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It is well known that look cross spectra processed from synthetic aperture radar (SAR) contain valuable information on ocean waves. With the launch of the European satellite ENVISAT, SAR look cross spectra (SLCS) have become available on an operational basis. Activities therefore exist at different European weather centres to use the data for assimilation into numerical wave models. Furthermore there is scientific interest in SLCS, e.g., concerning the estimation of the phase speed of ocean waves. For the estimation of ocean wave parameters, it is important to have information about the accuracy of SLCS. In this paper, errors of estimated SLCS due to SAR image speckle, spectral estimation errors, and image pattern decorrelation associated with ocean wave motion are analyzed. A probability model is proposed for the estimated SLCS based on the respective cross-spectrum coherence. The model is used to calculate signal-to-noise ratios and confidence limits for the SLCS phase and magnitude, as well as the real and imaginary part. The coherence is factored into a component describing look decorrelation due to SAR image speckle and a second factor describing the effect of sea surface motion. It is shown that the ocean-wave-dependent decorrelation can be simulated using existing nonlinear integral transforms for the look variance spectrum and the SLCS. The decorrelation effect associated with speckle noise is related to SAR system parameters, e.g., the spatial SAR resolution. The probability model is used to investigate the optimal choice of look processing parameters like the look separation time. A statistical analysis based on a global dataset of a reprocessed dataset of European Remote Sensing 2 satellite SLCS is presented confirming the applicability of the probability model. The implications of the results for the retrieval of two-dimensional wave spectra from SLCS are summarized. Possible future applications of the model like, for example, the investigation of the turbulent air flow over waves, are discussed. Index Terms--Coherence, cross spectrum, ocean waves, synthetic aperture radar (SAR).

A method is presented to derive two-dimensional sea surface elevation fields from complex synthetic aperture radar (SAR) data. Applied to spaceborne SAR data as acquired by European Remote Sensing 2 (ERS-2) or the Environmental Satellite (ENVISAT), the method allows to analyze the structure of ocean wave fields, e.g., wave grouping or individual wave heights on a global scale. The technique, thus, provides wave parameters not obtained with common SAR wave retrieval schemes, which are designed to estimate the 2-D wave spectrum, i.e., second-order statistical moments of the wave field. Estimates of sea surface elevation fields are obtained based on the existing theory of SAR ocean wave imaging, i.e., the modulation of the SAR image intensity due real aperture radar and motion-related effects. A power series expansion is derived for SAR intensity images that enables the analysis of nonlinear effects as well as to derive a quasi-linear approximation of the SAR imaging model in the spatial domain. A statistical analysis is performed based on a global dataset of 2-D wave spectra provided by the European Centre for Medium-Range Weather Forecast. Distributions are given for the relative error of the quasi-linear approximation in the spatial domain. It is shown that the error can be reduced by smoothing the SAR image in the azimuthal direction at the cost of lower resolution. Smoothed elevation fields are retrieved by the minimization of a cost function defined in the Fourier domain based on the quasi-linear approximation of the imaging process. A multilook technique is applied to infer the information on wave propagation directions, which is required because the SAR transfer function is non-Hermitian, i.e., the SAR image is not determined by the 'frozen' sea surface, but wave motion has a significant impact. The method is applied to simulated SAR images as well as to data acquired by ERS-2. The errors of the retrieved wave field due to image noise, uncertainties in the SAR imaging model, and bandwidth limitations are analyzed. In particular, the fact that the estimated elevation field is smoothed due to the finite system resolution and smearing effects associated with wave motion is discussed. A statistical test is proposed to check the homogeneity of the SAR image. The method makes sure that atmospheric effects are not misinterpreted as being caused by ocean waves. Index Terms--Individual waves, ocean waves, sea surface elevation, synthetic aperture radar (SAR).

The global availability of synthetic aperture radar (SAR) wave mode data from the European Remote Sensing (ERS) satellites ERS-1 and ERS-2, as well as ENVISAT, allows for the investigation of the wind field over the ocean on a global and continuous basis. For this purpose, 27 days of ERS-2 SAR wave mode data were processed, representing a total of 34310 imagettes of size 10 km x 5 km, available every 200 km along the satellite track. In this paper, two methods for retrieving wind speeds from SAR imagettes are presented and validated, showing the applicability of ENVISAT alike SAR wave mode data for global ocean wind retrieval. The first method is based on the well-tested empirical C-baud scatterometer (SCAT) models, which describe the dependency of the normalized radar cross section (NRCS) on wind speed and direction. To apply C-band models to SAR data, the NRCS needs to be accurately calibrated. This is performed by a new efficient method utilizing a subset of colocated measurements from ERS-2 SCAT and model winds from the European Centre for Medium-Range Weather Forecast (ECMWF). SAR wind speeds are computed from the calibrated imagettes and compared to the entire set of colocated ERS-2 SCAT and ECMWF model data. Comparison to ERS-2 SCAT winds result in a correlation of 0.95 with a bias of -0.0l [ms.sup.-1] and an rms error of 1.0 [ms.sup.-1] The second approach is based on neural networks (NNs), which allow the retrieval of wind speeds from uncalibrated SAR imagettes. NNs are trained using the mean intensity of ERS-2 SAR imagettes and colocated wind data from the ERS-2 SCAT and ECMWF model data. Validation of the NN-retrieved SAR wind speeds to ERS-2 SCAT and ECMWF model wind data result in a correlation of 0.96 with a bias of -0.04 [ms.sup.-1] and an rms error of 0.93 [ms.sup.-1]. Index Terms--Calibration, neural network, scatterometer, synthetic aperture radar (SAR), wind speed.

