PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

A data base of outdoor transfer functions
Sylvain CHEINET1; Loïc EHRHARDT; Matthias COSNEFROY; Adrien DAGALLIER
French-German Research Institute of Saint-Louis (ISL), FranceABSTRACT
In many outdoor acoustic applications, the propagation channel can be modeled as a transfer function. Forpropagation above a flat ground, the environmental conditions vary, and a representative data base of transfer
functions is needed. This study addresses the challenges of forming such a general data base. It uses athree-dimensional, Finite-Difference, Time-Domain (FDTD) model for propagating a reference wideband
signal up to 250 m above a finite-impedance ground, over a range of wind strengths and directions, withconsistent turbulence fluctuations. The database provides the amplitude and phase of the transfer function atfine spectral resolution. The sensitivity of the transfer functions to the various environmental parameters isanalyzed. The present database can be used to readily connect any near-field signature to its propagatedcounterpart, in a variety of open, flat environments. The signatures of an illustrative impulse sound at 200 m
in the various considered environments reproduce the large expected modulations and randomization due tothe ground, atmospheric stratification and turbulence. The database can easily be enlarged to otherenvironmental conditions with further computational resources.
Keywords: Propagation, Outdoors, Simulation

1. INTRODUCTION
Outdoor acoustics has an extensive scope of applications. In source sensing, the sound is used to
extract information on the emitting source (e.g. vehicle tracking, explosion localization etc.). In theseapplications, knowledge is required of the relationship between the signature emitted at a source, andthe signature received at a sensor or a sensors’ array. By extension, noise monitoring applications (forindustries, transports, entertainment, etc.) regard the human ear as sensor and the received sound as anannoyance. Last, outdoor acoustics intervenes in environmental remote sensing. The
environment-induced alterations of a (known) source sound are then used to characterize theenvironment.
How does the environment alter a source sound to form the acoustic signature at the receiver?
Formally, this issue can be assessed in the temporal or spectral domains, respectively with aconvolution by the environment impulse response, or a multiplication by the environment transferfunction. In simple environments, analytical solutions exist. In realistic outdoor environments,complex (e.g. 3D) propagation effects take place, and numerical solvers of sound propagation cancalculate the transfer function of a perfectly known environment.
The key challenge is the computation of the transfer function in the general case. Indeed, thefunction dramatically depends on the environment – which changes with place and time (if only due toweather), and is never perfectly known. One thus needs to calculate a database of transfer functions,which spans over all considered environmental parameters, and to the best of knowledge.
Numerical approaches have been proposed for propagation in many weather conditions, for averagesound level predictions in open, ground-to-ground propagation scenarii. These approaches focus on
the amplitude of the transfer function, averaged over relatively large frequency bands. For impulse
sounds, however, the phase of the transfer function is also required, on fine frequency bands. Besides,
because it is a heavy challenge, the description of the atmospheric turbulence is often limited to asimple threshold parameterization. The oversimplification of turbulence effects may lead to biased
estimates of the instantaneous and average noise level predictions (Cheinet, 2012), and biased and/orrandomized sensing performance of impulse sounds (e.g. Cheinet et al. (2018).
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The present paper follow the same strategy of investigating a variety of near-surface atmosphericconditions, within a ground-to-ground propagation scenario. It is meant to illustrate that overcoming
the above limitations becomes possible with present-day knowledge and resources. Specifically, itdemonstrates that one can form a database of transfer functions (1) including the amplitude and phase
information, (2) with explicit description of the ground and atmospheric effects (including turbulence).
It illustrates some salient results of such a database.
The paper is composed as follows. Section 2 presents the sound propagation scenario and numericalmodels used for the calculations. Section 3 illustrates the calculated transfer functions andsubsequently predicted sound signatures. Section 4 gives a conclusion.

