Parabolic Equation Propagation Model Research Articles

Environmental information-aided electromagnetic propagation testbed for maritime communication

Maritime channel modeling can be affected by some key time-varying environmental factors. The ducting effect is one of the thorniest factors since it causes anomalous propagation enhancement and severe co-channel interference. Moreover, the atmospheric attenuation is much more severe in the ocean environment, resulting in shorter coverage distance and more link outage. In this paper, we propose an environmental information-aided electromagnetic propagation testbed. It is based on complex refractivity estimation and improved parabolic equation propagation model, taking into account both ducting effect and atmospheric attenuation. A large-scale temporal and spatial propagation measurement was conducted with meteorological acquisition. We consider practical path loss and ducting conditions to verify the testbed feasibility in these long-distance radio links. The simulation results are in good agreement with the measured data, which further reveal the basic temporal and spatial distribution of ducting effect at 3.5 GHz band.

Criteria for the assessment of the influence of atmospheric turbulence on wind turbine noise propagation

This paper investigates the influence of atmospheric turbulence on the propagation of wind turbine noise using an aeroacoustic source model coupled with a parabolic equation propagation model. Sets of simulations with and without atmospheric turbulence are performed, allowing the determination of a simple formulation that quantifies the uncertainties of the A-weighted sound pressure level (SPL) when the modelling does not account for atmospheric turbulence. For the case study, the results show that atmospheric turbulence has a negligible effect on SPL up to 800 m from the wind turbine, even under upwind conditions. While the conclusions are specific to this case study, the method appears promising for simplifying the calculation of atmospheric turbulence effect in wind turbine noise studies. A freely accessible online application has been developed to present additional results.

Mapping of surface-generated noise coherence

The performance of a hydrophone array can be evaluated by its coherent gain, which depends on the spatial correlation of both the signal of interest and the background noise between different array elements, where one hopes to maximize the former while minimizing the latter with array signal processing. In this paper, a computational vertical noise coherence map of the first zero-crossing is generated near Alvin Canyon, south of Martha’s Vineyard, Massachusetts, to study its dependence on the spatial variation in bathymetry, water column sound speed and sediment type. A two and three-dimensional Parabolic Equation propagation model based on reciprocity theory were used for the simulation. The results showed that the seabed parameters have the greatest impact on vertical noise coherence at the array location in the Alvin Canyon area, when compared to 3-D bathymetric and water column sound speed profile variability, especially in the shallower water. The analysis reveals the ideal spacing for a vertical hydrophone array for better signal detection in acoustic experiments. In the continental shelf and slope regions, the ideal spacing lies between 3λ⁄8 in deep water and λ⁄2 in shallow water, and for areas with strong bathymetric variations the ideal spacing can be determined by comprehensive numerical models.

Spatial-resolution impacts on local infrasound propagation.

The accuracy of input meteorological data can significantly impact the successful prediction of infrasound propagation at local to near-regional distances. These meteorological inputs are often derived from weather model simulations when event-specific measurements are not available, but the ideal spatial resolutions of these simulations have not been determined. This study seeks to identify the ideal horizontal resolutions for input meteorological data via infrasound simulations conducted with both range-dependent and -independent inputs. Outputs from the Weather Research and Forecasting (WRF) model at 1, 3, 5, and 15 km horizontal resolutions enable these investigations. The parabolic equation propagation model is used to calculate transmission loss for an impulsive signal and is compared against experimental data obtained from a series of 1 lb spherical, suspended C4 shots recorded on the infrasound array on the Waterways Experiment Station in Vicksburg, MS, occurring throughout the diurnal cycle with an overall propagation distance of 14.5 km. Simulations for morning and nighttime correctly predict signal detection and non-detection. Transitional times of day (dawn, evening) were partially successful. Changing horizontal resolutions in WRF incurred greater differences in prediction results than use of range-dependence vs -independence. No clear picture emerged regarding the optimal horizontal resolution for meteorological inputs.

