Reichardt, J., M. Hess, A. Macke (2000): Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions, Appl. Opt., 39, 1895-1910.

Multiple-scattering correction factors for cirrus particle extinction coefficients measured with Raman and high spectral resolution lidars are calculated with a radiative-transfer model. Cirrus particle-ensemble phase functions are computed from single-crystal phase functions derived in a geometrical-optics approximation. Seven crystal types are considered. In cirrus clouds with height-independent particle extinction coefficients the general pattern of the multiple-scattering parameters has a steep onset at cloud base with values of 0.5-0.7 followed by a gradual and monotonic decrease to 0.1-0.2 at cloud top. The larger the scattering particles are, the more gradual is the rate of decrease. Multiple-scattering parameters of complex crystals and of imperfect haexagonal columns and plates can be well approximated by those of projected-area equivalent ice spheres, whereas perfect hexagonal crystals show values as much as 70% higher than those of spheres. The dependencies of the multiple-scattering parameters on cirrus particle spectrum, base height and geometric depth and on the lidar parameters laser wavelength and receiver field of view, are discussed, and a set of multiple-scattering parameter profiles for the correction of extinction measurements in homogeneous cirrus is provided.