Numerical implementation of local unified models for backscattering from random rough sea surfaces

In the context of electromagnetic wave backscattering from ocean-like surfaces, by using the lowest order of the SSA (SSA-1) model, Bourlier et al. proposed an original technique to reduce the number of numerical integrations to two for easier numerical implementation. To be consistent with microwave measurements, closed-form expressions of the Fourier coefficients with respect to the wind direction of the backscattering normalized radar cross-section (NRCS) are obtained. For Gaussian statistics, previous work is extended in this paper to kernels of unified models expanded up to second order, like full SSA and full LCA. Thus, with the help of Bessel functions and by analytical integrations over the azimuthal angles, the second-order backscattering (BNRCS) is expressed in terms of two-fold integrations and another independent integration instead of four-fold integrations, if no analytical integration is made. This approach allows us to obtain fast results (less than one second). Numerical results are then presented for different microwave frequencies and wind speeds.