Assessment of the COVID-19 infection risk at a workplace through stochastic microexposure modeling.

BACKGROUND: The COVID-19 pandemic has a significant impact on economy. Decisions regarding the reopening of businesses should account for infection risks. OBJECTIVE: This paper describes a novel model for COVID-19 infection risks and policy evaluations. METHODS: The model combines the best principles of the agent-based, microexposure, and probabilistic modeling approaches. It takes into account specifics of a workplace, mask efficiency, and daily routines of employees, but does not require specific inter-agent rules for simulations. Likewise, it does not require knowledge of microscopic disease related parameters. Instead, the risk of infection is aggregated into the probability of infection, which depends on the duration and distance of every contact. The probability of infection at the end of a workday is found using rigorous probabilistic rules. Unlike previous models, this approach requires only a few reference data points for calibration, which are more easily collected via empirical studies. RESULTS: The application of the model is demonstrated for a typical office environment and for a real-world case. CONCLUSION: The proposed model allows for effective risk assessment and policy evaluation when there are large uncertainties about the disease, making it particularly suitable for COVID-19 risk assessments.

Efficient prediction of acoustic pulses accounting for fractional travel time.

Predicting a full waveform of an acoustic broadband signal propagating over different impedance surfaces is a stringent test of both the method used in the modeling of propagation and the surface impedance models. It has been shown that predicted waveforms might be sensitive to the fractional travel time, when the propagation time of the pulse does not equal an integer number of computational time steps. A method overcoming this issue is developed and demonstrated for different propagation conditions: a pulse propagating over a snow layer, frozen ground, and their combinations along the propagating path with homogeneous and vertically stratified atmosphere for a range of 60 m. For the numerical simulations, a conventional one-way parabolic equation with the Crank-Nicholson numerical algorithm is modified to improve computational efficiency and insure that the experimental time of arrival and spatial location of the receiver are matched exactly to the digital grids used in the simulations. The results are in a good agreement with experimental measurements and prior knowledge, and confirm that physical properties of a snow layer, sublayer ground, atmospheric conditions, and the order of range dependent ground properties affect the pulse waveforms.

Spatial-temporal coherence of acoustic signals propagating in a refractive, turbulent atmosphere.

Propagation of acoustic signals above an impedance ground in a refractive, turbulent atmosphere with spatial-temporal fluctuations in temperature and wind velocity is considered. Starting from a parabolic equation, and using the Markov approximation and a locally frozen turbulence hypothesis, closed-form equations for the spatial-temporal statistical moments of arbitrary order of the sound-pressure field are derived. The general theory provides a basis for analysis of many statistical characteristics of broadband and narrowband acoustic signals for different geometries of propagation: line-of-sight propagation, multipath propagation in a refractive atmosphere above an impedance ground, and sound scattering into a refractive shadow zone. As an example of application of this theory, the spatial-temporal coherence of narrowband acoustic signals for line-of-sight propagation is calculated and analyzed. The coherence time of acoustic signals is studied numerically for meteorological conditions ranging from cloudy to sunny conditions, and with light, moderate, and strong wind. The results obtained are compared with available experimental data.

Description and quantification of uncertainty in outdoor sound propagation calculations.

The accuracy of outdoor sound propagation predictions is often limited by imperfect knowledge of the atmospheric and ground properties, and random environmental variations such as turbulence. This article describes the impact of such uncertainties, and how they can be efficiently addressed and quantified with stochastic sampling techniques such as Monte Carlo and Latin hypercube sampling (LHS). Extensions to these techniques, such as importance sampling based on simpler, more efficient propagation models, and adaptive importance sampling, are described. A relatively simple example problem involving the Lloyd's mirror effect for an elevated sound source in a homogeneous atmosphere is considered first, followed by a more complicated example involving near-ground sound propagation with refraction and scattering by turbulence. When uncertainties in the atmospheric and ground properties dominate, LHS with importance sampling is found to converge to an accurate estimate with the fewest samples. When random turbulent scattering dominates, the sampling method has little impact. A comprehensive computational approach is demonstrated that is both efficient and accurate, while simultaneously incorporating broadband sources, turbulent scattering, and uncertainty in the environmental properties.

Assessment of systematic measurement errors for acoustic travel-time tomography of the atmosphere.

