The reflection of impulses from a nonlinear random sea

Non‐Gaussian ocean wave statistics are accounted for in a simple model of the reflection of radar impulses from the sea at near‐vertical incidence. In the geometrical optics approximation to microwave backscatter, the impulse response of the sea surface is proportional to the joint probability density function (pdf) of wave height and slope, where the wave height corresponds to the appropriate propagation delay time and the slope satisfies the condition for specular reflection. The joint pdf is calculated according to the theory of Longuet‐Higgins (1963) on the distributions of variables in a ‘weakly nonlinear’ random sea. The long‐crested approximation is made, a Phillips wave spectrum is assumed, and the Gram‐Charlier series is truncated after skewness terms. It is found that the height and height‐slope skewness coefficients bear the ratio 1:2 and that consequently, the impulse response of the sea at vertical incidence is very nearly equal to wave height pdf. The mean of the distribution, however, is not located at true mean water level but is negatively biased in an amount equal to the height skewness coefficient times the rms wave height. The derived impulse response and conditional cross section versus wave height are in excellent agreement with the Yaplee et al. (1971) observations. It is suggested that the empirically determined and theoretically predicted sea state bias be corrected for in the routine processing of satellite radar altimeter data.