Aircraft Noise Measurement and Modeling

The following is an excerpt from Appendix A of Findings of the Low-Frequency Noise Expert Panel of the Richfield-MAC Noise Mitigation Agreement of 17 December 1998, Annotated, Sept. 30, 2000. The red italic type is text added after the final report was issued May 9, 2000, and was intended by the authors to indicate whether consensus had been reached on significant points. The illustrations are not yet available for reposting here (June 1, 2002).


Standardized procedures have evolved for both measuring and modeling aircraft noise for common purposes. These are outlined in the following subsections.

A.4.1 Frequency-Related Measurement Conventions

The human ear is capable in principle of detecting sounds within a ten octave range extending from about 20 Hz to 20 kHz. It has been well understood since the early 1920s, however, that sensitivity to sounds varies greatly over frequencies within this range. The greatest sensitivity is concentrated within a two octave range extending from roughly 1000 to 4000 Hz that includes many important speech sounds. At extremely low and extremely high frequencies, the ear is thousands of times less sensitive than in the speech range.

When systematic measurements of urban noise were first made in the late 1920s, it was quickly realized that an adjustment of some sort was needed to represent measurements of sounds of differing frequency content in terms meaningful for assessing effects of such noise on people. The simplest solution available at the time was to apply a "frequency weighting network" to measurements of environmental sounds. Three such networks were standardized initially during the 1930s: the A-weighting network for sounds of relatively low absolute sound pressure level, the B-weighting network for sounds of intermediate level, and the C-weighting network for relatively high level sounds. These weighting networks were intended as approximations to the inverse of human hearing sensitivity at increasing sound levels.

The A-weighting network eventually gained acceptance as the default weighting network for general environmental noise measurement purposes. When FAA was charged with regulating aircraft noise emissions, however, it adopted a different measurement procedure for the 1969 Part 36 of the Federal Aviation Regulations -- Perceived Noise Level, or PNL. PNL is a more complex frequency weighting network than the A-weighting network, that is slightly more sensitive than the A-weighting network to low-frequency sounds, and also to sounds in the vicinity of 1 to 3 kHz.

Most references to FAR Part 36 cite the standard in terms of the Effective Perceived Noise Level (EPNL). While an instantaneous level is given in terms of PNL, the level from an event (i.e., a takeoff or a landing) is given in terms of the EPNL. This is analogous to the instantaneous level being cited as an A-weighted level and the sound from an event as the Sound Exposure Level (SEL).

When the Office of Noise Abatement and Control of the Environmental Protection Agency recommended adoption of the Day-Night Average Sound Level for general assessments of environmental noise levels in 1974, readily available instrumentation could not conveniently measure PNL values. The A-weighting network was therefore retained as the basis for routine environmental noise measurements, such as monitoring of aircraft noise levels near airports.

A.4.2 Duration-Related Conventions

A.4.2.1 The "Equal Energy Hypothesis"

As a matter of regulatory policy, it is commonly assumed that people are indifferent between the annoyance of small numbers of very high-level noise events of short duration and the annoyance of large numbers of compensatingly lower level and/or longer duration noise events. In other words, it is conventionally assumed that the number, level, and duration of noise events are fully interchangeable determinants of annoyance, as long as their product (energy sum) remains constant. Thus, a small number of noisy aircraft operations is considered to create the same impact as that of a compensatingly greater number of operations by less noisy aircraft.

It is misleading to attribute the equal energy hypothesis to "regulatory policy." As part of its responsibilities under the mandates of the Noise Control Act of 1972, the EPA recommended adoption of DNL., based on A-weighted levels. As is clear from the report containing that recommendation, the "Levels Document," the EPA base its decision on previous research and experience in other countries, mainly in Europe, and in California, not regulatory policy. 28

