Closed-Form Anisotropic Polarimetric Two-Scale Model for Fast Evaluation of Sea Surface Backscattering

The polarimetric two-scale model (PTSM) was introduced a few years ago as an electromagnetic scattering model to be used within algorithms for soil moisture retrieval from polarimetric synthetic aperture radar (SAR) data. PTSM inherits the ability to account for depolarization effects from the original two-scale model (TSM), and, with respect to the latter, it has the advantage to provide closed-form expressions of the elements of the covariance matrix that hold for moderate large-scale surface slopes. This allows a very fast evaluation of scattering, since numerical integration needed by the original TSM is avoided. The TSM, also called composite model (CM), has been extensively used to study scattering from the sea surface, so that it is natural to explore the use of PTSM for the same purpose. However, in its current formulation, PTSM assumes that large-scale surface slope distribution and small-scale roughness spectrum are isotropic. This is not realistic for the sea surface, for which anisotropy is dictated by the wind direction. Accordingly, we here extend PTSM to account for surface roughness anisotropy, so obtaining the anisotropic PTSM (A-PTSM). In addition, as a second contribution, we provide A-PTSM expressions also in the circular polarization basis, which may be useful for some SAR sensor polarimetric configurations. Finally, we compare A-PTSM results with sea surface scattering measurements available in the literature and with results of the second-order small-slope approximation (SSA2). In particular, as a third original contribution of this paper, an analytical closed-form expression of the ratio of crosspolarized normalized radar cross sections (NRCSs) obtained by SSA2 and A-PTSM is provided.