Statistical Wave Model Research Articles

MONTHLY MEAN WAVE HEIGHT FORECASTS USING THE STATISTICAL WAVE MODEL BASED ON PCA ANALYSIS

Wave forecasts are refed in various fields such as fishing, surfing, ship navigation, and maritime construction. In addition, mild wave conditions are necessary during construction on the sea. Therefore, the accuracy of wave forecasting greatly influences marine construction management. In order to make a construction plan for marine construction, it is desired to estimate the wave height and frequency of construction several months ahead. The concern with long-term predictions has been growing because most wave forecasts are short-term predictions. In this study, a monthly ensemble mean wave height prediction was carried out using the statistical wave model, and the prediction accuracy was verified.

Predicting Statistical Wave Physics in Complex Enclosures: A Stochastic Dyadic Green's Function Approach

This article presents a physics-oriented, mathematically tractable, statistical wave model for analyzing the wave physics of high-frequency reverberation in complex cavity environments. The key ingredient is a vector dyadic stochastic Green's function (SGF) method that is derived from the Wigner's random matrix theory and Berry's random wave hypothesis. The SGF statistically replicates multipath, ray-chaotic communication between vector sources and vectorial electromagnetic fields at displaced observation points using generic, macroscopic parameters of the cavity environment. The work establishes a physics-based modeling and simulation capability that predicts the probabilistic behavior of backdoor coupling to complex electronic enclosures. Experimental results are supplied to validate the proposed work.

On the Importance of Using Event‐Specific Wave Diffusion Rates in Modeling Diffuse Electron Precipitation

AbstractA few to tens of keV electron precipitation that carries substantial energy source down to the upper atmosphere to create aurora is manifested as an important magnetosphere‐ionosphere coupling process. The precipitation is usually caused by scattering processes associated with plasma waves in the magnetosphere. The scattering process is often quantified by wave diffusion rates that indicate how fast an electron is scattered. Global models commonly use diffusion coefficients that are derived from statistical wave models. However, due to the statistical nature, many localized, transient features could be smeared out. In this study, we investigate electron precipitation using event‐specific diffusion coefficients that are obtained based on simultaneous in‐situ measured/inferred, rather than statistical, chorus wave dynamics. We find that the application of the event‐specific diffusion coefficients associated with a more dynamic and intense chorus wave model leads more electrons, particularly at several to tens of keV in the dawn‐to‐noon sector at L > 3, to precipitate than using statistical coefficients. The new simulation roughly captures both the intensity and variability of the precipitating flux as detected by the NOAA/POES satellites. Ionospheric electron density in the lower E region (100–120 km) observed by the mid‐latitude Millstone Hill radar is also much better reproduced, while the case using statistical diffusion coefficients underestimates the ionization rate. This study implies the importance of using event‐specific diffusion rates in simulating the diffuse electron precipitation and understanding the magnetosphere‐ionosphere coupling.

Long-term rogue wave occurrence probability from historical wave data on a spatial scale relevant for spar-type floating wind turbines

Very large waves, such as rogue waves, can be dangerous for ships and offshore structures. There is no consensus on the theoretical occurrence probability of these rogues and ocean measurements containing rogue waves are rare. This paper addresses the long-term occurrence probability of rogue waves using time-extreme (TE) and space–time extreme (STE) statistical wave models, evaluated with a significant amount of historical directional wave data from Monterey Bay, California, USA. A novel understanding of these models is obtained by exploring the area size for which the STE models estimate a higher rogue wave occurrence probability compared to the TE models. For four rogue wave and crest heights the return periods until a 95% rogue wave occurrence probability are estimated. To illustrate an application of this statistical analysis, the risk of rogue waves to a spar-type floating wind turbine is evaluated. Based on both the dynamic response and the long-term occurrence probability of the rogue wave, this research presents a new and advanced approach for a risk analysis of rogue waves to floating offshore structures.

