineering ◽  
Large Wave ◽  
Highly Nonlinear

The formation mechanism of extreme waves in the coastal areas is still an open contemporary problem in fluid mechanics and ocean engineering. Previous studies have shown that the transition of water depth from a deeper to a shallower zone increases the occurrence probability of large waves. Indeed, more efforts are required to improve the understanding of extreme wave statistics variations in such conditions. To achieve this goal, large scale experiments of unidirectional irregular waves propagating over a variable bottom profile considering different transition water depths were performed. The validation of two highly nonlinear numerical models was performed for one representative case. The collected data were examined and interpreted by using spectral or bispectral analysis as well as statistical analysis. The higher probability of occurrence of large waves was confirmed by the statistical distributions built from the measured free surface elevation time series as well as by the local maximum values of skewness and kurtosis around the end of the slope. Strong second-order nonlinear effects were highlighted as waves propagate into the shallower region. A significant amount of wave energy was transmitted to low-frequency modes. Based on the experimental data, we conclude that the formation of extreme waves is mainly related to the second-order effect, which is also responsible for the generation of long waves. It is shown that higher-order nonlinearities are negligible in these sets of experiments. Several existing models for wave height distributions were compared and analysed. It appears that the generalised Boccotti’s distribution can predict the exceedance of large wave heights with good confidence.

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 The Role of Spatio-Temporal Information to Govern the COVID-19 Pandemic: A European Perspective

2021 ◽  
Vol 10 (3) ◽  
pp. 166
Author(s):  
Hartmut Müller ◽  
Marije Louwsma
Keyword(s):  
European Union ◽  
Spatial Distribution ◽  
Spatial Information ◽  
National Level ◽  
Temporal Information ◽  
The European Union ◽  
Member States ◽  
Heavy Burden ◽  
Spatio Temporal

The Covid-19 pandemic put a heavy burden on member states in the European Union. To govern the pandemic, having access to reliable geo-information is key for monitoring the spatial distribution of the outbreak over time. This study aims to analyze the role of spatio-temporal information in governing the pandemic in the European Union and its member states. The European Nomenclature of Territorial Units for Statistics (NUTS) system and selected national dashboards from member states were assessed to analyze which spatio-temporal information was used, how the information was visualized and whether this changed over the course of the pandemic. Initially, member states focused on their own jurisdiction by creating national dashboards to monitor the pandemic. Information between member states was not aligned. Producing reliable data and timeliness reporting was problematic, just like selecting indictors to monitor the spatial distribution and intensity of the outbreak. Over the course of the pandemic, with more knowledge about the virus and its characteristics, interventions of member states to govern the outbreak were better aligned at the European level. However, further integration and alignment of public health data, statistical data and spatio-temporal data could provide even better information for governments and actors involved in managing the outbreak, both at national and supra-national level. The Infrastructure for Spatial Information in Europe (INSPIRE) initiative and the NUTS system provide a framework to guide future integration and extension of existing systems.

scholarly journals Spatio-Temporal Alignment and Trajectory Matching for Netted Radar Without Prior Spatial Information and Time Delay

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 126965-126976
Author(s):  
Xiaoyu Cong ◽  
Yubing Han ◽  
Weixing Sheng ◽  
Shanhong Guo ◽  
Renli Zhang
Keyword(s):  
Time Delay ◽  
Spatial Information ◽  
Temporal Alignment ◽  
Trajectory Matching ◽  
Spatio Temporal

VIDEO-SHOT TRANSITION DETECTION: A SPATIO-TEMPORAL SALIENCY APPROACH

2010 ◽  
Vol 24 (08) ◽  
pp. 1295-1309 ◽  
Author(s):  
XIAN WU ◽  
JIANHUANG LAI ◽  
PONG C. YUEN
Keyword(s):  
Error Probability ◽  
Spatial Information ◽  
Saliency Map ◽  
Detection Error ◽  
Novel Approach ◽  
Video Shot ◽  
Recent Method ◽  
Temporal And Spatial ◽  
Spatio Temporal ◽  
Shot Transitions

This paper proposes a novel approach for video-shot transition detection using spatio-temporal saliency. Both temporal and spatial information are combined to generate a saliency map, and features are available based on the change of saliency. Considering the context of shot changes, a statistical detector is constructed to determine all types of shot transitions by the minimization of the detection-error probability simultaneously under the same framework. The evaluation performed on videos of various content types demonstrates that the proposed approach outperforms a more recent method and two publicly available systems, namely VideoAnnex and VCM.

scholarly journals Focusing of long waves with finite crest over constant depth

2013 ◽  
Vol 469 (2153) ◽  
pp. 20130015 ◽  
Author(s):  
Utku Kânoğlu ◽  
Vasily V. Titov ◽  
Baran Aydın ◽  
Christopher Moore ◽  
Themistoklis S. Stefanakis ◽  
...  
Keyword(s):  
Source Region ◽  
Wave Theory ◽  
Long Waves ◽  
Constant Depth ◽  
Large Wave ◽  
Weakly Nonlinear ◽  
Scaling Relationships ◽  
2011 Japan Tsunami ◽  
Wave Heights ◽  
Run Up

Tsunamis are long waves that evolve substantially, through spatial and temporal spreading from their source region. Here, we introduce a new analytical solution to study the propagation of a finite strip source over constant depth using linear shallow-water wave theory. This solution is not only exact, but also general and allows the use of realistic initial waveforms such as N -waves. We show the existence of focusing points for N -wave-type initial displacements, i.e. points where unexpectedly large wave heights may be observed. We explain the effect of focusing from a strip source analytically, and explore it numerically. We observe focusing points using linear non-dispersive and linear dispersive theories, analytically; and nonlinear non-dispersive and weakly nonlinear weakly dispersive theories, numerically. We discuss geophysical implications of our solutions using the 17 July 1998 Papua New Guinea and the 17 July 2006 Java tsunamis as examples. Our results may also help to explain high run-up values observed during the 11 March 2011 Japan tsunami, which are otherwise not consistent with existing scaling relationships. We conclude that N -waves generated by tectonic displacements feature focusing points, which may significantly amplify run-up beyond what is often assumed from widely used scaling relationships.

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.

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