Normal mode acoustic modeling using measurements of ocean sound speed from the Beaufort Sea

Over the last few decades, environmental changes in the Arctic have resulted in a subsurface acoustic duct located between 100- and 300-m depth, known as the Beaufort Duct. This subsurface duct allows for long-range acoustic transmission with little to no interaction with the sea surface or seafloor. In a 2017 long-range acoustic tomography experiment, two Seagliders traversed between five active sources moored within the duct which transmitted linear frequency modulated (LFM) sweeps centered around 250 Hz. These Seagliders were equipped with conductivity, temperature, depth (CTD) sensors as well as passive acoustic receivers. The environmental measurements were used to create sound speed profiles for input into broadband parabolic equation and normal mode acoustic propagation models. The normal mode models provide physical insight into the relationship between the peak arrival and the final cutoff of the ducted acoustic receptions. Modal group speeds from the predictions are used to interpret the acoustic arrival patterns measured on the Seagliders.

Wind turbine noise uncertainty quantification for downwind conditions using metamodeling.

The influence of the ground and atmosphere on sound generation and propagation from wind turbines creates uncertainty in sound level estimations. Realistic simulations of wind turbine noise thus require quantifying the overall uncertainty on sound pressure levels induced by environmental phenomena. This study proposes a method of uncertainty quantification using a quasi-Monte Carlo method of sampling influential input data (i.e., environmental parameters) to feed an Amiet emission model coupled with a Parabolic Equation propagation model. This method allows for calculation of the probability distribution of the output data (i.e., sound pressure levels). As this stochastic uncertainty quantification method requires a large number of simulations, a metamodel of the global (emission-propagation) wind turbine noise model was built using the kriging interpolation technique to drastically reduce calculation time. When properly employed, the metamodeling technique can quantify statistics and uncertainties in sound pressure levels at locations downwind from wind turbines. This information provides better knowledge of sound pressure variability and will help to better control the quality of wind turbine noise prediction for inhomogeneous outdoor environments.

Frequency Diversity in Electromagnetic Remote Sensing of Lower Atmospheric Refractivity

This article explores the effects of system frequency on electromagnetic (EM) remote sensing of atmospheric refractivity. A frequency range of 2–40 GHz covering S- to Ka-bands is analyzed. A multifrequency inversion algorithm is developed to estimate the evaporation duct heights using a parabolic wave equation propagation model. The capabilities of a theoretical multifrequency system are explored for high and low signal-to-noise ratios for varying numbers of frequencies and bands. Experimental data were collected using the lower atmospheric propagation ultrawideband (LATPROP-UWB) system deployed during the Coupled Air-Sea Processes and EM Ducting Research (CASPER) East Campaign. Range-dependent propagation loss measurements at 53 frequencies ranging from 2 to 40 GHz were made. The evaporation duct refractivity profiles estimated from the multifrequency LATPROP-UWB data were compared to the profiles inferred from the concurrent meteorological and oceanographic measurements. Inversion results show that the optimal refractivity retrieval can be achieved using ten frequencies and results in a fourfold reduction in the estimation RMSE compared to a single-frequency inversion.

Accurate Computation of Scintillation in Tropospheric Turbulence With Parabolic Wave Equation

Parabolic wave equation (PWE) propagation models using multiple phase screens (MPS) are widely used to predict the log-amplitude variance of the signal propagating in tropospheric turbulence. Previous literature demonstrates the limitations of the MPS technique, usable only when the signal frequency is low (typically below 5 GHz for radio-wave propagation in the troposphere). In this article, we demonstrate that the accuracy of the MPS technique depends not only on the signal frequency but also on the outer scale length ( L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">os</sub> ) of the turbulent eddy. For example, when L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">os</sub> is on the order of tens of meters (e.g., in most terrestrial communication links), the MPS method is indeed unusable at high frequencies, but, when L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">os</sub> is on the order of hundreds of meters (e.g., in air-ground and satellite links), the method can be used even at millimeter-wave frequencies. Next, a correlated phase screen (CPS) implementation within the PWE is introduces, which avoids the condition of statistical noncorrelation of the phase screens in the MPS technique, and as such, it can be used for any signal frequency. Finally, an ad hoc error metric is provided, allowing for the selection of the appropriate phase screen model based on the signal frequency, turbulence outer scale length, and the electromagnetic (EM) link distance. The simulated signal log-amplitude variances as a function of range at microwave and millimeter-wave frequencies using the CPS method are reported here for the first time and are shown to be in excellent agreement with the analytically obtained values.

