The original Rudy model was constructed with no surface roughness, rather using a simple smooth sphere (and parameters were derived based on this). It is clear that surface roughness is not only present, but affects the outgoing thermal emission, as described in a number of papers (see e.g., Heiles & Drake 1963; Hagfors & Moriello 1965; Golden 1979; Mitchell & de Pater 1994).

I have implemented surface roughness within the Rudy model by modifying the emissivity of each surface facet before calculating the emission from it. I do this by pre-calculating the emissivity, given the roughness parameters, for the full range of outgoing emission angles, then interpolating into these pre-calculated values given the particular emission angle of a facet.

I allow for two ways of describing the surface roughness, either as a Gaussian distribution or as an exponential one (Muhleman 1964). For either of these cases, for the range of emission angles, I do a calculation of the average emissivity from 10000 randomly oriented facets with a deviation from normal given by the proper distribution. The only parameter necessary to the roughness model (aside from choosing between a Gaussian or exponential distribution of slopes) is the mean surface slope (very akin to the "surface rms roughness" often used in such models).

For a more in-depth description of the mathematics, go here.