Nonlinear influences on ocean waves observed by X-band radar

The purpose of this study is to discuss the influence of signal nonlinearity upon X-band radar observations. A method for estimating the degree of nonlinearity by bispectral analysis was applied and discussed. We found that bispectral analyses from spatial radar backscatter series are similar to results obtained from water level time series. In addition, the average nonlinear degree from radar backscatter is related to wind speed. The accuracy of wave observations derived by consideration of the nonlinear effect from radar backscatter was also investigated. The estimated error in wave height from the radar data is also related to the degree of nonlinearity. In order to improve accuracy, the modulation transfer function method was applied in order to eliminate the influence of nonlinearity.     

Nonlinear ocean internal waves observed by multifrequency synthetic aperture radar

A numerical model which consists of the Korteweg-de Vries (KdV) equation, the action balance equation and the radar backscat- tering model is developed to simulate the frequency dependence of synthetic aperture radar (SAR) remote sensing of nonlinear o- cean internal waves. Muhifrequency data collected by NASA SIR - C SAR and NASA JPL AIRSAR are used as comparison. Case studies show that the results of simulation agree well with the results of SAR data.     

Models of radar imaging of the ocean surface waves

A number of models which would explain ocean wave imagery taken with a synthetic aperture imaging radar are analyzed analytically and numerically. Actual radar imagery is used to support some conclusions. The models considered correspond to three sources of radar backscatter cross section modulation: tilt modulation, roughness variation, and the wave orbital velocity. The effect of the temporal changes of the surface structure, parametric interactions, and the resulting distortions are discussed.     

On the synthetic aperture radar imaging of ocean surface waves

A process of synthetic aperture radar imaging of ocean surface waves is considered on the basis of the two-scale model of microwave scattering by a disturbed sea surface. Analytical expressions are obtained to relate characteristics of a large-scale wave image, averaged over an ensemble of realizations of the small-scale ripple, with the wave, radar, and viewing scheme as parameters. It is shown that the wave image would be defocused as an image of a target moving in the along-track direction with a speed equal to a half of the wave phase speed projection on the line of flight. The defocusing magnitude was measured experimentally for the ocean swells images, obtained with an airborneS-band radar, and the results are found to be in satisfactory agreement with the model prediction.     

Synthetic aperture radar imaging of ocean waves during the marineland experiment

X- andL-band simultaneously obtained synthetic aperture radar (SAR) data of ocean gravity waves collected during the Marineland Experiment were analyzed using wave contrast measurements. The Marineland data collected in 1975 represents a unique historical data set for testing still-evolving theoretical models of the SAR ocean wave imaging process. The wave contrast measurements referred to are direct measurements of the backscatter variation between wave crests and troughs. These modulation depth measurements, which are indicators of wave detectability, were made as a function of: a) the settings used in processing the SAR signal histories to partially account for wave motion; b) wave propagation direction with respect to radar look direction for bothX- andL-band SAR data; c) SAR resolution; and d) number of coherent looks. The contrast measurements indicated that ocean waves imaged by a SAR are most discernible whenX-band frequency is used (as compared toL-band), and when the ocean waves are traveling in the range direction. Ocean waves can be detected by bothX- andL-band SAR, provided that the radar surface resolution is small compared to the ocean wavelength (at least 1/4 of the ocean wavelength is indicated by this work). Finally, wave detection withL-band SAR can be improved by adjusting the focal distance and rotation of the cylindrical telescope in the SAR optical processor to account for wave motion. The latter adjustments are found to be proportional to a value that is near the wave phase velocity.     

Dual frequency correlation radar measurements of the height statistics of ocean waves

A radar technique has been developed for measuring the statistical height properties of a random rough surface. This method is being applied to the problem of measuring the significant wave height and probability density function of ocean waves from an aircraft or spacecraft. Earlier theoretical and laboratory results have been extended to define the requirements and performance limitations of flight systems. Some details of the current airborne radar system are discussed and results obtained on several experimental missions are presented and interpreted.     

