The principle of ocean wave spectrometers was fi rst presented several decades ago to detect the directional wave spectrum with real-aperture radar (Jackson, 1981). To invert wave spectra using an ocean wave spectrometer, for simplicity, the hydrodynamic forcing and wave-wave interaction effect are neglected and a Gaussian slope probability density function (pdf) is used to calculate the normalized backscattering cross-section ( σ 0 ) of the ocean surface. However, the real sea surface is non-Gaussian. It is not known whether the non-Gaussian property of the sea surface will affect the performance of the inversion of the wave spectrum if following existing inversion steps and methods. In this paper, the pdf of the sea surface slope is expressed as a Gram-Charlier fourth-order expansion, which is quasi-Gaussian. The modulation transfer function (MTF) is derived for a non-Gaussian slope pdf. The effects of non-Gaussian properties of the sea surface slope on the inversion process and result are then studied in a simulation of the SWIM (Surface Waves Investigation and Monitoring) instrument confi guration to be used on the CFOSAT (China-France Oceanography Satellite) mission. The simulation results show that the mean trend of σ 0 depends on the sea slope pdf, and the peakedness and skewness coeffi cients of the slope pdf affect the shape of the mean trend of σ 0 versus incidence and azimuth; owing to high resolution of σ 0 in the range direction, MTF obtained using the mean trend of σ 0 is almost as accurate as that set in the direct simulation; in the inversion, if ignoring the non-Gaussian assumption, the inversion performances for the wave spectrum decrease, as seen for an increase in the energy error of the inverted wave slope spectrum. However, the peak wavelength and wave direction are the same for inversions that consider and ignore the non-Gaussian property.Keyword : slope probability density of the sea surface; ocean wave spectrometer; non-Gaussian; directional wave spectrum; energy error 1 INTRODUCTION

International audienceKnowledge of the distribution of wave slopes in the sea is important for understanding a number of processes occurring at or near the air-sea interface. The sea slope probability density function (pdf) of sea waves is quasi-Gaussian, being able to be expressed as a Gram-Charlier expansion to fourth-order. However, the method is absent for remote sensing the sea slope pdf in a large scale. SWIM (Surface Waves Investigation and Monitoring), used on the CFOSAT (China-France Oceanography Satellite) mission, the first space borne wave scatterometer in the world can obtain two dimensional (2D) scattering measurements of sea surface in the incidence and azimuth direction with high resolution, which made it possible to measure 2D slope pdf with high accuracy. In the paper, the feasibility of remote sensing quasi-Gaussian sea slope by SWIM is studied by the simulation