[28] Anon. "Information on Levels of Environmental Noise Requisite to Protect Public Health and Welfare with an Adequate Margin of Safety," EPA 550/9-74-004, March 1974.
The assumption of linearity of acoustic effects underlies reliance on t he equal energy hypothesis for purposes such as predicting the prevalence of annoyance from long-term, time-weighted average sound levels (such as Day-Night Average Sound Level). This assumption is untenable for present purposes, since the occurrence of noise-induced rattle is a threshold-like phenomenon. In residential settings, people hear rattle when outdoor noise levels exceed some structure-specific and frequency-specific sound level. Furthermore, sound levels of rattling objects do not necessarily increase in direct proportion to the amount by which sound levels exceed a rattle threshold (cf. Schomer et al., 1987a). [P.D. Schomer et al., "Expedient Methods for Rattle-proofing Certain Housing Components," U.S. Army Corps of Engineers, CERL Report N-87/24, 1987]

Under these circumstances, time-integrated noise exposure cannot be expected to predict the annoyance of rattle as well as quantities such as the number or temporal density of noise events in excess of a threshold of rattle.

A.4.2.2 Family of "equivalent level" noise metrics

Figure 76 shows the characteristic form of a time history of sound levels produced during an aircraft overflight of a fixed point on the ground. The sound pressure level at the measurement point initially rises to a maximum, after which it decreases. Since the sound pressure levels vary throughout the overflight, and since the durations of different overflights also vary, no single number can usefully characterize the moment-to-moment changes in sound levels. The usual method for representing the sound energy produced during the entire overflight is therefore to "normalize" the measurement to a standard time period (one second). This measure, "sound exposure level," simplifies the comparison of noise events of varying duration and maximum level by compressing the acoustic energy of the entire noise event into a standard time period.

Figure 76 (not available)

Relationship of sound exposure level (SEL) to time history of an aircraft overflight.

The concept of a sound exposure level can be generalized to an "equivalent level" of time periods longer than one second. For example, a full day’s worth of sound exposure can be expressed as a 24-hour equivalent level, symbolized as Leq24. If a different weighting factor is assigned to the equivalent level of day time (0700 - 2200 hours) and night time (2200-0700 hours), the noise metric becomes a time-weighted 24-hour metric. When the nighttime weighting of the time average is ten times greater than the daytime weighting, the noise measure is known as Day-Night Average Sound Level, abbreviated DNL and symbolized as Ldn.

A.4.3 Field Measurement of Aircraft Noise

Part 36 of the Federal Aviation Regulations specifies levels of noise emissions of commercial aircraft offered for sale or otherwise operating in the United States. Regulatory language indicates in great detail the conditions of measurements and analysis of sound level measurements made for purposes of certifying that air craft types are in compliance with Part 36. These include constraints on aircraft operating procedures, atmospheric conditions, multiple microphone positions, half-second sampling of one-third octave band levels from 50 to 10,000 Hz, calculation of variant forms of Perceived Noise Levels, and so forth.

Although Part 36 does not apply to aircraft noise measurements made for purposes other than certification, half-second sampling of one-third octave band sound levels in the 24 bands from 50 to 10,000 Hz are commonplace in field measurements made under less controlled circumstances as well. However, adventitious measurements of aircraft noise (those made under circumstances in which aircraft movements are unconstrained) are much more likely to be influenced by factors such as variability in aircraft operating conditions (thrust settings, flight profiles, etc.), weather conditions, and the presence of extraneous noise sources. These uncontrollable sources of error limit the precision of most field measurements of aircraft noise, and often contribute to the sort of scatter seen in Figures [ ].

Another obvious limitation of field measurement of aircraft noise is that it is applicable only to existing circumstances of noise exposure. Noise that has not yet been made cannot be measured, but only modeled.

A.4.4 Standard Approach to Modeling Aircraft Noise Exposure Near Airports

Aircraft noise can be modeled in as many ways as there are purposes for modeling. The standard approach to aircraft noise modeling in the immediate vicinity of civil airfields answers the question "How much noise does an airplane flying here make there?" To answer this question, mathematical models of atmospheric propagation of sound are applied to standard sets of aircraft noise levels, to propagate noise emissions away from aircraft (whether in flight or on the ground) in all directions. These calculations are summarized graphically as sets of source-based emission contours, or sometimes as point values. The goal of this form of aircraft noise modeling is protection of public investment in an airport.