Two algorithms are described for assessing systematic errors in acoustic travel-time tomography of the atmosphere, the goal of which is to reconstruct the temperature and wind velocity fields given the transducers' locations and the measured travel times of sound propagating between each speaker-microphone pair. The first algorithm aims at assessing the errors simultaneously with the mean field reconstruction. The second algorithm uses the results of the first algorithm to identify the ray paths corrupted by the systematic errors and then estimates these errors more accurately. Numerical simulations show that the first algorithm can improve the reconstruction when relatively small systematic errors are present in all paths. The second algorithm significantly improves the reconstruction when systematic errors are present in a few, but not all, ray paths. The developed algorithms were applied to experimental data obtained at the Boulder Atmospheric Observatory.

Effect of randomly varying impedance on the interference of the direct and ground-reflected waves.

A randomly varying ground impedance is introduced into the solution for the sound field produced by a point source in a homogeneous atmosphere above a flat ground. The results show that in general the ground with a random impedance cannot be represented by an effective, non-random impedance. The behavior of the solution is studied with a relaxation model for the impedance in which porosity and the static flow resistivity are random variables. Mean values and standard deviations are adopted from measurements of two types of ground surfaces. For both surfaces, the mean intensity of the sound field above a random-impedance ground deviates only slightly from the intensity above a non-random impedance. The normalized standard deviation of intensity fluctuations can, however, be greater than one, thus indicating that for a particular realization of the random impedance, the sound intensity might significantly deviate from the intensity for a non-random impedance.

Incorporating source directionality into outdoor sound propagation calculations.

Many outdoor sound sources, such as aircraft or ground vehicles, exhibit directional radiation patterns. However, long-range sound propagation algorithms are usually formulated for omnidirectional point sources. This paper describes two methods for incorporating directional sources into long-range sound propagation algorithms. The first is the equivalent source method (ESM), which determines a compact distribution of omnidirectional point sources reproducing a given directivity pattern in the far field. This method can be used with any propagation algorithm because it explicitly reconstructs a source function as a set of point sources with certain amplitudes and positions. The second is a directional starter method (DSM), which is developed specifically for the parabolic equation (PE) algorithms. This method derives narrow- or wide-angle directional starter fields, corresponding to a given source directivity pattern, without reconstructing the equivalent source distribution. Although the ESM can also be used for the PE, the DSM is simpler and can be more convenient, especially if the sound propagation is calculated only for one or a few azimuthal directions. While these two methods are found to produce generally distinct starter fields, they nonetheless yield identical directivity patterns.

Source localization from an elevated acoustic sensor array in a refractive atmosphere.

Localization of sound sources on the ground from an acoustic sensor array elevated on a tethered aerostat is considered. To improve estimation of the source coordinates, one should take into account refraction of sound rays due to atmospheric stratification. Using a geometrical acoustics approximation for a stratified moving medium, formulas for the source coordinates are derived that account for sound refraction. The source coordinates are expressed in terms of the direction of sound propagation as measured by the sensor array, its coordinates, and the vertical profiles of temperature and wind velocity. Employing these formulas and typical temperature and wind velocity profiles in the atmosphere, it is shown numerically that sound refraction is important for accurate predictions of the source coordinates. Furthermore, it is shown that the effective sound speed approximation, which is widely used in atmospheric acoustics, fails to correctly predict the source coordinates if the grazing angle of sound propagation is relatively large.

Tomographic reconstruction of atmospheric turbulence with the use of time-dependent stochastic inversion.

Acoustic travel-time tomography allows one to reconstruct temperature and wind velocity fields in the atmosphere. In a recently published paper [S. Vecherin et al., J. Acoust. Soc. Am. 119, 2579 (2006)], a time-dependent stochastic inversion (TDSI) was developed for the reconstruction of these fields from travel times of sound propagation between sources and receivers in a tomography array. TDSI accounts for the correlation of temperature and wind velocity fluctuations both in space and time and therefore yields more accurate reconstruction of these fields in comparison with algebraic techniques and regular stochastic inversion. To use TDSI, one needs to estimate spatial-temporal covariance functions of temperature and wind velocity fluctuations. In this paper, these spatial-temporal covariance functions are derived for locally frozen turbulence which is a more general concept than a widely used hypothesis of frozen turbulence. The developed theory is applied to reconstruction of temperature and wind velocity fields in the acoustic tomography experiment carried out by University of Leipzig, Germany. The reconstructed temperature and velocity fields are presented and errors in reconstruction of these fields are studied.