AbstractA global dataset of complex synthetic aperture radar (SAR) images processed from wave mode raw data acquired by the European remote sensing satellite ERS-2 is used to measure ocean waves. Cross spectra of two looks extracted from the azimuth spectrum of wave mode imagettes are used to derive ocean wave propagation directions on a global basis. Energy and propagation direction derived from wave mode cross spectra are compared with ocean wave model data from the European center for medium range weather forecasts (ECMWF). A new inversion scheme for the retrieval of two dimensional wave spectra from SAR cross spectra is presented. The algorithm is based on a maximum a posteriori estimation which combines the information from SAR measurements with a priori knowledge on short ocean waves. A new regularization approach is used to impose smoothness constraints on the retrieved wave spectra.