2. NUMERICAL MODELING APPROACH
2.1 Overall scenario
The following scenario is hereafter considered, which is inspired from the ADVISE experiment(Atmospheric-Driven Variability of Impulse Sounds Experiment, Cheinet et al., 2018). A near-surface
sound source (1.75 m height) emits a known sound, in the frequency range from 20 to 1250 Hz(wavelengths from 0.27 m to 17 m). The signature is desired at ranges up to 250 m – which implies
atmospheric heights of relevance to sound propagation up to 25 m. The ground is composed of longgrass. This scenario is rather simple, in that the source is punctual and omnidirectional, with nonon-linear propagation effects. Besides, the environment is flat and open, e.g. there are no obstacles
which could alter the acoustic or atmospheric fields. Last, at the considered ranges and frequencies,
gaseous absorption of sound is negligible compared to other propagation effects, and is ignored.
2.2 Sound propagation model
The sound propagation model used in this study is a Finite -Difference, Time-Domain (FDTD)
solution of the Linearized Euler Equations. The studies of Cheinet et al. (2012) and Ehrhardt et al.
(2013) have demonstrated the relevance of this solution for sound propagation modeling throughcomplex atmosphere and turbulence. An extensive description of the present FDTD model is given in
Cosnefroy (2019); the set-up used in this study is now discussed.
- The model uses a Cartesian grid of resolution 5 cm, with a 13-points interpolation scheme inspace. The spatial resolution used (0.2 times the smallest source wavelength) provides a major
computational gain compared to previous versions of the model.
- The calculation is made for a moving window for each selected propagation direction. Thewindow volume has 768 points (38.4 m width) x 512 points (25.6 m height) x 512 points (25.6m depth). There are 7500 time-step iterations, with a Courant number of approximately 0.7, so
the maximal range exceeds 260 m. Figure 1 sketches the computational approach.
- The lateral and top boundaries are modeled with perfectly matched layers (PMLs). The PMLparameterization is optimized for absorption at grazing angles, a fter Cosnefroy et al. (2019).
The front and back boundaries of the moving window also use PMLs.
- The source is taken to be a derivative-of-Gaussian pulse. It is implemented as an isotropic
spatial distribution of the acoustic pressure, with full-width at half maximum 10 times theresolution.

Figure 1 – Sketch of the computational approach. The acoustic signal propagating in the selected
direction toward virtual receivers is numerically resolved within the moving computational window.

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2.3 Environmental model
In the model, the environmental conditions respectively appear through the boundary conditions at
the bottom layer (ground) and inside the model domain (atmosphere). The ground is assumed not tovary from simulation to simulation, and is taken to be horizontally homogeneous. After Cosnefroy(2019), it is modeled with a reflexion coefficient, with physical parameters fitted to the ADVISE
measurements. Model-wise, the complex frequency dependence of the reflexion coefficient isapproximated with a rational expansion, which allows for an efficient implementation with auxiliary
differential equations in the FDTD model.
The 3D atmosphere (wind, temperature) directly enters into the Linearized Euler Equations. An
appropriate first-order model is a superposition of a mean vertical stratification (horizontal wind,temperature), and homogeneous and isotropic turbulence fluctuations. The parameterization of bothaspects combines the approaches of Cheinet (2012) and Cheinet et al. (2012), and is now recalled.
In the considered scenario, the atmospheric heights of relevance pertain to the surface layer, where
the Monin-Obukhov Similarity Theory (MOST) generally holds. Accordingly, the stratification inmean horizontal wind and temperature is modeled with MOST relationships, with a buoyancy forcing
of 0.01 mK/s, a temperature of 283 K at 2 m height, and a roughness length of 0.005 m. The friction
velocity is given three values: 0.15 m/s, 0.3 m/s and 0.6 m/s, to model low, moderate and strong winds.
The mean horizontal wind is assumed not to turn with height. The azimuthal angle between the mean
horizontal wind and the acoustic propagation direction is given three representative values: downwind,crosswind and upwind propagation.
A turbulence model is used to generate random realizations of 3D wind velocity fluctuations. The
selected von Karman spectrum has parameters (intensity, length scale) calculated with the MOSTparameters above – whereby a consistent prescription of the turbulence and stratification . For each setof MOST parameters, a Monte Carlo approach is adopted with 30 turbulence realizations. An
additional simulation with no turbulence is also performed. The temperature turbulence is ignored, as
it usually has a lesser effect than wind turbulence. Since the turbulence realizations are uncorrelated,
the temporal coherence of the atmospheric field (and of the propagated acoustic field) is ignored.
Overall, the database includes 3 wind forcings, 3 directions, 30+1 turbulence realizations, whichgives 279 simulations. The calculations are run on a high performance computational cluster, with amassively parallel interface programming. For each simulation, the pressure time series at many,
predefined receiver positions are stored in the database. Once this computational effort is carried out,
the database takes the form of a lookup table, which provides the transfer function, for each simulationand each receiver’s position.

