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Abstract and Figures

Numerical models are valuable tools to assess air pollutant concentrations in cities which can be used to define new strategies to achieve sustainable cities of the future in terms of air quality. Numerical results are however difficult to be directly compared to air quality standards since they are usually valid only for specific wind speed and direction while some standards are on annual values. The purpose of this paper is to present existing and new methodologies to turn numerical results into mean annual concentrations and discuss their limitations. To this end, methodologies to assess wind speed distribution based on wind rose data are presented first. Then, methodologies are compared to assess mean annual concentrations based on numerical results and on wind speed distributions. According to the results, a Weibull distribution can be used to accurately assess wind speed distribution in France, but the results can be improved using a sigmoid function presented in this paper. It is also shown that using the wind rose data directly to assess mean annual concentrations can lead to underestimations of annual concentrations. Finally, the limitations of discrete methodologies to assess mean annual concentrations are discussed and a new methodology using continuous functions is described.
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DOI : 10.1016/j.scs.2020.102221
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        
1

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Nicolas Reiminger1,2, Xavier Jurado1,2*, José Vazquez2, Cédric Wemmert2, Nadège Blond3,
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Jonathan Wertel1, Matthieu Dufresne1
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1AIR&D, 67000, Strasbourg, France
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2ICUBE Laboratory, CNRS/University of Strasbourg, 67000, Strasbourg, France
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3LIVE Laboratory, CNRS/University of Strasbourg, 67000, Strasbourg, France
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Corresponding author: Tel. +33 (0)6 31 26 75 88, Mail. nreiminger@air-d.fr
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*These authors contributed equally to this work
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Please cite this paper as : Reiminger, N., Jurado, X., Vazquez, J., Wemmert, C., Dufresne, M., Blond,
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N., Wertel, J., 2020. Methodologies to assess mean annual air pollution concentration combining
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numerical results and wind roses. Sustainable Cities and Society, 59,
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102221. DOI: 1016/j.scs.2020.102221
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ABSTRACT
16
Numerical models are valuable tools to assess air pollutant concentrations in cities which can
17
be used to define new strategies to achieve sustainable cities of the future in terms of air quality.
18
Numerical results are however difficult to be directly compared to air quality standards since
19
they are usually valid only for specific wind speed and direction while some standards are on
20
annual values. The purpose of this paper is to present existing and new methodologies to turn
21
numerical results into mean annual concentrations and discuss their limitations. To this end,
22
methodologies to assess wind speed distribution based on wind rose data are presented first.
23
Then, methodologies are compared to assess mean annual concentrations based on numerical
24
results and on wind speed distributions. According to the results, a Weibull distribution can be
25
used to accurately assess wind speed distribution in France, but the results can be improved
26
using a sigmoid function presented in this paper. It is also shown that using the wind rose data
27
directly to assess mean annual concentrations can lead to underestimations of annual
28
concentrations. Finally, the limitations of discrete methodologies to assess mean annual
29
concentrations are discussed and a new methodology using continuous functions is described.
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1. Introduction
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Over the past decades, outdoor air pollution has become a major issue, especially in highly
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densified urban areas where pollutant sources are numerous and air pollutant emissions high.
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In order to protect people from excessive exposure to air pollution, which can cause several
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diseases (Anderson et al., 2012; Kim et al., 2015), the World Health Organization (WHO) have
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recommended standard values that must not be exceeded for different pollutants such as
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nitrogen dioxide (NO2) and particulate matter (EU, 2008; WHO, 2017) to protect population
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health, and the European Union (EU) decided to respect the same or other standards depending
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on the air pollutants. Among the different types of values given as standards, studies have
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shown that annual standards are generally more constraining and harder to reach than the other
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standards (Chaloulakou et al., 2008; Jenkin, 2004).
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In the meantime, recent studies have shown that the indoor air quality is strongly correlated
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with the outdoor one: while for nitrogen dioxide a 5% increase in indoor air pollutant
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concentrations can be expected for only a 1% increase in outdoor concentrations (Shaw et al.,
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2020), for particulate matters such as PM2.5 the outdoor concentration can contribute from 27%
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to 65% of the indoor concentration (Bai et al., 2020). Being able to assess outdoor pollutant
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concentrations is therefore a necessity to improve air quality in the outdoor built environment,
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but also in the indoor one .
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Annual concentrations can be assessed using both on-site monitoring and numerical modeling.
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On site monitoring requires measurements over long periods to be able to assess mean annual
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concentrations of pollutants, although a recent study has shown that mean annual concentration
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of NO2 can be assessed using only one month of data (Jurado et al., 2020), which significantly
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reduces the measurement time required. Monitoring nonetheless has other limitations: it does
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not allow assessing the future evolution of the built environment or pollutant emissions, thus,
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limiting its applicability to achieve the smart sustainable cities of the future as defined by Bibri
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and Krogstie (2017). Numerical modelling can overcome these limitations and can help define
