Recent advances in ultraviolet (UV) semiconductor sources and detectors have inspired significant research activities in short-range UV communications, particularly in non-line-of-sight (NLOS) channel conditions due to atmospheric scattering. However, a scattering channel involves complex interactions of photons with atmospheric particles. This paper presents a parametric channel model that greatly simplifies channel characterization. For a short range link, single scattering may dominate in some scenarios. We model the channel impulse response with a gamma function as well as its variants to better fit the prediction by a widely adopted analytical single scattering model. Normalized mean square fitting error is adopted to validate our parametric model. Path losses and channel bandwidths are subsequently studied under different geometrical link configurations.