2.5  Models in general use and their intrinsic limitations and risks

Practical engineering methods:
The technique adopted by these models involves the calculation of noise levels by adding the separate contributions that each sound attenuation factor has on noise propagation. The common factor in all these models is that they are mainly based on empirical results. In general, they are simple and easy-to-use.

Approximate semi-analytical methods:
These methods retain the same practical structure as engineering methods, but are based on simplified analytical solutions of the acoustic wave equation rather than empirical results. While the practical engineering methods only take into account averaged meteorological effects, these methods allow a better tracking of the influence of specific meteorological conditions on noise levels, such as upwind or downwind situations. Simple ray tracing models are the most popular methods within this category.

Numerical methods:
This group includes methods such as the Fast Field Program (FFP), the Parabolic Equation (PE) and the Boundary Element Method (BEM). These methods are based on the numerical solution of the wave equation. The FFP and BE allow the calculation of sound propagation over non-complex level terrain with any user-specified atmospheric conditions. The BEM includes the effects of sound diffraction due to large obstacles and more complex terrains. Perhaps the most  powerful current outdoor sound propagation numerical models are Euler-type finite-difference time-domain models (see, e.g., D Heimann, “A linearized Euler finite-difference time-domain sound propagation model with terrain-following coordinates”, Journal of the Acoustical Society of America, vol. 119, issue 6, p. 3813, 2006).

The FFP (or "wave number integration method") gives the full wave solution for the field in a horizontally stratified medium. The method provides an exact solution of the Helmholtz equation, except within a wavelength or so of the source, but is restricted to systems with a layered atmosphere and a homogeneous ground surface. Therefore, systems with a range-dependent terrain (either in terms of ground impedance or terrain shape), or with a range-dependent atmospheric environment (variable sound speed profile with range) cannot be modelled with the FFP method. This makes the model inappropriate for use over long distances or with mixed ground conditions. Furthermore, the computing time is often considerable. FFP is not so efficient since the ground has to be flat and homogeneous, and the atmosphere is described by a succession of horizontal layers (no range-dependency).

In contrast to the FFP method, the Parabolic Equation (PE) method, which is based on an approximate form of the wave-equation, is not restricted to systems with a layered atmosphere and a homogeneous ground surface. The PE method, Euler-type finite-difference time-domain models and the Lagrangian sound particle model are the  only currents technique that can handle environmental range-dependent variations.

There are three limitations to the PE method: PE algorithms only give accurate results in a region limited by a maximum elevation angle, ranging from 10° to 70° or even higher depending on the angle approximation used in the derivation of the parabolic equation; the computing time for a complete spectrum is often considerable, particularly for to the calculation of frequencies above 600 Hz; scattering by sound speed gradients in the direction back to the source is neglected. In other words, a parabolic equation is a one-way wave equation, taking into account only sound waves travelling in the direction from the source to the receiver. As the sound speed is usually a smooth function of position in the atmosphere, the one-way wave propagation approximation is usually a good one, but, when turbulence is to be taken into account, this limitation must be considered.

Since hybrid methods can provide highly accurate representations of propagation effects for individual frequencies in certain conditions, they provide the basis for the 'reference model' used to validate the engineering method produced by HARMONOISE, an EU project which has produced methods for the prediction of environmental noise levels caused by road and railway traffic. These methods are intended to become the harmonized methods for noise mapping in all EU Member States. The methods are developed to predict the noise levels in terms of L_den and L_night, which are the harmonised noise indicators according to the Environmental Noise Directive 2002/49/EC. Since the techniques are computationally intense they are most commonly only employed for 2D prediction. Furthermore, the methods are not widely available within common commercial software.

In summary, numerical methods have many strengths, mainly in accuracy, and weaknesses, mainly in practical application. None of the methods is capable on its own of handling all possible environmental conditions, frequencies and transmission ranges of interest in practical applications. One method will be more appropriate than another for a particular problem scenario, and thus selection of the best method must be situation specific.

For information on the PE, see K E Gilbert, M J White, “Application of the parabolic equation to sound propagation in a refracting. atmosphere”, J. A. S. A. 85, pp.630-637, 1989. Details of the BEM are given in S N Chandler-Wilde, “The boundary element method in outdoor noise propagation”, Proceedings of the Institute of Acoustics 19(8), 27-50, 1997.