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new strategies to improve air quality in cities combining wind data, various air pollution
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scenarios and urban morphologies (Yang et al., 2020). Among the several models currently
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available, Computational Fluid Dynamics (CFD) has shown great potential for modeling
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pollutant dispersion from traffic-induced emissions by including numerous physical
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phenomena such as the effects of trees (Buccolieri et al., 2018; Santiago et al., 2019; Vranckx
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et al., 2015) and heat exchanges (Qu et al., 2012; Toparlar et al., 2017; Wang et al., 2011) on
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the scale of a neighborhood. However, this type of numerical result cannot be directly compared
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with the annual standards. Methodologies designed to assess mean annual concentrations based
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on numerical results, such as described by Solazzo et al. (2011), are thus required and further
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work is required to improve these methodologies and assess their limits.
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The aim of this study is to provide tools and methodologies to assess mean annual
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concentrations based on numerical results and wind rose data to improve air quality in built
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environment and cities. It is firstly to evaluate whether it is possible to assess continuous wind
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speed distributions based on wind rose data. To do so, a statistical law called Weibull
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distribution is compared with a new sigmoid-based function built for the purpose of this study.
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Secondly, it is to present and compare a discrete methodology usually used to assess mean
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annual concentrations based on numerical results with a continuous methodology built for the
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purpose of this study, and to discuss their respective advantages and limitations. The data used
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for the wind speed distribution assessments, the area modeled and the CFD model used for
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illustration purposes are presented in Section 2. Then, the description and the comparison of
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the different methodologies are presented in Section 3 and, finally, a discussion is provided in
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Section 4.
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2. Material and methods
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2.1. Meteorological data
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2.1.1. Data location
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This work uses wind velocity and wind direction data from four cities in France. These cities
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were chosen to cover most of France to obtain representative results and include the cities of
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Strasbourg (Grand-Est region), Nîmes (Occitanie region), Brest (Bretagne region) and Lille
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(Hauts-de-France region). In particular, the data were obtained from the stations named
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Strasbourg-Entzheim, Nîmes-Courbessac, Brest-Guipavas and Lille-Lesquin, respectively. The
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location of these stations and their corresponding regions are presented in Fig. 1.
90
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Fig. 1. Location of the different meteorological stations used.
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2.1.2. Data availability and data range
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The data used in this work were provided by Météo-France, a public institution and 
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official meteorology and climatology service. The data are mainly couples of wind velocity and
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wind direction over a twenty-year period from 1999 to 2018, except for the Strasbourg-
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Entzheim station where it is a ten-year period from 1999 to 2008. The data were obtained via a
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personal request addressed to Météo-France and were not available on open-access. A summary
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of the information of the stations is presented in Table 1, with the time ranges of the data and
99
the number of data available (the coordinates are given in the World Geodetic System 1984).
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Table 1. Summary of the available data.
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Station
Data availability
Location
Latitude
Altitude
Time range
Number of
valid cases
Number of
missing cases
Brest - Guipavas

94 m
2009 - 2018
29,171
45
Lille - Lesquin

47 m
2009 - 2018
29,185
31
Nîmes - Courbessac

59 m
2009 - 2018
29,214
2
Strasbourg - Entzheim

150 m
1999 - 2008
29,199
25
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All the data were monitored from wind sensors placed 10 meters from the ground and the wind
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frequencies are available for each wind direction with 20° steps for two distinct wind
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discretizations: a velocity ranges (from 0
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to 1.5 m/s, 1.5 to 3.5 m/s, 3.5 to 8 m/s and more than 8 m/s), illustrated in Fig. 2. (A); and a
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1 m/s steps except between 0 and 0.5 m/s,
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illustrated in Fig. 2. (B). zation is a common format mostly found in wind
108
 and
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more expensive.
110
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Fig. 2. Example of data for Strasbourg and a 200° wind direction with (A) only 4 ranges of velocities and (B) the detailed
112
data discretized in 18 ranges.
113
The wind roses for each meteorological station considered in this 
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4-velocity-range discretization described in Fig. 2. (A) are provided in Fig. 3. This figure shows
115
how the monitoring locations considered in this study give distinct but complementary
116
information, with for example many high velocities at Brest compared to Strasbourg and Nîmes,
117
where almost no velocities were monitored over 8 m/s, and with dominant wind directions at
118
Nîmes and Strasbourg compared to the other stations.
119
120
Fig. 3. Wind roses for each location considered.
121
122
2.1.3. Interpolation functions
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A two-parametric continuous probability function, the Weibull distribution, mainly used in the
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wind power industry, can be used to describe wind speed distribution (Kumar et al., 2019;
125

