With radar sounders, coherent backscattering simulations from global planetary DEMs typically display a deficit in diffuse clutter, which is mainly due to the implicit assumption that roughness at scales below the resolution of the DEM is absent. Indeed, while polynomial approximations of the phase evolution across the facet allow for fast and mathematically rigorous simulators, the coarse resolution of these planetary DEMs leads to a potentially significant portion of the backscattering response being neglected. In this paper, we derive the analytical phase response of a rough rectangular facet characterised by Gaussian roughness and a Gaussian isotropic correlation function under the linear phase approximation. Formulae for the coherent and incoherent power scattered by such an object are obtained for arbitrary bistatic scattering angles. Validation is done both in isolation and after inclusion in different Stratton-Chu simulators. In order to illustrate the different uses of such a formulation, we reproduce two lunar radargrams acquired by the LRS instrument with a Stratton-Chu simulator incorporating the proposed rough facet phase integral, and we show that the original radargrams are significantly better-reproduced than with state-of-the-art methods, at a similar computational cost. We also show how the rough facet integral formulation can be used in isolation to better characterise subglacial water bodies on Earth.

We evaluate several high-order quadrature schemes for accuracy and efficacy in obtaining orientation-averaged single-scattering properties (SSPs). We use the highly efficient MIDAS to perform electromagnetic scattering calculations to evaluate the gain in efficiency from these schemes. MIDAS is shown to be superior to DDSCAT, a popular discrete dipole approximation (DDA) method. This study is motivated by the fact that quality physical precipitation retrievals rely on using accurate orientation-averaged SSPs derived from realistic hydrometeors as input to radiative transfer Models (RTMs). The DDA has been a popular choice for single-scattering calculations, due to its versatility with respect to target geometry. However, being iterative-solver-based (ISB), the most used DDA codes, e.g. DDSCAT and ADDA, must solve the scattering problem for each orientation of the target separately. As the size parameter and geometric anisotropy of the hydrometeor increase, the number of orientations needed to obtain accurate orientation-averages can increase drastically and so does the computation cost incurred by the ISB-DDA methods. MIDAS is a Direct-Solver-Based (DSB) code, its decomposition of the original large matrix with a high rank into multiple more manageable smaller matrices of lower ranks makes it much more computationally efficient while maintaining excellent accuracy. In addition, direct solvers consider all requested orientations at once, giving MIDAS further advantage over popular ISB-DDA methods. MIDAS, when combined with high-order quadrature for orientation averaging, can be greater than three orders of magnitude more efficient in obtaining RTM-ready SSPs of complex-shaped hydrometeors than existing ISB-DDA methods, with the native quadrature schemes they offer.