Retrieval of the ocean wave spectrum in open and thin ice covered ocean waters from ERS Synthetic Aperture Radar images

This paper concerns with the task of retrieving ocean wave spectra from imagery provided by space-borne SAR systems such as that on board ERS satellite. SAR imagery of surface wave fields traveling into open ocean and into thin sea ice covers composed of frazil and pancake icefields is considered. The major purpose is to gain insight on how the spectral changes can be related to sea ice properties of geophysical interest such as the thickness. Starting from SAR image cross spectra computed from Single Look Complex (SLC) SAR images, the ocean wave spectrum is retrieved using an inversion procedure based on the gradient descent algorithm. The capability of this method when applied to satellite SAR sensors is investigated. Interest in the SAR image cross spectrum exploitation is twofold: first, the directional properties of the ocean wave spectra are retained; second, external wave information needed to initialize the inversion procedure may be greatly reduced using only information included in the SAR image cross spectrum itself. The main drawback is that the wind waves spectrum could be partly lost and its spectral peak wave number underestimated. An ERS-SAR SLC image acquired on April 10, 1993 over the Greenland Sea was selected as test image. A pair of windows that include open-sea only and sea ice cover, respectively, were selected. The inversions were carried out using different guess wave spectra taken from SAR image cross spectra. Moreover, care was taken to properly handle negative values eventually occurring during the inversion runs. This results in a modification of the gradient descending technique that is required if a non-negative solution of the wave spectrum is searched for. Results are discussed in view of the possibility of SAR data to detect ocean wave dispersion as a means for the retrieval of ice thickness

Development of a satellite SAR image spectra and altimeter wave height data assimilation system for ERS-1

The applicability of ERS-1 wind and wave data for wave models was studied using the WAM third generation wave model and SEASAT altimeter, scatterometer and SAR data. A series of global wave hindcasts is made for the surface stress and surface wind fields by assimilation of scatterometer data for the full 96-day SEASAT and also for two wind field analyses for shorter periods by assimilation with the higher resolution ECMWF T63 model and by subjective analysis methods. It is found that wave models respond very sensitively to inconsistencies in wind field analyses and therefore provide a valuable data validation tool. Comparisons between SEASAT SAR image spectra and theoretical SAR spectra derived from the hindcast wave spectra by Monte Carlo simulations yield good overall agreement for 32 cases representing a wide variety of wave conditions. It is concluded that SAR wave imaging is sufficiently well understood to apply SAR image spectra with confidence for wave studies if supported by realistic wave models and theoretical computations of the strongly nonlinear mapping of the wave spectrum into the SAR image spectrum. A closed nonlinear integral expression for this spectral mapping relation is derived which avoids the inherent statistical errors of Monte Carlo computations and may prove to be more efficient numerically

Visualizing characteristics of ocean data collected during the Shuttle Imaging Radar-B experiment

Topographic measurements of sea surface elevation collected by the Surface Contour Radar (SCR) during NASA's Shuttle Imaging Radar (SIR-B) experiment are plotted as three dimensional surface plots to observe wave height variance along the track of a P-3 aircraft. Ocean wave spectra were computed from rotating altimeter measurements acquired by the Radar Ocean Wave Spectrometer (ROWS). Fourier power spectra computed from SIR-B synthetic aperture radar (SAR) images of the ocean are compared to ROWS surface wave spectra. Fourier inversion of SAR spectra, after subtraction of spectral noise and modeling of wave height modulation, yields topography similar to direct measurements made by SCR. Visual perspectives on the SCR and SAR ocean data are compared. Threshold distinctions between surface elevation and texture modulations of SAR data are considered within the context of a dynamic statistical model of rough surface scattering. The result of these endeavors is insight as to the physical mechanism governing the imaging of ocean waves with SAR

An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra

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 dan be used in SAR wave data assimilation schemes

On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion

A new, closed nonlinear integral transformation relation is derived describing the mapping of a two-dimensional ocean wave spectrum into a synthetic aperture radar (SAR) image spectrum. The general integral relation is expanded in a power series with respect to orders of nonlinearity and velocity bunching. The individual terms of the series can be readily computed using fast Fourier transforms. The convergence of the series is rapid. The series expansion is also useful in identifying the different contributions to the net imaging process, consisting of the real aperture radar (RAR) cross-section modulation, the nonlinear motion (velocity bunching) effects, and their various interaction products. The lowest term of the expansion with respect to nonlinearity order yields a simple quasi-linear approximate mapping relation consisting of the standard linear SAR modulation expression multiplied by an additional nonlinear Gaussian azimuthal cutoff factor. The cutoff scale is given by the rms azimuthal (velocity bunching) displacement. The same cutoff factor applies to all terms of the power series expansion. The nonlinear mapping relation is inverted using a standard first-guess wave spectrum as regularization term. This is needed to overcome the basic 180° mapping ambiguity and the loss of information beyond the azimuthal cutoff. The inversion is solved numerically using an iteration technique based on the successive application of the explicit solution for the quasi-linear mapping approximation, with interposed corrections invoking the full nonlinear mapping expression. A straightforward application of this technique, however, generally yields unrealistic discontinuities of the best fit wave spectrum in the transition region separating the low azimuthal wave number domain, in which useful SAR information is available and the wave spectrum is modified, from the high azimuthal wave number region beyond the azimuthal cutoff, where the first-guess wave spectrum is retained. This difficulty is overcome by applying a two-step inversion procedure. In the first step the energy level of the wave spectrum is adjusted, and the wave number plane rotated and rescaled, without altering the shape of the spectrum. Using the resulting globally fitted spectrum as the new first-guess input spectrum, the original inversion method is then applied without further constraints in a second step to obtain a final fine-scale optimized spectrum. The forward mapping relation and inversion algorithms are illustrated for three Seasat cases representing different wave conditions corresponding to weakly, moderately, and strongly nonlinear imaging conditions

Statistical analysis and intercomparison of WAM model data with global ERS-1 SAR wave mode spectral retrievals over 3 years

Ocean wave spectra were retrieved from a set of ERS-1 synthetic aperture radar (SAR) wave mode (SWM) spectra between January 1993 and December 1995. An assessment is given of the SWM data quality and the retrieval performance as well as the operational feasibility of the retrieval algorithm. Sensitivity studies are performed to demonstrate the weak residual dependence of the retrieval on the first-guess input spectrum. The mean spectral parameters of the SWM retrievals are compared with spectral parameters from collocated wave model (WAM) spectra. The time series of SWM-retrieved and WAM-derived monthly mean significant wave heights H-s in various ocean basins show good overall agreement but with a small systematic underestimation of H-s by the WAM. A decomposition of the wave spectra into wind sea and swell reveals an average 10% overprediction of the wind sea by the WAM while swell is underpredicted by 20-30%. The positive wind-sea bias exhibits no clear wave height dependence, while the negative swell bias decreases with swell wave height. This could be due to a too strong damping in the WAM at low frequencies. Detailed regional investigations point to the existence of smaller-scale phenomena, which may not be adequately reproduced by the WAM at the present resolution of the wind forcing. Finally, an intercomparison is made of the observed and modeled azimuthal cutoff length scales, and global distributions are investigated. Ratios of the observed azimuthal cutoff wavenumber to the mean azimuthal wavenumber component indicate that about 75% of the swell can be directly resolved by the SAR, while about 70% of the wind sea lies at least partially beyond the cutoff