A 2-D nonlinear time domain computational model of sonic boom propagation has been modified to incorporate the effects of atmospheric turbulence. This model, based on the Nonlinear Progressive wave Equation (NPE) of McDonald and Kuperman, is used to propagate N-waves from the upper turbulent boundary layer (TBL) to the ground through different turbulence realizations. The output of the model provides detailed images of the full wave field at arbitrary heights above the ground, as well as shock profiles at specified locations along the wavefront. Preliminary results show multiple scales of spiking and rounding of shock profiles that are clearly correlated with wavefront focusing and defocusing, respectively. These waveform distortions, as well as their spatial variation along the wavefront, qualitatively match those seen in sonic booms recorded at the ground. These results are also consistent with earlier studies that applied the NPE to weak shocks with rippled wavefronts propagating through a homogeneous medium; these studies demonstrated that the combination of nonlinear and geometric effects arising from focusing wavefronts can produce the variety of distorted sonic boom waveforms observed in test flights. This paper describes the details of the sonic boom propagation code, including the implementation of turbulence effects, and discusses its performance on benchmark problems.