3. RESULTS
3.1 Transfer functions
We start the analysis with a discussion based on the transfer function amplitude. Figure 2 shows theenvironmental gain (in dB) with frequency, obtained at 200 m and at a height of 1.75 m. The sphericalspreading is compensated, so with no ground, the gain would be zero (dashed line), and withconstructive interferences above a perfectly reflective ground, the gain would be + 6 dB.
The case which minimizes the atmospheric effects has low wind, crosswind propagation, with noturbulence (panel d). The departure from the no-ground case reveals the impact of the ground:increased lower frequencies, with a dip at 250 Hz and larger frequencies. Turbulence tends torandomize the gain compared to the no-turbulence case - a process called scintillation. The
scintillation rate increases with frequency. The crosswind, no-turbulence simulations remain virtuallyunchanged as the wind increases, as the mean wind projection is nulled in crosswind propagation. On
the other hand, an enhanced wind implies an enhanced turbulence (by virtue of MOST relationships),
which in turn implies more scintillation. Hence, the wind increase has the indirect effect of increasing
the crosswind scintillation. The obtained result also illustrates the importance of a quantitativedescription of atmospheric turbulence, if one is to consider the variability of the pressure field.
In a general sense, the downwind direction features an increase of the highest frequencies, with aslightly more pronounced dip around 200 Hz. Both effects increase with the wind strength. Given themodest solar forcing, the downwind propagation essentially stands for downward refraction, whichcauses the noted features. Upwind propagation leads to upward refraction, with opposed effects.
The simulations with no turbulence ignore scintillation. Still, they provide a viable model of themean gain with turbulence, in configurations outside a shadow zone (downwind, crosswind, upwind

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with low wind). However, as the wind becomes non negligible, the no-turbulence simulation gain
undergoes a dramatic loss at high frequencies in the upwind case. Conversely, the simulations withturbulence feature a plateau between -25 to -20 dB. Hence, in such shadow zones, the no-turbulence
prediction becomes a poor estimator of the expected gain.
Qualitatively, the above effects are known. Their quantitative capturing in a systematic set of 3D
FDTD simulations appears to be original. Indeed, the present approach makes far less approximations
than, e.g., the study by Cheinet (2012). Among others, his parabolic equation approach (like manyothers) has a limited frequency range. It is solved on a 2D (range, height) domain, while thetransposition to 3D is not trivial in presence of turbulence. The solved stochastic equation makes useof the Markov approximation. None of these assumptions is required in the present 3D FDTD
approach.

Figure 2 – Environmental gain (in dB, taken as 20 Log 10(A FDTD /A FF), with A FDTD the amplitude of thetransfer function simulated with the environment, and A FF the amplitude of the free field transferfunction), with varying wind directions and strengths, at range 200 m and height 2 m. The dotted line
is in free-field, the red line is without turbulence, the blue lines show 10 simulations with turbulence.
3.2 Propagated signatures of arbitrary sounds
The above section considered the amplitude of the transfer function. The phase of the transfer
function further carries further time-domain information. Combining the two, one can readily derive
the time-domain signature at any receiver’s position, for any desired source signal and scenario (Sec.
1). A refinement is introduced for a more stable calculation of the transfer function at low frequencies(Cosnefroy, 2019).
As an example, the source signal is taken as the loudspeaker impulse sound measured in Cheinet etal. (2018). The near-field signature spans over the spectral range 150 – 1100 Hz, within the frequency
range under scope with the formed database. Figure 3 shows the derived signatures at 200 m, for themoderate wind case, in the upwind and downwind directions.
The sound convection by the mean wind explains the shorter times-of-arrival in the downwind
propagation, compared to upwind. At 200 m, the fluctuations in time-of-arrival are smaller than the3791

duration of the first peak. As a result, the wander of the pulses in presence of turbulence is not toomarked. Larger ranges may lead to larger wander. In the downwind direction, the pressure peaktypically reaches 0.15 Pa. The upwind peak is of the order of 0.005 Pa. Thus, the overall effect of achanging wind direction induces a difference of 30 dB in the peak pressure at 200 m. This can beunderstood in light of the +6 dB versus -20 to -25 dB amplitude gains noted downwind versus upwind.
Downwind, the signatures are dominantly driven by the deterministic mean downward refraction.
Thus, the downwind signature prediction without turbulence is rather representative of the averaged
signatures with turbulence. The scatter due to turbulence is of several dB, still. Conversely, thedeterministic contribution of mean refraction is a poor estimator of the transfer functions in the upwind
propagation case (see above). Hence, the predicted signature without turbulence is poorly informativeof the upwind signatures with turbulence. For example, there is a 12 dB difference between the peak of
the no-turbulence pressure time series, and the largest peak obtained among the simulations withturbulence (not shown here). The turbulence results also feature notably more high-frequency
oscillations than the result without turbulence. The impact of such differences is major for applications
like (impulse) noise pollution or source classification.

