Statistical exploration of small-scale variation in acoustic time series taking intoaccount micro-meteorological stability conditions

Olivier Baume, Benoît Gauvreau, Michel BérengierSection Acoustique Routière et Urbaine, Laboratoire Central des Ponts et Chaussées, route de Bouaye, BP 4129, 44341 Bouguenais Cedex, France,

{olivier.baume,benoit.gauvreau,michel.berengier}@lcpc.fr,

Fabrice JunkerÉlectricité de France, Recherche et Développement, 1 avenue du Général de Gaulle, 92141 Clamart Cedex, France,

fabrice.junker@edf.fr

Hans Wackernagel, Jean-Paul ChilèsCentre de Géostatistique, Centre de Recherche de l’École des Mines de Paris, 35 rue Saint-Honoré, 77305 Fontainebleau, France,

{hans.wackernagel,jean-paul.chiles}@ensmp.fr

In environmental noise propagation studies (road or railway traffic / industrial sources), a 10 minutes in-tegration time for acoustical sampling is quite standard. When attempting a related micro-meteorologicalcharacterization of these data, the average sound speed gradient within such a sampling period is knownto be a relevant parameter for classifying propagation conditions. Sound propagation phenomena and at-mospheric turbulence spectrum require to be examined at shorter time scales and statistical techniques takenfrom geostatistics have proven useful to analyse and model the small-scale behavior. In particular a toolcalled variogram which had already been successfully applied to indoor noise exposure time series in thepast, has improved insight. In this paper we present first results with acoustical data at a time scale of 1second (LAeq). First, we describe the experimental protocol of the campaign which took place in 2003. Thedata process includes validation of the acoustic and micro-meteorological samples as well as an applicationof Monin-Obukhov similarity theory for the calculation of the vertical sound celerity profiles. Second, theacoustic time series are explored at different time supports. The histogram and the cumulative distributionfunction are used to detect new information. The time lag variogram is utilized in order to characterize thetime structure of our acoustical data. Different time regimes are distinguished and then related to specificatmospheric stability conditions. Further exploration work is planned in which multi-dimensional analysisand spatial considerations on correlation length will be inserted. A new protocol which includes groundimpedance monitoring, spatial micro-meteorological and acoustical characterization is being presently de-signed and will be applied to an upcoming experimental campaign.

1 Introduction

Beyond the development of analytical and numerical cal-culations in Long Range Sound Propagation (LRSP), sev-eral important practical issues need to be considered.Among these, time and space representativity of "in situ"measurements, sampling design, influence of meteoro-logical parameters on acoustic exposure show to be a fewchallenges. They need to be investigated with statisti-cal tools taking into account spatial and temporal auto-correlation. Classical multi-dimensional analysis has al-ready been used in order to determine factorial corre-spondence between classified micro-meteorological con-ditions and sound propagation classes [1] and led to qual-itative results. In this contribution we present first resultsusing geostatistical methods for quantifying spatial andtemporal variation.

The Laboratoire Central des Ponts et Chaussées and theÉlectricité de France research center work together onthe impact of road traffic and industrial noise sources onthe environment. In this paper, we present experimental

data from a campaign which took place in 2003. Anexperimental site on an isolated plateau at Lannemezanin the Pyrénées mountains (F) was set up with anomnidirectional sound source. Both acoustical andmicro-meteorological data were recorded at small timescales.

In section 2 we describe in detail the experimental pro-tocol. It includes the site description, the sensor mastspecifications and the validation process. In section 3 wedescribe the data processing of the sonic anemometersto obtain vertical sound celerity profiles. We present theresulting data set for a sunny day in section 4. Synchro-nized time series of acoustical and micro-meteorologicalparameters are first drawn as a whole in one graph. Thenthe global LAeq is plotted every second with its meanvalue of ten minutes. In section 5 and 6 we discuss theinformation that can be found and interpreted when usinga 1 second period to sample the Leq series. Both classicaland geostatistical tools are introduced in the analysis. Insection 7 we present the future steps in data processing

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that will be performed after the large-scale experimentalcampaign to be carried out on the same site from June toAugust 2005.

