The sound-speed gradient and refraction in the near-ground atmosphere

A systematic description of sound refraction in the near-ground atmosphere is developed by modeling the effective sound-speed gradient with Monin-Obukhov similarity theory. The resulting gradient equation can be recast in a form involving just three nondimensional variables. The first is the ratio of a sound-speed scale (representing the strength of the turbulent fluctuations in the sound speed) to the friction velocity. The second is the ratio of the actual height to a transitional height where contributions from the near-ground wind-speed gradients and the adiabatic lapse rate are roughly balanced. The third is simply the cosine of the angle between the propagation direction and mean wind direction. When the magnitude of the sound-speed scale/friction velocity ratio is large, refraction is unconditionally upward or downward, depending on sign of the ratio. A small value for this ratio indicates nearly neutral atmospheric stratification, for which refraction is determined by the wind direction for small values of the nondimensional height and is upward for larger values. The contribution to refraction from air humidity is determined as a function of the Bowen ratio and found to be significant over wet surfaces. Weather conditions appropriate for measurement of sound pressure levels are also discussed.