The results of contouring exercises are usually summarized in terms of a time-weighted daily average exposure index devised by the Environmental Protection Agency (EPA, 1974), known as Day-Night Average Sound Level (DNL). DNL provides a convenient means for combining all of the noise energy created in the course of daily flight operations into a single number, for which interpretive criteria and regulatory policy have evolved. Airports routinely produce aircraft noise exposure contours in units of DNL for NEPA disclosure purposes; for purposes related to federal aviation regulations; for land use planning purposes; and for various other purposes.

FAA’s preferred aircraft noise prediction software, INM, can produce not only noise exposure (i.e., DNL or CNEL) contours, but with equal facility, contours of maximum noise levels and contours of duration of aircraft noise in excess of a user-specified threshold level ("time-above" contours). INM can also produce spot estimates (rather than entire contour sets) for various noise metrics.

For reasons discussed in Section 2.3 of Volume II, DNL contours are of no direct value as predictors of low-frequency sound level.

A.4.5 Overview of Airfield-Vicinity Noise Exposure Modeling

Computer-based aircraft noise exposure modeling began in the 1970s with the creation of early versions of the U.S. Air Force’s NOISEMAP software. FAA began construction of an "Integrated Noise Model" (Olmstead et al., 1997) several years later. [J. Olmstead et al., "INM Version 5.0 User's Guide," FAA Report FAA-AEE-95-01, 1997] Both noise modeling programs have been released in versions for different computing platforms and operating systems. Variants on both programs have also been produced by various government and commercial organizations worldwide.29

[29] For example, ARTS MAP is a commercial software package intended for retrospective use only. At airports with access to information produced by FAA’s ARTS III surveillance radars, ARTS MAP replaces assumptions about aircraft operating conditions with information developed from position reports made by aircraft transponders during actual operations.
Although the Air Force and FAA noise models were initially developed separately, recent versions share so me algorithms and software modules. NOISEMAP and INM may both be used for retrospective and prospective purposes: to produce noise contours for an historical set of operating conditions, or to predict the noise exposure resulting from alternate hypothetical operating conditions. FAA accepts contours produced by either INM or NOISEMAP as equivalent for regulatory purposes.

INM remains under active development, with Version 6.0 recently released. Differences in DNL contours from release to release for the same input specifications can be sizable. It is expected, for example, that sideline noise contours will be notably wider in Version 6.0 than in current versions of INM. Version 6.0 can also produce C-weighted noise exposure estimates in addition to the A-weighted metrics to which earlier versions of INM were limited.

A.4.6 General Properties of Aircraft Noise Exposure Contours

As a generality, aircraft noise exposure contours about an individual runway are elliptical, with the major axis oriented along the runway centerline and the minor axis perpendicular to the runway heading. Contours produced by aircraft arriving at an airport are usually straighter and narrower than departure contours, which often show bulges or lobes corresponding to turns away from the runway heading shortly after takeoff. At an airport with intersecting or multiple runways and operating patterns, the number, complexity and variability in aircraft flight paths tend to obscure the basic shapes of noise contours for individual runways. In such cases, noise exposure contours for the airport as a whole tend toward broader shapes.

Noise exposure gradients (rates of change of noise exposure with distance from runway ends) on the order of a thousand feet per decibel are common at large airports. In such cases, uncertainties of fractions of decibels in predicted noise levels may lead to mis-classification of the noise exposure of many city blocks.

A.4.7 Sensitivity of Contour Size And Shape to Modeling Assumptions

A.4.7.1 Major factors affecting noise contour shapes

The orientations of an airport’s runways have a major but not necessarily dominant effect on the shape of aircraft noise exposure contours. At an airport with a complex runway layout, assumed departure and arrival tracks can also have pronounced effects on contour shapes, depending on how they are populated with different types of aircraft at different times of day.

A.4.7.2 Major factors affecting contour size

The size of a set of aircraft noise exposure contours is sensitive to more factors than their shape. Two major operational factors affecting contour size are aircraft type and relative proportion of nighttime use. Numbers of operations, especially at large airports, may have a relatively minor effect on relative contour size as compared with flight profiles, stage length, and other factors. Under most conditions, aircraft ground operations do not greatly affect the size of A-weighted noise exposure contours more than a mile or two away from the airport.