2 Experimental protocol

2.1 Site description

The environmental acoustics experimental site is locatednear the town of Lannemezan on an isolated plateau area(Hautes-Pyrénées district - F). A map is displayed on fig-ure 1. The terrain is of a herbal nature and flat (maximumslope of 2.5 percent). The area is surrounded by an alleyof 20 meter high trees.

The disposable protocol is forced by the presence of awide marsh land zone. The mean wind situation of theregion is characterized by winds mainly from the west(ocean influence) and from the south (mountain influ-ence). For obtaining downward sound propagation condi-tions, the source had to be located in the south-east cornerof the site.

Figure 1: Sketch of the experimental protocol - Lan-nemezan 2003: acoustic channels 1 and 2 are located 200meters away from the artificial source whereas the refer-ence channel is a 15 meter distant microphone.

2.2 Acoustic and micro-meteorology speci-fications

The acoustic source S emits an omni-directional whitenoise. Its power level stability is controlled by a refer-ence microphone 15 meters away in the western direction(Aref ). Two other acoustical measurement devices (A1

and A2) are set 200 meters away from the source respec-tively along the northern and the western axes. Aref andA2 are recorded with the same acquisition system. A1 is

recorded separately. The source and the microphones areplaced at 2 meters height from the ground.

The micro-meteorological conditions are recorded withtwo towers. The first one consists in a 60 meter high typetower labelled M1 (figure 1) with 3 ultra-sonic anemome-ters respectively at 10, 35 and 60 meters height as wellas ventilated temperature sensors at 2, 10 and 60 me-ters height. As a result, statistical momentum of windspeed and temperature were measured in order to calcu-late characteristic scales of micro-meteorology such asfriction velocity u∗, surface heat flux Q0 and Monin-Obukhov length LMO - which were recorded every 10minutes with respect to a 10 Hz sampling frequency forcalculation.

The second micro-meteorological tower M2 yields com-plementary information with a classical anemometer andtwo temperature sensors at 1.5 and 6 meters height whichrecord 10 minute samples. In addition, the meteorologi-cal information is completed with precipitation and sunheating data from a Météo France (national) tower lo-cated 300 meters away from the site.

The ground acoustical impedance characterization hasnot been performed in the 2003 campaign.

2.3 Validation process of the samples

The validation process preceding the statistical analysisof the data consisted in checking :

1. the stability of the source using the acoustical refer-ence,

2. the presence of strong rainfall which is a dramaticnoise factor for outdoor acoustical data,

3. the coherence of M1 measurements in terms of winddirection between the ultra-sonic sensors.

Validation of the latter permits a Monin-Obukhov calcu-lation of micro-meteorological scales and correspondingvertical sound celerity profiles.

Measurements ran from the 23rd of March 2003 untilearly May. The source appeared to stabilize during 15days from April 1st to April 15th. During this period thewind direction ranged all possible angles with more er-ratic behavior during daytime. Up to 13 cumulative dayswhere recorded without rain.

Nevertheless periods of severe rainfall which appearedduring that fortnight could have influenced groundacoustical characteristics whose time variations were notmeasured.

Finally the validated data led to various micro-meteorological conditions for both channel 1 (A1) andchannel 2 (A2) with time varying ground properties interms of acoustical impedance at larger time scales.

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3 Calculation of vertical soundcelerity profiles

Monin-Obukhov similarity theory is the basis for com-puting wind and temperature profiles from ultrasonicanemometer when studying acoustic propagation condi-tions near open flat ground. The most representativemicro-meteorological scales of the atmospheric surfacelayer(u∗, Q0, LMO) are calculated from variances andcovariances of 3-D wind speed and temperature data sam-ples every 10 minutes, reading the 10 Hz time-ratedmeasurements. The scales also allow us to compute µ2

which is the experimental variance of the refraction indexn = c

c0. This latter is characteristic of the atmospheric

turbulence intensity.

Empirical functions, the so-called "universal functions"ψh( z

LMO) and ψm( z

LMO) , are then necessary to include

in the model, in order to obtain the computed profiles.The 10 minutes values of LMO are utilized to calculatethe functions ψh and ψm which are integrated along thez axis. The profiles of temperature and horizontal windspeed are combined to reach the effective sound celeritygradient along the Source-Receiver directions.