A minimum variance unbiased estimator for ocean surface currentsbased on multifrequency microwave radar observations

This paper presents a minimum variance unbiased (MVU) estimator for estimating an ocean surface current using the multifrequency microwave radar technique. In this technique the current information is obtained by finding the difference between the measured phase velocities of some specific surface gravity waves and the phase velocities calculated from the dispersion relation for still water. By defining the problem as a linear estimation problem, we develop an unbiased estimator for the current component along the radar look direction, which has a variance that is inversely proportional to the sum of the squared wavenumbers of the gravity waves used in the measurements. We also study the performance of an MVU vector estimator based on radar observations along two directions. Our analysis shows that the confidence region of this estimator has the shape of an elongated ellipse with semi-axes and orientation which are dependent on the angle between the observation directions, but independent on the true current vector. Furthermore, the theoretical models are thoroughly tested using both simulated and real radar data, and these tests show very good agreement with the model predictions     

Nonlinear response of membranes to ocean waves using boundary and finite elements

The behavior of a highly deformable membrane to ocean waves was studied by coupling a nonlinear boundary element model of the fluid domain to a nonlinear finite element model of the membrane. The hydrodynamic loadings induced by water waves are computed assuming large body hydrodynamics and ideal fluid flow and then solving the transient diffraction/radiation problem. Either linear waves or finite amplitude waves can be assumed in the model and thus the nonlinear kinematic and dynamic free surface boundary conditions are solved iteratively. The nonlinear nature of the boundary condition requires a time domain solution. To implicitly include time in the governing field equation, Volterra's method was used. The approach is the same as the typical boundary element method for a fluid domain where the governing field equation is the starting point. The difference is that in Volterra's method the time derivative of the governing field equation becomes the starting point.The boundary element model was then coupled through an iterative process to a finite element model of membrane structures. The coupled model predicts the nonlinear interaction of nonlinear water waves with highly deformable bodies. To verify the coupled model a large scale test was conducted in the OH Hinsdale wave Research Laboratory at Oregon State University on a 3-ft-diameter fabric cylinder submerged in the wave tank. The model data verified the numerical prediction of the structure displacements and of the changes in the wave field.The boundary element model is an ideal modeling technique for modeling the fluid domain when the governing field equations is the Laplace equation. In this case the nonlinear boundary element model was coupled with a finite element model of membrane structures, but the model could have been coupled with other finite element models of more rigid structures, such as a pontoon floating breakwater.     

Modelling ocean waves in ice-covered seas

Over the past decade there has been a rapid growth of interest in wave propagation through ice covers. This paper summarizes the author’s observation of the modeling efforts on this topic. Models can be theory-based, data-driven, or a combination of the two. A pure data-driven model relies on a large amount of observations and is only becoming available recently. Theory-based models on the other hand have a long history. They are always a simplified version of the reality. As our knowledge grows, theories become more complicated. A theory for waves-in-ice that captures all possible processes does not exist. However, when integrated with observation through calibration, these combined theory + data-based models may be used with some confidence. In this paper, different models, their basic concepts, their calibration and validation are discussed. The present theory-based models do not have the correct spectral attenuation trend as observed from field or laboratory experiments. Hence, through calibration they may fit different parts of the wave spectra but not all. Pure data-driven models can reproduce the correct trend, but its dependability outside the situation where the data are collected is uncertain. In addition to offering tools to forecast waves-in-ice, these model building and validating efforts point to missing mechanisms that should be carefully studied. Despite the many challenges towards building a satisfactory general waves-in-ice model, significant progress has been made for models that work reasonably well in the marginal ice zone. We anticipate much more data will become available in the coming years to help us improve the existing models.     

Non-hydrostatic Kelvin waves in the ocean

A theory of the coastal Kelvin wave is presented in which the pressure is assumed not to be hydrostatic. The results show that the non-hydrostatic Kelvin wave is dispersive and that the e^–1 decay distance of the wave amplitude from the coast decreases as the wave length becomes shorter. Similar conclusions can be drawn on the equatorial Kelvin wave.     

