The nonlinear evolution of deep-water wave groups, which are initiated by unstable three-wave systems, have been observed in a large wave tank (50 m long, 4.2 m wide, 2.1 m deep), equipped with a programmable, high-resolution wave generator. A large number of experiments were conducted (over 80 cases) for waves 1.0-4.0 m long, initial steepness ∈ = 0.10-0.28, and normalized sideband frequency differences, δω/∈ω, 0.2-1.4. Using an array of eight high-resolution wave wires distributed in range (up to 43 m fetch), spectral evolution was studied in detail including the effect of background disturbances on the evolution. Minimizing those, new observations were made which extend the pioneering work of Lake et al. (1977) and of Melville (1982). Foremost, near recurrence without downshifting was observed without breaking, despite a significant but reversible energy transfer to the lower sideband at peak modulation; complete recurrence was prevented by the spreading of discretized energy to higher frequencies. Strong breaking was found to increase the transfer of energy from the higher to the lower sideband and to render that transfer irreversible. The end state of the evolution following strong breaking is an effective downshifting of the spectral energy, where the lower and the carrier wave amplitudes nearly coincide; the further evolution of this almost two-wave system was not studied here. Breaking during strong modulation was observed not only for the fastest growing initial condition, but over a wide parameter range. An explanation of the sideband behaviour in both the breaking and non-breaking case was given based on wave energy and momentum considerations, including the separate effects of energy and momentum loss due to breaking, and transfer to discretized higher frequencies throughout the spectra. Attention was drawn to the latter, which was almost universally observed.

Laboratory observations of wave group evolution, including breaking effects

The European Space Agency (ESA) ERS-1 and ERS-2 C band VV polarization active microwave instrument (AMI) offers the unique ability to combine interlaced wind scatterometer and high-resolution synthetic aperture radar (SAR) wave mode imagettes. In this study, more than 2000 imagettes were considered. Eadi imagette has been statistically analyzed in comparison with normalized radar cross-section (NRCS) measurements from the scatterometer mode. During the ERS-1 AMI wave mode mission the incidence angle of the imagette center was modified from roughly 19.9° to 23.5°. Using ERS-1 and ERS-2 NRCS, calibration has thus been completed for both configurations, which allows a better characterization of some signal data saturation effects. However, since a SAR relies on platform displacement to achieve fine resolution, surface motions reduce its nominal resolution. As the wind speed increases, scatterer motion occurring during the SAR integration time also increases, causing the characteristic large azimuth cutoff wavelength. Acknowledging the strong dependence between sea state conditions and azimuth smearing effects, our results are highlighted by the global comparison with wind estimates derived from the scatterometer. The results demonstrate the ability to define a SAR wind algorithm from a kinematic point of view. Finally, a higher-order statistical analysis shows evidence of deviation from standard Rayleigh statistics, leading to a balance between K law and lognormal distributions. This deviation is mainly due to the SAR's high-resolution properties.

/pdf/analysis-of-ers-1-2-synthetic-aperture-radar-wave-mode-1oy335tbkv.pdf

Analysis of ERS-1/2 synthetic aperture radar wave mode imagettes

The recent use of along-track interferometry (ATI) in synthetic aperture radar (SAR) has shown promise for synoptic measurement of ocean surface currents. ATI-SARs have been used to estimate wave fields, currents, and current features. This paper describes and analyzes a dual-beam along-track interferometer to provide spatially resolved vector surface velocity estimates with a single pass of an aircraft. The design employs a pair of interferometer beams, one squinted forward and one squinted aft. Each interferometric phase is sensitive to the component of surface Doppler velocity in the direction of the beam. Therefore, a proper combination of these measurements provides a vector surface velocity estimate in one pass of the aircraft. The authors find that precise measurements dictate widely spaced beams and that the spatial resolution for the squinted SAR is essentially identical to the sidelooking case. Practical instrument design issues are discussed, and an airborne system currently in development is described. Through computer simulation, they observe the azimuthal displacement of interferometric phases by moving surfaces identical to those of conventional SAR and find that such displacement can bias the estimated surface velocity.

