A fast and accurate ray model is developed for sound propagation in a downward refracting atmosphere. The model employs a new approach to the classification and computation of ray paths and caustic curves. The approach is valid for a large set of smooth sound-speed profiles, including realistic, nonlinear profiles such as the logarithmic profile. An ordered series of rays and caustics is found in this case, including caustics with a cusp. The sound-pressure field is computed by combining geometrical acoustics and the theory of caustics. The field on the illuminated side of a caustic is computed by modifying the geometrical-acoustics solution. The field on the shadow side of a caustic, i.e., the caustic diffraction field, is computed by extrapolation of various quantities into the shadow region. Different approaches to this extrapolation are considered. It is found that horizontal extrapolation gives the best results. The accuracy of the ray model is demonstrated by comparison with numerical solutions of the one-way wave equation. If caustic diffraction fields are ignored, discontinuities of more than 10 dB occur in the sound-pressure field.