The interference spectrum between direct and ground‐reflected sound waves is strongly influenced by fluctuations in their phase and amplitude induced by propagation through turbulence. Measurements of the interference spectrum at distances up to 45 m over a flat asphalt surface were shown previously to be in satisfactory agreement with a spherical wave theory that allowed for partial covariance between the phases of the interfering waves. The amount of covariance was claculated from simultaneous measurements of wind and temperature fluctuations in the atmosphere. This theory has now been extended to include propagation over ground of finite acoustic impedance and provides an explanation for measurements of jet noise over grass to a distance of 1100 m. Above 300 Hz the sound levels are up to 10 dB higher than predicted by coherent acoustic theory. The meteorological parameters were used as constants adjusted for best fit and agreement is obtained by assuming standard deviations in phase velocity of about 1 in 1000, and a correlation length of about 1 m—typical of values measured in Ottawa. Covariance of sound amplitude, being relatively more important at long distances, is now also included—at short distances its effect is negligible compared with that of phase convariance. Phase‐amplitude convariance is negligible at all distances.