Wave Spectrum Model Research Articles

MEMS-based wave buoy: Towards short wind-wave sensing

Low-cost commercial micro-electro-mechanical system (MEMS)-based inertial motion unit is used for sea surface wave measurements. A buoy is developed based on the capacitive silicon-based accelerometer–gyroscope–magnetometer sensor with radically simplified architecture allowing a significant reduction of the buoy hull size down to 14-cm diameter and hence increased high-frequency sensitivity. The proposed buoy design is suitable for short-term manual wave measurements with minimal deployment–recovery efforts and/or experiments where knowledge of the high-frequency part of the spectrum is preferable. The buoy data is validated in a field experiment at the Black Sea stationary research platform using reference measurements of the six-wire resistive wave gauge. The strapped-down buoy measurements are transformed into the georeferenced buoy tilts and vertical acceleration using small wave slope approximation. The classical (Longuet-Higgins et al., 1961) approach is used for directional wave spectra estimation. Under 1 to 15 m/s wind speed, pure wind and mixed sea conditions, the significant wave height, wave peak period, wave direction, and spectral width are well reproduced by the buoy. The buoy geometric cut-off frequency, about 2.5 Hz, corresponding to wavelength twice the hull diameter, is at least 2.5 times better than that of commercially available buoys. The sub-peak low-frequency noise, typical for accelerometer-derived spectra, is wind-dependent and thus is clearly not the intrinsic sensor noise, but rather results from the buoy non-linear response to the waves. The detected high-frequency (4<f<80Hz) spectrum tail also depends on the wind speed in accord with the short-wave wind-driven wave spectrum model. The observed high-frequency sensitivity may be useful for short-wave sensing beyond the geometric cut-off frequency with MEMS-based sensors.

$L$ -Band Ocean Surface Roughness

Surface wave spectral properties of centimeter to decameter (cmDm) wavelengths are of great interest to microwave remote sensing of the ocean. They are obviously different from the high-frequency extension of the wind-wave spectrum models developed for ocean science and engineering applications, which focus on the longer waves in the energetic peak region of the wave spectrum. For more than six decades, the cmDm waves are generally considered to be in the equilibrium range, and its spectral function has a constant slope: −5 or −4 in the 1-D frequency spectrum, and −3 or −2.5 in the 1-D wavenumber spectrum. The observed wind-wave spectral slopes, however, are not constant. As a result, the cmDm wave properties are significantly different from those inferred from an equilibrium spectrum model. Surface slope measurements are more suited for studying the cmDm waves. Microwave radar backscattering cross sections have been used to study the shorter range of cmDm waves. L-band lowpass-filtered mean square slope (LPMSS) is contributed by waves longer than about 0.6 m, here referred to as the decimeter to decameter (dmDm) waves. The analysis of LPMSS has improved the modeling of dmDm waves. Ultimately, the spectral slope variation is a critical characteristic of cmDm waves. The wave spectrum model formulated with the variable spectral slope consideration produces very good agreement with L-band scatterometer and reflectometer measurements.

Research on the Applicability of the E Spectrum and PM Spectrum as the First Guess Spectrum of SAR Wave Spectrum Inversion

Synthetic aperture radar (SAR) is an important method for observing ocean waves, and inversion of the ocean wave spectrum is an important part of SAR ocean wave detection. For most wave spectrum inversion methods, the first guess spectrum is crucial to the accuracy of SAR wave spectrum inversion. The first guess spectrum can be provided by some existing fixed wave spectrum models, but the applicability of these wave spectrum models as the first guess spectrum has not been systematically studied. This paper focused on the applicability of the Elfouhaily spectrum (E spectrum) as a full wavenumber spectrum and the Pierson-Moscowitz spectrum (PM spectrum) as a wind wave spectrum as the first guess spectrum for inverting the wave spectrum. Based on the SENTINEL-1A and RADARSAT-2 SAR satellite data of the Maritime Silk Road, using the E spectrum and PM spectrum as the first guess spectrum by the Max Planck Institute (MPI) method, the ability of the E spectrum and PM spectrum as the first guess spectrum to retrieve the wave spectrum and wave parameters was systematically evaluated. The significant wave height (HS) and zero-crossing period (TZ) wave parameters obtained from SAR inversion were compared with the European Center for Medium-Range Weather Forecasts (ECMWF) wave data. By the comparison results, we analyzed the best wind speed and significant wave height ranges for the inversion of the PM spectrum and E spectrum as the first guess spectrum. The results showed that the E spectrum as the first guess spectrum had a good effect on the inversion at medium sea situation. It was suitable as the first guess spectrum of the SAR wave spectrum inversion.

