PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Global sensitivity analysis for urban noise modelling
Pierre AUMOND1; Arnaud CAN1; Viven MALLET2,3; Benoit GAUVREAU1;
Gwenaël GUILLAUME4
1

Ifsttar, Cerema, UMRAE, France
2

3

INRIA, France

Sorbonne université, CNRS, LJLL

4

Cerema, Ifsttar, UMRAE, France

ABSTRACT
Regulatory noise maps rely on many input data that can be incomplete, erroneous or inexistent. Thus,
operators have to complete/validate/qualify those data by prioritizing some information sources andparameters to the detriment of others. Consequently, the sensitivity of the noise model to such input
parameters should be determined to focus on the most influential input parameters. For this purpose, a global
sensitivity analysis is carried out on the CNOSSOS regulatory method, implemented in the open-source
software NoiseModelling, using the Morris screening method. As part of the ANR CENSE project(2016-2020), a global sensitivity analysis is presented on a case study in the city of Lorient in France. This
paper presents an example of a sensitivity analysis of the CNOSSOS model for 9 of its input parameters on
426 receivers (30 buildings) in this area.
Keywords: Open-Source, Noise mapping, Sensitivity analysis

1. INTRODUCTION
Strong relationships between noise levels and both annoyance and health effects are established (1).
It is therefore crucial to quantify the noise levels to which populations are exposed. Noise mapping isclassically used to quantify these exposure levels. In this objective, traffic and geometric datacollected feed noise emission and propagation models to generate sound maps at district or city scales.
Then, once crossed with the residential occupations, these sound maps give us access to noise
exposure (2).
It is important to use a stable methodology and modelling framework to compare the exposurelevels of different cities, or the evolution over time of exposure to a given city. T hus the CNOSSOS
model has been proposed to participate in this harmonization of calculation methods (3). However, alarge variability of the calculated exposures may remain due to the model configurations and to theaccuracy of the different types of input data. In addition, many input data are sometimes difficult toobtain or non-existent, requiring calculation assumptions that may influence the accuracy of thecalculated exposure levels. It is therefore necessary to be able to identify the most influential input
data and parameters in order to give them priority in the data collection and modelling process. This
article presents the framework for a sensitivity analysis performed w ith the open-source
NoiseModelling software v3.0 (4). Regarding screening technique, the Morris method is applied bymaking a number r of local changes at different points of the possible range of input values.

2. METHODOLOGY
2.1 Morris Method
The Morris method is widely used for global sensitivity analysis, since it is adapted to models with
1

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pierre.aumond@ifsttar.fr

quantitative inputs (or parameters) and outputs (5). It is part of the OAT (One At a Time) methods,
meaning that the process of exploring the definition domain makes the input parameters vary one at atime. It can be seen as a statistical analysis of empirical estimates of changes in the output of the modelwith respect to each parameter. In the case of a time-consuming model, or a model with a large numberof parameters, the method is a simple way to make a first selection among the parameters according totheir influence. A sufficient number of repetitions are still required to ensure confidence in the results
obtained.
Its principle is as follows. The method begins by sampling a set of start values within the defined
range of possible values for all input parameters, and next by calculating the subsequent modeloutcome. The second step changes the value for one variable (all other inputs remaining at their startvalues) and calculates the resulting change in model outcome compared to the first run. Next, the value
for another variable is changed (the previous variable is kept at its changed value and all other ones
kept at their start values) and the resulting change in model outcome compared to the second run iscalculated. This goes on until all input parameters have been changed. This procedure is repeated rtimes, each time with a different set of start values, which leads to a number of r(k + 1) runs, where kis the number of input parameters. Such number of runs is very efficient compared to more demanding
methods for sensitivity analysis (e.g. exhaustive research among each range values, Monte-Carlo,etc.).
For the sensitivity analysis presented in this paper, the total procedure will be repeated 10 times(r=10) for a group of 9 parameters (k=9), resulting in a number of 100 simulations. To ensure thatspace exploration does not favour any area, 300 trajectories have been drawn and only the ten
trajectories that maximize exploration are retained (6).
2.2 Framework
NoiseModelling (formerly NoiseM@p) is a free and open-source tool, integrated in the OrbisGIS
software, designed to produce environmental noise maps on very large urban areas, with few
computational resources (4). The CNOSSOS model is implemented for the estimation of road traffic
emission, as well as for the calculation of its attenuation along propagation paths (3). NoiseModelling
allows information to be stored at three levels: the noise sources and their sound levels, the geometryof the propagation paths and finally the transfer matrix for each of the source/receptor pairs and for agiven propagation path scheme. This choice was made because the computation time of such asoftware type is essentially concentrated into the calculation of geometric rays. Thus the calculation
costs of the CNOSSOS model for emission and for propagation are considerably lower once thegeometry is known and the rays are calculated. To launch a large number of replications of the model,
the idea is then to store the geometry of the rays. Then it is possible to recalculate several possible
emission levels for the sources, and several possible attenuations for the sources/receivers couples
according to the varying parameters.
Figure 1 presents the technical framework behind the global sensitivity analysis using
NoiseModelling: A groovy script has been created to interact with Noise Modelling. It also serves as
an interface with a database (PostgreSQL 2 or H23). From a configuration file containing the values on
the input varying parameters, many simulations are performed and the results are stored in compressedfolders.
2.3 Study parameters
When creating a noise map, all the varying input parameters (regarding sound emission andpropagation) will be considered as variables in the sensitivity analysis. For example, it will be possible
to observe the influence of a 10% variation in the hourly flow rate of light vehicles and to compare itwith a 5°C variation in atmosphere temperature. It is also possible to complete the sensitivity analysis
by varying the parameters related to Source-Receiver geometry, even if the calculation costs thenincreases – because the rays will have to be retraced – but without adding complexity to the process
and analysis.