Laser-like wave amplification in straits

We present the research of ocean surface wind waves excitation in non-homogeneous situations, on the example of deep water strait in presence of the constant wind, blowing perpendicular to the coastal line. The used statistical wave model is based on Hasselmann equation with high-wavenumbers wave-breaking dissipation, exact nonlinear four-waves interaction and ZRP wind input term. At the first stage, the waves propagate in the wind direction in a step-like moving front manner, which is the combination of self-similar fetch-limited and duration-limited solutions of Hasselmann equation. The second stage begins further, when sufficient amount of wave energy is concentrated at the incoming waves shore line. Beginning with that time, the nonlinear wave interactions start formation of the wave groups, propagating across and against the wind. Despite the absence of long-wave dissipation, the system asymptotically evolves into complicated quasi-stationary state, comprising of the self-similar ``wind sea'' in the wind direction, and quasi-monochromatic waves, radiated close to orthogonally with respect to the wind, while slightly tilting counter the wind direction with the angle increasing toward the wave turbulence origination shore line, and reaching $15^{\circ}$ close to it. The total wave energy in the asymptotic state surpasses the wave sea energy propagating along the wind by two times due to the presence of quasi-orthogonal and counter the wind wave fields. The very similar turbulence structure was previously observed experimentally, this paper presents theoretical explanation of these results. It is suggested to name this laser-like radiation phenomenon by Nonlinear Ocean Waves Amplifier, simplified to the abbreviation NOWA.

Comparison of two statistical wave models for fatigue and fracture analysis of ship structures

Ocean crossing ship structures are continuously suffering from wave loads when sailing at sea. The wave loads cause large variation of structural stresses, leading to fatigue accumulation in ship structures. For the fatigue life prediction of ship structures, it is important to obtain both the long-term distribution and the time history of wave-induced loads. An essential step is to get reliable wave statistics and accurate description of the stochastic nature of sea state along a ship's sailing routes during her service time. Generally, the wave statistics are provided by the classification societies as a joint probability of significant wave height and mean wave period, also known as wave scatter diagram. In addition, different statistical wave models have been developed to describe wave environments along arbitrary shipping routes based on different data sources, e.g., hindcast data, satellite measurements, buoys, etc. In this paper, two statistical wave models based on hindcast data and satellite wave measurements are briefly introduced and compared with the wave measurements carried out by onboard radar. Both of the wave models are then used to generate the wave environments along given shipping routes. The effectiveness of the wave models is demonstrated by comparing the stochastic nature and the statistical characteristics of simulated sea state histories with those of the source oceanographic data. Finally, an application of the wave model to the fatigue assessment is presented.

MISALIGNMENT AND LAG TIME OF WIND AND WAVE OCCURRENCE BASED ON 10 YEARS MEASUREMENTS IN THE NORTH SEA NEAR THE GERMAN COAST

There are several intentions to analyze the correlation of wind and wave data, especially in the North Sea. Fatigue damage is intensified by wind and wave loads acting from different directions, due to the misaligned aerodynamic damping of the rotor regarding the wave loads from lateral directions. Furthermore, construction time and costs are mainly driven by the operational times of the working vessels, which strongly depend on the wind and wave occurrence and correlation. Turbulent wind can rapidly change its direction and intensity, while the inert water waves react slowly in relation to the wind profile. Tuerk (2008) investigates the impact of wind and turbulence on offshore wind turbines by analyzing data of four years. The study shows that the wave height is increasing with higher wind speeds but when the wind speed drops the reaction of the waves is postponed. The dependence of the wave height on the wind speed is varying because of the atmospheric stability and different wind directions. Fischer et al. (2011) estimated absolute values of misalignment between wind and waves located in the Dutch North Sea. The study presents decreasing misalignment for increasing wind speeds, ranging up to 90 degrees for wind speeds below 12 m/s and up to 30 degrees for wind speeds above 20 m/s. Bredmose et al. (2013) present a method of offshore wind and wave simulation by using metocean data. The study describes characteristics of the wind and wave climate for the North and Baltic Sea as well as the directional distribution of wind and waves. Güner et al. (2013) cover the development of a statistical wave model for the Karaburun coastal zone located at the southwest coast of the Black Sea with the help of wind and wave measurements and showed that the height of the waves is directly correlating with the duration of the wind for the last four hours.

