sea surfaces scattering by multi-order small-slope approximation: a monte-carlo and analytical comparison

L-band electromagnetic scattering from two- dimensional random rough sea surfaces are calculated by first- and second-order small-slope approximation (ssa1, 2) methods. both analytical and numerical computations are utilized to calculate incoherent normalized radar cross-section (nrcs) in mono- and bi-static cases. for evaluating inverse fourier transform, inverse fast fourier transform (ifft) is performed to reduce computational burdens. for the ssa simulations, surface dimensions are large as all sea spectrum components are included. considering the integration domain of the analytical ssa (a-ssa), it requires huge computer memories especially at high frequencies and high wind speeds. in this regard, the numerical ssa (n-ssa) employs less memory, however, it requires more running time because of monte-carlo simulations. by applying tapered incident plane wave (tpw) to the n-ssa, dimensions are reduced to enhance computational efficiency in comparison with the a-ssa. as a result, the n-ssa with the tpw is applicable to high wind speeds, where the a-ssa may be limited. to validate the ssa, results are compared with those from the method of moments (moms) in vv polarization. the results of different methods show good agreements at low wind speeds and incident angles less than 60 degrees. at high wind speeds, there are some differences between the ssa1 and the ssa2 recommending on the ssa2 to use, due to the higher order of accuracy.