ISO 13474:2009
(Main)Acoustics — Framework for calculating a distribution of sound exposure levels for impulsive sound events for the purposes of environmental noise assessment
Acoustics — Framework for calculating a distribution of sound exposure levels for impulsive sound events for the purposes of environmental noise assessment
ISO 13474:2009 specifies the framework of an engineering method for calculating a statistical distribution of sound exposure levels for impulsive sound events for the purposes of environmental noise assessment. It is applicable to impulse sounds propagating over large distances (e.g. 0,5 km to 30 km) from sources, such as mine blasting, artillery fire and bomb explosions, using conventional explosives of moderate charge mass (e.g. 0,05 kg to 1 000 kg of TNT equivalent). The effects of meteorological conditions and terrain upon sound propagation are considered.
Acoustique — Cadre pour le calcul d'une distribution des niveaux d'exposition sonore pour les sons impulsionnels pour les besoins de l'évaluation du bruit environnemental
Akustika - Osnove za izračun porazdelitve ravni zvočne izpostavljenosti zaradi impulznih zvočnih dogodkov za potrebe vrednotenja hrupa v okolju
Ta mednarodni standard določa okvir inženirske metode za izračun statistične porazdelitve ravni zvočne izpostavljenosti zaradi impulznih zvočnih dogodkov za potrebe vrednotenja hrupa v okolju. Ta mednarodni standard se uporablja za impulzni hrup, ki se širi prek velike razdalje (npr. 0,5 km do 30 km) od virov, kot so miniranje, topniško orožje in bombne eksplozije, pri katerih se uporabljajo običajni eksplozivni materiali z zmerno maso naboja (npr. 0,05 kg do 1 000 kg ekvivalentne mase TNT). Vpliv meteoroloških razmer in terena na širjenje zvoka je upoštevan.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-februar-2012
$NXVWLND2VQRYH]DL]UDþXQSRUD]GHOLWYHUDYQL]YRþQHL]SRVWDYOMHQRVWL]DUDGL
LPSXO]QLK]YRþQLKGRJRGNRY]DSRWUHEHYUHGQRWHQMDKUXSDYRNROMX
Acoustics - Framework for calculating a distribution of sound exposure levels for
impulsive sound events for the purposes of environmental noise assessment
Acoustique - Cadre pour le calcul d'une distribution des niveaux d'exposition sonore pour
les sons impulsionnels pour les besoins de l'évaluation du bruit environnemental
Ta slovenski standard je istoveten z: ISO 13474:2009
ICS:
17.140.01 $NXVWLþQDPHUMHQMDLQ Acoustic measurements and
EODåHQMHKUXSDQDVSORãQR noise abatement in general
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 13474
First edition
2009-06-15
Acoustics — Framework for calculating a
distribution of sound exposure levels for
impulsive sound events for the purposes
of environmental noise assessment
Acoustique — Cadre pour le calcul d'une distribution des niveaux
d'exposition sonore pour les sons impulsionnels pour les besoins de
l'évaluation du bruit environnemental
Reference number
©
ISO 2009
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ii © ISO 2009 – All rights reserved
Contents Page
Foreword .v
Introduction.vi
1 Scope.1
2 Normative references.1
3 Terms and definitions .2
4 Basic equations .6
4.1 General .6
4.2 Probability of occurrence .6
4.3 Band sound exposure level.7
4.4 Frequency-weighted sound exposure level.8
4.5 Long-term average single-event sound exposure level.8
4.6 Equivalent level from multiple events.10
5 Calculation of a statistical distribution .10
6 Calculation of attenuation .14
6.1 General .14
6.2 Geometric divergence.14
6.3 Atmospheric absorption.14
6.4 Insertion loss by screening objects .15
6.5 Terrain shielding.15
6.6 Contributions to excess attenuation.16
6.6.1 General .16
6.6.2 Refraction.16
6.6.3 Ground reflection and absorption .17
7 Classification .19
7.1 General .19
7.2 Classification of atmospheric absorption.19
7.3 Classification of excess attenuation .19
7.3.1 General .19
7.3.2 Lookup table requirements .20
7.3.3 Range-dependent sound speed profiles.21
7.3.4 Directed sound speed profiles.21
8 Probability of occurrence of sound speed profiles .22
8.1 General .22
8.2 Using direct measurements of wind and temperature profiles .22
8.3 Similarity relationships for the atmospheric surface layer.23
8.4 Using measurements of turbulent fluxes.24
8.5 Using routinely gathered weather station data .25
8.6 Using directly measured or calculated sound speed profiles as input .26
9 The source .26
9.1 General .26
9.2 Demolition and muzzle blasts .26
9.2.1 General .26
9.2.2 Source descriptors.27
9.2.3 Determination by measurement.27
9.2.4 Determination by estimation .28
9.3 Projectile sound.28
9.3.1 General .28
9.3.2 Flat trajectories .28
9.3.3 High-elevation trajectories and rocket trajectories.28
10 Uncertainties .28
Annex A (informative) Example of the estimation of the statistical distribution of single-event
sound exposure levels .30
Annex B (informative) Uncertainty .37
Bibliography .40
iv © ISO 2009 – All rights reserved
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 13474 was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise.
It cancels and replaces ISO/TS 13474:2003, which has been technically revised.
Introduction
The aim of this International Standard is to provide a framework for the evaluation of descriptor quantities for
use in environmental noise assessment. Part of this framework includes an engineering method for calculating
a statistical distribution of event sound exposure levels at locations which are some distance from high-energy
impulsive sound sources. It is specifically intended for environmental noise assessment and not for the
assessment of the risk of damage to buildings or the risk of injury to animals or people.
In ISO 9613-2, the immission level from sources such as traffic and industry is calculated for a so-called
“downwind” condition. The long-term average level is estimated using a correction factor, C . This concept
met
holds for distances where sound from such sources is assessed as environmental noise. ISO 9613-2 excludes
impulses in its scope and holds only for A-weighting, for near-ground sources and receivers and for distances
up to about 1 000 m. For high-energy impulsive sound sources, the impulsive sound event duration is short,
and low frequencies are more prominent than for traffic and industrial sound sources. Lower-frequency
sounds are generally less attenuated over a given distance in the atmosphere than higher frequencies and, as
a consequence, the level-influencing effects of propagation over much larger distances need to be taken into
account.
A general outline is given of a method that takes into account ground reflection, shielding by topography and
the meteorological effects of refraction and turbulence. Starting from the source strength, this method
calculates a distribution of immission levels for a set of replica atmospheres, each replica being a specific
combination of atmospheric-absorption class and excess-attenuation class. To carry out practical calculations
using the procedure, it is useful to exploit the statistical contribution of the meteorological and ground surface
conditions. In particular, histograms of the frequencies of occurrence of the wind velocity, wind direction,
temperature, humidity and atmospheric stability can be used to describe the classes. From the distribution of
the immission levels, a number of assessment metrics can be obtained. For instance, the long-term averaged
immission level can be calculated as a weighted average. The weighting factors are determined by the
probability of occurrence of each replica atmosphere during the relevant time period for the location of interest.
