Forward Propagation Modeling Above Gaussian Rough Surfaces by the Parabolic Shadowing Effect

Abstract

Abstract-In this paper, a fast method is presented to model the forward propagation above Gaussian rough surfaces and taking into account atmospheric refraction. The method is based on the Discrete Mixed Fourier Transform (DMFT) solved by the Parabolic Wave Equation, in which the Ament boundary condition with shadowing effect is used at grazing angle.In this model, for a bistatic configuration, the surface height PDF of the illuminated points is derived and it is introduced in the boundary condition. Examples demonstrate the capacities of the method to compute propagation factor above rough surfaces following Gaussian statistics and Gaussian height correlation and the proposed method is validated by comparison to a Monte Carlo approach.

Forward Radar Propagation Over Oil Slicks on Sea Surfaces Using the Ament Model With Shadowing Effect

“…This phenomenon, which was subject to a recent publication in [8], is summarized in next subsection for the case of reflection from a single interface, in order to extend it to the case of a rough layer.…”

“…S 11 (θ i , ζ, γ) is the bistatic statistical illumination function of an arbitrary point of the surface, of height ζ and slope γ, for an incidence angle θ i . For any uncorrelated process between the surface heights and slopes, it is given by equation (15) of [8]; for an uncorrelated Gaussian process, it is given by equations (15) and (16) of [8]; and for a correlated Gaussian process, it is given by equation (17) of [8]. Hereafter, the Smith formulation of the bistatic statistical illumination function [13,14], denoted as S 11,S (θ i , ζ, γ), will be used, and we will consider uncorrelated process.…”

“…Thus, the Ament model [5], which is a fast and simple model that describes the forward (i.e., in the specular direction) radar propagation over rough surfaces, can be used for such a configuration. Here, based on the Parabolic Wave Equation [6][7][8], it is applied to the forward propagation over sea surfaces for coastal radar configuration. This model, which is based on a ray approach, uses the Rayleigh parameter to describe the scattering from the rough interface for grazing incidence in a simple way.…”

“…Nevertheless, as shown in the literature [9], this simple model enables fast results which are consistent with rigorous methods for R a 1.25 (R a = k 1 σ h cos θ i , with σ h the surface RMS height, k 1 the incident wave number, and θ i the incidence angle). The model was then improved in [8] by taking the shadowing effect into account.…”

Investigation of Low-Grazing-Angle Microwave Backscattering From Threedimensional Breaking Sea Waves

“…Although the sea surface scattering is successfully modeled based on the Bragg theory in small and moderate incidence angles [6][7][8][9][10][11][12][13], some discrepancies between the predictions and experiment observations still cannot be explained. The terminology "super events" refers to the special phenomenon observed from the measured sea clutters, which includes sea spikes [14], polarization independence [15], faster scatters [16] and expanded width of Doppler spectrum [17].…”