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




   
 
 
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Mahmood et al., 2019). The equation of the corresponding probability density function is given
126
in (1).
127

128
where is the wind velocity, is the shape parameter and is the scale parameter of the
129
distribution, with and being positive.
130
For the purpose of this study, an original 5-parametric continuous function was built to
131
determine         -velocity-range wind
132
discretization. This function, called Sigmoid function, based on the composition of two sigmoid
133
functions, is given in (2). The two functions will be compared in the results section.
134



135
where , , , and are positive parameters.
136
137
2.2. Numerical model
138
Simulations were performed using the unsteady and incompressible solver pimpleFoam from
139
OpenFOAM 6.0. A Reynolds-Averaged Navier-Stokes (RANS) methodology was used to solve
140
the Navier-Stokes equations with the RNG k-  , and the transport of
141
particulate matter was performed using a transport equation. This solver was validated
142
previously in Reiminger et al. (2020).
143
The area chosen to illustrate the methodologies discussed in this paper is located in
144
Schiltigheim, France (48°36'24", 7°44'00"), a few kilometers north of Strasbourg. This area, as
145
well as the only road considered as an emission source in this study (D120, rue de la Paix), are
146
illustrated in Fig. 4. (A). PM10 traffic-related emissions were estimated at 1.39 mg/s using daily
147
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annual mean traffic and were applied along the street considering its length in the numerical
148
domain (200 m), its width (9 m) and an emission height of 0.5 m to take into account initial
149
dispersion.
150
The recommendations given by Franke et al. (2007) were followed. In particular, with being
151
the highest building height (16 m), the distances between the buildings and the lateral
152
boundaries are at least 5, the distances between the inlet and the buildings as well as for the
153
outlet and the buildings are at least 5 and the domain height is around 6. An illustration of
154
the resulting 3D sketch is presented in Fig. 4. (B). A grid sensitivity test was performed and
155
showed that hexahedral meshes of 1 m in the study area and 0.5 m near the building walls are
156
sufficient, leading to a more comparable resolution than other CFD studies (Blocken, 2015) and
157
leading to a total number of around 800,000 cells. The resulting mesh is illustrated in Fig. 5.
158
159
Fig. 4. Illustration of (A) the area of Strasbourg modeled with the road considered for the traffic-related emissions (white
160
dashed lines), and (B) the corresponding area built in 3D for the numerical simulations with the emission source (red).
161
162

 
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No-slip conditions (U = 0 m/s) were applied to the building walls and ground, and symmetry
163
conditions to the lateral and the top boundaries. A freestream condition was applied to the outlet
164
boundary, and neutral velocity, turbulent kinetic energy and turbulent dissipation profiles
165
suggested by Richards and Norris (2011) were applied to the inlet boundary.
166
A total of 18 simulations were performed using the same wind velocity (U10 m = 1.5 m/s) but
167
with different wind directions from to 340° using a 20° step. Since the simulations were
168
performed in neutral conditions and without traffic-induced turbulence, the dimensionless
169
concentration given in (3) is a function only of the wind direction (Schatzmann and Leitl,
170
2011). In other words, this means that considering the previous hypothesis, and for a given
171
emission and building configuration (leading to constant  
ratio), only one simulation is
172
needed for each wind direction simulated. The pollutant concentrations for a non-simulated
173
wind velocity can therefore be computed using (4).
174


175
where is the dimensionless concentration, is the concentration, the wind velocity,
176
the characteristic building height and  the source strength of emission.
177