vi © ISO 2009 – All rights reserved
INTERNATIONAL STANDARD ISO 13474:2009(E)
Acoustics — Framework for calculating a distribution of sound
exposure levels for impulsive sound events for the purposes of
environmental noise assessment
1 Scope
This International Standard specifies the framework of an engineering method for calculating a statistical
distribution of sound exposure levels for impulsive sound events for the purposes of environmental noise
assessment. This International Standard is applicable to impulse sounds propagating over large distances
(e.g. 0,5 km to 30 km) from sources such as mine blasting, artillery fire and bomb explosions, using
conventional explosives of moderate charge mass (e.g. 0,05 kg to 1 000 kg of TNT equivalent). The effects of
meteorological conditions and terrain upon sound propagation are considered.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 1996-1, Acoustics — Description, measurement and assessment of environmental noise — Part 1: Basic
quantities and assessment procedures
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 9613-1, Acoustics — Attenuation of sound during propagation outdoors — Part 1: Calculation of the
absorption of sound by the atmosphere
ISO 9613-2, Acoustics — Attenuation of sound during propagation outdoors — Part 2: General method of
calculation
ISO 17201-1, Acoustics — Noise from shooting ranges — Part 1: Determination of muzzle blast by
measurement
ISO 17201-2, Acoustics — Noise from shooting ranges — Part 2: Estimation of muzzle blast and projectile
sound by calculation
ISO 17201-4, Acoustics — Noise from shooting ranges — Part 4: Prediction of projectile sound
ISO/IEC Guide 98-3, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
VDI MSR 8/559, Standard Method to Measure the Sound Exposure Emissions and Immissions from Large
Weapons (Standardmethode zur Messung der Geräuschemissionen und -immissionen von schweren Waffen),
Edmund Buchta (ed.), in Meß-, Steuerungs- und Regelungstechnik, No. 8/559, Fortschritt-Berichte, VDI
Verlag, Düsseldorf, 1996 (in English and German)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
atmospheric absorption
attenuation of sound by air, resulting from viscous molecular processes, molecular rotation and molecular
vibration
3.2
atmospheric-absorption class
range of meteorological parameters yielding approximately the same attenuation of sound by air, all within a
specified uncertainty
NOTE See also atmospheric absorption.
3.3
atmospheric stability
tendency of the atmosphere to reduce or enhance vertical motion of the air
NOTE Enhanced (or reduced) vertical motion of the air usually implies enhanced (or reduced) atmospheric
turbulence.
3.4
atmospheric-stability class
subset formed from partitioning the set of atmospheres according to stability
NOTE See also atmospheric stability.
3.5
direct path
position displacement vector, in metres, originating at the source and describing a straight trajectory
terminating at the receiver
NOTE The direct path may intercept objects such as buildings or terrain.
3.6
directed sound speed
algebraic sum of the adiabatic sound speed and the horizontal component of the wind velocity along the direct
path
NOTE Directed sound speed is expressed in metres per second.
3.7
directed sound speed profile
sound speed along the direct path, expressed as a function of height
NOTE See directed sound speed.
3.8
event
single short burst, or rapid sequence of bursts, associated with a sound source
NOTE A single activity, such as firing a gun, could produce multiple sound events. In the case of firing an explosive
projectile from a high-velocity gun, sound events are associated with each of the following sound sources: the muzzle
blast, the ballistic shock and the projectile impact.
2 © ISO 2009 – All rights reserved
3.9
event duration
T
time interval starting just before immission, at time t , and ending just after immission, at time t , to
1 2
encompass all significant sound of a single short blast or rapid sequence of blasts
NOTE The time interval t − t is expressed in seconds.
2 1
3.10
exceedance level
sound level of a stated type, in decibels, exceeded by no more and no less than a stated percentage of
samples
NOTE The sampling set shall be identified, e.g. percentage of times during a stated time interval or percentage of
firing events from an exercise.
3.11
excess attenuation
that part of sound attenuation not included when accounting for geometric divergence (from a small sound
source in non-refracting and non-moving air), atmospheric absorption of sound waves along the direct path
from source to receiver and attenuation of screens and/or barriers
NOTE Excess attenuation is expressed in decibels.
3.12
excess-attenuation class
range of combined directed sound speed profiles and ground types yielding approximately the same
attenuations, all within a specified uncertainty
3.13
ground condition
sound reflection and absorption properties of outdoor surface(s) along the sound path(s) between source and
receiver
3.14
impulsive sound event
occurrence of a single short blast or series of blasts of sound in which the pressure-time history, close to the
source, includes a rapid rise to the peak sound pressure followed by decay of the pressure
3.15
sound pressure
p
difference between instantaneous total pressure and static pressure
[ISO 80000-8:2007, 8-9.2]
NOTE 1 Sound pressure is expressed in pascals.
NOTE 2 The symbol p is often used without modification to represent a root-mean-square sound pressure. However,
root-mean-square values should preferably be indicated by the subscript “eff”.
[ISO/TR 25417:2007, 2.1]
3.16
open-air explosion
blast, taking place out-of-doors, in which no part of the exploding material or gaseous products is limited by a
container or any other obstructing surface
3.17
peak sound pressure
p
peak
greatest absolute sound pressure during a certain time interval
NOTE 1 Peak sound pressure is expressed in pascals.
NOTE 2 A peak sound pressure may arise from a positive or negative sound pressure.
[ISO/TR 25417:2007, 2.4]
NOTE 3 This definition is technically in accordance with ISO 10843.
3.18
peak sound pressure level
L
p, peak
ten times the logarithm to the base 10 of the ratio of the square of the peak sound pressure, p , to the
peak
square of a reference value, p , expressed in decibels
p
peak
L = 10 lg dB
p,peak
p
where the reference value, p , is 20 µPa
NOTE Because of practical limitations of the measuring instruments, p is always understood to denote the
peak
square of a frequency-weighted or frequency-band-limited peak sound pressure. If a specific frequency weighting as
specified in IEC 61672-1 is applied, this should be indicated by appropriate subscripts; e.g. L denotes the
p, C peak
C-weighted peak sound pressure level.
[ISO/TR 25417:2007, 2.5]
3.19
receiver height
h
r
distance, in metres, of the sound receiver above the local ground surface
NOTE This definition is technically in accordance with ISO 9613-2.
3.20
replica atmosphere
conditions representing the atmosphere corresponding to a stated excess-attenuation class and a stated
atmospheric-absorption class
3.21
roughness height
distance above local ground level to the elevation where the time-average horizontal wind velocity becomes
non-zero
NOTE 1 The roughness height is expressed in metres.
NOTE 2 The time interval over which the wind velocity is averaged is 300 s.
4 © ISO 2009 – All rights reserved
3.22
sound exposure
E
T
integral of the square of the sound pressure, p, over a stated time interval or event duration T (starting at t
and ending at t ) (see 3.9)
t
E = pt dt
()
T
∫
t
NOTE 1 Sound exposure is expressed in pascals squared seconds, Pa ⋅s.
NOTE 2 Because of practical limitations of the measuring instruments, p is always understood to denote the square of
a frequency-weighted and frequency-band-limited sound pressure. If a specific frequency weighting as specified in
IEC 61672-1 is applied, this should be indicated by appropriate subscripts; e.g. E denotes the A-weighted sound
A,1 h
exposure over 1 h.
NOTE 3 When applied to a single event of impulsive or intermittent sound, the quantity is called “single-event sound
exposure” and the symbol E is used without a subscript.
NOTE 4 This definition is technically in accordance with ISO 80000-8:2007, 8-18.
[ISO/TR 25417:2007, 2.6]
3.23
sound exposure level
L
E,T
ten times the logarithm to the base 10 of the ratio of the sound exposure, E , to a reference value, E ,
T 0
expressed in decibels
E
T
L = 10 lg dB
ET,
E
−10 2
where the reference value, E , is 4 × 10 Pa ⋅s
NOTE 1 If a specific frequency weighting as specified in IEC 61672-1 is applied, this should be indicated by
appropriate subscripts; e.g. L denotes the A-weighted sound exposure level over 1 h.
E,A,1 h
NOTE 2 When applied to a single event, the quantity is called “single-event sound exposure level” and the symbol L is
E
used without further subscript.
NOTE 3 This definition is technically in accordance with ISO 80000-8:2007, 8-24.
[ISO/TR 25417:2007, 2.7]
3.24
source height
h
s
distance of the sound source above the local ground surface
NOTE 1 The source height is expressed in metres.
NOTE 2 This definition is technically in accordance with ISO 9613-2.
3.25
source forward direction
horizontal and vertical rotation angles assigned as references in the source-directivity coordinate system
3.26
adiabatic sound speed
c
speed of sound in the absence of ambient flow
NOTE The speed is expressed in metres per second.
4 Basic equations
4.1 General
ISO 1996-1 suggests a number of descriptors for environmental noise, some of which can be calculated from
a statistically weighted summation of single-event sound exposures. Other descriptors can be evaluated by
using order statistics derived from the distribution.
