In this paper a series of numerical simulations of the effect of turbulence on the propagation of acoustic waves in the atmosphere are presented. First the technique of representing the turbulence as a set of realizations of a random field generated by a limited number of Fourier modes is described. Through each individual realization, the acoustic waves are propagated in a wide-angle parabolic approximation to obtain the sound-pressure level. Ensemble averaging is then performed to compute the statistical properties of the acoustic field: mean sound-pressure level, intensity fluctuations, and amplitude distributions. The method is applied first to a nonrefractive atmosphere, both in the presence of a rigid boundary and of an impedance ground, and then to an upward refractive atmosphere with an impedance ground. The model, which contains no adjustable parameters, is tested using the experimental data of Parkin and Scholes, Daigle, and Wiener and Keast. Good agreement between numerical simulations and experiments is obtained.