Estimating received levels for acoustically tracked whales from Navy mid-frequency active sonar

Multi-channel passive acoustic data were collected from bottom-mounted hydrophones off the coast of Kauai, HI at the U.S. Navy Pacific Missile Range Facility’s instrumented range. In February 2017, data were recorded during the Submarine Command Course (SCC) training event that included mid-frequency active sonar (MFAS). Data were post-processed for minke whale (Balaenoptera acutorostrata) vocalizations and MFAS with automated detection, classification, and localization algorithms. Semi-automated processes were used to perform spatio-temporal associations of whale localizations to create individual whale tracks and to associate localized MFAS transmissions with positional data from multiple ships. For each whale track, the received level from each MFAS transmission was estimated using a parabolic equation propagation model that statistically represented the uncertainty of whale location and depth. Exposures were accumulated over the duration of each whale track to estimate the cumulative sound exposure level (cSEL; dB re: 1μPa2s). Twenty-three minke whales were exposed to MFAS during the SCC; the maximum exposure was 169.8 dB cSEL, and the minimum distance to a ship transmitting MFAS was 4.8 km. Currently, statistical analyses of track kinematics and call characteristics are being conducted to quantify any significant changes between animal track kinematics with and without MFAS training presence.

Determining essential scales and associated uncertainties for regional atmospheric infrasound propagation by incorporating three-dimensional weather model forecasts

Understanding infrasound propagation is important for geophysical and military applications. Infrasound signatures can be detected from larger sources such as nuclear detonations and from smaller sources such as bridges, dams, and buildings. Infrastructure sources produce signals of lower amplitude, leading to more regional (up to 150 km) propagation. However, current methods for calculating regional infrasound propagation involve assumptions about the atmosphere, such as horizontal homogeneity, that deviate from more realistic environmental conditions and decrease the accuracy of the infrasound predictions. To remedy this issue, we have interfaced three-dimensional forecasts from the Weather Research and Forecasting (WRF) meteorological model with range-dependent parabolic equation propagation models. To test the improvement of infrasound propagation predictions with more realistic weather data, we conducted sensitivity studies with different propagation ranges and horizontal resolutions and compared the...

Three-dimensional noise modeling

The ambient sound field due to wind generated surface noise and distant ship generated noise may be highly axially non-symmetric in regions with rapidly changing bathymetry. Some of this asymmetry is due to bathymetric shadowing, while in other cases horizontal refraction contributes significantly. These propagation effects can alter the omnidirectional power spectral levels, as well as the horizontal and vertical noise coherence (directionality). The special case of an idealized Gaussian submarine canyon can be described using the method of normal mode decomposition applied to a three-dimensional longitudinally invariant wave-guide. The modal decomposition is carried out in the vertical and across-canyon horizontal directions and gives a semi-analytical solution describing the three-dimensional bathymetric effects on the noise field. Reciprocal three-dimensional cylindrical co-ordinates parabolic equation (PE) and Nx2D PE sound propagation models can be used to compute the noise field in arbitrary domains. Inter-comparison of these models highlights the effect of the three-dimensional topography on the vertical coherence and mean-noise level as a function of arrival direction relative to the canyon’s axis. These effects include the focusing of noise along the canyon axis and the frequency perturbation of vertical coherence minima. [Research supported by ONR.]