/pdf/dual-beam-interferometry-for-ocean-surface-current-vector-2exfbz1irq.pdf

Dual-beam interferometry for ocean surface current vector mapping

We show that if ocean surface waves of the order of a few meters long are frequently steep enough to generate bound centimetric waves, then composite surface scattering theory can account for many anomalous properties of microwave backscatter from the sea at high incidence angles. The model proposed here postulates that these intermediate waves are made sufficiently steep to generate bound centimetric waves because of their modulation by longer, dominant ocean surface waves. The bound centimetric waves have a nonzero mean tilt because they are located on the steep forward face of the intermediate waves, and they move at the speed of the intermediate waves. Applying composite surface scattering theory to this sea surface model, we show that much of the apparently anomalous behavior of microwave sea return measured at incidence angles between 50° and 80° during the Synthetic Aperture Radar and X Band Ocean Nonlinarities-Forschungsplatform Nordsee (SAXON-FPN) experiment can be explained using reasonable parameters to characterize the surface waves. In the SAXON-FPN measurements the mean values of the first moments of microwave Doppler spectra for horizontally polarized backscatter differ from those for vertically polarized backscatter by an amount which varies with the incidence angle and with the azimuthal angle between the radar look direction and the direction of the dominant wave. The modulation of this first moment by surface waves tens of meters in length is the same for the two polarizations at low to moderate incidence angles and can be interpreted in terms of the advection of free centimetric waves by the long waves. At higher incidence angles, however, this modulation is different for the two polarizations and cannot be explained by simple advection of free waves. Finally, microwave cross sections measured at high incidence angles using horizontal polarization are much larger than can be explained by a composite surface theory that includes only freely propagating centimetric waves. Most of these effects can be explained by the composite surface model presented here, which includes Bragg scattering from both free and bound, tilted waves.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JC01225

A model for microwave Doppler sea return at high incidence angles: Bragg scattering from bound, tilted waves

This work analyses the structure of the different contributions to the image spectrum derived by the three-dimensional Fourier decomposition of sea clutter time series measured by ordinary X-band marine radars. The goal of this investigation is to derive a method to estimate the significant wave height of the ocean wave fields imaged by the radar. The proposed method is an extension of a technique developed for the analysis of ocean wave fields by using synthetic aperture radar systems. The basic idea behind this method is that the significant wave height is linearly dependent on the square root of the signal-to-noise ratio, where the signal is assumed as the radar analysis estimation of the wave spectral energy and the noise is computed as the energy due to the sea surface roughness, which is closely related to the speckle of the radar image. The proposed method to estimate wave heights is validated using data sets of sea clutter images measured by a marine radar and significant wave heights derived from measurements taken by a buoy used as reference sensor.

/pdf/signal-to-noise-ratio-analysis-to-estimate-ocean-wave-1z1siz2kfw.pdf

Signal-to-noise ratio analysis to estimate ocean wave heights from X-band marine radar image time series

A 3-GHz Doppler radar has been used to study wave dynamics and backscatter from the sea surface at low grazing angles. Vertical polarization results are dominated by Bragg scatter even at low (∼8°) grazing angles. Horizontal polarization results, however, show a strong upwind-downwind asymmetry with additional, high-velocity intermittent scatter in the upwind direction associated with steep or breaking waves. These characteristics have been exploited to distinguish spilling breaking events from the background Bragg scatter. While these “spikes” at a single range may appear random in time, the combined range and time information reveals a well-determined propagation pattern. It is shown that for a developing sea in deep water, group behavior modulates the occurrence of wave breaking. The frequency-wavenumber spectrum shows a clear separation between the linear dispersion curve and nonlinear effects related to breaking. The most important nonlinear feature is a line near the dominant wave group velocity which is identified with the spectrum of breaking intermittency. The slope of this line suggests that the wave components which are most likely to break lie at frequencies significantly above the dominant wave frequency.