An across track interferometric synthetic aperture radar (InSAR) is used to image ocean waves. Across track InSAR data were acquired during the SAR INnterferometry Experiment for validation of ocean Wave imaging models (SINEWAVE) in the North Sea using an airborne X-band radar with horizontal polarization. A wind sea system was imaged at different flight levels and with different flight directions with respect to the ocean wave propagation direction. Simultaneously, ocean wave spectra were measured by a directional wave rider buoy. Thus, the experiment data comprises synthetic aperture radar (SAR) intensity, coherence, and phase images together with in situ measurements. As shown in a recent theoretical study by Schulz-Stellenfleth and Lehner [1], across track InSAR provides distorted (bunched) digital elevation models (DEMs) of the sea surface. Using SINEWAVE data the DEM bunching mechanism is verified with in situ ocean wave measurements available for the first time. It is shown that significant waveheight as well as one-dimensional (1-D) wavenumber spectra derived from bunched DEMs and buoy data are in good agreement for small nonlinearities. Peak wave directions and peak wavelength detected in bunched DEMs and SAR intensity images are compared with the buoy spectrum. Peak rotations of up to 30 [degrees] with respect to the buoy spectrum are found depending on flight direction and flight level. Two-dimensional (2-D) spectra of bunched DEMs, corresponding coherency maps, and SAR intensity images are intercompared. The signal-to-noise ratio (SNR) of bunched DEM spectra is shown to be about 5 to 10 dB higher than the SNR of SAR intensity image spectra. A new approach is presented to measure the real aperture modulation transfer function (RAR MTF), which describes the modulation of the normalized radar cross section by ocean waves. Estimates for RAR MTF modulus and phase are obtained by cross correlating bunched DEMs with coregistered SAR intensity images. Modulus and phase of the RAR MTF are compared to a theoretical two scale model for different levels of nonlinearity. Index Terms--Across track interferometry, ocean waves, synthetic aperture radar (SAR).

An airborne single pass across-track interferometric synthetic aperture radar (InSAR) is used to image ocean waves. A theoretical model explaining the imaging mechanisms is developed, and simulations of the interferogram as well as the conventional SAR intensity image are presented for given ocean wave spectra. Distortions of digital elevation models (DEM) derived from InSAR data are explained by the motion of the sea surface. A Monte Carlo method based on forward simulations is used to estimate variance spectra of the distorted elevation models. It is shown that a straightforward estimation of wave height using the distorted InSAR elevation model is in good agreement with true wave height for low amplitude swell with about 10% error depending on propagation direction and coherence time. However, severe underestimation of wave height is found for wind seas propagating in flight direction. Forward simulations show that the distorted InSAR DEM is less dependent on the model chosen for the real aperture radar mechanism than conventional SAR images. Data acquired during an experiment over the North Sea by a high precision InSAR system are compared with simulations. Index Terms--Interferometry, ocean waves, synthetic aperture radar (SAR).

A global dataset of complex synthetic aperture (SAR) images is processed from wave mode raw data acquired by the ERS-2 satellite. Using these data, different algorithms for wind and wave measurements recently developed in view of future ENVISAT ASAR data are analyzed on a statistical basis. Different aspects of complex SAR wave mode processing with the DLR processor BSAR are discussed and global statistics of processing parameters are presented. Single-look complex (SLC) imagettes give the opportunity to apply multilook techniques in range as well as in azimuth. Such methods are used to reduce speckle noise or to analyze the time evolution of the ocean surface cross section during SAR integration time. A global analysis of different new algorithms for wind and ocean wave measurements, taking advantage of SLC data, is given. Wind speed is estimated with the azimuthal cross-correlation algorithm (CCA). As a modification of the existing CCA, range multilooking is used to deal with the speckle bias. Homogeneity of the imagettes is considered. Wind speed is derived from mean SAR image intensities taking into account wind direction (CMOD algorithm). Comparison with collocated ERS-2 scatterometer data shows reasonable agreement with the CCA and good agreement for the CMOD approach. Using imagettes instead of image power spectra allows us to study ocean surface features caused by natural slicks, sea ice, or atmospheric processes. The impact of these phenomena on SCAT measurements is considered. Cross spectral methods are used to derive the ocean wave propagation direction from complex imagettes on a global basis. Comparison with model data provided by the European Center for Medium Range Weather Forecast (ECMWF), Reading, U.K., shows good agreement. Index Terms--ERS wave mode, ocean waves, SAR, wind speed estimation.