Atmospheric ice crystals scatter sunlight, affecting Earth’s climate through the radiation properties of cirrus clouds. Naturally occuring 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 $R_{\mathrm{q}}$. 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 $\mu$ m from both above and below the planar surface are studied. A refractive index for ice $m=1.313+\mathrm{i}5.889·{10}^{-10}$ is used throughout the computations. Results are averaged over ten rough surface realizations for a specific $H,$ $R_{\mathrm{q}}$-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 $R_{\mathrm{q}}$ 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.

大气冰晶散射阳光，通过卷云的辐射特性影响地球的气候。天然存在的表面粗糙度及其对冰晶散射特性的影响仍然未知。通过将有限，薄的表面粗糙度元素放置在无限大的平面真空冰边界上，研究了具有粗糙表面的冰晶的散射。使用基于分数布朗运动的统计模型生成元素。水平粗糙度标度由Hurst指数描述$H$ 以及垂直粗糙度标度和均方根粗糙度参数 ${\mathrm{[R}}_{\mathrm{q}}$。使用离散偶极近似软件ADDA（1.34b版）的表面模式执行计算。波长为0.5的几个入射方向$\mu$研究了平面上方和下方的m。冰的折射率$米=1.313+\mathrm{一世}5.889·{10}^{-10}$在整个计算中使用。针对特定表面，将十个粗糙表面实现的结果取平均值$H，$ ${\mathrm{[R}}_{\mathrm{q}}$-一对。

将粗糙元素的散射与相应光滑元素的散射进行比较。元素越粗糙，通过表面传输的散射强度越多。粗糙元件的线性极化度比光滑元件大得多。而且，发现粗糙度虽然本身会影响极化，但是确切的表面形态似乎没有显着影响。垂直粗糙度标尺${\mathrm{[R}}_{\mathrm{q}}$ 对光散射结果的影响比水平刻度更大 $H$。在几乎平行于冰介质内的真空冰边界的方向上检测到增强的角散射。可以通过强大的内部反射机制解释该现象。

可以将表面粗糙度模型以及此处使用的光散射方法结合到大冰晶和其他粒子的几何光学射线追踪计算中。