2
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www.postgresql.org
www.h2database.com

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Figure 1 – Sensitivy analysis framework using NoiseModelling
For this first sensitivity study, it is proposed to consider 9 parameters. The road parameters aresupposed to vary homogeneously across the network. For example, if the vehicle speed increases by
10%, this is the case for all road segments of the road network. Table 1 shows the parameters, theirsteps and ranges of variation.
Table 1 – Sensitivity analysis parameters, step and range of variation
Parameter

Code

Variation

Step

Parameter

Code

Variation

Step

Light Vehicle Flow
Rate (veh./hour)
Heavy Vehicle Flow
Rate (veh./hour)Light Vehicle Speed(km/h)
Heavy Vehicle Speed(km/h)
Temperature (°C)

Flow_lv[0.8;1.4]

0.1 (*)

Humidity (%)

Hum[20;80]20(+)

Flow_hv[0.8;1.4]

0.1 (*)

Refl

[0;1]

1 (+)

Speed_lv[0.8;1.4]

0.1 (*)

Dif_h[true/false]-

Speed_hv[0.8;1.4]

0.1 (*)

Order ofReflection
Horizontal
diffraction
Verticaldiffraction

Dif_v[true/false]

-

Temp

[5;30]

5 (+)

2.4 Score indicators
As an output of the analysis, sensitivity to the model's input parameters is observed on two
quantities:- for each receiver, the sound pressure level for day/evening/night periods (Lden ) expressed indB(A);- the inhabitants ratio exposed to a Lden value superior to 65 dB(A).
The Morris method allows us to access to three indicators:- µ is the arithmetic mean of the effect associated with the k-th parameter. In case of an
independent linear dependency, µ is the change in the output when the k-th parameter changes
changes by one step (as defined by its range of variation in Table 1),- µ* is the mean of the absolute effect associated with the k-th parameter. It is similar to µ but itis the average of the absolute differences caused by a change in the k-th parameter. This value
is interesting to avoid cancelation effects in the average (as it can be the case for a
non-monotonic function),- σ is the standard deviation of the effect associated with the k-th parameter. It tells how much theeffect of the k-th parameter changes depending on the value of this k-th parameter and thevalues of the other parameters. It gives an indication of the presence of nonl inearities orinteractions between the k-th parameter and other parameters.

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2.5 Study Area
The sensitivity analysis presented in this article is part of the CENSE project (Characterization ofurban sound environments using a comprehensive approach combining o pen data, measurements andmodeling), which includes a noise mapping case study based on both modelling and sensors
deployment, in the city of Lorient, France (7)4. It covers an area of about 1 km², in which 426 receivers(30 buildings) were randomly selected in order to serve as a support for this sensitivity analysis. The
influent input parameters (e.g. built-up characteristics, ground topology, road traffic data, groundcharacteristics, etc.) are a compilation of data collected from CEREMA, IGN and the city of Lorient.
Figure 2 shows an example of results through the median sound level of the 100 simulations in dB(A),where 30 buildings are assessed, representing 318 inhabitants and approximatively 17% of them areexposed to L den levels above 65 dB(A).

Figure 2 – Noise map of the study area computed with NoiseModelling (median sound level of the 100
simulations). Following this map, the inhabitants ratio exposed to Lden>65 dB(A) is about 17 %.