The Influence of Solar Wind and Geomagnetic Indices on Lower Band Chorus Emissions in the Inner Magnetosphere

AbstractStatistical wave models, describing the distribution of wave amplitudes as a function of location, geomagnetic activity, and other parameters, are needed as the basis to describe the wave‐particle interactions within numerical models of the radiation belts. In this study, we widen the scope of the statistical wave models by investigating which of the solar wind parameters or geomagnetic indices and their time lags have the greatest influence on the amplitudes of lower band chorus (LBC) waves in the inner magnetosphere. The solar wind parameters or geomagnetic indices with the greatest control over the waves were found using the error reduction ratio (ERR) analysis, which plays a key role in system identification modeling techniques. In this application, the LBC magnitudes at different locations are considered as the output data, while the lagged solar wind parameters are the input data. The ERR analysis automatically determines a set of the most influential parameters that explain the variations in the emissions. Both linear and nonlinear applications of the ERR analysis are compared using solar wind inputs and show that the linear ERR analysis can be misleading. The linear results show that the interplanetary magnetic field (IMF) factor has the most influence on at each magnetic local time (MLT) sector. However, the nonlinear ERR analysis shows that the IMF factor coupled with the solar wind velocity has the main contribution to the LBC wave magnitudes. When geomagnetic indices are included as inputs with the solar wind parameters to the nonlinear ERR analysis, the results show that the majority of the variation in emissions may be attributed to the Auroral Electrojet (AE) index. In the dawn sectors between 00 and 12 MLT and 5 < L < 7, the AE index multiplied by the solar wind velocity with zero time lag has the most influence on the amplitudes of LBC. For 5 < L < 7, the parameters with the highest ERR are the AE index multiplied by the solar wind velocity with a 2‐hr time lag at 12–16 MLT, the linear AE index with a 2‐hr time lag at 16–20 MLT, and AE index multiplied by the IMF factor with zero lag at 20–00 MLT. For 4 < L < 5, the parameters with the highest ERR are the AE index multiplied by the solar wind dynamic pressure with zero time lag at 00–04 MLT, the AE index multiplied by the solar wind velocity with zero time lag between 14 and 12 MLT, the AE index multiplied by the solar wind velocity with a 2‐hr time lag at 12–16 MLT, the Dst index with a 6‐hr time lag at 12–16 MLT, and the AE index multiplied by the IMF factor with zero lag at 20–00 MLT.

선박운항 시뮬레이터를 위한 풍파와 너울의 실시간 시뮬레이션

Seas and swells are basic wave types in ocean surface simulation and are very important elements in the simulation of ocean background. In this paper, we propose a real-time simulation method, for reproducing realistic seas and swells, to be used in real-time simulators such as ship maneuvering simulators. Seas and swells have different visual properties. Swells have relatively longer wavelengths and round crests compared with seas, therefore they are visualized globally with large meshes and procedural methods. Parameters to illustrate swells are extracted from ocean wave spectra. Conversely, seas have shorter wavelengths and their characteristics are only clearly apparent near to the observation point. Here, we present visualization of seas based on a statistical wave model using ocean wave spectra, which provides realistic results in a reactively small area.

Development of a Spectral Method and a Statistical Wave Model for Crack Propagation Prediction in Ship Structures