The calculation steps are performed when computing thevertical gradients except that other universal functions φh

and φm are introduced which are first order derivation ofψh and ψm.

The choice of empirical functions was refined thanks toa comparative study of several expressions to be found inthe literature [3, 4, 5, 6].

4 Description of the time series

We plot on figure 2 all relevant parameters, i.e. acousti-cal exposure (Leq), vertical celerity gradient calculatedat 6 meters height, horizontal wind speed modulus, winddirection, rainfall and sun heating. The data to be seenon figure 2 corresponds to an entirely sunny day (on the8th of April) which is typical of the vertical temperaturegradient inversion between night and day. The calcula-tion of Monin-Obukhov similarity was held however witha limited number of samples on that day because of thenon-validated inconsistencies in the wind series.

The micro-meteorological data values are averages over10 minute intervals. The acoustic data is available everysecond which allows to explore small-scale time struc-ture. We plot the time series of the global acoustical level(LAeq) at the 2 different sample supports (see figure 3): 10 minute averages and 1 second averages which arecloser to the order of the acoustical travel time. In termsof micro-meteorological conditions, the first sampling in-terval is meant to be typical of mean refraction conditionswhereas the second is linked to the fluctuating part of the

Leq (dB)

Global A1/3 oct. 500 Hz

0 3 6 9 12 15 18 21 24

2040

60

2040

60

GRAD C (1/s) ++++

++ + +

++++++++++++++++

++++++++++++++++++

+

−0.

40.

41

−0.

40.

41

WIND SPEED (m/s)

04

04

WIND ANGLE (°)

027

0

027

0

RAIN (mm)

04

04

SUN HEAT (W)

0 3 6 9 12 15 18 21 24

0 0

DAYTIME

Figure 2: Acoustical and micro-meteorological seriesduring the 8th of April, 2003: the A2 series is displayedconcerning the acoustical data.

DAYTIME

L(eq

,A)

IN D

EC

IBE

LS

3540

4550

5560

65

0 3 6 9 12 15 18 21 24

Figure 3: A2 acoustical time series of LAeq for 10minutes samples (yellow line) and 1 second samples(black marks) - Lannemezan 2003, the 8th of April, 2003.

refraction index.

Figure 3 shows a huge variability of the short time sam-ples around their mean value of 10 minutes. The overallstructure of this time series is typical for a sunny day. Itcan be split into three main periods :

nighttime: average acoustic level is most important atnight at a fairly constant level of 54 dB(A),

daytime: at sunrise the level drops quickly down to40 dB(A) with a few isolated events reaching 50dB(A),

evening: after sunset acoustic level smoothly rises overa period of 3 hours.

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5 Histogram and cumulative distri-bution function

Clearly the variability of acoustical data depends uponthe sampling support. This is a well know characteris-tic in LRSP measurements. To illustrate this, we chosefour different averaging intervals of 6 hours, 10 minutes,1 minute and 1 second, using the full series of 15 days(which includes some rainy periods). We show on figure4 the histograms as well as the cumulative distributionfunctions for the four supports.

var = 9.6 , n = 60 (6 h)

Min = 40.2 dB Max = 54.9

30 40 50 60 70

010

20

var = 16.8 , n = 2160 (10 min)

Min = 37.9 dB Max = 66.5

30 40 50 60 70

020

0

var = 19.4 , n = 21581 (1 min)

Min = 35.9 dB Max = 76.3

30 40 50 60 70

020

00

var = 24.5 , n = 1294352 (1 s)

Min = 33.3 dB Max = 83.4

30 40 50 60 70

080

000

35 40 45 50 55 60 65

0.0

0.2

0.4

0.6

0.8

1.0

y=ACOUSTIC LEVEL (dB)

F(y

)

6 hours support10 minutes support1 minute support1 second support

Figure 4: Histograms and cumulative distribution func-tions of the LAeq time series for different sampling pe-riods - Lannemezan 2003, data taken from the 1st to the15th of April, 2003. var is the variance and n the numberof samples.

