Examining an empirical relationship between Lnight and the
probability of awakening
Nicholas P. Millera)
Harris Miller Miller & Hanson Inc.
Burlington, Massachusetts, USA
The World Health Organization, WHO, has proposed “Night Noise Guidelines for Europe”
which it recommends in terms of Lnight (11 p.m. to 7 a.m.). The target recommended is
Lnight,outside of 40 dB with an interim target of 55 dB. Sleep disturbance, however, is
acknowledged to be a reaction to single events. Hence, any single value of Lnight can be a
result of many combinations of single event levels and hence could result in different
degrees of sleep disturbance. This paper uses measured values of indoor night time Sound
Exposure Levels produced by aircraft overflights, applies the methods of ANSI Standard
S12.9-2008, Part 6, “Methods for Estimation of Awakenings Associated with Outdoor Noise
Events Heard in Homes,” and compares the resulting probabilities of awakening with the
associated computed Lnight values. The author finds some correlation of Lnight with the
probability of awakening and ponders the selection of a quantitative sleep disturbance
guideline.
1
THE PROBLEM OF RATIONALLY ADDRESSING NIGHT TIME NOISE
Government policy related to analysis and control of airport noise has traditionally been
based on equivalent metrics such as Ldn and CNEL in the U.S. and LDEN in Europe. There is
concern that these and similar metrics of 24-hour exposure do not fully characterize the effects of
night time noise. In 2009, the World Health Organization Regional Office for Europe published
“Night noise guidelines for Europe.”1 These guidelines recommend that “…an Lnight,outside of 40
dB should be the target of the night noise guideline (NNG) to protect the public, including the
most vulnerable groups such as children, the chronically ill and the elderly. Lnight,outside value of
55 dB is recommended as an interim target for the countries where the NNG cannot be achieved
in the short term for various reasons, and where policy-makers choose to adopt a stepwise
approach.”b)
However, research on sleep disturbance has found that disturbance, being a reaction to
single noise events, is not correlated with equivalent metrics of exposure such as Lnight.2
a)
b)
email: [email protected]
WHO night guidelines assume a 21 dB reduction of outside to inside levels. Hence values of Lnight,outside of 40
dB and 55 dB translate to Lnight,inside of 19 dB and 34 dB.
Research on sleep disturbance, and follow-on analyses3 resulted in an American National
Standards Institute Standard for estimation of awakenings from noise events.4 This paper applies
the ANSI standard method to measured indoor SEL values collected in a previous sleep
awakening study.2 The same SEL values are used to compute Lnight, and resultant probability of
awakening (PA) and Lnight are compared and analyzed.
2
COMPUTING PROBABILITY OF AWAKENING AND LNIGHT
Indoor SEL data measured around Castle Air Force Base, Fig. 1 were used because of the
wide range of SEL values, Fig. 2.
2.1 Computing Probability of Awakening (PA)
The PAs were computed for each subject (Fig. 2) for each night. The number of nights of
data varied from subject to subject, from a low of 2 nights to as many as 16 nights. For most of
the analyses, only SEL values from subjects with at least 6 nights of data were used.
Computation of the probability of awakening from a single SEL used equation 1, from the ANSI
standard, repeated here as Eqn. (1).
ܲ௔௪ ௔௞௘ǡ௦௜௡௚௟௘ =
1
ͳ ൅ ݁ି௓
(1)
ܼ ൌ െ͸Ǥͺ ͺ ͺ Ͷ ൅ ͲǤͲͶͶͶͶ ‫ܮܧܵכ‬
The ANSI standard provides a method for extending the computation of PA to include all SEL
that occur during a night. The method first computes the probability of not awakening from any of
the events and then subtracts the result from 1 to yield x% probability of awakening at least once –
which can also be interpreted as the probability that x% of the population will be awakened at least
once.
2.2 Computing Lnight
Lnight is an equivalent level for the night hours and was computed as the energy sum of all
SEL during a night, adjusted for a nine hour night time [-10xLog10 (9x3600)].
