Light scattering by random convex polyhedron in geometric optics approximation

Abstract

Based on the convex hull construction algorithm, a new geometrical model of ice crystals is proposed to investigate the scattering properties of cirrus clouds particles. Light scattering matrices involving complete polarization information are calculated in geometric optics approximation for randomly oriented large crystals with random and given convex polyhedron shape. The proposed model construction method and computational scheme of light scattering matrix works 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 and absorption are not considered in this work. The calculated results for the classical hexagonal column model show 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.

Figures (7)

• Figure 1: Demonstration of mesh optimization: before (left) and after (right) merging coplanar triangular faces.
• Figure 2: Examples of random irregular convex polyhedron generated by the program MMCP.
• Figure 3: Examples of regular convex polyhedron generated by the program MMCP.
• Figure 4: Schematic representation of the incident, reflected, and refracted rays, together with the unit vectors defining the polarization configuration. The vectors $\hat{v}_{i,r,t}$ point out of the paper. Unlike Fig.2.2 in yang2006light, the diagrams presented here are consistent with the assumption that all unit vectors $\hat{n}$, which are locally normal to the polyhedron faces, are directed outward.
• Figure 5: Comparison of six Mueller matrix elements for randomly oriented hexagonal column obtained by the program MMCP (black solid line) and by Macke's method macke1993scatteringmacke1996singlemacke_2020_3965488 (red short dash). The horizontal axis represents the scattering angle (in degrees).