The mean of the data is understood as a physical para-meter. Its value is computed in Pascal and subsequentlyexpressed in decibels. Remember the decibel is purelyconventional and cannot be justified, neither on physicalnor on statistical grounds whatsoever. The mean is inde-pendent of the support, i.e. the overall mean of the meansof subsets from a partition of the data should not be de-pendent on the way the data set is partitioned.

The variance is interpreted as a statistical descriptor of the

the data dispersion. The smaller the support the larger isthe variance of the data. This can be seen on figure 4.

The 1 second sampling period best displays the two sepa-rate populations to be seen on the histograms. The lowlevel population (in the interval [35 dB, 50 dB]) ex-hibits the daytime distribution for sunny days; for cloud-covered sky and nighttime the acoustic levels are distrib-uted according to the right hand sub-population.

The cumulative distribution function (cdf) plot allows tooverlay the curves obtained with different supports. Withincreasing support the curves become more and moresteep. The cdf can be interpreted in terms of one of thepossible annoyance indicators : it represents the probabil-ity of the noise level being below a given threshold levelP (LAeq < LAeq,Threshold).

6 Experimental variogram

The variogram is the preferred tool in geostatistics for an-alyzing the autocorrelation structure of the data. It is cal-culated from the quadratic difference between two sam-ple times t1 and t2 and is denoted γ∗

γ∗(t2 − t1) =12(y(t2)− y(t1))

2. (1)

The average value is computed for any pair of samplesseparated by the time lag h = (t2 − t1). Then the cor-responding function γ(h) called the experimental vari-ogram is equal to

γ(h) =1

2nh

nh∑

i=1

(y(ti + h)− y(ti))2

. (2)

We computed the experimental variograms of the acousti-cal data for the 8th of April, taking great care of distin-guishing the variability regimes that we could detect onfigure 3 in the time series. For each microphone, figure5 shows results for the variogram plotted for a time lagranging from 0 to 10 minutes. Three different series wereselected: respectively for the nighttime, the daytime andthe evening.

The general shape of the variograms shows a definiteslope at the origin h = 0 which means that the acousticaltime series of Lannemezan 2003 are autocorrelated.

We can note that the variograms of the reference channel(Aref ) for the 3 regimes are well different even thoughthe microphone is only 15 meters away from the source.Comparing channels 1 and 2, the variograms have thesame level of variability. Levels at daytime are lowest,which is well known in long range sound propagation.Nighttime is a stable period for the atmospheric surfacelayer and induces more steady sound levels. Wind di-rection seems to have a great impact on the variogram

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TIMELAG (MINUTES)

VA

RIO

GR

AM

(dB

²)

0 2 4 6 8 10

0.0

0.5

1.0

1.5

0h to 6h8 h to 14 h17 h to 23 h

a- channel Aref

TIMELAG (MINUTES)

VA

RIO

GR

AM

(dB

²)

0 2 4 6 8 10

01

23

45

67

0h to 6h8 h to 14 h17 h to 23 h

b- channel A1

TIMELAG (MINUTES)

VA

RIO

GR

AM

(dB

²)

0 2 4 6 8 10

01

23

45

67

0h to 6h8 h to 14 h17 h to 23 htotal for 15 days

c- channel A2

Figure 5: Variograms of acoustical time series Leq,A forthe 3 channels (Aref , A1 and A2): 3 regimes detectedduring the 8th of April, Lannemezan 2003. Variogramof complete data from the 1st to the 15th of April (blackcontinuous line) for channel A2.

structure at nighttime as can be seen on the channel 1 andchannel 2 variograms.

The recordings of channel 1 include some artefact de-tectable on the variograms. We suspect an electronic ca-pacity effect in the acquisition system which was inde-pendent for channel 1 from the two other channels.

On figure 5 (A2) the black curve plotted represents theexperimental variogram computed for the whole periodof 15 days validated data. This average computation ofthe variogram includes a cumulated rainy period of 11/2

days. The graph shows some small periodic fluctuationswhich could hardly be interpreted.