178
where is the pollutant concentration for the wind velocity not simulated and  the
179
pollutant concentration for the simulated wind velocity .
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181
Fig. 5. Illustration of the meshes in the computational domain with the emission source (red), with 0.5 m meshes near the
182
buildings and 1 m in the study area.
183
3. Results
184
3.1. Wind data interpolation
185
3.1.1. Comparison between the Weibull distribution and the sigmoid function
186
The best fitting parameters of the two functions were determined for the whole dataset using a
187
non-linear solver -velocity-range wind data. The solver was set up to solve
188
equation (5) for the four-velocity ranges [0, 1.5[, [1.5, 4.5[, [4.5, 8[ and [8, +[ for both the
189
Weibull and the sigmoid functions. This equation reflects that the sum of the frequencies
190
between two wind velocities (i.e. the area under the curve) must be equal to the frequency given
191
-velocity-range wind data. Since the sigmoid function has five parameters, a
192
fifth equation to be solved was added only for this function and corresponds to (6). With this
193
equation, it is assumed that the wind frequency tends toward 0% when the wind speed tends
194
toward 0 m/s, as for the Weibull distribution.
195


196

197
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where is the Weibull or the sigmoid function and  is the wind frequency given in
198
the 4-velocity-range data for wind velocities ranging from included to excluded.
199
Fig. 6 (AD) shows a comparison between the Weibull distribution, the sigmoid function and
200
 -velocity-range data for one wind direction of each meteorological station.
201
According to these figures, the two functions generally give the same trends, and both appear
202
   However, depending on the case, the
203
Weibull function can provide improvements in comparison to the sigmoid function, as in Fig.
204
6. (A), or vice versa, the sigmoid function can provide improvements in comparison to the
205
Weibull function, as in Fig. 6. (D).
206
207
Fig. 6. (AD) Weibull distribution and sigmoid function results compared to the detailed meteorological wind frequency data
208
for one wind direction at each station considered and (E) a notched box plot of the mean error over one wind direction with
209
all stations included for both functions.
210
To better compare the two functions, a notched box plot of the mean error over one wind
211
direction is given in Fig. 6. (E). According to this figure, the sigmoid function gives generally
212
better results compared to the Weibull distribution, with a lower maximal error (30.0% and
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33.1% respectively); a lower first quartile (8.1% and 9.5% resp.); a lower third quartile (13.8%
214
and 14.5% resp.); a lower mean (11.7% and 13.5% resp.); and a lower median (10.6% and
215
12.4% resp.). The differences are, however, small and may not be significant, especially for the
216
median because the notches slightly overlap. These differences between the Weibull
217
distribution and the sigmoid function are also location dependent, with for example better
218
prediction of the wind distribution in Strasbourg using the sigmoid function and an equivalent
219
prediction in Brest. Finally, it should be noted that both functions can lead to underestimations
220
of the lower wind velocity frequencies, as shown in Fig. 6. (A) and (D).
221
According to the previous results, the Weibull distribution and the sigmoid function can
222
          -velocity-range
223
discretization with an average error of around 12% over the four stations considered in France.
224
They can nonetheless lead to underestimations of the low wind velocity frequencies, for which
225
the highest pollutant concentrations appear.
226
227
3.1.2. Optimization of the sigmoid function interpolation for low wind velocities
228
The parametrization of the sigmoid function, called standard sigmoid function, was modified
229
to improve the estimation of the low wind velocity frequencies in order to avoid
230
underestimating pollutant concentrations.
231
Based on all the meteorological data considered in this study, it was found that the
232
underestimation of low wind velocity frequencies occurs mostly when the frequency of the first
233
velocity range is lower than the frequency of the second velocity range. In this specific case,
234
the optimized sigmoid function still needs the equation (5) for the four-velocity ranges given in
235
 , but equation (6) is replaced by equation (7); otherwise, the previous
236
parametrization using equations (5) and (6) is kept.
237
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

