Directional Ocean Wave Spectra Research Articles

Ocean surface waves in Hurricane Ike (2008) and Superstorm Sandy (2012): Coupled model predictions and observations

Forecasting hurricane impacts of extreme winds and flooding requires accurate prediction of hurricane structure and storm-induced ocean surface waves days in advance. The waves are complex, especially near landfall when the hurricane winds and water depth varies significantly and the surface waves refract, shoal and dissipate. In this study, we examine the spatial structure, magnitude, and directional spectrum of hurricane-induced ocean waves using a high resolution, fully coupled atmosphere–wave–ocean model and observations. The coupled model predictions of ocean surface waves in Hurricane Ike (2008) over the Gulf of Mexico and Superstorm Sandy (2012) in the northeastern Atlantic and coastal region are evaluated with the NDBC buoy and satellite altimeter observations. Although there are characteristics that are general to ocean waves in both hurricanes as documented in previous studies, wave fields in Ike and Sandy possess unique properties due mostly to the distinct wind fields and coastal bathymetry in the two storms. Several processes are found to significantly modulate hurricane surface waves near landfall. First, the phase speed and group velocities decrease as the waves become shorter and steeper in shallow water, effectively increasing surface roughness and wind stress. Second, the bottom-induced refraction acts to turn the waves toward the coast, increasing the misalignment between the wind and waves. Third, as the hurricane translates over land, the left side of the storm center is characterized by offshore winds over very short fetch, which opposes incoming swell. Landfalling hurricanes produce broader wave spectra overall than that of the open ocean. The front-left quadrant is most complex, where the combination of windsea, swell propagating against the wind, increasing wind–wave stress, and interaction with the coastal topography requires a fully coupled model to meet these challenges in hurricane wave and surge prediction.

Development of HF radar inversion algorithm for spectrum estimation (HIAS)

AbstractA method for estimating ocean wave directional spectra using an HF (high‐frequency) ocean radar was developed. This method represents the development of work conducted in previous studies. In the present method, ocean wave directional spectra are estimated on polar coordinates whose center is the radar position, while spectra are estimated on regular grids. This method can be applied to both single and multiple radar cases. The area for wave estimation is more flexible than that of the previous method. As the signal to noise (SN) ratios of Doppler spectra are critical for wave estimation, we develop a method to exclude low SN ratio Doppler spectra. The validity of the method is demonstrated by comparing results with in situ observed wave data that it would be impossible to estimate by the methods of other groups.

Simulation of Ocean Wave-Generated Magnetic Field Disturbance Observed above Sea-Surface Based on Directional Spectrum

Ocean wave have a magnetic field disturbance, caused by the motional induction of sea water moving in the steady main field of Earth. Mass experiment indicates ocean wave-generated magnetic field disturbance can be a major limitation on the performance of airborne magnetic anomaly detection. To check the character of such disturbance observed above sea-surface, a harmonic ocean wave-generated magnetic field disturbance mathematical model based on Weavers monochromatic wave-generated magnetic field model and ocean wave directional spectrum is proposed. Algorithm is presented for real-time simulation of ocean wave-generated magnetic field disturbance corresponding to the proposed mathematical model. Numerical simulations of ocean wave-generated magnetic field disturbance are sampled above sea-surface by a stationary magnetometer and an airborne magnetometer moving steadily along a rectilinear path. Spectrum analysis of the samples is performed. Simulations results indicate that the proposed harmonic ocean wave magnetic field disturbance mathematical model can well-simulate the real sea conditions. Numerical simulations also reveal that there is a Doppler frequency shift with the increase of magnetometer flight speed. Moreover, energy of the magnetic field disturbance is more dispersed and frequency band is wider with the increase of magnetometer flight speed.

Dynamical partitioning of directional ocean wave spectra

Directional wave spectra generally exhibit several peaks due to the coexistence of wind sea generated by local wind conditions and swells originating from distant weather systems. This paper proposes a new algorithm for partitioning such spectra and retrieving the various systems which compose a complex sea-state. It is based on a sequential Monte-Carlo algorithm which allows to follow the time evolution of the various systems. The proposed methodology is validated on both synthetic and real spectra and the results are compared with a method commonly used in the literature.