Doppler radar measurements of wave groups and breaking waves

Increasing interest is being shown in frequency modulated continuous wave (FMCW) radars due to their advantages of compact size, low peak power requirement, good range resolution and low interference to other systems. A major disadvantage of FMCW systems is the need to use two separate, well shielded antennas for transmission and reception. Several schemes have been devised to enable FMCW radars to operate with a single antenna. The authors describe a ground based S-band ocean surface remote sensing FMCW radar that has been adapted for single antenna operation by alternately switching the single antenna between the transmitter and the receiver. Even though this frequency modulated interrupted continuous wave (FMICW) system is no longer a true continuous wave radar, the essential properties of the FMCW waveform are preserved, provided some conditions on the switching speed and FMCW parameters are met. The purpose of the radar is to deduce ocean wave and current parameters by measuring ocean surface velocities. The radar was tested operationally by comparing ocean surface data from both the single antenna (FMICW) and dual antenna (FMCW) systems recorded under similar conditions.

Switching system for single antenna operation of an S-band FMCW radar

Resonant Bragg scattering forms the basis for the composite or dual-scale model for microwave backscatter from the sea surface. The scatterers are short surface waves that are spatially resonant with the incident electromagnetic waves. Bragg scattering is most easily identified when the intrinsic velocity of the scattering agents can be deduced and compared with theoretical surface wave phase velocities. In this paper we present S band (wavelength 10 cm) microwave backscatter data taken at low grazing angles for three situations where the scatterer velocity could be separated from the surface currents. These include a situation where pack ice acts as an additional tracer on the water surface, a wind direction reversal, and an azimuthal scan during low wind speed conditions where two Bragg peaks are visible in the Doppler spectra. These data show that under these conditions the scattering is dominated by propagating 5-cm resonant waves. Doppler spectra recorded at low grazing angles are interpreted in terms of the angular distribution of the scattering waves, the contributions of wave orbital velocities, and the effects of geometric shadowing.

Microwave backscatter from the sea surface: Bragg scattering by short gravity waves

Transformation of sea-surface Doppler microwave backscatter observations from the space-time domain to the wavenumber-frequency domain separates linear wave energy from nonlinear effects. Here observations and modeling are used to investigate the sources of these nonlinearities. Wave breaking and electromagnetic shadowing are examined with emphasis on their relative effects both inside and outside the region of the wavenumber-frequency spectrum associated with the linear dispersion equation. Shadowing significantly reduces the variance levels within the linear spectral region. In addition, shadowing is less directly related to changes in variance outside this region, i.e., that region associated with nonlinearity in the wave field. Wave breaking has less of an effect on the variance within the linear region than shadowing. However, the modeled wave breaking does have a greater tendency to increase variance levels at frequencies less than that of the linear wave field, for any given wavenumber. Aliasing and emphasis of crest backscatter are also explored to explain features seen in some wavenumber-frequency intensity images. Two-dimensional data allow the linear wave spectrum to be separated from nonlinear effects. This results in improved wave height spectrum estimation.

Nonlinear features in wave-resolving microwave radar observations of ocean waves

A ground-based frequency-modulated continuous wave microwave radar has been developed and applied to the measurement of ocean surface velocities. Full Doppler spectra are available, and both range and lime variations of the surface drifts can be recorded with resolutions down to 2.5 m and 0.3 s, respectively, over range extents of up to 1000 m. The ability of the radar to provide information over a wide range of sea conditions is demonstrated. These range from the identification of 5-cm scattering waves and their damping by a surface slick, to the propagation characteristics of long (∼200 m) ocean waves in deep and shallow water. The longwave propagation is in accord with linear wave theory. The relationship of the backscattered power at low grazing angles to the wave features is also demonstrated. The consequences of measuring radial velocity components at low grazing angles with a narrow beam antenna are considered. In this situation, wave height spectra and the principal wave direction are wel...

E. M. Poulter

Papers

Doppler radar measurements of wave groups and breaking waves

Switching system for single antenna operation of an S-band FMCW radar

Microwave backscatter from the sea surface: Bragg scattering by short gravity waves

Nonlinear features in wave-resolving microwave radar observations of ocean waves

S-Band FMCW Radar Measurements of Ocean Surface Dynamics