The single-event sound exposure level is subject to variation, in large part due to the effects of weather on the
propagation to the receiver. In sound propagation measurements, it has been observed, for example, that the
received sound level of a steady source can vary by several decibels from moment to moment, as well as
from day to day or from season to season. Because the atmospheric temperature and wind can vary from
point to point and from time to time, it is impractical to measure these values at all points during each event. It
would also be equally impractical to employ so many measurements within a detailed calculation for making a
routine noise assessment.
As a practical approach, the detailed atmosphere is described by several replica atmospheres, each being the
(short term) average state of the atmosphere for various atmospheric conditions and ground conditions.
Computations can be performed to estimate the single-event sound exposure level for the prevailing
conditions for each replica atmosphere. For practical computations, only a limited number of representative
situations can be managed. Therefore, the atmosphere is subject to classification in which each replica
atmosphere is representative of its class. Histograms of the frequencies of occurrence of the wind velocity,
wind direction, temperature, humidity and atmospheric stability are used to describe the different classes.
In this International Standard, two different classifications are used: atmospheric-absorption classes and
excess-attenuation classes. Each replica atmosphere represents a combination of an atmospheric-absorption
class with an excess-attenuation class. Using the calculated values of the short-term single-event sound
exposure level, combined with the frequencies of occurrence of the various classes, as shown in this
International Standard, it is feasible to calculate the sound exposure level as well as the exceedance level for
a long-term interval.
4.2 Probability of occurrence
Consider a continuous random variable X. For any particular x, one can consider the likelihood that X u x.
Accordingly, the cumulative distribution function is defined as:
F()xX=P ux (1)
()
r
where
X is a random variable (possibly with dimensional units);
x is any value (with the dimensional units of X).
The cumulative distribution function is a monotonically increasing one and ranges in value from 0 to 1, as x
ranges from −∞ to +∞.
Here and below, the role of the random variable can be taken by any of several types of quantity. The role
includes, for example, such things as atmospheric parameters, sound exposure levels or sound attenuations.
Two examples follow.
6 © ISO 2009 – All rights reserved
EXAMPLE 1 A measurement is performed to evaluate the probability distribution of the weather by atmospheric
stability (see 8.4). In this case, the Monin-Obukhov length (see 8.3) is the random variable. The sample space is the list of
all possible values of the Monin-Obukhov length.
EXAMPLE 2 The experiment is conducted to measure the probability distribution of the Z-weighted (unweighted) event
sound exposure level of cannon fire measured at the receiver, for a specified type of cannon, ammunition, direction and
elevation of fire, firing position and receiver position. In this case, the random variable is L . The sample space is the set of
E
all values of the event sound exposure level.
For practical use, it is convenient to segment the range of a continuous distribution into several intervals. To
this end, the following bin is defined:
xx: −<δδxux+ (2)
{ }
ii i i
and the discrete probability:
℘=()xxP −δδ
()
iir i ii ii ii
where
℘ is the probability (dimensionless) of obtaining an outcome in the ith bin;
i
x is the central value of the ith bin (possibly with dimensional units);
i
δ is the bin half-width (with the dimensional units of x );
i i
i is the index of the bin.
NOTE For simplicity, the probability bins are chosen to be equally spaced and contiguous, so that the sum of the
probability of occurrence over the discrete domain is equal to one.
4.3 Band sound exposure level
The band sound exposure level, in decibels, from an impulse sound source shall be calculated by:
L (jS)=−()j ⎡A+A (j)+A ()j+A ()j+A (j)⎤ (4)
Ek, ,l φθ, div atm,k rec diff exc,l
⎣ ⎦
where
L (j) is the band sound exposure level, in decibels, under the conditions described by the kth
E,k,l
atmospheric-absorption class and the lth excess-attenuation class;
j is the frequency band index;
S (j) is the direction-dependent source band sound exposure level, in decibels, using a reference
φ,θ
distance of one metre (see Clause 9);
φ is the (azimuth, yaw) angle, in degrees, between the source forward direction and the direct-
path direction when all angles are projected onto the horizontal plane;
θ is the (elevation, pitch) angle, in degrees, between the source forward direction and the
horizontal plane;
A is the attenuation, in decibels, due to geometric divergence (see 6.2);
div
A (j) is the band attenuation, in decibels, due to atmospheric absorption under conditions described
atm,k
by the kth atmospheric-absorption class (see 6.3);
A (j) is the band attenuation, in decibels, due to the presence of barriers that can affect propagation
rec
(e.g. walls, berms or sound-attenuating screens) not already included in the source description
(see 6.4);
A (j) is the band attenuation, in decibels, due to shielding by terrain (see 6.5);
diff
A (j) is the band excess attenuation, in decibels, under conditions described by the lth excess-
exc,l
attenuation class (see 6.6).
NOTE 1 For complex cases, the source sound exposure may include the combined effects of the source and sound-
absorbing or -reflecting screens or barriers near to the source that affect propagation. The diffraction insertion loss of
barriers or screens may be affected by meteorological conditions, requiring this to be accounted for separately.
NOTE 2 For omni-directional sources, such as open-air explosions, the source sound exposure is constant with
respect to angles θ and φ.
4.4 Frequency-weighted sound exposure level
The frequency-weighted sound exposure level, L , in decibels, shall be calculated by summation over bands,
E,w
in accordance with
N
⎡⎤
max
0,1⎡⎤Lj( )+w(j)
⎣⎦E
⎢⎥
L = 10 lg 10 dB (5)
E,w ∑
⎢⎥
jN=
⎣⎦min
where
L (j) is the band sound exposure level, in decibels, for the jth frequency band;
E
w is the type of frequency weighting (A-weighting or C-weighting, for example);
w(j) is the frequency weighting, in decibels, for the jth frequency band;
N is the lower band index;
min
N is the upper band index.
max
Bandwidths equal to one-third of an octave are preferred.
Contributions to the summation above from bands having values of L (j) + w(j) within twenty decibels of the
E
maximum value of L (j) + w(j) for bands extending from band index 0 (1 Hz) to band index 40 (10 kHz) are
E
considered significant and are required in the summation.
4.5 Long-term average single-event sound exposure level
For a single event with all source and receiver properties held constant, only the atmospheric absorption and
excess attenuation can be subject to change. Using this fact, the probability of occurrence is the joint
probability of the kth atmospheric-absorption class and the lth excess-attenuation class:
℘=Lx= ℘ ×℘ (6)
()
E,wa∑tm,klexc,
()kl,|L =x
{}
Ek,,w ,l
where
℘(L = x) is the probability of occurrence of the equality L = x (see ISO 3534-1 for notation);
E,w E,w
L is the frequency-weighted single-event sound exposure level for all combinations of
E,w
excess-attenuation class and atmospheric-absorption class considered;
8 © ISO 2009 – All rights reserved
x is a variable parameter, in decibels;
℘ is the probability of occurrence of the kth atmospheric-absorption class;
atm,k
℘ is the probability of occurrence of the lth excess-attenuation class.
exc,l
NOTE 1 It is implicit in Equation (6) that the joint probabilities of the atmospheric-absorption classes and the excess-
attenuation classes are mutually independent, so that they appear only as multiplicands within the sum.
NOTE 2 The summation is performed as indicated by including those combinations, (k,l), which cause the frequency-
weighted single-event sound exposure level to be equal to x.