A Review of Wave Spectrum Models as Applied to the Problem of Radar Probing of the Sea Surface

AbstractThe most common models of the wind wave spectrum are reviewed, and the compliance of the studied spectra with several fundamental criteria is estimated. These criteria are the ability to simulate diverse wave climate and agreement between model‐based calculations of the mean square slope and experimental data. The spreading function of the spectrum should also correspond to the experimentally measured Doppler spectrum, while the dependence of the radar backscatter cross section should conform to geophysical model functions for various wavelength ranges of incident electromagnetic radiation at moderate incidence angles (20–60°). An analysis has shown that none of the considered spectrum models fully satisfies all the criteria; thus, a new spectrum model for wind waves was developed. Boundary wave numbers for various wavelength ranges of incident electromagnetic radiation within the framework of a two‐scale surface model were determined for the new model. The spectrum model can be used to simulate ripple attenuation in oil slicks and to calculate the radar backscatter cross section inside slick.

Hydrodynamic-Interaction Analysis of an Autonomous Underwater Hovering Vehicle and Ship with Wave Effects

A new vertical axis-symmetrical dish-shaped autonomous underwater vehicle (AUV) with excellent maneuverability, known as the autonomous underwater hovering vehicle (AUH), is proposed. This study investigates an important working model of the AUH approaching a host ship in waves. The working model of AUH–Ship interactions deals with hydrodynamic interaction, seakeeping performance for communication, launch, and recovery near a free surface. The AUH is able to navigate and implement homing automation through acoustic positioning equipment, a depth sensor, a heading compass, and a Doppler velocity log (DVL) in the working area based on numerical analysis of AUH–Ship hydrodynamic performance in this study. The hydrodynamic-interaction performance of the AUH and ship near free surfaces is analyzed in the frequency and time domains using a potential-based surface-panel method based on a commercial computational fluid dynamics (CFD) solver (ANSYS-AQWA), i.e., a 3D panel code of seakeeping performance module in the ANSYS platform where the fluid is assumed to be irrotational, inviscid, and incompressible. The motion performance of the AUH approaching the host ship, with a dynamic positioning system in waves, is studied by estimating interactive response-amplitude operators (RAOs) of the AUH and host ship in 6-DOF that were estimated and analyzed at different wave amplitudes and frequencies. In the ship and AUH interaction simulations, the host ship is assumed to be a well-posed station keeping in waves with zero service speed. The AUH and ship interference effect is studied at different distances to appropriate recovery and launch positions for the AUH at the following sea and beam sea, i.e., wave-encounter angles 0° and 90°, respectively. In addition, the hydrodynamic interaction of the AUH and ship in yaw and roll at different AUH velocities is estimated. The AUH motion performance approaching the ship in long-crested irregular seas is analyzed in the time domain using the Pierson–Moskowitz wave spectrum model. Viscid hydrodynamic force on AUH motion in roll near a free surface was significant. A damping model was adopted to formulate the viscid effect to enhance the effectiveness of the ANSYS-AQWA inviscid potential-based solver. Numerical analysis of motion RAO of the AUH in roll with the damping effect was compared to the experimental data in wave-frequency range 0.2–1.0 Hz, resulting in the average error being reduced from 21.03% to 9.95% to verify the method’s accuracy. The proposed method conveniently and accurately predicted hydrodynamic-interaction characteristics and motion RAO for a dish-type AUH and host ship for the precise use of mounted sensors in waves. The results of these simulations can be used to analyze the homing automation and adaptive controllability to advance the AUV development and design.

