The principal of conservation of action is applied to derive a spectral form for short, wind-generated waves on the ocean which is valid to second order in the slopes of longer surface waves. Using this form, composite surface theory is applied to microwave backscatter from the ocean surface in the Bragg regime to derive an expression for the normalized radar cross section of the sea, &sgr;0, which is also valid to second order in long-wave slope. This expression is compared with previous data and empirical models of &sgr;0 and is shown to account for the observed incidence angle, azimuth angle, wind speed, and polarization dependence. Comparisons are made at Ku and C band for incidence angles between 20¿ and 70¿. The theory indicates the manner in which atmospheric stability, long-wave spectra, and sea surface temperature may influence &sgr;0. Upwind-downwind asymmetry of &sgr;0 is shown to occur because of the second-order interaction of short-wave modulation with the orbital velocities of long waves. Furthermore, the results suggest that the wind speed dependence of &sgr;0 varies only slightly with microwave frequency, while the magnitude of &sgr;0 increases somewhat with frequency until viscous or turbulent dissipation reduces short-wave growth rates and thus amplitudes. Implications for scatterometer algorithm devleopment are discussed. |