The effects of surface roughness on the scattering properties of hexagonal columns with sizes from the Rayleigh to the geometric optics regimes

Effects of surface roughness on the optical scattering properties of ice crystals are investigated using a randomwave superposition model of roughness that is a simplification of models used in studies of scattering by surface water waves. Unlike previous work with models of rough surfaces applicable only in limited size ranges, such as surface perturbation methods in the small particle regime or the tilted-facet (TF) method in the large particle regime, ours uses a single roughness model to cover a range in sizes extending from the Rayleigh to the geometric optics regimes. The basic crystal shape we examine is the hexagonal column but our roughening model can be used for a wide variety of particle geometries. To compute scattering properties over the range of sizes we use the pseudo-spectral time domain method (PSTD) for small to moderate sized particles and the improved geometric optics method (IGOM) for large ones. Use of the PSTD with our roughness model is straightforward. By discretizing the roughened surface with triangular sub-elements, we adapt the IGOM to give full consideration of shadow effects, multiple reflections/refractions at the surface, and possible reentrance of the scattered beams. We measure the degree of roughness of a surface by the variance ðs2Þ of surface slopes occurring on the surfaces. For moderately roughened surfaces ðs2 ≤0:1Þ in the large particle regime, the scattering properties given by the TF and IGOM agree well, but differences in results obtained with the two methods become noticeable as the surface becomes increasingly roughened. Having a definite, albeit idealized, roughness model we are able to use the combination of the PSTD and IGOM to examine how a fixed degree of surface roughness affects the scattering properties of a particle as the size parameter of the particle changes. We find that for moderately rough surfaces in our model, as particle size parameter increases beyond about 20 the influence of surface roughness on the scattering properties of randomly oriented hexagonal particles starts to become evident. Somewhat surprisingly, in calculations using the IGOM certain qualitatively clear differences in patterns of roughness that have the same s2 result in negligible difference in scattering effects. The phase matrix elements given by the IGOM for smooth and roughened hexagonal columns with the “large” size parameter 100 agree very well with the PSTD results, and the integral scattering properties given by the PSTD for small-to-moderate sized particles are shown to merge smoothly with those given by the IGOM for moderate-to-large sizes. & 2013 Elsevier Ltd. All rights reserved. All rights reserved.