Scattering cross sections for composite rough surfaces using the unified full wave approach

EM models for evaluating rain perturbation on the NRCS of the sea surface observed near nadir

“…Under the hypothesis that the ring-wave phenomenon is independent of the angular direction (azimuth-symmetric surface), such spectra can be expressed in terms of the radial wavenumber spectrum 221 (RWS), as shown in the following Section. As suggested in [SI, the dependence of the RWS on rainfall intensity can indeed be approximated as follows: (6) where& -6Hz, Af -SHz and qo depends on R. Fig. 2 (after [5]) shows how such a log-Gaussian model fits the aforementioned experimental data relative to a normalised frequency spectrum.…”

“…2 (after [5]) shows how such a log-Gaussian model fits the aforementioned experimental data relative to a normalised frequency spectrum. Here we report, for ease of reference, the basic expressions of the adopted EM model, based on the FWM for the backscatter case, described in detail in [6,71, utilising the same original notation. The two-dimensional surface spectrum for an azimuth-symmetric surface, disregarding a normalisation factor, can be expressed as [17, 181…”

“…If the mean square slope CT?~ of the rough surface is small, say o?l < 0.2, the effects of height-slope correlation can be neglected [19]; 02, is then calculated as in [6,191, and for ring-waves corrugation with spectrum W,(K) we obtained os? = 3.34 x 10-2(h2).…”

“…Thus, condition c& < 0.2 is met for all values of (h2) considered in the following Section. Under this hypothesis, the unified FWM expressions of the likeand cross-polarised backscattering cross sections &' become [6,19,201 (12) 1"' are defined as in [6]. Expressions for the coefficients DPq in eqn.…”

“…Eqn. 12 reports the Q( iif, iiq function explicitly valid for the azimuthal symmetry case; it involves the Bessel function of zero order J,, where v : , vector E, locally perpendicular to the surface, is a function of the surface slopes h,, h, along the x, z directions, and p(h,, h,) is the slopes probability density function (PDF), assumed Gaussian with variance c& [7, 211, calculated as in [6, 191. The characteristic function (CF) and the joint characteristic functions (JCF) of the surface height h, are evaluated assuming a Gaussian PDF; they are, respectively [6] = v? + v, is the transverse component of 7.…”