Impacts of scattering plane randomization on lidar multiple scattering polarization signals from water clouds

Under a general approximation of multiple scattering paths involving small-angle scatterings interspersed with occasional large-angle scatterings, we performed Monte Carlo vector radiative transfer simulations to investigate the spatial and temporal distribution of the reduced Mueller matrix (RMM) of lidar returns from water clouds. Our findings indicate that the normalized RMM elements ${\tilde{M}}_{22}^{\prime }$ and ${\tilde{M}}_{33}^{\prime }$ are highly affected by two types of scattering plane randomizations: the overall rotation of scattering planes along multiple scattering paths, and the correlation of the rotation of scattering planes along sub-paths separated by large-angle scatterings. The simulation results reveal that the specific geometries of lidar multiple scattering paths, driven by strong forward-scattering in water clouds, result in the two scattering plane randomizations producing markedly different effects on the linear polarization. This insight not only elucidates the varying decline rates in linearly cross-polarized pattern contrast and linear polarization degree observed in current on-beam lidars but also establishes a basis for analyzing polarized signals in potential future off-beam lidar systems.