238
where  is the wind frequency for the first range of velocities given in the 4-velocity-
239
range data and  is the wind frequency for the second range of velocities (e.g., in this
240
study = 1.5 and = 4.5).
241
The methodology for the optimized sigmoid function is illustrated in Fig. 7. (AB): when the
242
frequency of the first velocity range is higher than the second, as in Fig. 7. (A1), the standard
243
parametrization of the sigmoid function can be used because the low wind velocity frequencies
244
are estimated accurately, as in Fig. 7. (A2), when the frequency of the first velocity range is
245
lower than the second, as in Fig. 7. (B1), the standard parametrization leads to underestimations
246
of low wind velocity frequencies and the optimized parametrization should be used instead,
247
leading to a better estimation of the frequencies, as shown by the blue curve in Fig. 7. (B2)
248
compared to the red curve.
249
250
Fig. 7. (AB) Illustration of the optimized sigmoid function methodology and (C) comparison with the standard sigmoid
251
function results.
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The improvements with the optimized sigmoid function compared to the standard function were
253
assessed and the results are presented in Fig. 7. (C). For this comparison, only the wind
254
directions where the optimized function was applied are considered and the errors compared to
255
 -velocity-range data were calculated for the low wind velocity frequencies
256
(between 0 and 3.5 m/s). According to this figure, the optimized sigmoid function gives
257
improvements over the standard sigmoid function with a lower maximal error (41.0% and
258
44.4% respectively); a lower first quartile (9.2% and 12.9% resp.); a lower third quartile (22.4%
259
and 25.5% resp.); a lower mean error (15.2% and 19.4% resp.); and a lower median (13.0% and
260
19.6% resp.). The improvements using the optimized function are significative, in particular for
261
the median since the box plot notches do not overlap; they are also location dependent. A global
262
improvement of the wind distribution prediction ranging between 20% and 45% is observed in
263
Strasbourg, Lille and Nîmes while no improvement is observed in Brest.
264
According to the previous results, using the optimized sigmoid function can improve the
265
-velocity-range compared
266
to the standard sigmoid function, especially for low wind velocities.
267
3.2. Mean annual concentration assessment
268
3.2.1. Discrete methodology with intermediate velocities
269
Initially, mean annual concentrations based on the CFD results can be calculated using a
270
discrete methodology. This methodology considers that the mean annual concentration at a
271
given location is composed of several small contributions of different wind velocities and wind
272
directions. The mean concentration over one wind direction can be calculated with equation (8)
273
and the mean annual concentration with equation (9). A similar methodology can be found in
274
(Solazzo et al., 2011).
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


 
276

 
277
where is the mean concentration over one wind direction,  is the concentration for a
278
given wind direction and a given wind velocity range ,  is the frequency for a given wind
279
direction and a given wind velocity range,  is the background concentration, is the mean
280
annual concentration and the total frequency of a given wind direction.
281
With this methodology, it is necessary to choose a wind velocity in each velocity range for
282
which the concentration will be calculated based on the CFD result. A simple choice is to
283
consider an intermediate velocity, noted , corresponding to the average between the minimal
284
and the maximal value of the velocity range (e.g., for the velocity range [1.5, 4.5[, the
285
intermediate value is 3 m/s).
286
A comparison of results for this methodology is given in Fig. 8. with distinct cases considering
287
-velocity--velocity-range frequencies,
288
(C) the frequencies calculated with the sigmoid function, and (D) the frequencies calculated
289
with the optimized sigmoid function. No background concentration is considered in this study
290
to permit better comparison of the results.
291
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292
-velocity-range monitoring
293
-velocity-range monitoring data, (C) the sigmoid interpolation data and (D) the optimized sigmoid
294
interpolation data.
295
Initially-velocity-range data leads to an underestimation
296
of the concentrations compared -velocity-range data by around
297
19%. 
298
the sigmoid function, the difference is reduced to 12.9%. Finally, the best results are obtained
299
when using the optimized sigmoid function with an underestimation of 3.4%. According to
300
these results, -velocity-range frequencies can give an estimation of the mean
301
annual concentrations but is not sufficient to reach good accuracy compared to the mean annual
302
          
303
sigmoid function and especially the optimized variant significatively improves the results,
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leading to almost the same results as those      
305
distribution.
306
3.2.2. Discrete methodology with representative velocities
307
The previous methodology used to compute annual concentrations, which was easy to set up,
308
nonetheless has certain weaknesses that mostly concern the choice of the wind velocity for
309
which the concentrations will be calculated, based on the CFD results. Using an intermediate
310
velocity corresponding to the average between the minimal and the maximal value of the
311
velocity range can lead to underestimations of the mean annual concentrations. Indeed, in doing
312
so, it is implicitly assumed that the concentration is constant with the wind velocity in a given
313
wind velocity range. However, according to equation (4), this assumption is wrong because the
314
concentration evolves hyperbolically with velocity. The representative velocity over one
315
velocity range, considering the hyperbolic evolution of the concentration, is given in (11) as a
316
result of (10) and (4).
317
 

  
 