3
COMPARISONS OF PROBABILITY OF AWAKENING AND LNIGHT
3.1 Compare All Subject Nights
Fig. 3 shows a general trend in the relationship between PA and Lnight, though with
considerable scatter. Each point in Fig. 3 represents a single night for one subject. As a metric
of the relationship, we use linear regression and the associated correlation coefficient.
3.2 Examine Subjects Independently
Examining one subject at a time suggests that the PA versus Lnight relationship can be more
highly correlated. Fig. 4 separately plots individual nights for three subjects and shows the
regression results. Not surprisingly, for a single subject (single location), PA and Lnight can be
highly correlated. At a given location, one would expect similar SEL values, night-to-night, with
variability being primarily in the number of events and hence, some sort of reasonable
correlation between PA and Lnight. Table 1 gives linear regression slopes, intercepts and
correlation coefficients for all subjects examined (225 and 227 were eliminated either for too few
SEL values of because of data that appear spurious). Though showing considerable variability, a
trend is apparent in Fig 5, which plots the regressions for each of the subjects retained.
3.3 Use Energy Average Night for Each Subject
Not only do the night guidelines apply to a full year of exposure, but noise compatibility
policies have for the most part been based on annual average exposures. We have nowhere near
a full year, but computing for each subject an energy average Lnight of all nights measured is the
best we can do. Using the energy average Lnight for each subject, the probability of awakening is
computed using the subject’s regression equation. Fig. 6 compares the probability of awakening
to Lnight for each subject. The regression is weighted for the number of nights of data for each
subject. Clearly the two subjects with the lowest awakening probabilities alter the otherwise
linear relationship of PA and Lnight. (Without these two subjects, R2 is 0.7123.) An examination
of SEL distributions by subject suggests some hypotheses about the relationship between PA and
Lnight.
3.3 Examine SEL Distributions for Select Subjects
Fig. 7 identifies subjects whose SEL distributions may be illuminating. The distributions
are presented as the average of all the nights for which data were collected.
Fig.s 8, 9 and 10 show the distributions for three subjects that lie close to the regression
line. Note that each subject has an average of 12 to 13 events per night and that the distributions,
while not identical, are similar, but of increasing levels – and hence increasing probability of
awakening and increasing Lnight. Fig.s 11 and 12 are the distributions of the two subjects that lie
well below the regression line. Each averages 7 to 8 events per night, but the range of levels for
Fig. 11 and Fig. 12 are somewhat similar to Fig. 9 (subject 224) and to Fig. 10 (subject 205),
respectively.
4
DISCUSSION AND CONCLUSIONS
Though the data analyzed are quite limited, it is possible to draw some tentative conclusions.
1. At individual locations, PA and Lnight can be linearly related with reasonable to high
correlations (Table 1, Fig. 4).
2. From location to location, this linear relationship (and correlation) can be highly variable
(Table 1, Fig. 5).
3. For locations that have similar annual night time operations, there can be a linear
relationship between PA and Lnight (Fig. 6 and Fig.s 8, 9, 10).
4. For locations that have very different numbers of night time operations, PA and Lnight
may bear no relationship (Fig. 6 and Fig.s 8-10 compared with Fig.s 11, 12).
5. Though it is possible to conclude from Fig. 3 that providing an indoor Lnight of 35 dB
could limit PA to 10% or less, Fig. 6 suggests (by extrapolation) that if there are enough
night time operations (e.g. a dozen or so), even this value of Lnight could still result in a
fairly high PA (about 25% to 30%). Note that the subject nights in Fig. 3 with Lnight of 35
dB to about 37 dB have generally low level SELs (low 80’s or below) and 4 or fewer
events.
Taken objectively, and assuming that the data used in this analysis are reasonably
representative of aircraft noise in the vicinity of airports, targeting a specific value of Lnight as a
means to limit sleep disturbance appears to be a very imprecise method. We should note that this
conclusion, drawn from the present data set, depends on relatively modest numbers of fairly high
values of indoor SEL at each location. Locations / airports with many more nighttime events at
lower levels may give different relationships of PA and Lnight, as might locations affected by rail
or road traffic noise.