A. Aircraft type

The proportion of airport operations flown by older (Stage II) aircraft has a major effect on the size of DNL contours. The increasing proportion of Stage III aircraft operations in recent years has been a main factor in shrinking departure contours at many airports. Approach contours are less sensitive to the proportion of Stage II aircraft operating at an airport, since airframe noise may contribute substantially to an aircraft’s total A-weighted emissions during approach. Low-frequency noise produced by jet aircraft is more closely related to engine power than to the classification of an aircraft as Stage II or Stage III.

A. Fleet mix

All other things being equal, greater proportions of larger (three- and four-engine) jet transports in the fleet serving an airport will lead to larger noise contours. Greater numbers of operations of smaller commuter aircraft (both turboprop and jet) do not generally compensate for their lower noise levels on departures, so that increasing representation of smaller aircraft in an airport’s fleet mix does not necessarily expand an airport’s noise contours.

A. Time of day

The 10 dB nighttime "penalty" incorporated into DNL treats a single nighttime operation as the equivalent of ten daytime operations by the same aircraft. Thus, the 10% of operations that often occur at night at large airports have an effect on contour size equivalent to the 90% of daytime operations. Even small changes in the proportion of nighttime operations can thus have a substantial effect on the size of a set of noise exposure contours.

A. Indirect factors

Certain assumptions made in creating a noise model can also affect contour size substantially through their indirect influences on operational factors. These include assumptions about wind speed and direction and air temperature, which affect engine power settings, and hence, noise levels.

A. Propagation assumptions

FAA has not published figures on the fundamental precision of the acoustic propagation algorithms of INM. It is unlikely, however, that INM’s air-to-ground acoustic propagation algorithms are much more precise than about ±1 dB directly beneath an airplane’s flight path. Algorithms in past and current versions of INM that are intended to account for "lateral attenuation" -- the absorption of noise inpassage over the ground to the side of an aircraft flight track -- are considerably less precise. Bias or random errors in these algorithms can lead to mis-prediction of contour size and shape undersome conditions.

A.4.8 Manner of Use of INM

INM is a sufficiently complex program that operates on so many variables that it is possible to use the software in more than one way to accomplish the same end. In particular, a program parameter intended by INM developers to model a particular phenomenon may be used as a de facto means for modeling a different phenomenon, often for reasons of convenience. Rather than creating a custom flight profile for a particular aircraft type as flown from a particular runway, for example, a user might intentionally instruct the program that the destination of a particular flight was closer or farther than is actually the case. This might provide a conveniently simple method for taking into consideration air traffic constraints that prevent a departure stream from gaining altitude as rapidly as might otherwise be the case.

Likewise, rather than creating a unique noise-power-distance curve to describe the manner of operation of a certain class of aircraft at a particular airport, a user might instruct INM to achieve the same effect by treating the approach and departure noise of a particular aircraft type as though it were created by two different aircraft: one for approaches, and a different one for departures. From the perspective of engineering expedience, use of INM parameters in ways unintended by its developers may be viewed as no more than a harmless tactic to save time, effort, and cost in creating an aircraft noise exposure model. Such expedients might also permit a complex noise model to execute on an available computing platform.

From other perspectives, however, such uses of INM carry certain disadvantages. Perhaps the most basic of these is directness of application. If there is reason to believe that INM does not operate appropriately on some particular information, is it preferable to correct the information or the algorithm that operates on it, or to manipulate the program into producing a modified prediction by other means? From the perspective of improving INM, it is clear that the only way to make progress in correcting potential deficiencies in the program is by addressing them directly rather than working around them. This is also the case from the longer term perspective of recurring uses of INM at the same airport.

Ultimately, the issue is whether INM is viewed as a means for inferring the size and shape of noise exposure contours from first principles -- as intended by its developers -- or whether it is simply an elaborate tool for drawing arbitrary shapes resembling aircraft noise contours. In practice, both the imperfections of modeling and measurement of aircraft noise, as well as differing short- and long-term perspectives on modeling purposes, create a gray area in which professional opinions may differ about the appropriateness of various uses of INM.