Hydroacoustic measurements and modeling of pile driving operations in Ketchikan, Alaska

Underwater acoustic measurements of pile driving operations were made at the Ketchikan ferry terminal in July 2016. At the time of the measurements, marine mammal injury and disturbance criteria developed by the National Marine Fisheries Service (NMFS) were based on sound pressure level (SPL) thresholds. Shortly after the measurements, NMFS changed the injury thresholds to a dual criteria involving peak pressure and sound exposure levels specific to marine mammal functional hearing groups. This paper presents distances to both injury criteria and the (unchanged) SPL-based disturbance criteria for vibratory driving and impact hammering 30-inch diameter cylindrical piles. Threshold distances were obtained using empirical regressions of sound levels measured by seabed-mounted recorders at 10 and 1000 m nominal range. A finite-difference method pile driving source model was used with a parabolic equation propagation model to compare measurements with simulations and to estimate received levels at all ensonifi...

Estimating refractivity from propagation loss in turbulent media

AbstractThis paper estimates lower atmospheric refractivity (M‐profile) given an electromagnetic (EM) propagation loss (PL) measurement. Specifically, height‐independent PL measurements over a range of 10–80 km are used to infer information about the existence and potential parameters of atmospheric ducts in the lowest 1 km of the atmosphere. The main improvement made on previous refractivity estimations is inclusion of range‐dependent fluctuations due to turbulence in the forward propagation model. Using this framework, the maximum likelihood (ML) estimate of atmospheric refractivity has good accuracy, and with prior information about ducting the maximum a priori (MAP) refractivity estimate can be found. Monte Carlo methods are used to estimate the mean and covariance of PL, which are fed into a Gaussian likelihood function for evaluation of estimated refractivity probability. Comparisons were made between inversions performed on propagation loss data simulated by a wide angle parabolic equation (PE) propagation model with added homogeneous and inhomogeneous turbulence. It was found that the turbulence models produce significantly different results, suggesting that accurate modeling of turbulence is key.

PSO ALGORITHM OF RETRIEVING SURFACE DUCTS BY DOPPLER WEATHER RADAR ECHOES

Doppler weather radar is an effective tool for monitoring mesoscale and small scale weather systems, quantitatively estimating precipitation and guarding against severe convective weather. The quality of the data obtained by Doppler weather radar will be seriously affected by the anomalous propagation of electromagnetic wave in tropospheric ducts. A novel method is introduced in this paper to retrieve the surface ducts, and it is based on the Principal Component Analysis (PCA) method for modeling M profile and Parabolic Equation (PE) propagation model which is a well-established technique for efficiently solving the equations for beam propagation in an inhomogeneous atmosphere. The inversion echo powers and equivalent reflectivity factor are in accordance with the measured data, which indicates that the surface ducts can be effectively retrieved by this method.

Source Localization in the Duct Environment with the Adjoint of the PE Propagation Model

Owing to the absorbing, refracting and scattering effects of the propagation medium, electromagnetic (EM) energy will degrade with the increment of propagation range, and the maximum value exists at the point of the radiating source. Employing this phenomenon, this paper introduces a novel approach to detect the location of EM transmitters in an atmospheric duct environment. Different from previous matched-field processing (MFP) methods, the proposed method determines the source location through reconstructing the forward propagation field pattern by the backward adjoint integration of the parabolic equation (PE) propagation model. With this method, the repeated computations of PE used in the MFP methods are not needed. The performance of the method is evaluated via numerical simulations, where the influences of the measurement noise and the geometry of the receiver array on the localization results are considered.

Predicting range-frequency interference patterns from broadband sources in a range-dependent, continental shelf environment

The 2007 CALOPS dataset contains horizontal line array received signals from numerous surface vessels transiting an area off the coast of southeast Florida. Parabolic equation propagation models using measured bathymetric, sound velocity profile, and sediment parameter data suggest that substantial mode coupling should be occurring for several down-slope propagation scenarios in the dataset. However, received acoustical data for these scenarios, in the form of range-frequency interference patterns, are best described by adiabatic propagation. This discrepancy has implications that affect waveguide invariant parameter estimation, which is necessary for invariant-based passive ranging. The causes of the incongruous model output will be discussed, as well as their effects on estimating waveguide invariant distributions for these scenarios. [This research was supported by the Applied Research Laboratory, at the Pennsylvania State University through the Eric Walker Graduate Assistantship Program.]

