The along-track interferometric synthetic aperture radar (AT-INSAR) has the potential to measure ocean surface currents and ocean surface waves. The authors have derived a new nonlinear integral transform that relates the ocean wave spectrum to the AT-INSAR phase image spectrum. This integral transform is obtained from an approximation of the mapping integral that includes the radial component of the velocity of the scatter elements and velocity bunching. However, it neglects the modulation of the normalized radar cross section by the long ocean waves, which has a small effect on the AT-INSAR phase. Under the assumption that the imaging is only weakly nonlinear, the nonlinear integral transform can be further simplified. In this case, the relationship between the AT-INSAR phase image spectrum and the ocean wave spectrum can be described by a linear transfer function.

A two-dimensional (2D) model for describing the imaging of ocean waves by an along-track interferometric synthetic aperture radar (AT-INSAR) is derived. It includes the modulation of the normalized radar cross section by the long waves, velocity bunching, and azimuthal image smear due to orbital acceleration associated with long waves and due to the orbital velocity spread within the AT-INSAR resolution cell (parameterized by the scene coherence time). By applying the Monte-Carlo method, AT-INSAR amplitude and phase image spectra are calculated for different sea states and radar configurations. The Monte-Carlo simulations show that velocity bunching affects the AT-INSAR imaging mechanism of ocean waves, and that a unimodal ocean wave spectrum may be mapped into a bimodal AT-INSAR phase image spectrum due to an interference between the velocity term and the velocity bunching term in the AT-INSAR imaging model. It is shown that the AT-INSAR imaging mechanism of ocean waves depends on the ratio of the scene coherence time and the time separation between the observations by the two antennas. If this ratio is larger than one, the AT-INSAR phase image spectra are distorted. Furthermore, the simulations show that the AT-INSAR phase image spectrum is quite insensitive to the ocean wave-radar modulation transfer function. Comparing AT-INSAR with conventional SAR imaging of ocean waves, the authors find that the azimuthal cut-off in AT-INSAR phase image spectra is shifted toward higher wavenumbers than in conventional SAR image spectra. This implies that AT-INSAR can resolve shorter azimuthal wavenumbers than conventional SAR. Thus the authors conclude that AT-INSAR phase images are better suited for measuring ocean waves spectra than conventional SAR images.

An earlier algorithm for retrieving two‐dimensional wave spectra from synthetic aperture radar (SAR) image spectra is improved by using a modified cost function and introducing an additional iteration loop in which the first‐guess input spectrum is systematically updated. For this purpose a spectral partitioning scheme is applied in which the spectrum is decomposed into a finite number of distinct wave systems. At each iteration step, the individual wave systems of the partitioned nth‐guess wave spectrum are adjusted to agree in mean energy, frequency, and direction with the corresponding mean values of the associated wave systems of the SAR‐inverted wave spectrum. The algorithm retrieves smooth wave spectra, avoiding the discontinuities which tended to arise in the previous algorithm in the transition region near the azimuthal wavenumber cutoff of the SAR image spectrum. The azimuthal cutoff of the SAR spectrum is also reproduced more accurately. The greatest improvement of the new retrieval algorithm is obtained when the discrepancies between the initial first‐guess wave spectrum and the observed SAR spectrum are large. In this case the additional updating loop for the input spectrum enables the retrieved spectrum to adjust such that the simulated SAR spectrum matches more closely the observed SAR spectrum. The overall correlation of a large set of simulated SAR spectra with the measured SAR spectra is found to be significantly higher than with the previous algorithm, indicating that the algorithm not only overcomes isolated shortcomings of the earlier algorithm but also yields retrieved wave spectra which are generally more consistent with the input SAR data. An additional practical advantage of the new algorithm is that it returns spectral partioning parameters which can be used in SAR wave data assimilation schemes.

First results of the imaging of ocean waves by SIR-C/X-SAR over the North Sea and North Atlantic are presented. It is shown that the SAR imaging of ocean waves depends only weakly on the radar frequency and polarization, but depends strongly on wind speed and direction. Wind streaks are imaged best at high radar frequencies and VV polarization

The nonlinear INSAR imaging mechanism of ocean waves is studied by applying an INSAR velocity bunching model and by using Monte-Carlo simulation techniques. Furthermore, a simplified INSAR phase imaging model is presented, which includes velocity bunching. A nonlinear integral ocean wave-INSAR phase spectral transform is derived. It is shown that the modulation by velocity bunching also enters into the INSAR imaging mechanism of ocean waves and gives rise to nonlinearity effects in the INSAR imaging mechanism. In some cases the INSAR phase image spectrum is split into two parts due to the interference between the velocity bunching term and the velocity term