A.4.9 Limitations of Interpretations of Aircraft Noise Contours

Aircraft noise contours are often presented in the form of sets of detailed concentric closed form curves overlaid on street grids. This creates the impression that the contours are as fixed, precise, and real as the underlying mapping of streets. In reality, aircraft noise contours are mathematical constructs whose size, shape, and position depend wholly on computational algorithms and assumptions. A given set of assumptions will lead to one set of contours, while a slightly different set of assumptions (about numbers, and types and times of day of aircraft operations from particular runways, on varying flight paths, with different stage lengths and flight profiles, under various meteorological conditions) can lead to very different sets of noise contours. Since there are no facts about the future, any set of prospective noise contours is necessarily speculative and arbitrary to some extent.

All interpretations of aircraft noise contours made for purposes of prospective land use planning must take into consideration the uncertainties inherent in modeling aircraft noise that has not yet occurred.


All measurement and modeling is intrinsically imperfect, in that no real world measurement can be absolutely accurate, precise, and reliable, and no modeling is free of simplifying assumptions and approximations. Some of the factors that lead to imperfections of measurement and modeling are manageable, while others are not. Factors that introduce uncertainty into field measurements of aircraft noise include the vagaries of atmospheric propagation of sound (e.g., atmospheric gradients of wind, temperature, humidity, and surface impedance in various propagation paths between the noise source and its measurement), calibration of instrumentation, operational variability in noise sources, and many other "nuisance" variables. Factors that can affect the credibility of aircraft noise modeling include the representativeness of a large number of unverifiable modeling assumptions (e.g., numbers, types, flight paths, and stage lengths of future aircraft operations) and the adequacy of propagation calculations. Factors that can affect measurements of attitudes (such as annoyance) include representativeness and size of samples, as well as wording of questionnaire items.

In the best of circumstances, the inevitable uncertainties of measurement and modeling lead to random errors of specifiable size in estimates of quantities such as sound levels in one-third octave bands, noise reductions of structures, positions of aircraft noise contours, percentages of survey respondents highly annoyed, and so forth. Under less benign circumstances, these uncertainties can lead to systematic errors of unknown size. As a rule of thumb, it may be assumed that errors of estimation and measurement of acoustic quantities described in this report are generally on the order of ± 2.5 dB, and that errors of measurement of the prevalence of annoyance are generally on the order of ± 5%.


The following subsections answer frequently asked questions about errors of aircraft noise measurement and modeling.

A.6.1 What is Measurement?

Measurement is a means of associating numbers with quantities such that the ordinary mathematical properties of numbers apply to the quantities of interest. The length of a hanging spring, for example, increases as the weight suspended from it increases. The deflection of a pointer attached to the spring measures weight by pointing to increasingly larger numbers as the weight attached to the spring increases.

A.6.2 What is Modeling?

In the present sense, "modeling" is the process of creating a computer simulation of real world phenomena for purposes of efficiently characterizing the effects of varying assumptions on model predictions. The basic rationale for modeling is cost-effectiveness: since the real world phenomena of interest are too expensive or otherwise inconvenient to characterize directly, a computer-based model of the phenomena is studied instead. The gross behavior of the model — its treatment of major influences on the phenomena of interest, its sensitivity to factor s affecting t he modeled real world phenomena, and so forth — is intended to resemble the phenomena of interest at a level of detail adequate to provide useful insights.

A.6.3 What is Error?

In the context of the present discussion, error is a technical term that describes a difference between one or more estimates of the numeric value of a quantity. The term does not carry any connotation of intentional or unintentional fault or mistake.

A.6.4 What is Error of Measurement?

Error of measurement is inescapable. No form of measurement, whether of length, weight, economic activity, political preferences, or aircraft noise, is ever error-free. Although more elaborate and costly measurement procedures may produce smaller errors, no amount of money can purchase perfectly error-free measurements. For most practical purposes, what matters is not whether a measurement system is perfect or imperfect, but whether the measurements it produces are adequate to support whatever decisions are made on their basis. It is therefore helpful to understand not only the nature of errors of measurement, but also the purposes for which the measurements are made in the first place.

A.6.5 What is Error of Estimation?

"Error of estimation" is a statistical term that refers to the probability that a given estimate lies within a certain interval about a true (but unknowable) exact value. Just as no measurement can ever be perfect, no prediction produced by a software model of long-term aircraft noise levels can be perfect. The statistical term "error of estimation" is sometimes borrowed to describe the inevitable discrepancies between modeled and actual quantities.