As a result of the wide use of high-tensile steel and the imperfect fabrication process in ship construction as well as some uncertainties in ship fatigue design, cracks could be initiated much earlier than expected. The presence of fatigue cracks greatly affects a ship's structural safety and serviceability. To ensure structural safety and perform reliable crack inspection and maintenance planning, it is important to know how fast cracks can grow in ship structures. In the current study, the principles of fracture mechanics are used for crack propagation analysis in ships. By taking into account the special properties of a ship's stress response, an efficient spectral method is proposed and validated for the prediction of crack propagation in ship structures. In this spectral method, structural stresses are assumed to be narrow-band Gaussian processes. Furthermore, for crack inspection and maintenance planning based on crack growth, it is essential to know the wave environments encountered in a ship's future operations. Therefore, a spatiotemporal statistical wave model based on both satellite and buoy measurements is briefly introduced. It is developed to generate wave environments along arbitrary ship routes. Finally, the deck longitudinal stiffener of a 2800TEU containership is used to demonstrate the application of the spectral method and the wave model for the prediction of crack propagation in ships. The route information and operating conditions are taken from full-scale measurements of this ship. In the case study, the scatter of crack propagation associated with the wave environments encountered is also investigated. The results from this investigation indicate possible potentials of crack inspection and maintenance optimization to enable more efficient ship operation.

Development of a Spectral Method and a Statistical Wave Model for Crack Propagation Prediction in Ship Structures

As a result of the wide use of high-tensile steel and the imperfect fabrication process in ship construction as well as some uncertainties in ship fatigue design, cracks could be initiated much earlier than expected. The presence of fatigue cracks greatly affects a ship's structural safety and serviceability. To ensure structural safety and perform reliable crack inspection and maintenance planning, it is important to know how fast cracks can grow in ship structures. In the current study, the principles of fracture mechanics are used for crack propagation analysis in ships. By taking into account the special properties of a ship's stress response, an efficient spectral method is proposed and validated for the prediction of crack propagation in ship structures. In this spectral method, structural stresses are assumed to be narrow-band Gaussian processes. Furthermore, for crack inspection and maintenance planning based on crack growth, it is essential to know the wave environments encountered in a ship's future operations. Therefore, a spatiotemporal statistical wave model based on both satellite and buoy measurements is briefly introduced. It is developed to generate wave environments along arbitrary ship routes. Finally, the deck longitudinal stiffener of a 2800TEU containership is used to demonstrate the application of the spectral method and the wave model for the prediction of crack propagation in ships. The route information and operating conditions are taken from full-scale measurements of this ship. In the case study, the scatter of crack propagation associated with the wave environments encountered is also investigated. The results from this investigation indicate possible potentials of crack inspection and maintenance optimization to enable more efficient ship operation.

Estimation of wave parameters based on nearshore wind–wave correlations

A statistical wave model for a specific region was developed to generate long-term wave data in case of the absence of any measured data or to fill the data gaps which occur in a measurement data. Wind data, wave measurement data and a third generation numerical wave model (MIKE21 SW) were used to develop a wave model that is applicable for the research area. The aim of to use such a model is to gain a practical and quick estimation of the wave parameters by using a meteorological station’s wind parameters without having need for a sophisticated wave model which demands more complicated input parameters. In addition, previously developed wave prediction models which are less complicated should not be appropriate for every coastal zone for various reasons. Therefore, the best way to estimate the wave climate for a region is to obtain a site-specific wave model. The Karaburun coastal zone located at the southwest coast of the Black Sea was chosen as the study field. Wind, wave and water level measurements were performed to determine the field data. Wave measurements were carried out at the site by an ultrasonic and pressure type wave gauge between the dates of August 2003 and March 2005. Wave measurement data was used both for the development and calibration of the statistical wave model. The results obtained from the statistical wave model have an RMSE value of 0.29m for the significant wave heights which is very reasonable when the model is considered to be simple and demanding less input data (wind speed, wind direction and fetch length).

Oscillatory Bottom Boundary Layers

A turbulence closure model is applied to the case of an oscillating boundary layer; model calculations compare favorably with data. Wave-induced oscillations can be temporally resolved in a one-dimensional model but not in three-dimensional ocean models, and, indeed, statistical wave models, working in consort with ocean models, can only provide information on expected wave periods and amplitudes. Therefore, in this paper, a way has been found to parameterize the effects of bottom flow oscillations; it entails augmenting the turbulence shear production as a function of amplitude and period of the oscillation, the bottom shear stress of the mean current flow, and the angle between the directions of the oscillations and the mean flow. The more conventional method of solving for an apparent wall roughness is also investigated in an appendix.