Ocean wave directional spectrum measurement using microwave coherent radar with six antennas

Ocean wave directional spectrum measurement using microwave coherent radar with six antennas

VERIFICATION OF A MODIFIED BAYESIAN METHOD FOR ESTIMATING DIRECTIONAL WAVE SPECTRA FROM HF RADAR

A Modified Bayesian Method (MBM) for estimating directional wave spectra from Doppler spectra obtained by HF radar is examined using field data which were employed in the verification of Bayesian Method (BM). Applicability, validity and accuracy of the MBM are demonstrated compared with the directional wave spectra estimated by BM and observed by buoy acquired from the reliable field data obtained from Surface Current and Wave Variability Experiments (SCAWVEX) project. The necessary conditions of the Doppler spectral components to be used to estimate a reliable directional spectrum are correspondingly estimated by BM. The results clearly demonstrate that directional wave spectra can be estimated by MBM on the basis of Doppler spectra. In addition, though BM shows very time consuming in computations, BM is more robust against the presence of noise than MBM.
 
 
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Satellite-based RAR performance simulation for measuring directional ocean wave spectrum based on SAR inversion spectrum

Some missions have been carried out to measure wave directional spectrum by synthetic aperture radar (SAR) and airborne real aperture radar (RAR) at a low incidence. Both them have their own advantages and limitations. Scientists hope that SAR and satellite-based RAR can complement each other for the research on wave properties in the future. For this study, the authors aim to simulate the satellite-based RAR system to validate performance for measuring the directional wave spectrum. The principal measurements are introduced and the simulation methods based on the one developed by Hauser are adopted and slightly modified. To enhance the authenticity of input spectrum and the wave spectrum measuring consistency for SAR and satellite-based RAR, the wave height spectrum inversed from Envisat ASAR data by cross spectrum technology is used as the input spectrum of the simulation system. In the process of simulation, the sea surface, backscattering signal, modulation spectrum and the estimated wave height spectrum are simulated in each look direction. Directional wave spectrum are measured based on the simulated observations from 0° to 360°. From the estimated wave spectrum, it has an 180° ambiguity like SAR, but it has no special high wave number cut off in all the direction. Finally, the estimated spectrum is compared with the input one in terms of the dominant wave wavelength, direction and SWH and the results are promising. The simulation shows that satellite-based RAR should be capable of measuring the directional wave properties. Moreover, it indicates satellite-based RAR basically can measure waves that SAR can measure.

Monte Carlo Simulation for SAR Ocean Wave Directional Spectrum

Using the Longuet-Higgins linear model of ocean wave and JONSWAP spectrum,the ocean wave directional spectrum is represented.Supposing bragg scattering,the mapping transform between ocean spectrum and SAR imagery spectrum is deduced,which is adapted to the linear wave-SAR imaging scope.Using Monte Carlo method,we can generate ocean direction spectrum which have characteristics of random.For Gaussian sea surface,the computation efficiency of the method is moderated.The simulation results are shows that there are distortions,split spectrum in range and the azimuth displacement between ocean spectrum and SAR imagery spectrum.

A simplified model of frequency distortion in ocean acoustic signals by multiple interactions with a moving ocean surface and its use in oceanographic inversions.

Received omnidirectional spectra of low frequency narrowband tones measured in a shallow ocean waveguide exhibit Doppler-shifted sidebands at frequencies whose offsets are integer multiples of the dominant surface wave frequencies. These observations suggest that higher order scattering is important. However, higher-order perturbation theory involving only a single surface interaction does not predict the observed relative sideband levels. In particular, the higher order sidebands were often observed to increase in relative level to the main spectral peak during smaller surface wave, and, therefore, smaller kh, conditions. A simplified model is presented that simulates the surface wave-induced frequency distortions as path-length modulation caused by the vertical motions of the surface. The model incorporates multiple interactions with the moving surface, and quantitatively predicts the effects on the received spectra of the spatial coherence of the surface waves along the propagation path. The model results are identical to those from higher order perturbation with a single interaction. The simplified nature of this model allows it to be readily used to invert for various properties of the ocean surface wave directional spectrum. [Work supported by ONR, Code 321(US).]