Each of the acoustic propagation effects modeled by INM has some associated error, ranging from fractions of a decibel to several decibels under differing conditions. For example, predictions of sound exposure levels at points on the ground directly beneath and relatively close to flight tracks can often be made to agree within a decibel of physical measurements, whereas prediction of sound exposure levels to the sides of flight tracks can be considerably greater.

A.6.6 What is a Confidence Interval?

A confidence interval is a range of values that has a high probability of encompassing a true ("population") value of some parameter. Different sets of measurements ("samples") of the same quantities virtually always differ from one another to some degree for various reasons. For example, average aircraft noise levels observed at the same point near a runway will almost certainly differ from one day to the next. A 90% confidence interval on the mean of a large set of such daily observations encompasses 90% of the daily values. To say that the 90% confidence interval about a mean noise level of 80 dB is 5 dB wide is thus to say that the means of 90% of all sets of measurements of this average noise level will lie between 75 and 85 dB.

The width of a confidence interval depends in large part on (the square root of) the number of observations on which it is based. All other things being equal, small numbers of observations will produce wide confidence intervals, while large numbers of observations will produce narrow confidence intervals. By itself, a wide confidence interval about a data point suggests only that relatively few measurements have been made of its value, not that the underlying variable is somehow incapable of supporting informed decision making.

A.6.7 What are Error Bars?

Error bars attached to data points in charts and graphs are visual indications of the extent of some measure of uncertainty. Plotting a data point with associated error bars serves as a reminder that the point is not the result of a measurement of infinite precision. Figure 77 illustrates error bars plotted for both the independent variable and the dependent variable for a hypothetical data point.30 The ends of the error bars are often used to indicate the upper and lower bounds of confidence intervals. The interval between the upper and lower bounds of error bars need not necessarily be a well defined confidence interval. Charts and graphs are sometimes marked with upper and lower bounds of the envelope of all observations within a data set, or with even less formal ranges of values (such as a range of typical values).

[30] When it is desirable to emphasize errors of measurement on both the abscissa and ordinate, data points are sometimes plotted as ellipses of varying size. The area within an ellipse then serves as a graphic reminder of the uncertainties of measurement associated with each observation. The dashed lines outlining a rectangle in Figure 71 define a region of joint uncertainty of measurement of both the independent and dependent variables.

Figure 77 (not available)

Illustration of the use of error bars to indicate measures of uncertainty for both independent and dependent variables.

A.6.8 Why Are Simplifying Assumptions Necessary for Modeling?

Computer models of real-world phenomena are necessarily simpler than the phenomena themselves. This simplification is necessary both for tractability of calculation, and also because a software model as complex as the modeled phenomena would be both unwieldy and uneconomical. A good software model seeks a balance between excessive and insufficient complexity in its algorithms; between the cost of its construction and use and the savings it yields in study of model rather than real-world behavior; and between accuracy and precision of prediction and the burden it imposes on users for detailed input information.

A.6.9 What is the Difference between Accuracy and Precision?

Errors of estimation may occur either systematically or randomly. Systematic errors (bias errors) affect the accuracy of a measurement or model prediction, while random errors affect its precision. A pattern of target shots is a common metaphor useful for illustrating the two kinds of errors. The bull’s eye represents the "true" value of a measurement. The pattern of shots illustrates the accuracy and precision of the measurement. The shot patterns in the four bull’s eyes in Figure 78 represent (from top to bottom and left to right) measurements (or predictions) of low accuracy and low precision, low accuracy but high precision, high accuracy and low precision, and high accuracy and high precision.

Figure 78 (not available)

Shot patterns representing four combinations of low and high precision and accuracy in errors of measurement.

In statistical terms, accuracy reflects the difference between the mean of a sample of (say) aircraft noise measurements and the "true" (but unknowable) central tendency. Precision is a measure of the dispersal (variance) of a distribution of measurements. Both the accuracy and precision of measurement of a quantity can be improved by making repeated measurements, as long as the errors of successive measurement are not systematically related to one another. Accuracy and precision of modeling are generally improvable only through more sophisticated algorithms or more comprehensive input information.