Evaluation of a Linear Inversion Method for retrieval of directional wave spectra from SAR look cross spectra

The feasibility of a Linear Inversion Method applied to Synthetic Aperture Radar cross spectra to retrieve wave directional spectra is investigated. The proposed method is computationally efficient and does not require any a priori information from wave or atmospheric models, as is usually the case with other approaches. It is also comparatively less sensitive to low signal-to-noise ratio image spectra, which in general hinders the disambiguation of the retrieved directional wave spectrum. Several test cases were computed employing a simulator of complex SAR image spectra considering a broad range of values of steepness for the Envisat and Sentinel-1 satellite configurations. The results of the simulated cases were employed as lookup tables to correct biases while retrieving directional wave spectra from Level 1 cross spectra. As the nonlinearities, not accounted for when applying a linear inversion, are dependent on satellite configuration and on the relative position of the peak wave spectrum in relation to the azimuth cut-off, it is possible to quantify them through numerical simulations. The SAR wave spectra retrieved with the Linear Inversion Method from an Envisat ground track were evaluated against the ECMWF reanalysis ERA5 and compared to the results of ESA Level 2 WVW wave mode spectra. The SAR-inverted wave spectra, retrieved with both methods, presented similar results in terms of root-mean-square error (RMSE) and scatter index (SI) for significant wave height, peak wavelength and peak propagation direction. Specifically for significant wave height, the Linear Inversion Method yielded a bias of −0.14 m, a SI of 0.34 and a RMSE of 0.44 m for a segment of ground track over the Pacific Ocean employed in our validations. The directional wave spectra retrieved with the Linear Inversion Method presented better similarity with the ERA5 spectra, in comparison with the WVW spectra. Moreover, in around one third of the cases, the ESA method did not resolve the directional ambiguity. The preliminary results employing the Linear Inversion Method are encouraging, specially considering its simplicity and performance against the ESA distributed wave spectra.