The long-term average single-event sound exposure level, in decibels, can be found from the expectation
value:
NN
⎡⎤atm exc
0,1L
Ek,w, ,l
⎢⎥
L=℘10 lg ℘ 10 dB (7)
Ek,w ∑∑ atm, exc,l
LT
⎢⎥
kl==11
⎣⎦
Alternatively, the long-term average single-event sound exposure rating level, in decibels, is
NN
⎡⎤atm exc
0,1LK+
()
Ek,w, ,l
⎢⎥
L=℘10 lg ℘ 10 dB (8)
r ∑∑ atm,klexc,
LT
⎢⎥
kl==11
⎣⎦
where
〈 〉 indicates the long-term average;
LT
K is the rating level adjustment for highly impulsive sounds, if applicable (see ISO 1996-1);
℘ is the probability of occurrence of the kth atmospheric-absorption class;
atm,k
℘ is the probability of occurrence of the lth excess-attenuation class;
exc,l
L is the single-event sound exposure rating level, in decibels;
r
L is the frequency-weighted sound exposure level, in decibels, under the conditions described
E,w,k,l
by the kth atmospheric-absorption class and the lth excess-attenuation class;
w is the type of frequency weighting, e.g. A-weighting or C-weighting;
N is the number of atmospheric-absorption classes;
atm
N is the number of excess-attenuation classes.
exc
The calculations in Equations (7) and (8) satisfy a key objective of this International Standard. The quantity
〈L〉 is suitable for use in ISO 1996-1 as a frequency-weighted (and adjusted) single-event sound exposure
r LT
level.
NOTE The method given above covers a unique single event, i.e. a single source, operated in the same mode, at the
same location, in the same orientation, with the same intervening path to the receiver, etc. The only aspects allowed to
vary are the atmospheric and ground parameters.
If a rating level is required (such as the day-evening-night level), this quantity shall take into account the
penalties for the various assessment periods.
4.6 Equivalent level from multiple events
For the case of calculating the equivalent level from multiple events, the summation runs through the list of
events, as follows:
N
⎡⎤evt
01, L
t
Ev,w,
LT
L =10 lg⎢⎥10 dB (9)
w,eq,T ∑
T
⎢⎥
v=1
⎣⎦
where
L is the frequency-weighted equivalent level;
w,eq,T
t is the reference time period, in seconds, and is equal to 1 s;
T is the assessment time period, in seconds;
〈L 〉 is the long-term average frequency-weighted single-event sound exposure level;
E,w,v LT
N is the number of events within the assessment time period;
evt
v is the event index.
If a rating level is required (such as the day-evening-night level), this quantity shall take into account the
penalties for the various assessment periods.
5 Calculation of a statistical distribution
To estimate a statistical distribution of the frequency-weighted sound exposure levels, all combinations of k
and l shall be placed in sorted order with increasing values of level:
L<=Lm,,with 2…,M (10)
Em,,w1− Em,,w
where
M is the number of combinations (M = N × N );
atm exc
N is the number of atmospheric-absorption classes;
atm
N is the number of excess-attenuation classes.
exc
This can be seen as a new classification of the sound exposure levels with M classes, in which each class is a
unique combination of the kth atmospheric-absorption class and lth excess-attenuation class. The class width
is chosen in such a way that there are no gaps between adjacent classes. The lower and upper boundaries,
g and g , between adjoining classes are chosen to lie half-way between consecutive values:
L,m U,m
⎛⎞LL+
Em,w, −1 Em,w,
g==gmfor 2=,…,M (11)
⎜⎟
L,mmU, −1
⎝⎠
The extreme lower and upper boundaries shall be chosen such that
gL=−()g−L (12)
L,1EE,w,1 U,1 ,w,1
and
gL=+()L −g (13)
U,M EM,w, E,w,M L,M
10 © ISO 2009 – All rights reserved
The probability of occurrence of each class, m, is calculated by
℘= PgL<
{ }
mmr L, E,w,m U,m atm,k exc,l
where
℘ is the probability of occurrence for the interval m [of combination (k,l)];
m
℘ is the probability of occurrence of atmospheric-absorption class k;
atm,k
℘ is the probability of occurrence of excess-attenuation class l.
exc,l
A probability density function ρ (x) can then be defined:
m
⎧ ℘
m
forgx<
⎪ L,mmU,
gg−
⎪
U,mmL,
ρ ()x = (15)
⎨
m
⎪
0 elsewhere
⎪
⎩
In the rare case that L = L = L , the probability function ρ (x) is not defined. In this case,
E,w,m−1 E,w,m E,w,m+1 m
classes with the same level shall be combined.
The overall probability density function, ρ(x), is defined as
M
ρρ()xx= ( ) (16)
∑ m
m=1
1 1
so ρ(x) × δx is the probability that the level is within the interval between xx− δ and xx+ δ . As a
2 2
consequence of the method used [Equation (16)], the function ρ(x) has discontinuities at the class boundaries,
g and g (see Figure 1).
L,m U,m
Figure 1 — Probability density function, ρ(x), with constant values within classes m
In practice, the number of classes, M, is limited to a value of, typically, 10 to 100. Each class therefore
represents a range of atmospheric conditions which are assumed to have an equal probability of occurrence
in that class. The discontinuities in the function ρ(x) cause discontinuities in calculated statistical distributions
of the sound exposure level.
To obtain the final statistical distribution, the following has to be taken into account. The calculations are
performed without taking into account the random perturbations of the sound speed profile (turbulence).
Therefore, the different classes represent sample values from within a small range of different atmospheric
and ground conditions. Field measurements indicate that the spread in levels due to turbulence can be
described by a normal distribution with a standard deviation equal to 5 dB. However, depending on the local
situation, other distributions may be more appropriate. If more information is available about the distribution of
levels, this should be taken into account.
NOTE The purpose of the distribution is to quantify the spreading of the levels due to turbulence, which can occur in
a particular combination of one atmospheric-absorption class and one excess-attenuation class. What must be considered
is spreading of the levels over a short time interval, typically shorter than 15 minutes. The distribution is not meant to
describe the spreading of levels due to changing weather conditions.
Key
1 Gaussian function
Figure 2 — Probability density function, with each class, m, divided into N subclasses (top) and with
sub
subclass {m, j} replaced by a continuous Gaussian function (bottom)
This spreading of levels due to turbulence will be taken into account by a convolution of the function ρ(x) with
a normal distribution having a standard deviation of 5 dB (the value typically used). This operation is carried
out in two steps (see Figure 2):
First, each class, m, is divided into N equal, contiguous subclasses labelled by an index, j (= 1,.,N ).
sub sub
1 1
Subclass {m, j} runs from xb=−µ to xb=+µ , where b is the width of each subclass and is
mj, m mj, m
m
2 2
given by
gg−
U,mmL,
b = (17)
m
N
sub
12 © ISO 2009 – All rights reserved
and µ is the centre of the subclass and is given by
m,j
µ =+g ()jb− (18)
mj,L,m m
Each subclass corresponds to a probability density given by
⎧
ρµ()xbfor −
⎪mm,,jmj m,jm,j
ρ ()x = (19)
⎨
mj,
0elsewhere
⎪
⎩
The total probability density function is therefore given by
N
M
sub
ρρ()xx= () (20)
∑∑ mj,
==
mj11
Next, the discontinuous probability density functions, ρ (x), are replaced by continuous normalized Gaussian
m,j
functions to give
⎧⎫
⎡ ⎤
x−−()µµ∆
1⎪⎪mj,
⎣ ⎦
*
ρρ()xb=−(µ ) exp (21)
⎨⎬
mj,,m m j m,j
σ 2π 2σ
⎪⎪
⎩⎭
where σ is the standard deviation, for which a value of 5 dB is typically used.
The shift ∆µ is introduced to ensure that the energetically averaged level remains at the value µ . The value
m,j
of ∆µ can be obtained using Equation (22):
∞
⎡⎤2
⎛⎞
1 x
01, x
⎢⎥
∆=µ 10 lg 10 exp − dx dB (22)
⎜⎟
∫ 2
⎜⎟
⎢⎥
σ 2π
2σ
⎝⎠
−∞
⎣⎦
The continuous overall probability density function is defined as
N
M
sub
**
ρρ()xx= () (23)
mj
∑∑ ,
mj==11
*
From the continuous function ρ (x), various types of statistical quantities or functions can be derived. For
example, the cumulative probability that the frequency-weighted sound exposure level is higher than a value
of x dB is given by
∞
* ′′
P(L >=xx) ρ ( )dx (24)
r,Ew
∫
x
where x′ is an integration variable.
