Environmental noise modelling describes the process of theoretically estimating noise levels within a region of interest under a specific set of conditions.
The specific set of conditions for which the noise is being estimated will be a fixed representation or ‘snapshot’ of a physical environment of interest. However, in practice the physical environment will usually not be fixed, but will be characterised by constantly varying conditions. These variations in real world conditions will subsequently cause the actual sound field to vary in time and space. Thus it is important to recognise that the output of an environmental noise model will only represent an estimate for a ‘snapshot’ of the range of actual environmental noise levels that could occur in time and space.
Recognising that modelling is a means of estimating noise for a specific set of conditions, attention is now directed to defining what these conditions are. The key conditions that a noise model relates to are:
- An approximation of the noise source, or sources, for which associated environmental noise levels are of interest
- An approximation of the physical environment through which noise will transmit from the noise source(s) to the location or region of interest. This includes the ground terrain, the built environment, and atmospheric conditions (e.g. wind, temperature, humidity)
- An approximation of the way in which sound will travel from the input noise source(s) via the input physical environment, to the receiver location or region of interest
Thus, producing an environmental noise model involves defining a series of noise sources to be investigated, describing acoustically significant features of the environment through which sound will propagate to the receiver, and then applying a calculation method that accounts for these descriptions to produce an estimated noise level at a location or region of interest. The simplest type of environmental noise model, involves a single sound source, radiating sound via a single transmission path, to a single location in the surrounding space.
In practice, environmental noise models will often be more complex, involving multiple sound sources, transmitting via multiple complex transmission paths, to multiple locations of interest.
In these more complex scenarios, the environmental noise model is repetitiously calculated for each sound source, via each transmission path to each and every receiver location. The total sound level at each position is then calculated by summing the contribution of each source and transmission path.
Application of these calculations to each point on a uniformly distributed grid enables a noise contour map to be developed to depict regions of equal estimated noise level and depict trends in the spatial pattern of the sound field.
What are environmental noise models used for?
Environmental noise predictions are used in an increasing range of decision-making applications. The most common application is for assessments where a decision is to be made regarding some future change to an environmental noise field. However, given the practical and technical challenges to noise measurement strategies, there are an increasing number of situations in which predictions complement or substitute for measurement-based noise assessment techniques.
Common uses of predictions for practical noise assessment purposes are as follows:
- Forecasting the impacts or benefits of proposed changes to an environmental noise field such as introduction, change or removal of a commercial/industrial installation, or modification of significant features in the physical environment that affect noise propagation, such as the construction or removal of barriers or enclosures
- Assessment of existing commercial/industrial installations where the effectiveness of different noise mitigation strategies needs to be evaluated. Predictions can be used to rank the relative contributions of individual component sources of an installation comprising multiple complex sources. These rankings can then be used to focus noise mitigation resources on to the component sources whose treatment will enable the greatest reduction in total noise levels
- Investigating the results of a measurement study to better understand the causes of the measured levels. For example, predictions may be used to assist the investigation of observed but unexplained variability in measurement results. Alternatively, predictions may be used to provide an estimate of the extent to which a particular source, or group of sources, may have influenced the total noise level measured from all sources affecting the environment in question.
Complementing the results of measurement studies to investigate a wider range of locations, time periods or noise sources than could be directly investigated with measurements.
Assisting the design of measurement studies by using predictions to understand the possible criticality of the situation before committing to expensive measurement studies. The predictions can be used to identify situations that are most critical to the assessment outcome, such as locations where noise levels might be expected to be similar to some threshold value where the assessment outcome significantly differs. This knowledge can then be used to design the measurement study in a way that focuses the available resources on the most effective strategy. A further benefit of predictions used in this way is the reference it provides when conducting post measurement analysis to judge the validity of a set of measurements, and whether there are any aspects of the results that differ from original expectations and subsequently warrant specific explanation or further investigation.
What information is needed to construct a noise model?
Approaches to environmental noise modelling vary in terms of the complexity with which each element of the model is described and analysed. However, irrespective of the chosen approach, the key information to all predictive studies is the systematic representation of the noise sources to be investigated, and the physical environment through which noise will transmit to the receivers. Once these are defined, an estimate of the way in which noise will travel from the noise sources to the receivers is also required. Table 1 shows the requirements for specifying a noisy environment.
To estimate the way in which noise will travel from the noise sources to the receivers, a range of sound propagation methodologies may be employed. Methods vary widely in their complexity and the scope of applications for which they can offer meaningful predictions.
The most basic form of propagation methodology is described as ‘spherical’ or ‘hemi-spherical’ spreading. This method simply accounts for the reduction in sound intensity as a sound wave front spreads over a larger area.
For common types of noise sources in relatively simple environments, as may be the case where separating distances are relatively small and there are no intervening structures to impede noise propagation, this type of method is often sufficient for estimation purposes.
In instances where the noise sources are more complex and/or account must be made of the influence of significant features of the physical environment, more robust and detailed information is needed to describe the propagation of noise. In most types of practical applications, engineering methods will provide the most viable basis for predicting environmental noise levels. These methods rely on a combination of acoustic principles and empirical knowledge to provide a means of estimating the influence of a range of phenomena, including:
- The absorption associated with the passage of noise through the atmosphere
- The change in noise level that occurs as a result of interactions between the sound wave travelling directly to the receiver and those reflected from the ground, accounting for influence of the ground cover type
- The attenuation offered by obstacles that fully or partly obstruct line of sight between a source and a receiver location
- The influence of atmospheric conditions that can change the direction of an advancing sound wave front by refracting the wave at points where there are significant changes in wind speed and/or temperature
- The influence of reflecting surfaces that re-direct an advancing sound wave front
Engineering methods can therefore take account of a wide range of factors that influence noise propagation, and their use for multi-source industrial/commercial installations can become complex when all relevant paths of sound transmission are taken into account.
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.
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
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.
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 Lden and Lnight, 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.
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.
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 Environmental Noise (“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
How reliable is environmental noise modelling?
The reliability of environmental noise modelling is a very important question, but one that is all too often addressed by potentially misleading statements about ‘accuracy’ in the sense of the closeness between measured and predicted values.
A noise model represents an estimate of a ‘snapshot’ in time. Environmental noise fields tend to be inherently variable in both time and space. This variability introduces a difficulty in defining the accuracy of a model, as it is a function of the relationship between a constant predicted value and a potentially widely varying noise level that could be measured in practice.
The value of a model cannot be measured by accuracy per se, but rather on a judgement of its reliability as a tool in decision making, and this judgement should be made according to the specific application and situation under consideration. Providing that modelling studies are used with an awareness of the relative benefits and limitations of predictions when compared to other possible bases upon which a decision could be made, such studies can provide a reliable basis for decision making purposes. In other words, a reliable model is one that is fit for purpose.
The National Physical Laboratory (NPL) is the UK’s National Measurement Institute and is a world-leading centre of excellence in developing and applying the most accurate measurement standards, science and technology.
Published: 01st Sep 2009 in AWE International