## 2 Bistatic Anisotropic Polarimetric Two-Scale Model  
Sea surface scattering is here described via the BA-PTSM, a recent advanced scattering model suited to anisotropic surfaces and bistatic geometries [26]. It is an evolution of the original two-scale model (TSM) firstly proposed about fifty years ago to evaluate EM scattering from random rough surfaces [29], including sea surfaces [30]. Within TSM, the scattering surface is expressed as the superposition of two random rough surfaces at different scales: a small-scale roughness whose horizontal scale is comparable to the EM wavelength and whose height is much smaller than wavelength; a large-scale roughness, whose horizontal scale is very large with respect to wavelength and height comparable to wavelength or larger. Scattering from the small-scale roughness is responsible for diffuse scattering, i.e., scattering in far-from-specular observation directions, and is modeled according to the Small Perturbation Method (SPM) [31]. Conversely, scattering from large-scale roughness accounts for scattering at and around the specular reflection direction and is described through GO. Accordingly, within TSM, surface scattering is completely characterized by the power spectral density (PSD) of the small-scale roughness (also referred to as surface spectrum) and by the probability density function (PDF) of the large-scale roughness slopes. The TSM described in [29; 30] allows for closed-form expressions of only the co-polarized normalized RCS (NRCS), which are obtained by a proper combination of the large- and small-scale scattering contributions. As a matter of fact, a fully polarimetric analysis of the scattered field requires an appropriate modeling of cross- and de-polarization effects, even within the incidence plane. This in turn calls for an accurate evaluation of the off-diagonal terms of the covariance matrix. However, such covariance matrix entries can be obtained only by averaging the SPM term over the large-scale roughness PDF. In the original formulation of TSM, this is accomplished via numerical evaluation of four-fold integrals, which is computationally demanding. Accordingly, TSM cannot be fruitfully exploited in applications where real-time monitoring of wide regions is crucial. In order to overcome this limitation, a fully polarimetric closed-form evaluation of the scattered field can be obtained using Polarimetric TSM (PTSM), which is based on a second-order power series expansion of the tilted-facet SPM covariance matrix around zero large-scale slopes [32]. Accordingly, PTSM is applicable to large-scale RMS slopes up to 0.3 [32]. PTSM was originally derived for monostatic radar systems, e.g., SAR, and, therefore, it is suited to an accurate evaluation of the backscattered signal strength. Later, PTSM has been extended to anisotropic surfaces in the so-called Anisotropic PTSM (A-PTSM) in [33] and, further, to the bistatic case (BA-PTSM) in [26]. In order to implement BA-PTSM, the PSD of the small-scale roughness and the PDF of the slopes of the large-scale roughness must be specified. The two-dimensional (2-D) anisotropic surface spectrum is expressed around the Bragg resonant surface wavenumber as [26]  
\[W_{2D}(\kappa,\phi)=W(\kappa)\Phi(\kappa,\phi) \tag{1}\]  
where \(\kappa\) and \(\phi\) stand for the module and phase of the surface wavenumber vector; \(W(\kappa)\) is the omnidirectional part of the 2-D surface spectrum and \(\Phi(\kappa,\phi)\) is the angular spreading function, which accounts for the anisotropy of the scattering surface. In BA-PTSM, the small-scale roughness PSD \(W_{2D}(\kappa,\phi)\) is described via the high-frequency portion of the Elfouhaily spectrum, whose detailed expression is reported in [33].