An n-percent exceedance level, L (for instance, L ), can be obtained by solving Equation (25) for x:
E,w,n E,A,95
∞
* ′′
P(Lx>=) ρ(x)dx=0,95 (25)
95 E,A
∫
x
where
n is the percentage of values that exceed x [in Equation (25) above, n = 95];
x is the exceedance level, in decibels.
6 Calculation of attenuation
6.1 General
Attenuation of sound during propagation is the result of several effects. Geometric divergence of sound away
from a compact source is discussed in 6.2, atmospheric absorption in 6.3, insertion loss by receiver site
screening objects in 6.4 and shielding by terrain in 6.5. It is common to include all other effects under the term
“excess attenuation”, as can be seen in 6.6.
6.2 Geometric diver
...
INTERNATIONAL ISO
STANDARD 13474
First edition
2009-06-15
Acoustics — Framework for calculating a
distribution of sound exposure levels for
impulsive sound events for the purposes
of environmental noise assessment
Acoustique — Cadre pour le calcul d'une distribution des niveaux
d'exposition sonore pour les sons impulsionnels pour les besoins de
l'évaluation du bruit environnemental
Reference number
©
ISO 2009
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ii © ISO 2009 – All rights reserved
Contents Page
Foreword .v
Introduction.vi
1 Scope.1
2 Normative references.1
3 Terms and definitions .2
4 Basic equations .6
4.1 General .6
4.2 Probability of occurrence .6
4.3 Band sound exposure level.7
4.4 Frequency-weighted sound exposure level.8
4.5 Long-term average single-event sound exposure level.8
4.6 Equivalent level from multiple events.10
5 Calculation of a statistical distribution .10
6 Calculation of attenuation .14
6.1 General .14
6.2 Geometric divergence.14
6.3 Atmospheric absorption.14
6.4 Insertion loss by screening objects .15
6.5 Terrain shielding.15
6.6 Contributions to excess attenuation.16
6.6.1 General .16
6.6.2 Refraction.16
6.6.3 Ground reflection and absorption .17
7 Classification .19
7.1 General .19
7.2 Classification of atmospheric absorption.19
7.3 Classification of excess attenuation .19
7.3.1 General .19
7.3.2 Lookup table requirements .20
7.3.3 Range-dependent sound speed profiles.21
7.3.4 Directed sound speed profiles.21
8 Probability of occurrence of sound speed profiles .22
8.1 General .22
8.2 Using direct measurements of wind and temperature profiles .22
8.3 Similarity relationships for the atmospheric surface layer.23
8.4 Using measurements of turbulent fluxes.24
8.5 Using routinely gathered weather station data .25
8.6 Using directly measured or calculated sound speed profiles as input .26
9 The source .26
9.1 General .26
9.2 Demolition and muzzle blasts .26
9.2.1 General .26
9.2.2 Source descriptors.27
9.2.3 Determination by measurement.27
9.2.4 Determination by estimation .28
9.3 Projectile sound.28
9.3.1 General .28
9.3.2 Flat trajectories .28
9.3.3 High-elevation trajectories and rocket trajectories.28
10 Uncertainties .28
Annex A (informative) Example of the estimation of the statistical distribution of single-event
sound exposure levels .30
Annex B (informative) Uncertainty .37
Bibliography .40
iv © ISO 2009 – All rights reserved
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 13474 was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise.
It cancels and replaces ISO/TS 13474:2003, which has been technically revised.
Introduction
The aim of this International Standard is to provide a framework for the evaluation of descriptor quantities for
use in environmental noise assessment. Part of this framework includes an engineering method for calculating
a statistical distribution of event sound exposure levels at locations which are some distance from high-energy
impulsive sound sources. It is specifically intended for environmental noise assessment and not for the
assessment of the risk of damage to buildings or the risk of injury to animals or people.
In ISO 9613-2, the immission level from sources such as traffic and industry is calculated for a so-called
“downwind” condition. The long-term average level is estimated using a correction factor, C . This concept
met
holds for distances where sound from such sources is assessed as environmental noise. ISO 9613-2 excludes
impulses in its scope and holds only for A-weighting, for near-ground sources and receivers and for distances
up to about 1 000 m. For high-energy impulsive sound sources, the impulsive sound event duration is short,
and low frequencies are more prominent than for traffic and industrial sound sources. Lower-frequency
sounds are generally less attenuated over a given distance in the atmosphere than higher frequencies and, as
a consequence, the level-influencing effects of propagation over much larger distances need to be taken into
account.
A general outline is given of a method that takes into account ground reflection, shielding by topography and
the meteorological effects of refraction and turbulence. Starting from the source strength, this method
calculates a distribution of immission levels for a set of replica atmospheres, each replica being a specific
combination of atmospheric-absorption class and excess-attenuation class. To carry out practical calculations
using the procedure, it is useful to exploit the statistical contribution of the meteorological and ground surface
conditions. In particular, histograms of the frequencies of occurrence of the wind velocity, wind direction,
temperature, humidity and atmospheric stability can be used to describe the classes. From the distribution of
the immission levels, a number of assessment metrics can be obtained. For instance, the long-term averaged
immission level can be calculated as a weighted average. The weighting factors are determined by the
probability of occurrence of each replica atmosphere during the relevant time period for the location of interest.
vi © ISO 2009 – All rights reserved
INTERNATIONAL STANDARD ISO 13474:2009(E)
Acoustics — Framework for calculating a distribution of sound
exposure levels for impulsive sound events for the purposes of
environmental noise assessment
1 Scope
This International Standard specifies the framework of an engineering method for calculating a statistical
distribution of sound exposure levels for impulsive sound events for the purposes of environmental noise
assessment. This International Standard is applicable to impulse sounds propagating over large distances
(e.g. 0,5 km to 30 km) from sources such as mine blasting, artillery fire and bomb explosions, using
conventional explosives of moderate charge mass (e.g. 0,05 kg to 1 000 kg of TNT equivalent). The effects of
meteorological conditions and terrain upon sound propagation are considered.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 1996-1, Acoustics — Description, measurement and assessment of environmental noise — Part 1: Basic
quantities and assessment procedures
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 9613-1, Acoustics — Attenuation of sound during propagation outdoors — Part 1: Calculation of the
absorption of sound by the atmosphere
ISO 9613-2, Acoustics — Attenuation of sound during propagation outdoors — Part 2: General method of
calculation
ISO 17201-1, Acoustics — Noise from shooting ranges — Part 1: Determination of muzzle blast by
measurement
ISO 17201-2, Acoustics — Noise from shooting ranges — Part 2: Estimation of muzzle blast and projectile
sound by calculation
ISO 17201-4, Acoustics — Noise from shooting ranges — Part 4: Prediction of projectile sound
ISO/IEC Guide 98-3, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
VDI MSR 8/559, Standard Method to Measure the Sound Exposure Emissions and Immissions from Large
Weapons (Standardmethode zur Messung der Geräuschemissionen und -immissionen von schweren Waffen),
Edmund Buchta (ed.), in Meß-, Steuerungs- und Regelungstechnik, No. 8/559, Fortschritt-Berichte, VDI
Verlag, Düsseldorf, 1996 (in English and German)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
atmospheric absorption
attenuation of sound by air, resulting from viscous molecular processes, molecular rotation and molecular
vibration
3.2
atmospheric-absorption class
range of meteorological parameters yielding approximately the same attenuation of sound by air, all within a
specified uncertainty
NOTE See also atmospheric absorption.
3.3
atmospheric stability
tendency of the atmosphere to reduce or enhance vertical motion of the air
NOTE Enhanced (or reduced) vertical motion of the air usually implies enhanced (or reduced) atmospheric
turbulence.
3.4
atmospheric-stability class
subset formed from partitioning the set of atmospheres according to stability
NOTE See also atmospheric stability.
3.5
direct path
position displacement vector, in metres, originating at the source and describing a straight trajectory
terminating at the receiver
NOTE The direct path may intercept objects such as buildings or terrain.
3.6
directed sound speed
algebraic sum of the adiabatic sound speed and the horizontal component of the wind velocity along the direct
path
NOTE Directed sound speed is expressed in metres per second.
