A novel multiple small-angle scattering framework for interpreting anisotropic polarization pattern of lidar returns from water clouds

Abstract This paper presents a novel mathematical framework to interpret the polarized lidar backscattering pattern for 1D water clouds. The framework is based on the multiple scattering of the lidar signals within small-angle range. An approximation is made that both the outgoing and returning trajectories are assumed to be along nearly planar forward scattering sequences. For lidar axial symmetrical system, a quasi-linear mathematical relationship is built between the observed reduced Mueller matrix and the backscattering phase matrix, and can be generalized to arbitrary scattering orders. For validation, we extend the radiative transfer model MSCART to simulate linearly- and circularly-polarized lidar signals. Meanwhile, we propose the azimuthal Fourier expansion to extract the reduced Mueller matrix results from the MSCART simulation. The numerical evaluation experiments demonstrate that our derived mathematical expressions could extend the polar-angle dependence of the reduced Mueller matrix from second-order to higher-order multiple scatterings. The relation can serve as a useful tool in understanding lidar polarization observations and designing a CCD polarized lidar instrument.