These methods are extremely useful for analysing the propagation under specific meteorological conditions. The problem is that they yield results for only those specific conditions and give little indication of statistical mean values of sound levels. Also, the user must provide substantial amounts of information. This information can be difficult to generate, such as complete profiles of wind and temperature..

Hybrid models:
A group of hybrid, numerically-derived methods is used for complex situations. The general principle of these methods is to solve the wave equation or Helmholtz equation to deduce the sound field. The procedure for solving the wave equation is generally difficult to implement due to the complexity of the atmospheric-acoustic environment. In fact, except for the very simplest boundary conditions and uniform media (which rarely occur in reality), it is not possible to obtain a complete analytic solution for either the wave or Helmholtz equation, therefore it is necessary to use numerical methods. Several different types of solution for the sound field have evolved over the past few decades: ray tracing provides a visual representation of the field, the FFP is accurate but computationally intensive and the PE is an approximation to the wave equation that has been solved using explicit and implicit finite different schemes.

Ray-tracing models are fast to compute and providing a pictorial representation, in the form of ray diagrams, of the sound field. Further advantages of ray tracing are that the directionality of the source and receiver can be fairly easily accommodated, by introducing appropriate launch- and arrival-angle weighting factors; and rays can be traced through range-dependent sound speed profiles.

Ray-tracing models are limited in capability only as a consequence of the approximation leading to the ional equation. This imposes restrictions on the physics, which in turn limit the applicability of ray theory. Two major anomalies can arise from these limitations: predictions of infinite intensity in regions around caustics, and predictions of zero intensity in shadow areas (where in reality sound energy will be present through diffraction and scattering). Such difficulties can be overcome by introducing different modifications, accounting to some extent for caustics and diffraction. For instance, Sachs and Silbiger describe a caustic correction (Sachs, D. A., Silbiger, A., "Focusing and refraction of harmonic sound and transient pulses in stratified media" J. Acoust. Soc. Am. 49, pp. 824-840, 1971) and Jensen et al explain a way to deal with shadow areas based on considering complex take-off angles (Jensen, F. B., Kuperman, W. A., Porter, M. B., Schmidt, H., "Computational Ocean Acoustics" American Institute of Physics Press, New York, p 605). However, in practical applications, such modifications are almost never used due to their complexity. Simplified variants of ray tracing have also been developed, notably a technique for tracing Gaussian beams ("fuzzy rays") is described by Porter and Bucker (Porter, M. B., Bucker, H.P., "Gaussian beam tracing for computing ocean acoustic fields" J. Acoust. Am. 82, pp. 1349-1359, 1987). However, this technique presents problems when applied to propagation over an irregular terrain in an inhomogeneous atmosphere.

The Lagrangian sound particle model is another approach which considers complex terrain and meteorological fields which are consistent with that terrain (Heimann D., de Franceschi M., Emeis S., Lercher P., Seibert P. (Eds.), 2007: “Air Pollution, Traffic Noise and Related Health Effects in the Alpine Space − A Guide for Authorities and Consulters.” ALPNAP comprehensive report. Università degli Studi di Trento, Dipartimento di Ingegneria Civile e Ambientale, Trento, Italy, 335 pp).

For more background information on propagation effects, see:

J.E. Piercy, T.F.W. Embleton and L.C. Sutherland : ”Review of noise propagation in the atmosphere.” J.A.S.A. 61, pp1403-1418, 1977 (general effects)

Attenborough, Keith, “Ground parameter information for propagation modelling” , The Journal of the Acoustical Society of America, Volume 92, Issue 1, pp.418-427, July 1992 (ground impedance effects)

Ingard, Uno "A Review of the Influence of Meteorological Conditions on Sound Propagation," Journal of the Acoustical Society of America, 25, p. 405, 1953 (meteorological effects)

Table 2 summarises and supplements the above. For comparison purposes the practical engineering method ISO 9613 has also been included.

For details of the CNPE and GFPE, see ACTA ACUSTICA UNITED WITH ACUSTICA, Vol. 93 (2007) 213 – 227, “Outdoor Sound Propagation Reference Model Developed in the European Harmonoise Project” Defrance et al.

 Table 2:  Characteristics of commonly used environmental noise modelling methods