3.7
directed sound speed profile
sound speed along the direct path, expressed as a function of height
NOTE See directed sound speed.
3.8
event
single short burst, or rapid sequence of bursts, associated with a sound source
NOTE A single activity, such as firing a gun, could produce multiple sound events. In the case of firing an explosive
projectile from a high-velocity gun, sound events are associated with each of the following sound sources: the muzzle
blast, the ballistic shock and the projectile impact.
2 © ISO 2009 – All rights reserved
3.9
event duration
T
time interval starting just before immission, at time t , and ending just after immission, at time t , to
1 2
encompass all significant sound of a single short blast or rapid sequence of blasts
NOTE The time interval t − t is expressed in seconds.
2 1
3.10
exceedance level
sound level of a stated type, in decibels, exceeded by no more and no less than a stated percentage of
samples
NOTE The sampling set shall be identified, e.g. percentage of times during a stated time interval or percentage of
firing events from an exercise.
3.11
excess attenuation
that part of sound attenuation not included when accounting for geometric divergence (from a small sound
source in non-refracting and non-moving air), atmospheric absorption of sound waves along the direct path
from source to receiver and attenuation of screens and/or barriers
NOTE Excess attenuation is expressed in decibels.
3.12
excess-attenuation class
range of combined directed sound speed profiles and ground types yielding approximately the same
attenuations, all within a specified uncertainty
3.13
ground condition
sound reflection and absorption properties of outdoor surface(s) along the sound path(s) between source and
receiver
3.14
impulsive sound event
occurrence of a single short blast or series of blasts of sound in which the pressure-time history, close to the
source, includes a rapid rise to the peak sound pressure followed by decay of the pressure
3.15
sound pressure
p
difference between instantaneous total pressure and static pressure
[ISO 80000-8:2007, 8-9.2]
NOTE 1 Sound pressure is expressed in pascals.
NOTE 2 The symbol p is often used without modification to represent a root-mean-square sound pressure. However,
root-mean-square values should preferably be indicated by the subscript “eff”.
[ISO/TR 25417:2007, 2.1]
3.16
open-air explosion
blast, taking place out-of-doors, in which no part of the exploding material or gaseous products is limited by a
container or any other obstructing surface
3.17
peak sound pressure
p
peak
greatest absolute sound pressure during a certain time interval
NOTE 1 Peak sound pressure is expressed in pascals.
NOTE 2 A peak sound pressure may arise from a positive or negative sound pressure.
[ISO/TR 25417:2007, 2.4]
NOTE 3 This definition is technically in accordance with ISO 10843.
3.18
peak sound pressure level
L
p, peak
ten times the logarithm to the base 10 of the ratio of the square of the peak sound pressure, p , to the
peak
square of a reference value, p , expressed in decibels
p
peak
L = 10 lg dB
p,peak
p
where the reference value, p , is 20 µPa
NOTE Because of practical limitations of the measuring instruments, p is always understood to denote the
peak
square of a frequency-weighted or frequency-band-limited peak sound pressure. If a specific frequency weighting as
specified in IEC 61672-1 is applied, this should be indicated by appropriate subscripts; e.g. L denotes the
p, C peak
C-weighted peak sound pressure level.
[ISO/TR 25417:2007, 2.5]
3.19
receiver height
h
r
distance, in metres, of the sound receiver above the local ground surface
NOTE This definition is technically in accordance with ISO 9613-2.
3.20
replica atmosphere
conditions representing the atmosphere corresponding to a stated excess-attenuation class and a stated
atmospheric-absorption class
3.21
roughness height
distance above local ground level to the elevation where the time-average horizontal wind velocity becomes
non-zero
NOTE 1 The roughness height is expressed in metres.
NOTE 2 The time interval over which the wind velocity is averaged is 300 s.
4 © ISO 2009 – All rights reserved
3.22
sound exposure
E
T
integral of the square of the sound pressure, p, over a stated time interval or event duration T (starting at t
and ending at t ) (see 3.9)
t
E = pt dt
()
T
∫
t
NOTE 1 Sound exposure is expressed in pascals squared seconds, Pa ⋅s.
NOTE 2 Because of practical limitations of the measuring instruments, p is always understood to denote the square of
a frequency-weighted and frequency-band-limited sound pressure. If a specific frequency weighting as specified in
IEC 61672-1 is applied, this should be indicated by appropriate subscripts; e.g. E denotes the A-weighted sound
A,1 h
exposure over 1 h.
NOTE 3 When applied to a single event of impulsive or intermittent sound, the quantity is called “single-event sound
exposure” and the symbol E is used without a subscript.
NOTE 4 This definition is technically in accordance with ISO 80000-8:2007, 8-18.
[ISO/TR 25417:2007, 2.6]
3.23
sound exposure level
L
E,T
ten times the logarithm to the base 10 of the ratio of the sound exposure, E , to a reference value, E ,
T 0
expressed in decibels
E
T
L = 10 lg dB
ET,
E
−10 2
where the reference value, E , is 4 × 10 Pa ⋅s
NOTE 1 If a specific frequency weighting as specified in IEC 61672-1 is applied, this should be indicated by
appropriate subscripts; e.g. L denotes the A-weighted sound exposure level over 1 h.
E,A,1 h
NOTE 2 When applied to a single event, the quantity is called “single-event sound exposure level” and the symbol L is
E
used without further subscript.
NOTE 3 This definition is technically in accordance with ISO 80000-8:2007, 8-24.
[ISO/TR 25417:2007, 2.7]
3.24
source height
h
s
distance of the sound source above the local ground surface
NOTE 1 The source height is expressed in metres.
NOTE 2 This definition is technically in accordance with ISO 9613-2.
3.25
source forward direction
horizontal and vertical rotation angles assigned as references in the source-directivity coordinate system
3.26
adiabatic sound speed
c
speed of sound in the absence of ambient flow
NOTE The speed is expressed in metres per second.
4 Basic equations
4.1 General
ISO 1996-1 suggests a number of descriptors for environmental noise, some of which can be calculated from
a statistically weighted summation of single-event sound exposures. Other descriptors can be evaluated by
using order statistics derived from the distribution.
The single-event sound exposure level is subject to variation, in large part due to the effects of weather on the
propagation to the receiver. In sound propagation measurements, it has been observed, for example, that the
received sound level of a steady source can vary by several decibels from moment to moment, as well as
from day to day or from season to season. Because the atmospheric temperature and wind can vary from
point to point and from time to time, it is impractical to measure these values at all points during each event. It
would also be equally impractical to employ so many measurements within a detailed calculation for making a
routine noise assessment.
As a practical approach, the detailed atmosphere is described by several replica atmospheres, each being the
(short term) average state of the atmosphere for various atmospheric conditions and ground conditions.
Computations can be performed to estimate the single-event sound exposure level for the prevailing
conditions for each replica atmosphere. For practical computations, only a limited number of representative
situations can be managed. Therefore, the atmosphere is subject to classification in which each replica
atmosphere is representative of its class. Histograms of the frequencies of occurrence of the wind velocity,
wind direction, temperature, humidity and atmospheric stability are used to describe the different classes.
In this International Standard, two different classifications are used: atmospheric-absorption classes and
excess-attenuation classes. Each replica atmosphere represents a combination of an atmospheric-absorption
class with an excess-attenuation class. Using the calculated values of the short-term single-event sound
exposure level, combined with the frequencies of occurrence of the various classes, as shown in this
International Standard, it is feasible to calculate the sound exposure level as well as the exceedance level for
a long-term interval.
4.2 Probability of occurrence
Consider a continuous random variable X. For any particular x, one can consider the likelihood that X u x.
Accordingly, the cumulative distribution function is defined as:
F()xX=P ux (1)
()
r
where
X is a random variable (possibly with dimensional units);
x is any value (with the dimensional units of X).
The cumulative distribution function is a monotonically increasing one and ranges in value from 0 to 1, as x
ranges from −∞ to +∞.