Modeling L-Band Reflection and Emission From Seawater, Foam, and Whitecaps Using the Finite-Difference Time-Domain Method

Reflection and emission from flat and rough seas with embedded whitecaps (WCs) are investigated at L-band using a custom finite-difference time-domain electromagnetic model. The model is applied to multiple layers, with vertically inhomogeneous dielectric profiles representing foam and spray overlying a homogeneous seawater layer. The foam and spray layers are adapted from an L-band radiative transfer model, and the rough sea surface is a statistical realization of the Kudryavtsev wave spectrum model. The 1-D and 2-D model versions are validated for a flat sea with optional foam cover, and the emissivity effects of WCs embedded in flat and rough seas are investigated. An overlying spray layer is found to markedly reduce WC detectability. Possible applications are the stochastic simulation of WC cover and its effect on emissivity at various wind speeds, and the effects of wave and WC shape on emissivity.

Offshore Electromagnetic Spectrum Distribution Prediction Model Based on Ray Tracing Method and PM Wave Spectrum

Electromagnetic spectrum distribution prediction is the basis for the development of wireless communication technology. Due to the high randomness of the rough sea surface, it is difficult to accurately predict the offshore electromagnetic spectrum distribution. We present a prediction model of offshore electromagnetic spectrum distribution based on ray tracing method and Pierson-Moskowitz (PM) wave spectrum model. Based on the antenna attitude and the antenna directional pattern, the field strength calculation formulas of the electromagnetic wave sight line ray (SLR) propagation and the electromagnetic wave reflecting line ray (RLR) propagation off the sea surface are established. As the sea surface and the antenna attitude change, the effective rays from the transmitting antenna to the receiving antenna also change. This paper focus on the electromagnetic spectrum distribution prediction by calculating the effective angle (EA) of the transmitting antenna. We relate the EA to the antenna tilt angle and the antenna directional pattern, and combine the PM wave spectrum to establish the offshore electromagnetic spectrum distribution prediction models. Finally, we simulated the electromagnetic spectrum distribution prediction based on specific PM wave spectrum data.

Numerical modeling of wave-current interaction in Merak Port, Indonesia

This study aimed to investigate the effects of currents to wave height in the waters of Merak Port, Banten using wave spectrum model. The wave-current interaction simulation was performed by utilizing SWAN (Simulating Waves Nearshore) in stationary mode and using the unstructured triangular grid. Data of wind velocity and direction as model inputs were obtained from BMKG (Indonesian Agency for Meteorology, Climatology, and Geophysics), whereas tidal current velocity data was obtained from TMD (Tide Model Driver). The model was simulated in two different scenarios, i.e. without and with following (adverse) current which is same (opposite) with wave propagation. The model input of dominant west wind was used to represent the west monsoon, while the dominant wind from the north was used to represent the east monsoon. The simulation results show that the maximum wave height is 2.98 m in the west monsoon and 1.9 m in east monsoon. In the west (east) monsoon the following current decrease wave height to 9.26% (5.09%), while the adverse current increase wave height up to 9.07% (6.56%).

