Light scattering by a random convex polyhedron in the geometric optics approximation

Understanding the optical scattering properties of cirrus ice particles is crucial for optimizing atmospheric circulation models, improving radiative transfer simulations, and advancing our understanding of global climate change, including the assessment of cirrus cloud thinning geoengineering strategies. However, due to the limited understanding of cirrus microphysics and the enormous diversity of ice crystal geometries, the microphysical scattering characteristics of cirrus clouds remain an active and challenging topic of research. In this work, based on the convex hull construction algorithm, a new geometrical model of ice crystals, to our knowledge, is proposed to investigate the scattering properties of cirrus cloud particles. A program named Mueller matrix of convex polyhedron (<i>MMCP</i>) has been developed. Light scattering matrices involving complete polarization information are calculated in geometric optics approximation for randomly oriented large crystals with random and given convex polyhedron shapes. The proposed model construction method and computational scheme of the light scattering matrix work for any convex polyhedron within the scope of geometrical optics. To illustrate the broad applicability of the proposed ice crystal model, scattering matrices for three ice crystal examples with different geometrical shapes are calculated under a unified computational framework. Diffraction, interference, and absorption are not considered in this work. The calculated results for the classical hexagonal column model show the overall agreement with those reported by other authors. The crystal model and scattering matrix computational framework developed in this study are applicable to radiative transfer simulations and remote sensing data interpretation in terrestrial and planetary atmospheres.