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Surface roughness of ice crystals is a morphological parameter important to the scattering characteristics of these particles. The intent of this paper, reported in two parts (hereafter, Parts I and II), is to investigate the accuracy associated with some simplifications in calculating the single-scattering properties of roughened ice crystals and to quantify the effect of surface roughness on the retrieval of the optical and microphysical properties of ice clouds from satellite observations. In Part I, two ray-tracing schemes, a rigorous algorithm and an approximate algorithm with a simplified treatment of surface roughness, are employed to calculate the single-scattering properties of randomly oriented hexagonal ice crystals with size parameters in the geometric optics regime. With the rigorous approach, it requires substantial computational effort to accurately account for the multiple external reflections between various roughness facets and the reentries of outgoing rays into the particles in the ray-tracing computation. With the simplified ray-tracing scheme, the ray-tracing calculation for roughened particles is similar to that for smooth particles except that, in the former case, the normal of the particle surface is statistically perturbed for each reflection-refraction event. The simplified ray-tracing scheme can account for most the effects of surface roughness on particle single-scattering properties without incurring substantial demand on computational resources and, thus, provides an efficient way to compute the single-scattering properties of roughened particles. The effect of ice-crystal surface roughness on the retrieval of the optical thicknesses and effective particle sizes of cirrus clouds is reported in Part II.