Long term response analysis of TLP-type offshore wind turbine

The performance of offshore wind turbine supported with different configurations of Tension-leg-platform (TLP) are studied for vertical plane motion responses (surge, heave, and pitch) along with the side-to-side, fore–aft, and yaw tower base bending moments. The long-term distribution is carried out using the short-term floating wind turbine responses based on Rayleigh distributions and North Atlantic wave data. The long-term response analysis is performed for the 5 MW TLP-type offshore wind turbine. The study aims at predicting the most probable maximum values of motion amplitudes that can be used for design purposes. The transfer functions for surge, heave and pitch motions of the floater are obtained using the FAST code. The performance of floating structure in the long-term analysis not only depends on the transfer functions but also on the careful selection of design wave spectrum model. Among different theoretical design wave spectrum models, three models are chosen that closely represents the sea states and the response spectrums are computed for these models. As the nature of the response spectrum of the floating structure is analogous with the input wave spectrum model, it can be assumed to have the same probabilistic properties and modeled as a stationary stochastic process. The long-term probability distributions for TLP-type floater configuration for surge, heave and pitch motion amplitudes along with the tower base bending moments are used for design purposes, so as to guarantee the safety of the floating wind turbines against overturning/capsizing in high waves and wind speed. The calculation of the long-term distribution using FAST will help in the preliminary analysis of the performance of floaters in the study of wave-induced response of floaters.

Comparison of Various Spectral Models for the Prediction of the 100-Year Design Wave Height

Offshore structures are exposed to random wave loading in the ocean environment, and hence the probability distribution of the extreme values of their response to wave loading is required for their safe and economical design. In most cases, the dominant load on offshore structures is due to wind-generated random waves where the ocean surface elevation is defined using appropriate ocean wave energy spectra. Several spectral models have been proposed to describe a particular sea state that is used in the design of offshore structures. These models are derived from analysis of observed ocean waves and are thus empirical in nature. The spectral models popular in the offshore industry include Pierson-Moskowitz spectrum and JONSWAP spectrum. While the offshore industry recognizes that different methods of simulating ocean surface elevation lead to different estimation of design wave height, no systematic investigation has been conducted. Hence, the aim of this study is to investigate the effects of predicting the 100-year responses from various wave spectrum models. In this paper, the Monte Carlo time simulation (MCTS) procedure has been used to compare the magnitude of the 100-year extreme responses derived from different spectral models. Additionally, the linear random wave theory (LRWT) was implemented to simulate the offshore structural responses due to random wave loading. The models have been tested for three different environmental conditions represented by Hs = 15m, 10m and 5m respectively. The accuracy of the predictions of the 100-year responses from Pierson-Moskowitz and JONSWAP spectrums will then be investigated.

Analysis of ocean wave characteristic in Western Indonesian Seas using wave spectrum model

Understanding the characteristics of the ocean wave in Indonesian Seas particularly in western Indonesian Seas is crucial to establish secured marine activities in addition to construct well-built marine infrastructures. Three-years-data (July 1996 - 1999) simulated from Simulating Waves Nearshore (SWAN) model were used to analyze the ocean wave characteristics and variabilities in eastern Indian Ocean, Java Sea, and South China Sea. The interannual or seasonal variability of the significant wave height is affected by the alteration of wind speed and direction. Interactions between Indian Ocean Dipole Mode (IODM), El Niño Southern Oscillation (ENSO) and monsoon result in interannual ocean wave variability in the study areas. Empirical Orthogonal Functions (EOF) analysis produces 6 modes represents 95% of total variance that influence the wave height variability in the entire model domain. Mode 1 was dominated by annual monsoon and has spatial dominant contribution in South China Sea effected by ENSO and Indian Ocean influenced by IODM. Java Sea was influenced by Mode 2 which is controlled by semi-annual monsoon and IODM. A positive (negative) IODM strengthens (weakens) the winds speed in Java Sea during the East (West) season and hence contributes to Mode 2 in increasing (decreasing) the significant wave in Java Sea.

