Approaches to stratified sampling and variance reduction in outdoor sound propagation calculations

As an aid to efficiently predicting outdoor sound propagation, meteorological and refractive conditions are often partitioned into classes or (in statistical terminology) strata. Average predictions are then made by weighting individual predictions from each stratum. Some examples are Marsh's scheme based on Pasquill stability classes, the Harmonoise scheme based on a log-linear parameterization of the effective sound-speed profile, and various schemes utilizing Monin-Obukhov similarity theory parameters. Latin hypercube sampling (LHS) is a general approach to stratified sampling that may also be used for outdoor sound propagation. The success of stratified sampling depends on whether useful classes can be chosen, in the sense of efficiently capturing the diversity of propagation conditions, while reducing the variance within the classes. The overall reduction in error variance can be quantified using equations known from statistics. In this paper, we adopt such an approach to analyzing the performance of several diverse stratified sampling schemes. The analysis utilizes a large synthetic database of excess attenuation calculations, which is generated by the parabolic equation method and spans a large range of ground, refractive, and turbulence conditions.