LAUSR

By expanding the first-order small-slope approximation (SSA-1) scattering model in the polynomial terms containing convolutions of the sea wave spectrum, this letter quantitatively investigated how the convolutions of the sea wave spectrum affect the normalized backscattering cross section (NBCS) under various wind speeds, radar frequencies, and incident angles. First, numerical results show that only a portion of convolution powers of the sea wave spectrum contribute significantly to the NBCS, and such a portion of convolution powers are defined as the “effective convolutions” (ECs). Based on this, an empirical model related to the radar frequency, incident angle, and wind speed is established to determine the ECs to reduce the computation cost. Finally, the NBCSs using the ECs by the empirical model and the reference data calculated by the direct numerical integration are compared. The comparison results indicate that compared to the direct numerical integration, implementing the first-order SSA with the ECs has high accuracy and relatively low computational cost, notably with small Rayleigh parameters.