23 Jul 2024

Signal Power Distributions for Simulated Outdoor Sound Propagation in Varying Refractive Conditions

Abstract: 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.

1 Aug 2023

Phase-Modulated Rice Model for Statistical Distributions of Complex Signals

Abstract: The basic Rice model is commonly used to describe complex signal statistics from randomly scattered waves. It correctly describes weak (Born) scattering, as well as fully saturated scattering, and smoothly interpolates between these extremes. However, the basic Rice model is unsuitable for situations involving scattering by random inhomogeneities spanning a broad range of spatial scales, as commonly occurs for sound scattering by turbulence in the atmospheric boundary layer and other scenarios. In such scenarios, the phase variations are often considerably stronger than those predicted by the basic Rice model. Therefore, the basic Rice model is extended to include a random modulation in the signal phase, which is attributable to the influence of the largest, most energetic inhomogeneities in the propagation medium. Various joint and marginal distributions for the complex signal statistics are derived to incorporate the phase-modulation effect. Approximations of the phase-modulated Rice model involving the Nakagami distribution for amplitude, and the wrapped normal and von Mises distributions for phase, are also developed and analyzed. The phase-modulated Rice model and various approximations are shown to greatly improve agreement with simulated data for sound propagation in the near-ground atmosphere.

25 Oct 2022

Numerical Modeling of Mesoscale Infrasound Propagation in the Arctic

Abstract: The impacts of characteristic weather events and seasonal patterns on infrasound propagation in the Arctic region are simulated numerically. The methodology utilizes wide-angle parabolic equation methods for a windy atmosphere with inputs provided by radiosonde observations and a high-resolution reanalysis of Arctic weather. The calculations involve horizontal distances up to 200 km for which interactions with the troposphere and lower stratosphere dominate. Among the events examined are two sudden stratospheric warmings, which are found to weaken upward refraction by temperature gradients while creating strongly asymmetric refraction from disturbances to the circumpolar winds. Also examined are polar low events, which are found to enhance negative temperature gradients in the troposphere and thus lead to strong upward refraction. Smaller-scale and topographically driven phenomena, such as low-level jets, katabatic winds, and surface-based temperature inversions, are found to create frequent surface-based ducting out to 100 km. The simulations suggest that horizontal variations in the atmospheric profiles, in response to changing topography and surface property transitions, such as ice boundaries, play an important role in the propagation.

12 Jul 2022

A Tutorial on the Rapid Distortion Theory Model for Unidirectional, Plane Shearing of Homogeneous Turbulence

Abstract: The theory of near-surface atmospheric wind noise is largely predicated on assuming turbulence is homogeneous and isotropic. For high turbulent wavenumbers, this is a fairly reasonable approximation, though it can introduce non-negligible errors in shear flows. Recent near-surface measurements of atmospheric turbulence suggest that anisotropic turbulence can be adequately modeled by rapid-distortion theory (RDT), which can serve as a natural extension of wind noise theory. Here, a solution for the RDT equations of unidirectional plane shearing of homogeneous turbulence is reproduced. It is assumed that the time-varying velocity spectral tensor can be made stationary by substituting an eddy-lifetime parameter in place of time. General and particular RDT evolution equations for stochastic increments are derived in detail. Analytical solutions for the RDT evolution equation, with and without an effective eddy viscosity, are given. An alternative expression for the eddy-lifetime parameter is shown. The turbulence kinetic energy budget is examined for RDT. Predictions by RDT are shown for velocity (co)variances, one-dimensional streamwise spectra, length scales, and the second invariant of the anisotropy tensor of the moments of velocity. The RDT prediction of the second invariant for the velocity anisotropy tensor is shown to agree better with direct numerical simulations than previously reported.

29 Dec 2021

Infrasound Propagation in the Arctic

Abstract: This report summarizes results of the basic research project “Infrasound Propagation in the Arctic.” The scientific objective of this project was to provide a baseline understanding of the characteristic horizontal propagation distances, frequency dependencies, and conditions leading to enhanced propagation of infrasound in the Arctic region. The approach emphasized theory and numerical modeling as an initial step toward improving understanding of the basic phenomenology, and thus lay the foundation for productive experiments in the future. The modeling approach combined mesoscale numerical weather forecasts from the Polar Weather Research and Forecasting model with advanced acoustic propagation calculations. The project produced significant advances with regard to parabolic equation modeling of sound propagation in a windy atmosphere. For the polar low, interesting interactions with the stratosphere were found, which could possibly be used to provide early warning of strong stratospheric warming events (i.e., the polar vortex). The katabatic wind resulted in a very strong low-level duct, which, when combined with a highly reflective icy ground surface, leads to efficient long-distance propagation. This information is useful in devising strategies for positioning sensors to monitor environmental phenomena and human activities.

22 Sep 2021

Extra-Wide-Angle Parabolic Equations in Motionless and Moving Media

Abstract: Wide-angle parabolic equations (WAPEs) play an important role in physics. They are derived by an expansion of a square-root pseudo-differential operator in one-way wave equations, and then solved by finite-difference techniques. In the present paper, a different approach is suggested. The starting point is an extra-wide-angle parabolic equation (EWAPE) valid for small variations of the refractive index of a medium. This equation is written in an integral form, solved by a perturbation technique, and transformed to the spectral domain. The resulting split-step spectral algorithm for the EWAPE accounts for the propagation angles up to 90􀀁 with respect to the nominal direction. This EWAPE is also generalized to large variations in the refractive index. It is shown that WAPEs known in the literature are particular cases of the two EWAPEs. This provides an alternative derivation of the WAPEs, enables a better understanding of the underlying physics and ranges of their applicability, and opens an opportunity for innovative algorithms. Sound propagation in both motionless and moving media is considered. The split-step spectral algorithm is particularly useful in the latter case since complicated partial derivatives of the sound pressure and medium velocity reduce to wave vectors (essentially, propagation angles) in the spectral domain.

25 Jun 2021

A Physics-Informed Neural Network for Sound Propagation in the Atmospheric Boundary Layer

Abstract: We describe what we believe is the first effort to develop a physics-informed neural network (PINN) to predict sound propagation through the atmospheric boundary layer. PINN is a recent innovation in the application of deep learning to simulate physics. The motivation is to combine the strengths of data-driven models and physics models, thereby producing a regularized surrogate model using less data than a purely data-driven model. In a PINN, the data-driven loss function is augmented with penalty terms for deviations from the underlying physics, e.g., a governing equation or a boundary condition. Training data are obtained from Crank-Nicholson solutions of the parabolic equation with homogeneous ground impedance and Monin-Obukhov similarity theory for the effective sound speed in the moving atmosphere. Training data are random samples from an ensemble of solutions for combinations of parameters governing the impedance and the effective sound speed. PINN output is processed to produce realizations of transmission loss that look much like the Crank-Nicholson solutions. We describe the framework for implementing PINN for outdoor sound, and we outline practical matters related to network architecture, the size of the training set, the physics-informed loss function, and challenge of managing the spatial complexity of the complex pressure.