Utilization of the energy in ocean waves

The characteristics of ocean wind waves place certain constraints upon devices designed to convert their energy to a useful form. Here we consider the nature of these constraints and the theoretical analysis of a wave power generator that conforms to the design criteria. We also present the results of field tests with several models of the wave power generator. The experimental results support the theory and indicate that such a wave pump is suitable for power generation in a variety of circumstances.     

High-frequency radar measurements of the ocean wave-directionalspectrum

Measurements of the ocean wave directional spectrum using a dual, high-frequency (HF) radar system are presented. A model-fitting technique is used to obtain wave measurements from the radar Doppler spectra. Over 100 h of data, collected NURWEC2 (Netherlands-UK Radar Wavebuoy Experimental Comparison), have been compared with measurements using a WAVEC directional wave buoy. The amplitude and directional characteristics of long-wave components at frequencies of 0.07-0.1 Hz in general show good agreement. Reasonable estimates of the directional spectrum across the whole frequency range are obtained when the assumptions of the model-fitting technique are appropriate. Remaining problems in radar measurement and difficulties in assessing accuracy are discussed     

On the growth of ocean waves

The availability of 10 h of continuous, uninterrupted field measurements of wind waves recorded in the western Pacific and containing a complete wave growth episode, has provided a distinct opportunity for us to make a novel, unprecedented examination of detailed wave growth processes. We found that the significance of the size of data used in the measurement, which can only be addressed with continuous and uninterrupted measurements, reflected the ineptness of the conventional approach toward further detailed understanding of realistic wave growth processes, as the conventional 20 min data size essentially stamped out any dynamics with time scale below 20 min. While our conventional understanding and modeling were generally operative and useful, they left no real vestige on time localized mechanisms such as wave grouping or wave breaking processes all with time scales much less than 20 min.     

On ensemble prediction of ocean waves

The numerical ensemble prediction is a well accepted method for improving the performance of atmospheric models. In the context of ocean wave modeling little has been researched or documented about this technique. An essential study of the method of ensemble prediction applied to deep water waves has been carried out. A framework is defined for obtaining perturbations of the directional wave spectra and for employing an ensemble of wind fields generated by an atmospheric model. The third-generation global wave model WAM is used with real atmospheric conditions to investigate the effect on wave predictions of perturbed initial conditions and atmospheric forcing. Due to spectral shape stabilisation, perturbing wave initial conditions has limited utility in ensemble prediction. However, the members could be used in wave data assimilation schemes in an interactive way. Using ensembles of the atmospheric condition can generate diverging solutions, justifying the ensemble procedure by itself. In the cases studied, it is observed that the ensemble mean outperformed the other members. The solution behaviour suggests using a lower-order approximation of the model to generate ensemble members with less computational cost.     

Generation of internal waves in a three-layer ocean

Within the framework of the linear theory of long waves taking into account the action of the Coriolis force, we solve the problem of generation of internal waves by a barotropic tide impinging on a bottom irregularity of the sea-ridge type. The cross section of the ridge is assumed to be rectangular and the stratification of the ocean is regarded as stepwise with two thermoclines (three-layer model). We study the dependences of the characteristics of generated waves on the parameters of stratification and the period of the impinging barotropic tide. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Simulation-based evaluations of HF radar ocean current algorithms

A computer simulation is used to analyze errors in high-frequency (HF) radar ocean surface current measurements. Two pointing algorithms used for current extraction, a direction finding approach using MUltiple SIgnal Characterization (MUSIC) developed by Schmidt (1986), and conventional beam forming, are compared in terms of the effect of variations in sea state parameters on current measurement error. The radar system parameters used in the simulation were taken from the University of Michigan's multi-frequency coastal radar (MCR), which operates on four frequencies from 4.8 to 21.8 MHz and employs an eight-element linear phased array for its receive antenna. Results show MUSIC direction finding to be applicable to phased array systems and to have a better sensitivity to sharp current features, but larger random error than traditional beam forming methods. Also, for cases where beam forming errors are dominated by beam width or low signal to noise ratio, results show MUSIC to be a viable alternative to beam forming     

Instability analysis of three-dimensional ocean shear waves

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