The effect of atmospheric turbulence on the loudness of shaped supersonic signatures perceived at the ground may be an important consideration for the certification and design of civil supersonic aircraft. To quantify the effect of turbulence, a numerical model suitable for predicting variations in the Perceived Level (PL) metric has been developed. The model solves a nonlinear propagation equation accounting for turbulence in two or three spatial dimensions, illuminating the variation of the PL across the ground. Inclusion of the third spatial dimension is shown to increase the predicted PL range and the standard deviation. Because both transverse dimensions are accounted for in the three-dimensional simulations, the distorted waveforms may be sampled with “virtual” arrays to estimate the performance of different microphone array types in sampling the PL distribution statistics. Repeated random sampling finds that the PL standard deviation is underpredicted by the arrays, while the mean is unbiased. Some strategies are suggested by the analysis for improving array performance in terms of increasing the accuracy and precision of the array-sampled PL standard deviation and mean.