Wind Profiles and Wave Spectra for Potential Wind Farms in South China Sea. Part II: Wave Spectrum Model

Along with the commercialization of offshore wind energy in China, the South China Sea has been identified as ideal for constructing offshore wind farms, especially for farms consisting of floating wind turbines over deep waters. Since the wind profiles and wave spectra are somewhat primitive for the design of an offshore wind turbine, engineering models describing the wind and wave characteristics in the South China Sea area are necessary for the offshore wind energy exploitation given the meteorological, hydrological, and geographical differences between the South China Sea and the North/Norwegian Sea, where the commonly used wind profile and wave spectrum models were designated. In the present study; a series of numerical simulations were conducted to reveal the wave characteristics in the South China Sea under both typhoon and non-typhoon conditions. By analyzing the simulation results; the applicability of the Joint North Sea Wave Project (JONSWAP) spectrum model; in terms of characterizing the wind-induced wave fields in the South China Sea; was discussed. In detail; the key parameters of the JONSWAP spectrum model; such as the Phillips constant; spectral width parameter; peak-enhancement factor, and high frequency tail decay; were investigated in the context of finding suitable values.

Wind Profiles and Wave Spectra for Potential Wind Farms in South China Sea. Part I: Wind Speed Profile Model

With the setting of wind energy harvesting moving from coastal waters to deep waters, the South China Sea has been deemed to offer great potential for the construction of floating wind farms thanks to the abundance of wind energy resources. An engineering model describing the wind profiles and wave spectra specific to the South China Sea conditions, which is the precondition for offshore wind farm construction, has, however, not yet been proposed. In the present study, a series of numerical simulations have been conducted using the Weather Forecast and Research model. Through analyzing the wind and wave information extracted from the numerical simulation results, engineering models to calculate vertical profiles of wind speeds and wave spectra have been postulated. While the present paper focuses on the wind profile model, a companion paper articulates the wave spectrum model. For wind profiles under typhoon conditions, the power-law and log-law models have been found applicable under the condition that the Hellmann exponent α or the friction velocity u * are modified to vary with the wind strength. For wind profiles under non-typhoon conditions, the log-law model is revised to take into consideration the influence of the atmospheric stability.

The Active Element Patterns of a Finite Array-Space Wave and Leaky Wave Perspective

The active element patterns (AEPs) of a finite array of parallel-plate waveguides are studied. It is shown that an excited element in array environment produces a number of space and leaky wave modes (but no surface wave mode) that can be expressed in terms of branch-cut integrals and residues, respectively, in the complex wavenumber plane. The dominant space wave mode has a very sharp radiation pattern with large phase variation near its peak causing constructive and destructive interferences with the primary pattern of the excited element within a small angular region. As a result, the AEP exhibits sharp dips that are very close to the local peaks. The number and the extent of excited modes that cause interference depend on the location of the excited element in a finite array. Consequently, the shape of the AEP changes with the element location. It is found that an array generates forward and backward waves on its aperture, and for element spacing less than one wavelength, the backward wave dominates. As a result, the AEP for the left-edge element has a dip at the left-hand side of the boresight and the beam tilts toward the left. For large element spacing, multiple dips may occur on both sides. The present analysis explains several interesting characteristics of finite and infinite arrays and very closely agrees with the plane wave spectrum model.

Validation of naval vessel spectral fatigue analysis using full-scale measurements

Full-scale measurements taken during a naval vessel sea trial are compared to calculated stress spectra and associated fatigue damage estimates using linear frequency-domain hydrodynamic and finite element analysis codes. Results were generated using four different wave spectrum models to better understand their influence on fatigue damage estimates. The results using measured two-dimensional wave spectra were most similar to measurements, but the agreement with measurements for each of the spectrum models was acceptable. Significant improvement in calculation accuracy was observed when adding a spreading function to longcrested wave spectra. The use of ±90° as the extent of wave spreading gave results with minimal differences from the use of measured spreading angles. The agreement between measurements and calculations using longcrested wave spectra with a constant spreading function is fortunate because available seaway data are commonly limited to wave height and period combinations. The results of this study suggest the spectral fatigue analysis method can be used to generate reasonable estimates of stress spectra and resulting fatigue damage for a naval vessel.