Ambient noise modeling using sound field reciprocity

An efficient numerical calculation of the vertical and horizontal coherence of the noise field in the ocean due to a distributed sheet of sources can be carried out using a parabolic equation (PE) propagation model and the reciprocity property of the complex pressure field. In the case of an infinite sheet of sources near the surface in an infinitely deep, isovelocity ocean, the calculation of vertical coherence using this method is in agreement with the Cron and Sherman model for wind-driven surface noise, as well as with measurements made of vertical coherence in the Philippine Sea. This numerical model also gives the effective surface-listening radius for a single hydrophone by calculating the contribution to the noise field at the receiver from a small noise patch at the surface, as a function of range. The model is capable of calculating the vertical and horizontal coherence (directionality) of the noise field and the depth-dependent surface-listening radius of a hydrophone in a shallow water waveguide and over range-dependent environments, such as a wedge, canyon, or shelf break. Additionally, this technique can be used to calculate the spatial properties of the noise field due a finite patch of surface sources in motion, such as a rainstorm.

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian—MCMC method

The estimation of lower atmospheric refractivity from radar sea clutter (RFC) is a complicated nonlinear optimization problem. This paper deals with the RFC problem in a Bayesian framework. It uses the unbiased Markov Chain Monte Carlo (MCMC) sampling technique, which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework. In contrast to the global optimization algorithm, the Bayesian—MCMC can obtain not only the approximate solutions, but also the probability distributions of the solutions, that is, uncertainty analyses of solutions. The Bayesian—MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar sea-clutter data. Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter. The inversion algorithm is assessed (i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data; (ii) the one-dimensional (1D) and two-dimensional (2D) posterior probability distribution of solutions.

Modeling underwater impact pile driving noise in shallow, inhomogeneous channels

The broadband synthesis of a parabolic equation (PE) propagation model for shallow water acoustic propagation in inhomogeneous channels is presented to account for the noise produced by impact pile driving. The PE model utilizes sediment information obtained from boring measurements and detailed bathymetry to model range dependent propagation in the Columbia River between Portland, OR and Vancouver, WA. The impact pile driving source is modeled in two ways: first, as a reverberating impulse source that emits Mach-wave radiation [Reinhall, Dahl, J. Acoust. Soc. Am. 130, 1209 (2011)]; and second, with a structural acoustic finite-difference time-domain (FDTD) model [Shahab, Woolfe, and Hastings, J. Acoust. Soc. Am. 130, 2558 (2011)]. Model results using both source models are shown to be in good agreement with acoustic measurements of test pile operations in the Columbia River at multiple locations from 10 to 800 meters from the pile driving source. Implications for noise levels in river systems with varying bottom sediment characteristics are presented and discussed. [This research is supported with funding from the Oregon Department of Transportation.]

Use of Galerkin's method using variable depth grids in the parabolic equation model

Choice of a depth grid affects the accuracy of a parabolic equation (PE) propagation model, as well as the speed of execution. Choice of a fine grid step may result in lower discretization errors, but will lengthen computation times. Moreover, application of a sampling requirement (e.g. N samples per wavelength) to the water column results in oversampling in the bottom. Since an artificial absorbing later in the bottom is often employed, a large part of the computational domain is oversampled. Fine depth sampling is only needed in the region about the water sediment interface. Hence, Galerkin’s method using a variable depth grid is implemented. This is demonstrated to achieve the same error as a uniform grid with fine spacing over the entire depth domain, while taking a fraction of the run time. This is particularly important in models where nested PE models are required, as with noise models (so called N by 2D runs), full 3D, or broadband models. The variable grid Galerkin’s method is also used in an elastic PE model, in which sampling requirements for low-shear speed sediments require much finer sampling than that in the water column.