Light scattering by fractal roughness elements on ice crystal surfaces

Abstract

Atmospheric ice crystals scatter sunlight, affecting Earth’s climate through the radiation properties of cirrus clouds. Naturally occurring surface roughness and its effect on the scattering properties of ice crystals remain largely unknown. Scattering by ice crystals with rough surfaces is studied by placing a finite, thin surface-roughness element on an infinitely large, planar vacuum-ice boundary. The elements are generated using a statistical model based on fractional Brownian motion. The horizontal roughness scale is described by the Hurst exponent H and the vertical roughness scale with the root-mean-square roughness parameter Rq. The computations are performed with the surface mode of the Discrete Dipole Approximation software ADDA (version 1.34b). Several incident directions for wavelength of 0.5 µm from both above and below the planar surface are studied. A refractive index for ice m=1.313+i5.889×10−10 is used throughout the computations. Results are averaged over ten rough surface realizations for a specific H,Rq-pair.Scattering by the rough elements is compared to that by the corresponding smooth elements. The rougher the element is, the more of the scattered intensity is transmitted through the surface. The rough elements have distinctively smoother angular distributions for the degree of linear polarization than their smooth counterparts. Also, it is found that while roughness itself affects polarization, the exact surface morphology does not seem to have a significant effect. The vertical roughness scale Rq has a larger effect on the light scattering results than the horizontal scale H. Enhanced angular scattering is detected in directions nearly parallel to the vacuum-ice boundary within the ice medium. The phenomenon is explained with a strong internal reflection mechanism.The model for surface roughness, along with the light scattering methodology used here, could be incorporated into geometric optics ray-tracing computations for large ice crystals and other particles.