Urban noise distributions and the influence of geometric spreading on skewness

Statistical distributions of urban noise levels are influenced by many complex phenomena, including spatial and temporal variations in the source level, multisource mixtures, propagation losses, and random fading from multipath reflections. This article provides a broad perspective on the varying impacts of these phenomena. Distributions incorporating random fading and averaging (e.g., gamma and noncentral Erlang) tend to be negatively skewed on logarithmic (decibel) axes but can be positively skewed if the fading process is strongly modulated by source power variations (e.g., compound gamma). In contrast, distributions incorporating randomly positioned sources and explicit geometric spreading [e.g., exponentially modified Gaussian (EMG)] tend to be positively skewed with exponential tails on logarithmic axes. To evaluate the suitability of the various distributions, one-third octave band sound-level data were measured at 37 locations in the North End of Boston, MA. Based on the Kullback-Leibler divergence as calculated across all of the locations and frequencies, the EMG provides the most consistently good agreement with the data, which were generally positively skewed. The compound gamma also fits the data well and even outperforms the EMG for the small minority of cases exhibiting negative skew. The lognormal provides a suitable fit in cases in which particular non-traffic noise sources dominate.