The reflection of impulses from a nonlinear random sea

Abstract

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 heightslope 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 skewhess 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.

Statistical Non-Gaussian Model of Sea Surface with Anisotropic Spectrum for Wave Scattering Theory. Part I

“…The random Gaussian field ξ (q) , entering in (117), is completely auxiliary and has no direct meaning. The model of [26] was used in [27] for description of radar impulses reflection from the sea surface in GO approximation. This model was extended in [28] for the joint PDF of elevation and two slopes, and applied to radar altimetry.…”

“…Note that all of the values ∆ 1 , (27) to (29) in terms of conditional mean values (13) to (17), we obtain:…”

Evaluation of GEOSAT data and application to variability of the Northeast Pacific Ocean

“…narrow high peaks and broad shallow troughs) that tends to further bias the altimetry measurement towards the troughs. Lipa and Barrick (1981), extending the theory of Jackson (1979) (1982). For these reasons, the present recommendation for GEOSAT is that the sea surface heights should be increased by 2% of the significant wave height (Cheney et al, 1987).…”

SEASAT altimeter height calibration

“…The amount of the shift is a function of SWH and probably other surface properties. The latter are at least partially characterized by height skewness, According to Jackson (1979), sea state bias may bl^ approximated by the product of RMS waveheight and height skewness. For "typical" values of height skewness of 0.2, this bias reduces to 5% of SWH.…”