Kalman filtering of vessel motions for ocean wave directional spectrum estimation

This paper proposes a high-speed iterative procedure for estimating the ocean wave directional spectrum from vessel motion data. It uses as input data, the measurements from motion sensors that are commonly available on dynamically positioned vessels and which may easily be installed on any ship. Because the necessary sensors are relatively inexpensive or may already be installed, it becomes an ideal solution to provide initial estimates to offline estimation procedures and to give spectral updates under quickly changing weather conditions. The Kalman filtering algorithm, for iterative harmonic detection, and frequency domain vessel response data are used in the estimation procedure. The results and conclusions are still based on synthesized data, but very promising.

Extraction of Ocean Wave Spectra From Simulated Noisy Bistatic High-Frequency Radar Data

An algorithm is developed for the inversion of bistatic high-frequency (HF) radar sea echo to give the nondirectional wave spectrum. The bistatic HF radar second-order cross section of patch scattering, consisting of a combination of four Fredholm-type integral equations, contains a nonlinear product of ocean wave directional spectrum factors. The energy inside the first-order cross section is used to normalize this integrand. The unknown ocean wave spectrum is represented by a truncated Fourier series. The integral equation is then converted to a matrix equation and a singular value decomposition (SVD) method is invoked to pseudoinvert the kernel matrix. The new algorithm is verified with simulated radar Doppler spectrum for varying water depths, wind velocities, and radar operating frequencies. To make the simulation more realistic, zero-mean Gaussian noise from external sources is also taken into account

Ocean Wave Directional Spectra Estimation from an HF Ocean Radar with a Single Antenna Array: Methodology

Abstract A method to estimate ocean wave directional spectra using a high-frequency (HF) ocean radar was developed. The governing equations of wave spectra are integral equations of first- and second-order radar cross sections, the wave energy balance equation, and the continuity equation of surface winds. The parameterization of the source function is the same as that in WAM. Furthermore, the method uses the constraints that wave spectral values are smooth in both wave frequency and direction and that the propagation terms are small. The unknowns to be estimated are surface wind vectors at radial grids whose centers are the radar position, and wave spectral values at radial and wave frequency–direction grids. The governing equations are discretized in the radial and wave frequency–direction grids and are converted into a nonlinear minimization problem. Identical twin experiments showed that the present method can estimate wave spectra and dynamically extrapolate wave spectra, even in an inhomogeneous wave field.

Ocean wave directional spectra estimation from an HF ocean radar with a single antenna array: Observation

A method of estimating ocean wave directional spectra using a]high‐frequency (HF) radar with a single antenna array was applied to actual ocean data. This method incorporates the wave energy balance equation and the continuity equation of wind vectors into the inversion method to solve the integral equation which relates a Doppler spectrum to wave spectra. This method uses dynamic extrapolation to estimate wave spectra at positions where the signal‐to‐noise (SN) ratio in Doppler spectra is not high. The agreement of wave heights with in situ observation is good. Additionally, there is a correlation between radar‐estimated sea surface winds and winds near the HF radar observation area. The method under consideration was found to be able to estimate wave directional spectra in swell conditions.

