Long-range outdoor sound propagation is characterized by a large variance in sound pressure levels due to factors such as refractive gradients, turbulence, and topographic variations. While conventional numerical methods for long-range propagation address these phenomena, they are costly in computational memory and time. In contrast, machine-learning algorithms provide very fast predictions, which this study considers. Observations from either experimental data, or surrogate data from a numerical method, are required for the training of machine-learning models. In this study, a comprehensive training set for the machine learning was created from excess attenuation predictions made with a Crank-Nicholson parabolic equation (CNPE) model. Latin hypercube sampling of the parameter space (source frequency, meteorological factors, boundary conditions, and propagation geometries) generates a set of input for the CNPE model and machine-learning models. Consideration is given to ensemble decision trees, ensemble neural networks, and cluster-weighted models for nonlinear regression. The large variance in excess attenuation, from the CNPE model, presents a challenge for accurate machine-learning model predictions. For example, given 5000 samples the overall root-mean-square error for an ensemble decision tree model is 6.7 dB. Errors related to sample size, modeling approaches, and propagation ranges are quantified in this study.

Atmospheric conditions greatly affect the propagation of the sound. Currently, little information exists regarding the amount of variation in level and spectra of blast noise that is caused by changing meteorological conditions along the propagation path. Available meteorological models accurately predict vertical sound speed profiles only up to the top of the boundary layer. For long-range propagation, this is inadequate. Vertical sound speed profile data and resulting propagation effects will help to better explain the effects of atmospheric refraction in sound propagation. This report detailed the procedures and equipment used to carry out a series of blast noise experiments at White Sands Missile Range, NM and Fort Leonard Wood, MO from 2007 to 2009. The data provided by this large-scale experiment comprise a definitive dataset for the effects of a wide range of meteorological conditions on long-range high-energy blast sound propagation in climate types similar to the majority of continental United States (CONUS) military installations (arid desert and temperate vegetated). The experiment also captured a comprehensive set of meteorological measurements over the duration of the experiments.

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