Figure 3 – Acoustic signatures derived from the database for an impulse sound at range 200 m. The redline is without turbulence, the blue lines show 10 simulations with turbulence.

4. Conclusions
Many, if not all, applications of outdoor acoustics require the relationship between a near -fieldsource signature, and the signature received at distant receivers. Forming databases of such transfer
functions for representative outdoor conditions has been investigated for decades. Previous proposals
in this line focus on the ground and meteorological effects, in a ground-to-ground propagation scenario.
They generally suffer from limitations, such as missing information on the time-domain content of thepropagated signal, missing information due to averaging over frequency bands, or absence ofsignificant propagation effects due to turbulence (scintillation, and scattering in shadow zones).
The present paper pursues the strategy of spanning over a representative variety of environmentalconditions in a ground-to-ground propagation scenario. It demonstrates that one can form a database ofcomplex transfer functions with explicit description of the turbulence effects. To this purpose, theenvironmental conditions are consistently modeled, with physical descriptions of the ground reflexion,
meteorological gradients and 3D wind turbulence. The source sound is propagated with a 3D FDTD
model which correctly predicts sound propagation in presence of complex ground and atmosphericeffects.
The formed database provides the complex transfer function at ranges up to 250 m, over 1 groundtype, 3 wind strengths, 3 wind directions, without and with turbulence (30 realizations). It can be used
to readily derive the signature at a distant receiver, for any desired source signal within the frequency
range of relevance. Analysis reveals the major effects of the environment (including turbulence) on an
exemplary impulse sound.
Now that the transfer functions database is formed, it can be applied to analyze other source signals,
and the signals at other receiver’s ranges and heights, at no additional computational expense. This
opportunity appears to be original and of notable practical significance. In effect, it implies that thepresent database can cover, or give a good approximation, of a very large number of propagation
scenarii in open, flat environments.

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There are some assumptions in the present approach, which may require careful considerations if tobe revised: punctual and omnidirectional source, applicability of MOST and of the selected model ofturbulence, flat and horizontally homogeneous ground etc. On the other hand, the present database
could readily include other parameters of sensitivity, e.g. the buoyancy forcing (due to e.g. surface
heat fluxes), the ground type or the source height. Adaptations of the source, model domain andresolution would also extend the frequencies and ranges of interest. Such extensions raise no otherchallenge than the available power for computation.

ACKNOWLEDGEMENTS
This work was granted access to the HPC resources of IDRIS under the allocation
2016-A0022A07720 and A0042A07720 attributed by GENCI (Grand Equipement National de Calcul
Intensif).

REFERENCES
1. Cheinet, S., M. Cosnefroy, F. Königstein, W. Rickert, M. Christoph, S. L. Collier, A. Dagallier, L.
Ehrhardt, V. E. Ostashev, A. Stefanovic, T. Wessling, D. K. Wilson, 2018, An experimental study of theatmospheric-driven variability of impulse sounds, J. Acoust. Soc. Am., 144, 822-840.
2. Cheinet, S., L. Ehrhardt, D. Juvé and Ph. Blanc-Benon, 2012, Unified modeling of turbulence effects
on sound propagation, J. Acoust. Soc. Am., 132, 2198-2209.
3. Cheinet, S., 2012, A numerical approach to sound levels in near-surface refractive shadows, J. Acoust.
Soc. Am., 131, 1946-1958.
4. Cosnefroy, M., S. Cheinet, L. Ehrhardt, A. Dagallier, D. Dragna and D. Juvé, 2019, Perfectly MatchedLayers for acoustic waves at extreme grazing angles, J. Comput. Phys., Accepted pending revisions, pp.
28.
5. Cosnefroy, M., Simulation numérique de la propagation dans l'atmosphère de sons impulsionnels etconfrontations expérimentales [Numerical simulation of the impulse sound propagation in theatmosphere and experimental comparisons], 2019, PhD Thesis of Ecole Centrale de Lyon, pp. 190.
6. Ehrhardt, L., S. Cheinet, D. Juvé and Ph. Blanc-Benon, 2013, Evaluating a linearized Euler equations
model for strong turbulence effects on sound propagation, J. Acoust. Soc. Am., 133, 1922-1933.

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