Directional ocean wave spectra obtained with a fully non-linear inversion scheme from synthetic aperture radar (SAR) ocean image spectra collected by SARs onboard ERS-1 and the space shuttle (SIR-C/X-SAR) are compared. First results using spectra obtained within 500 km and five hours of each other indicate that the resulting spectral shapes and wave directions agree well. Spectral intensities and significant wave heights, however, are found not to agree well when the theoretical form of a hydrodynamic modulation transfer function (MTF) derived from orbital velocity straining alone is used. Agreement is improved when an empirical hydrodynamic MTF obtained from tower-based measurements is used

An improvement of an earlier algorithm for retrieving ocean wave spectra from SAR image spectra is presented. The scheme uses a modified cost function and an additional iteration loop. A spectral partitioning scheme decomposes the spectrum into a finite number of wave systems. At each iteration step the individual wave systems of the first guess spectrum are modified to agree in mean wave height, mean wave frequency and direction with the corresponding values of the SAR-inverted wave spectrum, thus yielding a new first guess for a new iteration, if necessary. The algorithm retrieves smooth wave spectra and in addition provides consistent spectral partitioning parameters which can be used in combined wind-and-wave data assimilation. Two assimilation schemes are presented: an optimal interpolation scheme which uses the first guess and SAR-retrieved characteristic parameter as input data and a Green's function approach which inverts the differential operator of the wave transport equation. The schemes are applied to the ERS-1 SAR data for the Atlantic Ocean and the resulting local wind corrections are intercompared

For the inversion of SAR image spectra into ocean wave spectra the ocean wave-radar modulation transfer function (MTF) plays an important role for waves traveling in or near the range direction. MTFs can be measured from sea-based platforms or inferred from the comparison of measured and simulated SAR image spectra. The MTFs determined by the two experimental methods have comparable moduli, but different phases. Also they do not agree with the values derived from various modulation theories. A short summary of the present status is given and possible reasons for the observed discrepancies are discussed

An interferometric synthetic aperture radar (INSAR) is capable of measuring ocean surface waves and surface currents. An INSAR velocity bunching model is derived which includes the radar cross section modulation and the velocity bunching modulation, as well as the velocity spread within the SAR resolution cell (parameterized by a scene coherence time). The authors simulate INSAR images of two-dimensional ocean wave fields by using the Monte-Carlo method, from which the INSAR amplitude and phase image spectra are calculated. It is shown that the INSAR phase image spectrum is almost independent of the radar cross section modulation, while the conventional SAR image spectra are more strongly affected by the interference of the radar cross section and the velocity bunching modulations. The authors find that the scene coherence time and the distance between the two antennas are the limiting parameters for imaging of ocean waves by INSAR.

Hasselmann's closed forward integral transform and its inversion includes, in addition to motion induced effects, the modulation of the normalized radar cross section (NRCS) due to long ocean waves. This modulation is described by a linear ocean wave-radar modulation transfer function (MTF). The authors compute the forward mapping integral by using a 'theoretical' and a parameterized form of the MTF with variable moduli and phases. For range propagating waves the transformation of SAR image spectra into ocean wave spectra depends strongly on this MTF. Significant wave heights (H/sub s/) derived from inverted wave spectra decrease by 15-20% when increasing the modulus of the MTF by a factor of 2. Furthermore, H/sub s/ increases up to 50% if a phase of 0/spl deg/ is used in the forward mapping integral instead of the most likely phase of the MTF which is 90.<>

Estimates of the ocean wave‐radar modulation transfer function (MTF) are derived from synthetic aperture radar (SAR) imagery acquired by the American Naval Air Development Center airborne three‐frequency SAR over the North Sea during the U.S./German SAR and X Band Ocean Nonlinearities‐Forschungsplattform Nordsee experiment in November 1990. This is achieved by comparing measured and simulated SAR image spectra. The simulated SAR image spectra are computed from ocean wave height spectra measured by a pitch and roll buoy and by applying the generalized velocity‐bunching model. First, SAR simulations are carried out by using the theoretical MTF which contains the tilt and range‐bunching MTFs as well as the hydrodynamic MTF calculated from the relaxation time model. Second, SAR simulations are carried out by taking the modulus and phase of the MTF as free parameters. For waves traveling toward the radar antenna, best agreement is achieved when using the following values for the modulus |M0| and phase η of the nondimensional MTF defined by (5) and (10): |M0| = 8 ‐ 13 for VV polarization and |M0| = 12 ‐ 15 for HH polarization; η = 60° ‐ 90° past the long‐wave crest when the wind is blowing downwave, and η = 0° ‐ 60° past the long‐wave crest when the wind is blowing upwave. The values derived for the modulus of the MTF are in good agreement with values obtained from tower‐based radar backscatter measurements. However, for the downwave case the phase of the MTF disagrees with the phase obtained from tower‐based measurements, where usually values between 20° and 60° are found.

