A noise model for estimated synthetic aperture radar look cross spectra acquired over the ocean

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.