Here and below, the role of the random variable can be taken by any of several types of quantity. The role
includes, for example, such things as atmospheric parameters, sound exposure levels or sound attenuations.
Two examples follow.
6 © ISO 2009 – All rights reserved
EXAMPLE 1 A measurement is performed to evaluate the probability distribution of the weather by atmospheric
stability (see 8.4). In this case, the Monin-Obukhov length (see 8.3) is the random variable. The sample space is the list of
all possible values of the Monin-Obukhov length.
EXAMPLE 2 The experiment is conducted to measure the probability distribution of the Z-weighted (unweighted) event
sound exposure level of cannon fire measured at the receiver, for a specified type of cannon, ammunition, direction and
elevation of fire, firing position and receiver position. In this case, the random variable is L . The sample space is the set of
E
all values of the event sound exposure level.
For practical use, it is convenient to segment the range of a continuous distribution into several intervals. To
this end, the following bin is defined:
xx: −<δδxux+ (2)
{ }
ii i i
and the discrete probability:
℘=()xxP −δδ
()
iir i ii ii ii
where
℘ is the probability (dimensionless) of obtaining an outcome in the ith bin;
i
x is the central value of the ith bin (possibly with dimensional units);
i
δ is the bin half-width (with the dimensional units of x );
i i
i is the index of the bin.
NOTE For simplicity, the probability bins are chosen to be equally spaced and contiguous, so that the sum of the
probability of occurrence over the discrete domain is equal to one.
4.3 Band sound exposure level
The band sound exposure level, in decibels, from an impulse sound source shall be calculated by:
L (jS)=−()j ⎡A+A (j)+A ()j+A ()j+A (j)⎤ (4)
Ek, ,l φθ, div atm,k rec diff exc,l
⎣ ⎦
where
L (j) is the band sound exposure level, in decibels, under the conditions described by the kth
E,k,l
atmospheric-absorption class and the lth excess-attenuation class;
j is the frequency band index;
S (j) is the direction-dependent source band sound exposure level, in decibels, using a reference
φ,θ
distance of one metre (see Clause 9);
φ is the (azimuth, yaw) angle, in degrees, between the source forward direction and the direct-
path direction when all angles are projected onto the horizontal plane;
θ is the (elevation, pitch) angle, in degrees, between the source forward direction and the
horizontal plane;
A is the attenuation, in decibels, due to geometric divergence (see 6.2);
div
A (j) is the band attenuation, in decibels, due to atmospheric absorption under conditions described
atm,k
by the kth atmospheric-absorption class (see 6.3);
A (j) is the band attenuation, in decibels, due to the presence of barriers that can affect propagation
rec
(e.g. walls, berms or sound-attenuating screens) not already included in the source description
(see 6.4);
A (j) is the band attenuation, in decibels, due to shielding by terrain (see 6.5);
diff
A (j) is the band excess attenuation, in decibels, under conditions described by the lth excess-
exc,l
attenuation class (see 6.6).
NOTE 1 For complex cases, the source sound exposure may include the combined effects of the source and sound-
absorbing or -reflecting screens or barriers near to the source that affect propagation. The diffraction insertion loss of
barriers or screens may be affected by meteorological conditions, requiring this to be accounted for separately.
NOTE 2 For omni-directional sources, such as open-air explosions, the source sound exposure is constant with
respect to angles θ and φ.
4.4 Frequency-weighted sound exposure level
The frequency-weighted sound exposure level, L , in decibels, shall be calculated by summation over bands,
E,w
in accordance with
N
⎡⎤
max
0,1⎡⎤Lj( )+w(j)
⎣⎦E
⎢⎥
L = 10 lg 10 dB (5)
E,w ∑
⎢⎥
jN=
⎣⎦min
where
L (j) is the band sound exposure level, in decibels, for the jth frequency band;
E
w is the type of frequency weighting (A-weighting or C-weighting, for example);
w(j) is the frequency weighting, in decibels, for the jth frequency band;
N is the lower band index;
min
N is the upper band index.
max
Bandwidths equal to one-third of an octave are preferred.
Contributions to the summation above from bands having values of L (j) + w(j) within twenty decibels of the
E
maximum value of L (j) + w(j) for bands extending from band index 0 (1 Hz) to band index 40 (10 kHz) are
E
considered significant and are required in the summation.
4.5 Long-term average single-event sound exposure level
For a single event with all source and receiver properties held constant, only the atmospheric absorption and
excess attenuation can be subject to change. Using this fact, the probability of occurrence is the joint
probability of the kth atmospheric-absorption class and the lth excess-attenuation class:
℘=Lx= ℘ ×℘ (6)
()
E,wa∑tm,klexc,
()kl,|L =x
{}
Ek,,w ,l
where
℘(L = x) is the probability of occurrence of the equality L = x (see ISO 3534-1 for notation);
E,w E,w
L is the frequency-weighted single-event sound exposure level for all combinations of
E,w
excess-attenuation class and atmospheric-absorption class considered;
8 © ISO 2009 – All rights reserved
x is a variable parameter, in decibels;
℘ is the probability of occurrence of the kth atmospheric-absorption class;
atm,k
℘ is the probability of occurrence of the lth excess-attenuation class.
exc,l
NOTE 1 It is implicit in Equation (6) that the joint probabilities of the atmospheric-absorption classes and the excess-
attenuation classes are mutually independent, so that they appear only as multiplicands within the sum.
NOTE 2 The summation is performed as indicated by including those combinations, (k,l), which cause the frequency-
weighted single-event sound exposure level to be equal to x.
The long-term average single-event sound exposure level, in decibels, can be found from the expectation
value:
NN
⎡⎤atm exc
0,1L
Ek,w, ,l
⎢⎥
L=℘10 lg ℘ 10 dB (7)
Ek,w ∑∑ atm, exc,l
LT
⎢⎥
kl==11
⎣⎦
Alternatively, the long-term average single-event sound exposure rating level, in decibels, is
NN
⎡⎤atm exc
0,1LK+
()
Ek,w, ,l
⎢⎥
L=℘10 lg ℘ 10 dB (8)
r ∑∑ atm,klexc,
LT
⎢⎥
kl==11
⎣⎦
where
〈 〉 indicates the long-term average;
LT
K is the rating level adjustment for highly impulsive sounds, if applicable (see ISO 1996-1);
℘ is the probability of occurrence of the kth atmospheric-absorption class;
atm,k
℘ is the probability of occurrence of the lth excess-attenuation class;
exc,l
L is the single-event sound exposure rating level, in decibels;
r
L is the frequency-weighted sound exposure level, in decibels, under the conditions described
E,w,k,l
by the kth atmospheric-absorption class and the lth excess-attenuation class;
w is the type of frequency weighting, e.g. A-weighting or C-weighting;
N is the number of atmospheric-absorption classes;
atm
N is the number of excess-attenuation classes.
exc
The calculations in Equations (7) and (8) satisfy a key objective of this International Standard. The quantity
〈L〉 is suitable for use in ISO 1996-1 as a frequency-weighted (and adjusted) single-event sound exposure
r LT
level.
NOTE The method given above covers a unique single event, i.e. a single source, operated in the same mode, at the
same location, in the same orientation, with the same intervening path to the receiver, etc. The only aspects allowed to
vary are the atmospheric and ground parameters.
If a rating level is required (such as the day-evening-night level), this quantity shall take into account the
penalties for the various assessment periods.
4.6 Equivalent level from multiple events
For the case of calculating the equivalent level from multiple events, the summation runs through the list of
events, as follows:
N
⎡⎤evt
01, L
t
Ev,w,
LT
L =10 lg⎢⎥10 dB (9)
w,eq,T ∑
T
⎢⎥
v=1
⎣⎦
where
L is the frequency-weighted equivalent level;
w,eq,T
t is the reference time period, in seconds, and is equal to 1 s;
T is the assessment time period, in seconds;
〈L 〉 is the long-term average frequency-weighted single-event sound exposure level;
E,w,v LT
N is the number of events within the assessment time period;
evt
v is the event index.