The performance of the synthetic aperture radar (SAR) aboard the Russian ALMAZ-1 and the European ERS-1 satellites for imaging ocean surface waves is investigated. Collocated ALMAZ-1 and ERS-1 SAR images were acquired quasi-simultaneously on Oct. 6 and Oct. 8, 1992, over the North Atlantic in the vicinity of the island of Iceland. The SAR image spectra calculated from the ALMAZ-1 and ERS-1 images are compared with simulated SAR image spectra which are obtained from a wave spectrum hindcast by the WAM wave prediction model

Ocean wave height spectra are extracted routinely from ERS-1 synthetic aperture radar (SAR) wave mode image spectra since July 1, 1992 by applying a SAR inversion scheme based on Hasselmann's closed nonlinear spectral integral transform. The scheme requires a first-guess wave height spectrum as regularization term obtained from the WAM wave prediction model. Global monthly statistics of integrated spectral wave parameters, such as significant wave height, mean wavenumber, mean wave direction and directional spread, are calculated from wave model and SAR extracted wave spectra. The general agreement between the mean spectral wave parameters is quite good. They have a correlation between 0.83 and 0.94. However, the SAR extracted mean wave height is 10-15% larger and the mean wavenumber is about 10% smaller than the wave model values. The results demonstrate the good performance and high accuracy of the SAR ocean wave inversion scheme.<>

It is widely accepted that the imaging of ocean surface waves by synthetic aperture radar (SAR) can be adequately described by velocity bunching theory in conjunction with the two-scale wave model. However, it has been conjectured that this theory is incapable of explaining why, under certain conditions, the image contrast of airborne SAR imagery of ocean waves can be enhanced by defocusing the SAR processor. In the present study the velocity bunching theory is defended.< >

The SAR ocean images obtained in the Tower Ocean Wave and Radar Dependence Experiment (TOWARD) are carefully analyzed at different focus settings and compared with simulated results based on various theories for imaging surface waves. The agreement between the experimental data and all of the SAR simulations except one is found to be favorable. There is also surprisingly close agreement among the different theoretical models themselves, suggesting a closer fundamental similarity among the contending theories than was previously thought. It is shown that the width of the focusing curve has an inverse dependence on the SAR integration time. For the TOWARD conditions it is found that the image modulation due to azimuth-traveling surface waves is greater than that due to range-traveling waves.

The imaging of ocean surface waves by synthetic aperture radar (SAR) is investigated using two-dimensional Monte-Carlo simulations. The properties of the SAR imaging mechanism for windseas and swell in the Bragg scattering regime are discussed as a function of a few governing non-dimensional parameters formed from a combination of SAR and ocean wave parameters. The parameter ranges may be classified into three regimes corresponding to linear and weakly nonlinear, medium nonlinear and strongly nonlinear imaging. The nonlinearities are induced by motion effects (velocity bunching, velocity spread and acceleration smearing), while the real aperture radar (RAR) tilt and hydrodynamic modulation processes are regarded as linear. In the strongly nonlinear imaging regime, the velocity bunching mechanism causes a rotation of the spectral peak towards the range direction and a stretching of the peak wavelength. In addition, the azimuthal resolution is degraded through the Doppler spreading arising from the different facet velocities within a SAR resolution cell. The imaging properties in this regime are largely governed by two non-dimensional parameters, the velocity bunching and velocity smearing parameter. The nonlinear imaging distortions are strongest for broad spectra (windseas) and are significantly weaker for narrow-band swell. In the linear and weakly nonlinear imaging regime, the superposition of the hydrodynamic and tilt cross-section modulation and the velocity bunching transfer function normally produces a rotation of the spectral peak towards the azimuthal direction. The interference characteristics of these different modulation mechanisms depends on the wave propagation direction and can lead to a significant distortion of the image. This is often seen in large differences in the image modulation depths of waves propagating parallel and anti-parallel to the flight direction.