Simultaneous Measurement of Ocean Winds and Waves with an Airborne Coherent Real Aperture Radar

AbstractA coherent, X-band airborne radar has been developed to measure wind speed and direction simultaneously with directional wave spectra on the ocean. The coherent real aperture radar (CORAR) measures received power, mean Doppler shifts, and mean Doppler bandwidths from small-resolution cells on the ocean surface and converts them into measurements of winds and waves. The system operates with two sets of antennas, one rotating and one looking to the side of the airplane. The rotating antennas yield neutral wind vectors at a height of 10 m above the ocean surface using a scatterometer model function to relate measured cross sections to wind speed and direction. The side-looking antennas produce maps of normalized radar cross section and line-of-sight velocity from which directional ocean wave spectra may be obtained. Capabilities of CORAR for wind and wave measurement are illustrated using data taken during the Shoaling Waves Experiment (SHOWEX) sponsored by the Office of Naval Research. Wind vectors measured by CORAR agree well with those measured by nearby buoys. Directional wave spectra obtained by CORAR also agree with buoy measurements and illustrate that offshore winds can produce dominant waves at an angle to the wind vector that are in good agreement with the measurements. The best agreement is produced using the Joint North Sea Wave Project (JONSWAP) parameterizations of the development of wave height and period with fetch.

An investigation of altimeter sea state bias theories

Two theoretical formulations of the sea state bias (SSB) by Srokosz [1986] (hereafter S86) and Elfouhaily et al. [2000] (hereafter E00) are applied to directional ocean wave spectra from WAM and from NDBC moored buoys collocated with Topex altimeter data. S86 SSB computations obtained for WAM with idealized ocean current fields reveal a quasi‐linear relationship between the SSB coefficient and the r.m.s. ocean slope, which remains valid for a wide range of wind/wave/current conditions. The SSB coefficient is shown to be better parameterized in terms of slope, instead of the significant wave height and wind speed presently used in empirical models. The theoretical SSB for the buoys' 2‐D wave spectra are compared with estimates from five recent empirical SSB models calculated from the collocated Topex data. The magnitude of the E00 SSB shows a strong sensitivity to the choice of high frequency tail model used to extend the 2‐D wave spectra. We find that the E00 theory can adequately model the radar frequency dependence of the SSB given a suitable choice of high frequency tail. However, the E00 theory is found to systematically underestimate the magnitude of the SSB coefficient with respect to empirical SSB models. In contrast, the long‐waves‐only S86 theory displays good agreement with the empirical SSB estimates. Thus our calculations suggest that the sea state bias may be primarily governed by the slope of long gravity waves, presumably through its well‐documented influence on the modulation of short waves, as also suggested by recent empirical findings.

Polarisation orientation angle measurements of ocean internal waves and current fronts using polarimetric SAR

Recent studies have shown that polarimetric synthetic aperture radar (POLSAR) data may be used to measure parameters such as bare surface roughness. Polarisation orientation angles, derived from POLSAR data, can be utilised to produce estimates of topography. Orientation angles have been used for SAR data compensation, in areas of rugged terrain, to ensure accurate estimation of geophysical parameters such as biomass and soil moisture. Orientation angles have also recently been investigated for use in measuring directional ocean wave spectra. Studies of these ocean features are conventionally done by measuring feature-related microwave backscatter intensity perturbations. In the work presented, a new approach is taken. Investigations have been made of changes in the polarisation orientation angle caused by ocean wave–current interaction features. The study uses airborne POLSAR data obtained in the New York Bight and in the Gulf Stream, east of Cape Hatteras. A model is used to determine the parametric dependencies of the orientation angle on internal wave current, wind–wave direction and wind–wave speed. An empirical relation is proposed to relate orientation angle perturbations to the underlying internal wave current strength.

SWIMSAT: A Real-Aperture Radar to Measure Directional Spectra of Ocean Waves from Space—Main Characteristics and Performance Simulation

Abstract The project SWIMSAT aims to measure the directional spectra of waves from space using a real-aperture radar with a low-incidence, conical-scanning beam. This system’s design is based on airborne versions developed in France and the United States. In this paper, the authors present the satellite measurement principle and instruments. For this study, the authors developed a simulation method to analyze the sensitivity of wave spectra, taking into account radar observation conditions (spatial resolution, signal-to-noise ratio, integration time, etc.) and inversion processing parameters (noise level and range displacements during temporal integration). The simulation method and results are presented in this paper. The study enabled validation and refinement of the satellite concept. The simulations show that in the chosen configuration, SWIMSAT is capable of measuring wave spectral properties in wind–sea conditions (at dominant wavelengths over approximately 70 m) and swell conditions (at significant...