An appropriate unidirectional wave spectrum model for the Strait of Hormuz

The objective of this paper is to introduce an appropriate unidirectional wave spectrum model for the Strait of Hormuz. The research is focused on assessing performance of standard wave spectrum models in the region. By evaluating such models based on valuable measurement data recently published, the calibration procedure has been conducted on such standard models to reach a better concordance between a modified standard spectral model and observed field spectra. The calibration is performed initially with respect to four distinct directions related to four available measurement stations. So, it results in four sets of coefficients for a nominated model. Next, it is continued to reach just one model insensitive to directions. Results clearly showed that the International Towing Tank Conference (ITTC) model is more appropriate than Joint North Sea Wave Project (JONSWAP) and Pierson and Moskowitz (PM) models in this area, even without any calibration. However, modifications have been successful on improving the conformity of the model.

너울성파랑 정의를 위한 파랑스펙트럼의 형상모수 특성 분석

In the present study, the characteristics of spectral peakedness parameter Qp, bandwidth parameter e, and spectral width parameter ν were analyzed as a first step to define the swell waves quantitatively. For the analysis, the joint probability density function of significant wave heights and peak periods were newly developed. The MCMC(Markov Chain Monte Carlo) simulations have been performed to generate the significant wave heights and peak periods from the developed probability density functions. Applying the simulated significant wave heights and peak periods to the theoretical wave spectrum models, the spectral shapes parameters were obtained and analyzed. Among the spectral shape parameters, only the spectral peakedness parameter Qp, is shown to be independent with the significant wave height and peak wave period. It also best represents the peakedness of the spectral shape, and henceforth Qp should be used to define the swell waves with a wave period. For the field verification of the results, wave data obtained from Hupo port and Ulleungdo were analyzed and results showed the same trend with the MCMC simulation results.

Multiple Model Adaptive Nonlinear Observer of Dynamic Positioning Ship

Considering the filtering problem of dynamic positioning (DP) ship for the slowly varying sea state, a multiple model adaptive observer (MMAO) for dynamic positioning ship is presented. The MMAO consists of a bank of nonlinear subobserver and a dynamic weighting signal generator, in which each sub-observer is designed based on different peak frequency of wave spectrum model. To improve the performance of the observer, subobserver using the measurement of position, velocity, and acceleration is used to update the estimated velocity of ship. The observer parameters are optimized using particle swarm optimization (PSO). Finally, the method is verified effective by the computer simulation.

Study on effect of wind waves on radar echoes in atmosphere duct oversea

The Wen's wave spectrum model is adopted to describe the rough sea surface, and the relation between wind and ocean waves using sea wave spectrum theory is derived. The improved discrete mixed Fourier transform algorithm and the modified rader scattering coefficient model are used to calculate radio propagation loss and radar cross section respectively. On this basis, the influence of wind waves on radar echoes in the environment of atmosphere ducts is analysed by using numerical calculations. The results show that the influences of wind on propagation loss at different heights are different; wich respect to the propagation loss, rader scattering coefficient influenced by waves of factors is large, which results in large change in the radar echo power.

An Advanced Roughness Spectrum for Computing Microwave L-Band Emissivity in Sea Surface Salinity Retrieval

The influence of sea surface roughness dominates the error budget of satellite sea surface salinity (SSS) retrieval from L-band radiometers; thus, accurate roughness correction models are needed. Semi-analytical SSS correction models, as used in the soil moisture and ocean salinity satellite Level 2 processor, combine an emissivity model with an ocean wave spectrum model that describes the rough sea surface. Previous findings indicate that the errors contributed by ocean roughness model exceed those of the emissivity model. In this paper, we compare the performance of three well-known spectrum models and a new one as inputs to the small slope approximation/small perturbation method emissivity model. The new spectrum model, which is developed from empirical parameterization of short water wave spectra measured in the ocean and incorporates swell effects, performs very well in comparison with the other spectrum models, and we propose its consideration for future SSS roughness correction models.