These latter considerations take a step in the direction ofdistinguishing acoustical time samples with both meanlevel and variability level. Both of these informationsseem characteristic of the atmospheric conditions of thesound propagation between the source and the receiver.

7 Future work

On the one hand the Lannemezan 2003 campaign has pro-vided us mainly with time series and so the geostatisticalinterpretation of the data is limited to the time structure.A new campaign is going on during 2005 and will provideus with a good spatial sample coverage : 47 microphones,about 70 micro-meteorological sensors and periodic im-pedance measurements of the ground (see the conferencepaper by Junker et al. [8]). This extensive data set willbe completed by numerical simulations using referencemodels (ray tracing, PE, BEM, etc.) for typical micro-meteorological situations.

On the other hand Séchet et al. [1] have provideda French standard in qualitative correspondance be-tween micro-meteorological and sound propagation con-ditions using multi-dimensional analysis. An exten-sion of this standard is worth examining by introduc-ing further acoustical and turbulence parameters relatedto time or space variability. Geostatistical analysis con-sists in computing and modelling variograms taking ac-count of spatial anisotropy. The acoustic exposure canthen be estimated by geostatistical methods like krig-ing and conditional simulation for characteristic micro-meteorological situations. Furthermore the numericalmodel runs could be integrated into the acoustic exposureestimation process.

8 Conclusion

It has been shown that information at short time scale(1 second) exists in acoustical time series and is relevantto characterize the situations of propagation encounteredduring a whole day. The variogram has shown to be of

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special interest to explore different fluctuation structures.

As a conclusion, time variability in acoustical data hasits own evolution and the information which belongs toshort time variability must also be used to classify propa-gation conditions. Our example consisted in a single daywith nighttime acoustical levels higher than daytime andevening levels. On the contrary the lowest variability inLAeq appeared at nighttime.

Crossed information between 10 minutes samples ofacoustical mean value and variance would strengthen theclassification of propagation conditions.

In future work new micro-meteorological criteria will beincluded in the classification methods. The campaign ofLannemezan 2005 will bring new statistical knowledgeof the phenomena and a refined classification of propa-gation conditions will allow us to use reference calcula-tions of numerical models to study spatial variability ofthe acoustical field and analyse its correspondence withmicro-meteorology.

References

[1] E. Séchet et V. Zouboff, ’Application des méth-odes factorielles à la caractérisation des effetsmétéorologiques sur la propagation du bruit à grandedistance’. Bulletin de liaison Laboratoire des Pontset Chaussées 1995, Vol. 198. référence 3908 (1995)

[2] O. Baume, ’Choix des fonctions universelles dansl’application de la théorie de la similitude de Monin-Obukhov’, Private Communication.

[3] J.A. Businger, J.C. Wyngaard, Y. Izumi et E.F.Bradley, ’Flux profile relationships in the at-mospheric surface layer’, Journal of AtmosphericScience, Vol. 28. pp. 181-189. (1971)

[4] D.J. Carson et P.J.R. Richards, ’Modelling surfaceturbulent fluxes in stable conditions’, Boundary-Layer Meteorology, Vol. 14. pp. 67-81. (1978)

[5] D. Randerson, Technical report in Atmospheric sci-ence and power production, United States Depart-ment of Energy, Office of Scientific and Technical In-formation, DOE/TIC-27601 (DE84005177). (1984)

[6] Y. Brunet, J.C. Laporte et V. Zouboff, ’Estimatinglong term microclimatic conditions for long rangesound propagation model’, In 7th Intern. Symp. onLong Range Sound Propagation, pp. 123-136. (1996)

[7] H. Wackernagel, C. Lajaunie, L. Thierry et M.Grzebyk, ’Evaluation de l’exposition sonore en mi-lieu professionnel : application des méthodes géo-statistiques à l’estimation du Leq et conséquences

sur les stratégies de mesurage’, Institut National deRecherche et de Sécurité, Note technique 373. (1998)

[8] F. Junker, B. Gauvreau, C. Cremezi et Ph. Blanc-Benon, Classification of relative influence of physi-cal parameters for long range sound propagation, InProc. Forum Acusticum 2005.

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