Ocean wave extraction from RADARSAT synthetic aperture radar inter-look image cross-spectra

This study is concerned with the extraction of directional ocean wave spectra from synthetic aperture radar (SAR) image spectra. The statistical estimation problem underlying the wave-SAR inverse problem is examined in detail in order to properly quantify the wave information content of SAR. As a concrete focus, a data set is considered comprising six RADARSAT SAR images co-located with a directional wave buoy off the east coast of Canada. These SAR data are transformed into inter-look image cross-spectra based on two looks at the same ocean scene separated by 0.4 s. The general problem of wave extraction from SAR is cast in terms of a statistical estimation problem that includes the observed SAR spectra, the wave-SAR transform, and prior spectral wave information. The central role of the weighting functions (inverse of the error covariances) is demonstrated, as well as the consequence of approximate (based on the quasilinear wave-SAR transform) versus exact linearizations on the convergence properties of the algorithm. Error estimates are derived and discussed. This statistical framework is applied to the extraction of spectral wave information from observed RADARSAT SAR image cross-spectra. A modified wave-SAR transform is used to account for case-specific geophysical and imaging effects. Analysis of the residual error of simulated and observed SAR spectra motivates a canonical form for the SAR observation error covariance. Wave estimates are then extracted from the SAR spectra, including wavenumber dependent error estimates and explicit identification of spectral null spaces where the SAR contains no wave information. Band-limited SAR wave information is also combined with prior (buoy) spectral wave estimates through parameterization of the wave spectral shape and use of regularization.

Limits to the Inversion of HF Radar Backscatter for Ocean Wave Measurement

Abstract The power spectrum of backscatter from the ocean surface at HF radio frequencies is characterized by two large peaks called the first-order Bragg peaks. These are surrounded by a continuum due to second-order effects. The power spectrum can be described in low to moderate sea states by a nonlinear integral equation relating it to the ocean wave directional spectrum. Inverting this equation provides an estimate of the directional spectrum. A number of inversion methods have been published. In this paper, the Wyatt method is discussed. This method uses the part of the backscatter power spectrum that surrounds the larger Bragg peak. An extension of the method to include the spectrum around the weaker peak is discussed, and some improvements in the solution are demonstrated. Until recently, all published work in this area concerned solutions to a linearized version of the equation. The second extension presented here tackles the nonlinear problem but points out the limitations of the approach and sho...

Directional spectrum of ocean waves from array measurements using phase/time/path difference methods

Wave direction has for the first time been consistently, accurately and unambiguously evaluated from array measurements using the phase/time/path difference (PTPD) methods of Esteva in case of polygonal arrays and Borgman in case of linear arrays. We have used time series measurements of water surface elevation at a 15-gauge polygonal array, in ≅8 m water depth, operational at the CERC's Field Research Facility at Duck, North Carolina, USA. Two modifications have been made in the methodology. One modification is that we use the true phase instead of the apparent phase, the other modification being that estimates of wave direction are registered only if the relevant gauges in the array are coherent at 0.01 significance level. PTPD methods assume that in a spectral frequency band the waves approach from a single direction, and are simple, expedient and provide redundant estimates of wave direction. Using Esteva's method with the above modifications, we found that at Duck: (i) the directions of swell and surf beat, when energetic swell is present, conform to the schematic diagram of surf beat generation given by Herbers et al., (ii) surf beat of remote origin occurs when the significant wave height, H mo, falls below 0.41 m, (iii) the surf beat of remote origin is not normally incident at the shore contrary to Herbers et al. In fact we found that the surf beat of remote origin is incident at angles in excess of 45° with respect to the shore normal, and (iv) the surf beat of remote origin is largely trans-oceanic in origin.