Signal power distributions for simulated outdoor sound propagation in varying refractive conditions.

Probability distributions of acoustic signals propagating through the near-ground atmosphere are simulated by the parabolic equation method. The simulations involve propagation at four angles relative to the mean wind, with frequencies of 100, 200, 400, and 800 Hz. The environmental representation includes realistic atmospheric refractive profiles, turbulence, and ground interactions; cases are considered with and without parametric uncertainties in the wind velocity and surface heat flux. The simulated signals are found to span a broad range of scintillation indices, from near zero to exceeding ten. In the absence of uncertainties, the signal power (or intensity) is fit well by a two-parameter gamma distribution, regardless of the frequency and refractive conditions. When the uncertainties are included, three-parameter distributions, namely, the compound gamma or generalized gamma, are needed for a good fit to the simulation data. The compound gamma distribution appears preferable because its parameters have a straight forward interpretation related to the saturation and modulation of the signal by uncertainties.

Vertical and slanted sound propagation in the near-ground atmosphere: Coherence and distributions.

Atmospheric turbulence causes acoustic signals to fluctuate and diminishes their coherence. These phenomena are important in applications such as source localization and sonic boom propagation. This article provides formulations for the spatial, cross-frequency, and temporal coherences of narrowband acoustic signals propagating over vertical and slanted paths in the atmosphere. Formulations for single- and two-point distributions of acoustic signals are also overviewed. The theoretical formulations are compared with data from a comprehensive sound propagation experiment carried out in 2018 at the National Wind Technology Center (Boulder, CO). The theories for sound propagation in a turbulent atmosphere, when combined with turbulence models incorporating shear and buoyancy instabilities, correctly predict the measured spatial coherence, which is primarily affected by small-scale isotropic turbulence. For relatively small coherence times, this approach also correctly predicts the temporal coherence. However, the approach underpredicts the cross-frequency coherence and temporal coherence for relatively large coherence times, which are affected by large-scale anisotropic buoyancy-driven velocity fluctuations. For different regimes ranging from unsaturated to fully saturated scattering, the measured distributions agree well with the theoretical predictions.

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.

Vertical and slanted sound propagation in the near-ground atmosphere: Amplitude and phase fluctuations.

Sound propagation along vertical and slanted paths through the near-ground atmosphere impacts detection and localization of low-altitude sound sources, such as small unmanned aerial vehicles, from ground-based microphone arrays. This article experimentally investigates the amplitude and phase fluctuations of acoustic signals propagating along such paths. The experiment involved nine microphones on three horizontal booms mounted at different heights to a 135-m meteorological tower at the National Wind Technology Center (Boulder, CO). A ground-based loudspeaker was placed at the base of the tower for vertical propagation or 56 m from the base of the tower for slanted propagation. Phasor scatterplots qualitatively characterize the amplitude and phase fluctuations of the received signals during different meteorological regimes. The measurements are also compared to a theory describing the log-amplitude and phase variances based on the spectrum of shear and buoyancy driven turbulence near the ground. Generally, the theory correctly predicts the measured log-amplitude variances, which are affected primarily by small-scale, isotropic turbulent eddies. However, the theory overpredicts the measured phase variances, which are affected primarily by large-scale, anisotropic, buoyantly driven eddies. Ground blocking of these large eddies likely explains the overprediction.

Extending standard urban outdoor noise propagation models to complex geometries.

A hybrid method that combines a noise engineering method and the 2.5D boundary element method approximates outdoor sound propagation in large domains with complex objects more accurately than noise engineering methods alone and more efficiently than reference methods alone. Noise engineering methods (e.g., ISO 9613-2 or CNOSSOS-EU) efficiently approximate sound levels from roads, railways, and industrial sources in cities for simple, box-shaped geometries by first finding the propagation paths between the source and receiver, then applying attenuations (e.g., geometrical divergence and atmospheric absorption) to each path, and finally incoherently summing all of the path contributions. Standard engineering methods cannot model more complicated geometries but introducing an additional attenuation term quantifies the influence of complex objects. Calculating this extra attenuation term requires reference calculations but performing reference computations for each path is too computationally expensive. Thus, the extra attenuation term is linearly interpolated from a data table containing the corrections for many source/receiver positions and frequencies. The 2.5D boundary element method produces the levels for the real and simplified geometries and subtracting them yields a table of corrections. For a T-shaped barrier with two buildings, this approach reduces the mean error by approximately 2 dBA compared to a standard engineering method.