

A parametric inversion scheme for the SAR retrieval of 2D ocean wave spectra
Johannes SchulzStellenfleth^{(1)} and Susanne Lehner^{(1)}
^{(1)}
German Aerospace Center (DLR),
Oberpfaffenhofen,
82234 Wessling,
Germany
Abstract
A parametric inversion scheme for the retrieval of twodimensional ocean wave spectra from look cross spectra (SLCS) acquired by spaceborne synthetic aperture radar (SAR) is presented. The scheme uses prior information from numerical wave models to deal with the information loss caused by the nonlinear SAR ocean wave imaging mechanism.
The Partition Rescaling and Shift Algorithm (PARSA) is based on a maximum a posteriori approach in which an optimal estimate of a wave spectrum for a given measured SLCS and additional prior knowledge is calculated. The method is based on explicit models for measurement errors, as well as uncertainties in the SAR imaging model and the model wave spectra used as prior information. The correction parameters for the SAR imaging model are estimated as part of the retrieval process. The rigorous stochastic approach enables the estimation of the error covariance matrix of the retrieved parameters.
Uncertainties in the prior wave spectrum are expressed in terms of transformation variables, which are defined for each wave system in the spectrum, describing rotations, rescaling of wavenumbers and energy, as well as changes of directional spreading. A new partitioning method is used which allows overlapping partitions and thus avoids discontinuities occurring in algorithms used so far.
The PARSA wave spectra retrieval is equivalent to a minimization problem with regard to the transformation variables and parameters of the imaging model. A Levenberg Marquard method is used to find a numerical solution. The inversion is performed on a polar grid with a dimension, which is an order of magnitude smaller than the typical cartesian grids used so far. The reduced dimension enables the use of an extended quasilinear approximation of the imaging model with nondiagonal Jacobian matrix, leading to a high stability of the algorithm.
The scheme is tested using both ERS2 SAR and ENVISAT ASAR data. It is shown that the method is able to extract information from cross spectra even if there are strong errors in the SAR imaging model. It is demonstrated that the algorithm makes use of the new phase information contained in cross spectra, which is of particular importance for multimodal sea states. Global statistics are presented for a global data set of reprocessed ERS2 SAR wave mode SLCS acquired in southern winter 1996. Comparisons with NDBC buoy data are presented.
The statistical analysis includes standard wave parameters like the significant wave height as well as parameters which are relevant for the investigation of extreme wave conditions like,e.g., the Benjamin Feir Index.
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