Research On The Mechanism Of Multiple Small-angle Scattering For Interpreting Polarization Pattern Of Lidar Returns From Water Clouds

Accurately determining cloud microphysical properties is of great significance for the earth-atmosphere radiation budget and the climate change.Lidar polarization technique is one of the main sounding tools in retrieving cloud microphysical parameters.For water clouds,mul-tiple scattering contribution is significant in lidar return signals due to the short mean free path-length of laser beams.Meanwhile,consider that single backscattering from water cloud does not change the polarization state of laser beams,lidar depolarization ratio and anisotropic polar-ization patterns thus results from water cloud multiple scattering.Currently,lidar water cloud multiple scattering polarization signal interpretation is majorly based on lidar polarized radiative transfer simulations or a simplified mathematical relation between lidar depolarization ratio and particle scattering phase matrix,which is derived by the second-order small-angle scattering ap-proximation.The physical explanation in the Mueller matrix pattern of lidar returns applicable to arbitrary scattering orders doesn't yet exist.However the 2D angular backscattering Mueller matrix pattern of lidar returns contains the most complete information about experimental ob-servations.Therefore,this paper aims to establish theoretical relationship between multiple scattering Mueller matrix pattern of lidar returns and water cloud scattering phase matrix,and further reveal multiple scattering mechanism in lidar water cloud backscattering polarization pattern.In this paper,the fundamental starting point is classic multiple small-angle scattering ap-proximation in lidar polarized radiative transfer.That is,lidar signals are mainly contributed by laser beams that undergone many small-angle forward scatterings and only one large-angle backward scattering.Based on it,we further assume that multiple forward scatterings,regard-less of an outgoing or return light beam,almost occur on a fixed plane.Under this theoretical approximation,we establish a quasi-linear simplified mathematical relationship between lidar reduced Mueller matrix and particle backscattering phase matrix.Specifically,the normalized reduced Mueller matrix elements are quasi-linearly proportional to the normalized backscat-tering phase matrix elements.Meanwhile,the ensemble-averaging dihedral angle between the outgoing and return scattering plane and the ensemble-averaging rotation angle of multiple for-ward scattering planes with respect to the fixed scattering plane can affect the linear correlation between the reduced Mueller matrix and the scattering phase matrix to a certain extent.The derived mathematical exprresions are applicable to arbitrary scattering orders.In order to com-prehensively verify and evaluate the theoretical relation,we firstly extend the three-dimensional vector radiative transfer model MSCART to simulating the CCD Stokes vector signal of lidar multiple scattering returns.The numerical simulation accuracy of this model has been validated by the experimental observation results of polystyrene sphere solution and the corresponding second-order analytical results.Secondly,a large number of Stokes vector patterns of polarized lidar returns are simulated for water cloud layer with different water cloud droplet effective radii and effective variances.Meanwhile,we propose an azimuthal Fourier expansion technique.It can improve numerical simulation efficiency and thus make a large number of simulation ex-periments possible.Because this technique ensures that we can derive complete polar angle dependent reduced Mueller matrix only from the Stokes vector patterns of horizontal linear po-larization lidar returns and right-handed circular polarization lidar returns.Finally,the numer-ical evaluation results demonstrate that,regardless of the second-order or multiple scattering results,the mathematical relation we established can successfully predict the lidar receiving polar-angle dependence of reduced Mueller matrix elements.This relation also reveals that the sensitivity of lidar polarized signals to water cloud particle size distribution parameters is mainly due to the backscattering phase matrix elements(especially P₃₃).In addition,the other two influencing factors will also adjust the sensitivity of the lidar polarized signal to particle size to a certain extent.In summary,we present a new multiple small-angle scattering framework to establish a simplified mathematical relationship in this paper,which can serve as a useful theoretical tool in understanding lidar polarization observations and designing a polarized lidar instrument.