Conditional sea surface statistics and their impact on geophysical sea surface parameters retrieved from SAR altimetry signals

In this study we present an analytical formulation of synthetic-aperture radar (SAR) altimetry signals including narrow banded nonlinear wave fields and conditional statistics between wave elevation displacements, horizontal wave slopes and vertical wave particle velocities. Considering the wave elevation displacements coskewness with respect to horizontal slopes leads to an analytical formulation of the electromagnetic bias within a SAR-mode altimeter stack. This formulation can be either parametrized by the significant wave height (SWH) and mean wave steepness, or in terms of the variance of vertical wave velocities. The effect of conditional vertical wave particle velocity variances with respect to the observed horizontal wave slopes close to nadir incidence angles leads to an effective reduction of the azimuth blurring of SAR-mode stacks. We present here a formulation of this effect by examining JONSWAP ocean wave spectra. In most cases this effect reduces the azimuth blurring by 10% to 30%. Additionally we investigate the effect of a nonlinear wave elevation displacement probability density function (PDF) on estimated geophysical parameters. We were able to show that including an elevation displacement skewness of 0.13 improves significantly the SWH consistency between altimetry and ECMWF Reanalysis v5 ERA5 results.All of these effects are validated with respect to ERA5 model data in the North East Atlantic region and in situ data located in the German Bight and Baltic Sea.The developed model can be used in both SAR and conventional altimetry retrackers.