Scattering and Doppler Spectral Analysis for Two-Dimensional Linear and Nonlinear Sea Surfaces

Two-dimensional linear and second-order Creamer [Creamer (2)] nonlinear sea-surface models are combined with the second-order small-slope approximation method to comparatively study the electromagnetic scattering and the Doppler spectral characteristics from sea surfaces. Due to nonlinear hydrodynamics, the bistatic normalized radar cross section (NRCS) calculated from Creamer (2) surfaces is slightly larger than its linear surface counterpart for scattering angles departing from the specular direction, and the Creamer (2) surface backscattering coefficient increases as well for wind direction angles around upwind and downwind, whereas, for the crosswind direction, it is interesting to note that the observations are contrary. However, as was pointed out by Toporkov in a 1-D surface case, the effect of the nonlinear surface model on the average NRCS is minute. In particular, the Doppler spectra of the backscattered echoes are compared for the linear and Creamer (2) surfaces at various incident angles. It is seen, as expected, that the Doppler shifts and spectral widths of 2-D Creamer (2) surfaces exhibit different features compared with those of the linear surfaces, agreeing with the 1-D cases. However, for larger incident angles, the Doppler spectral broadening for Creamer (2) surfaces is not as severe as was reported in previous 1-D studies that used full Creamer model. The reason for this discrepancy appears to be the reduced nature of the Creamer (2) approximation. Moreover, studies of the Doppler characteristics for different wind directions demonstrate that nonlinear effects become weaker as the wind direction varies from upwind to crosswind.