Notably, the WHO report has gone to some considerable effort to relate Lnight,outside to sleep
effects and has provided an interim target of 55 dB, which is likely more feasible than 40 dB in
the near future. But one wonders, would it not be better to specify the target in terms of percent
of people awakened which after all, is the effect of interest. The ANSI standard assumes a
specific relationship of SEL to PA (Eqn. 1). If that relationship is too insensitive to other types of
sleep disturbance, alternative relationships could be used to estimate the percent of people
experiencing sleep disturbance. The author believes computing PA or a similar sleep disturbance
metric need be no more difficult that computing Lnight and, like Lnight, contours of equal PA can
be constructed around airports as a tool for exploring noise control alternatives.
5
ACKNOWLEDGEMENTS
This comparison is one of the key issues identified during the FAA supported Workshop on
Aircraft Noise Impacts Research, Washington, DC, December 10-11, 2009.5
6
REFERENCES
1. WHO Regional Office for Europe, “Night noise guidelines for Europe,” available on line
at: http://www.euro.who.int/__data/assets/pdf_file/0017/43316/E92845.pdf , accessed
April 2012.
2. Fidell, S. et al, “Noise-Induced Sleep Disturbance in Residential Settings,” page 64,
Armstrong Laboratory, AL/OE-TR-1994-0131, February 1994
3. Anderson, G.S. and N.P. Miller, “Alternative analysis of sleep-awakening data,” Noise
Control Eng. J. 55 (2), 2007 March-April
4. ANSI/ASA S12.9-2008 / Part 6, “Quantities and Procedures for Description and
Measurement of Environmental Sound — Part 6: Methods for Estimation of Awakenings
Associated with Outdoor Noise Events Heard in Homes.”
5. Available: http://www.fican.org/pdf/faa/DC_Final_Summary_Report.pdf
Table 1 – Linear Regression Coefficients for each Subject and Number of Nights of Data
Subject
201
202
203
204
205
206
207
209
212
213
214
215
216
217
218
219
220
221
222
223
224
Intercept
-1.94
-1.94
-2.08
-2.33
-0.86
-2.53
-0.56
-1.41
-0.68
-0.61
-0.83
-0.77
-0.41
4.71
-0.60
-0.84
-0.38
-0.31
-0.87
-1.00
-0.99
Slope
0.04
0.04
0.05
0.05
0.02
0.05
0.02
0.03
0.02
0.02
0.03
0.02
0.01
-0.09
0.02
0.03
0.01
0.01
0.02
0.03
0.03
R^2
0.73
0.74
0.75
0.97
0.59
0.77
0.69
0.38
0.62
0.83
0.78
0.81
0.17
1.00
0.35
0.78
0.65
0.58
0.78
0.85
0.78
# Nights
9
11
3
4
10
8
9
9
12
12
14
13
6
2
9
10
15
16
7
11
12
Fig. 1 – Location of Sleep Research Subjects, Castle AFB (from Fidell, reference 2).
Fig. 2 – Distributions of indoor SEL Values for each subject (from Anderson, reference 3).
Fig. 3 – Probability of awakening versus Lnight for each subject night.
Fig. 4 – Probability of awakening versus Lnight for three subjects for each night.
Fig. 5 – Probability of awakening v. Lnight for all subjects with regression lines.
Fig. 6 – Probability of awakening v. weighted energy average Lnight for subjects with six or
more nights of data.
Fig. 7 – Probability of awakening v. weighted energy average Lnight for subjects with six or
more nights of data, five specific subjects identified.
Fig. 8 – Distribution of SEL, average night, subject 219.
Fig. 9 – Distribution of SEL, average night, subject 224.
Fig. 10 –
Distribution of SEL, average night, subject 205.
Fig. 11 –
Distribution of SEL, average night, subject 216.
Fig. 12 –
Distribution of SEL, average night, subject 209.