3. RESULTS
3.1 Sensitivity analysis regarding the ratio number of exposed people
Figure 3 shows the sensitivity analysis of the ratio number of inhabitants exposed to Lden > 65
dB(A) levels using the CNOSSOS method for its nine varying input parameters (See section 2.3).
Results are expressed in percentage of inhabitants exposed to Lden > 65 dB(A).

4

http://cense.ifsttar.fr/en

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Figure 3 – Results of the sensitivity analysis for the 9 input parameters with NoiseModelling
The most influential parameters in terms of the number of inhabitants exposed to more than
65 dB(A) Lden values are the speed and flow of light vehicles parameters and temperature, which canlead to an increment of approximatively 1.5% on the affected population, ranging from 15.5% to19.5%. These are three parameters that affect noise emission - temperature is an influential parameterof the CNOSSOS emission model - and they are therefore particularly influential on noise levels
around 65 dB(A) because they are often observed at the edge of the roads and therefore with shortpropagation distances. As a result, receivers with Lden values close to 65 dB(A) will switch above or
below the 65 dB(A) threshold, when these two parameters vary.The range of variation from 0.8 to 1.4
times the nominal value is then sufficient to vary the number of inhabitants exposed to Lden values
exceeding 65 dB(A).
The parameters related to sound propagation have a greater impact on isolated receivers, which
may or may not be reached by sound rays, depending for example on the fact the reflection ordiffraction are taken or not into account. As a result, these parameters have little effect on noise levels
in a range around 65 dB(A), so that the number of exposed persons varies little.
3.2 Sensitivity analysis regarding the sound exposure by receivers
Figure 4 shows the sensitivity analysis of the Lden sound level using the CNOSSOS model at 3 of its
varying input parameters, namely the speed of light vehicle, the order of reflection, and whether or not
horizontal diffractions are taken into account.

(a) – Order of reflections (1/0) - Refl

1636(b) – horizontal diffraction (true/false) - Dif_h(c) – Speed of light vehicles - Speed_lv
Figure 4 –Lden variation (μ*) by receiver of the sensitivity analysis for 3 input parameters
The Figure 4 confirms the high homogeneity in the variations in Lden values according to the speedof light vehicles, while the impact of taking into account or not reflections or horizontal diffractions insound levels calculation is very heterogeneous on the network. In particular, receivers located inbuilding yards are highly affected by parameters such as diffractions. This can be explained by thevery high errors made when the number of rays in the simulation reaching certain isol ated points, suchas building yards, falls drastically when diffractions or reflections are not allowed in the simulation. It
is even possible that for some simulations no rays reach the receiver. For these receivers, the variationon these parameters (diffractions, reflections) can therefore induce very large variations on theobserved sound levels. It is likely that if indicators of the type "number of persons exposed to less than
40 dB(A)" were considered, these indicators would be very sensitive to thes e calculation parameters.

Figure 5 – μ* for each receiver depending on Lden sound levels for 4 varying input parameters

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Figure 5 shows the existing links between the Lden sound level and four parameters:The Figure 5 confirms the high sensitivity of low noise levels to whether or not diffractions
are taken into account, with receivers that can potentially receive no energy for somesimulations (see μ* >30 dB(A) on the top-left figure);
When noise levels are low, the impact to whether or not reflections are taken into accountcan be significant. As for diffractions, receivers that are not in direct field compared tonoise sources often have the lowest noise levels and are also those most affected by thisparameter;
The influence of the temperature and the speed of light vehicles on Lden values increases
with sound levels because the receivers nearest to the streets are the ones with highest
sound levels and also those for whom the parameters related to the emission are the mostinfluential ;4. CONCLUSION
A global sensitivity analysis of the CNOSSOS model at 9 of its varying input parameters ispresented in this paper. The screening technique is based on Morris' method and simulations were
performed with the NoiseModelling v3.0 tool. The results presented in this article are preliminary
results and further research should be carried out in order to propose more general results that can betransposed to other district (or even city) typologies. However, any user can reproduce thismethodology for his case study and the groovy script and NoiseModelling are available on the
open-source platform Github5.
Other applications as dynamic noise mapping, uncertainty propagation or meta-model development
can benefit from the same structure of the NoiseModelling software.

ACKNOWLEDGEMENTS
This work is currently carried out in the framework of the CENSE project which aims at proposing
a new methodology for the production of more realistic noise maps, based on an assimilation ofsimulated and measured data through a dense network of low-cost sensors (http://cense.ifsttar.fr). This
project is supported by the French National Agency for Research (ANR) under ref. 16-CE22-0012.

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173rd Meeting of the Acoustical Society of America and the 8th Forum Acusticum.
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