If a rating level is required (such as the day-evening-night level), this quantity shall take into account the
penalties for the various assessment periods.
5 Calculation of a statistical distribution
To estimate a statistical distribution of the frequency-weighted sound exposure levels, all combinations of k
and l shall be placed in sorted order with increasing values of level:
L<=Lm,,with 2…,M (10)
Em,,w1− Em,,w
where
M is the number of combinations (M = N × N );
atm exc
N is the number of atmospheric-absorption classes;
atm
N is the number of excess-attenuation classes.
exc
This can be seen as a new classification of the sound exposure levels with M classes, in which each class is a
unique combination of the kth atmospheric-absorption class and lth excess-attenuation class. The class width
is chosen in such a way that there are no gaps between adjacent classes. The lower and upper boundaries,
g and g , between adjoining classes are chosen to lie half-way between consecutive values:
L,m U,m
⎛⎞LL+
Em,w, −1 Em,w,
g==gmfor 2=,…,M (11)
⎜⎟
L,mmU, −1
⎝⎠
The extreme lower and upper boundaries shall be chosen such that
gL=−()g−L (12)
L,1EE,w,1 U,1 ,w,1
and
gL=+()L −g (13)
U,M EM,w, E,w,M L,M
10 © ISO 2009 – All rights reserved
The probability of occurrence of each class, m, is calculated by
℘= PgL<
{ }
mmr L, E,w,m U,m atm,k exc,l
where
℘ is the probability of occurrence for the interval m [of combination (k,l)];
m
℘ is the probability of occurrence of atmospheric-absorption class k;
atm,k
℘ is the probability of occurrence of excess-attenuation class l.
exc,l
A probability density function ρ (x) can then be defined:
m
⎧ ℘
m
forgx<
⎪ L,mmU,
gg−
⎪
U,mmL,
ρ ()x = (15)
⎨
m
⎪
0 elsewhere
⎪
⎩
In the rare case that L = L = L , the probability function ρ (x) is not defined. In this case,
E,w,m−1 E,w,m E,w,m+1 m
classes with the same level shall be combined.
The overall probability density function, ρ(x), is defined as
M
ρρ()xx= ( ) (16)
∑ m
m=1
1 1
so ρ(x) × δx is the probability that the level is within the interval between xx− δ and xx+ δ . As a
2 2
consequence of the method used [Equation (16)], the function ρ(x) has discontinuities at the class boundaries,
g and g (see Figure 1).
L,m U,m
Figure 1 — Probability density function, ρ(x), with constant values within classes m
In practice, the number of classes, M, is limited to a value of, typically, 10 to 100. Each class therefore
represents a range of atmospheric conditions which are assumed to have an equal probability of occurrence
in that class. The discontinuities in the function ρ(x) cause discontinuities in calculated statistical distributions
of the sound exposure level.
To obtain the final statistical distribution, the following has to be taken into account. The calculations are
performed without taking into account the random perturbations of the sound speed profile (turbulence).
Therefore, the different classes represent sample values from within a small range of different atmospheric
and ground conditions. Field measurements indicate that the spread in levels due to turbulence can be
described by a normal distribution with a standard deviation equal to 5 dB. However, depending on the local
situation, other distributions may be more appropriate. If more information is available about the distribution of
levels, this should be taken into account.
NOTE The purpose of the distribution is to quantify the spreading of the levels due to turbulence, which can occur in
a particular combination of one atmospheric-absorption class and one excess-attenuation class. What must be considered
is spreading of the levels over a short time interval, typically shorter than 15 minutes. The distribution is not meant to
describe the spreading of levels due to changing weather conditions.
Key
1 Gaussian function
Figure 2 — Probability density function, with each class, m, divided into N subclasses (top) and with
sub
subclass {m, j} replaced by a continuous Gaussian function (bottom)
This spreading of levels due to turbulence will be taken into account by a convolution of the function ρ(x) with
a normal distribution having a standard deviation of 5 dB (the value typically used). This operation is carried
out in two steps (see Figure 2):
First, each class, m, is divided into N equal, contiguous subclasses labelled by an index, j (= 1,.,N ).
sub sub
1 1
Subclass {m, j} runs from xb=−µ to xb=+µ , where b is the width of each subclass and is
mj, m mj, m
m
2 2
given by
gg−
U,mmL,
b = (17)
m
N
sub
12 © ISO 2009 – All rights reserved
and µ is the centre of the subclass and is given by
m,j
µ =+g ()jb− (18)
mj,L,m m
Each subclass corresponds to a probability density given by
⎧
ρµ()xbfor −
⎪mm,,jmj m,jm,j
ρ ()x = (19)
⎨
mj,
0elsewhere
⎪
⎩
The total probability density function is therefore given by
N
M
sub
ρρ()xx= () (20)
∑∑ mj,
==
mj11
Next, the discontinuous probability density functions, ρ (x), are replaced by continuous normalized Gaussian
m,j
functions to give
⎧⎫
⎡ ⎤
x−−()µµ∆
1⎪⎪mj,
⎣ ⎦
*
ρρ()xb=−(µ ) exp (21)
⎨⎬
mj,,m m j m,j
σ 2π 2σ
⎪⎪
⎩⎭
where σ is the standard deviation, for which a value of 5 dB is typically used.
The shift ∆µ is introduced to ensure that the energetically averaged level remains at the value µ . The value
m,j
of ∆µ can be obtained using Equation (22):
∞
⎡⎤2
⎛⎞
1 x
01, x
⎢⎥
∆=µ 10 lg 10 exp − dx dB (22)
⎜⎟
∫ 2
⎜⎟
⎢⎥
σ 2π
2σ
⎝⎠
−∞
⎣⎦
The continuous overall probability density function is defined as
N
M
sub
**
ρρ()xx= () (23)
mj
∑∑ ,
mj==11
*
From the continuous function ρ (x), various types of statistical quantities or functions can be derived. For
example, the cumulative probability that the frequency-weighted sound exposure level is higher than a value
of x dB is given by
∞
* ′′
P(L >=xx) ρ ( )dx (24)
r,Ew
∫
x
where x′ is an integration variable.
An n-percent exceedance level, L (for instance, L ), can be obtained by solving Equation (25) for x:
E,w,n E,A,95
∞
* ′′
P(Lx>=) ρ(x)dx=0,95 (25)
95 E,A
∫
x
where
n is the percentage of values that exceed x [in Equation (25) above, n = 95];
x is the exceedance level, in decibels.
6 Calculation of attenuation
6.1 General
Attenuation of sound during propagation is the result of several effects. Geometric divergence of sound away
from a compact source is discussed in 6.2, atmospheric absorption in 6.3, insertion loss by receiver site
screening objects in 6.4 and shielding by terrain in 6.5. It is common to include all other effects under the term
“excess attenuation”, as can be seen in 6.6.
6.2 Geometric divergence
The attenuation, A , in decibels, due to geometrical divergence shall be calculated assuming spherical
div
spreading of the wave front surface area with distance from a point sound source in non-moving and
non-refracting air. This calculation is as follows:
Ad= 20 lg /d dB (26)
()
div 0
where
A is the attenuation of geometric divergence, in decibels;
div
d is the distance from the source to the receiver, in metres;
d is the reference distance for source sound exposure, equal to one metre (d = 1 m).
0 0
6.3 Atmospheric absorption
Tabulations of atmospheric-absorption attenuation coefficients can be found in ISO 9613-1 for frequencies of
50 Hz and above and for one static atmospheric pressure only. For the purposes of this International Standard,
the equations given in ISO 9613-1 are adequate for calculating attenuation by atmospheric absorption at other
frequencies and at other static atmospheric pressures. The values of atmospheric temperature and humidity
can also be partitioned into discrete ranges (atmospheric-absorption classes) before calculating the
atmospheric absorption. In this way, band attenuation coefficients (see ISO 9613-1) and their probabilities of
occurrence can be calculated and stored for subsequent rapid retrieval. The relevant heights and quantities
for evaluation of atmospheric absorption appear in ISO 9613-1.
The band attenuation, in decibels
...
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