318


319
where  and  are respectively the maximal and the minimal velocities of the velocity
320
range, is the representative velocity of the velocity range and the equation describing
321
the evolution of the concentration as a function of the wind velocity, i.e. equation (4).
322
The representative velocities were calculated with equation (11) and compared to the
323
intermediate velocities . It is noteworthy that for a velocity range with a minimal velocity of
324
0 m/s, it is mathematically not possible to compute the representative velocity due to the domain
325
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definition of the function. A choice is therefore required; for the purpose of this study, the same
326
ratio  as for [0.5, 1.5[ was considered.
327
According to the results summarized in Table 2. for wind velocities ranging from 0 to 6.5 m/s,
328
the intermediate velocity can be much higher than the representative velocity for low velocities.
329
For example, for wind velocities ranging from 0.5 to 1.5 m/s, the intermediate velocity of 1 m/s
330
is almost twice as high as the representative velocity of 0.67 m/s. For higher velocity ranges,
331
such as [2.5, 3.5[ or more, the differences can be neglected. This last statement is true for 1 m/s
332
steps between the minimal and the maximal velocities of the velocity range but can become
333
wrong for higher velocity steps.
334
335
Table 2. Comparison between the intermediate velocity and the representative velocity (*: the representative velocity was
336
calculated considering the same ratio  as for [0.5, 1.5[ ).
337
 [m/s]
0
0.5
1.5
2.5
3.5
4.5
5.5
 [m/s]
0.5
1.5
2.5
3.5
4.5
5.5
6.5
[m/s]
0.25
1.00
2.00
3.00
4.00
5.00
6.00
[m/s]
0.1675*
0.67
1.82
2.88
3.90
4.92
5.94

0.67*
0.67
0.91
0.96
0.97
0.98
0.99
338
Fig. 9. shows a comparison of the mean annual concentrations when using the intermediate
339
velocity and when using the representative velocity, -velocity-range
340
wind distribution. According to the results, using the intermediate velocity leads to considerable
341
underestimations of the mean annual concentrations compared to the use of the representative
342
velocity. The underestimation is about 20%. When using the discrete methodology presented
343
in Section 3.2.1., it is therefore suggested to use the representative velocity instead of the
344
intermediate velocity to better take into account the hyperbolic evolution of the pollutant
345
concentrations with the wind velocity to avoid underestimating the concentrations.
346
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347
Fig. 9. Comparison of the mea-velocity-range wind distribution using (A)
348
the intermediate velocity and (B) the representative velocity.
349
350
3.2.3. Continuous methodology using the sigmoid function
351
For the last approach, mean annual concentrations based on CFD results can be calculated using
352
a continuous methodology. This methodology is a combination of equation (4), describing the
353
evolution of pollutant concentration with wind velocity, and equation (2), describing the
354
evolution of wind velocity frequency with wind velocity. The equation to compute the mean
355
annual concentrations continuously is given in (12).
356





357
where is the mean annual concentration, is the function describing the evolution of the
358
concentration with the wind velocity, is the function describing the evolution of the wind
359
velocity frequency with the wind velocity, and  is the background concentration.
360
Taking equation (4) for and equation (2) for leads to a mathematical problem. Indeed,
361
is not defined for = 0 and the limit of tends toward infinity when tends
362
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toward 0. To avoid this problem, equation (13) is suggested instead of equation (12). With this
363
equation, it is considered that a minimal velocity () exists for which the pollutant
364
concentration will no longer increase when the wind velocity decreases. This hypothesis can be
365
justified by the additional effects, such as traffic-induced turbulence (Vachon et al., 2002) and
366
atmospheric stability (Qu et al., 2012) that may participate in pollutant dispersion for low wind
367
velocities or become preponderant. We suggest applying a constant pollutant concentration for
368
wind velocities ranging from 0 to  and suggest using . The choice of 
369
is particularly important when using the optimized sigmoid function.
370










371
where is the mean annual concentration,  is the maximal concentration accepted for the
372
calculation,  is the velocity under which is considered equal to , is equation
373
(2), is equation (4) and  is the background concentration.
374
Fig. 10. shows a comparison between the discrete methodology with the representative
375
velocities and the continuous methodology using the optimized sigmoid function. It can be seen
376
that the results of the discrete methodology given in Fig. 10. (A) can be reached by the
377
continuous methodology. Nonetheless, the difference of 5% reached using  = 0.01 m/s can
378
increase when changing the value of : lower values will lead to higher concentrations
379
whereas higher values will lead to lower concentrations. The value of  must therefore be
380
chosen carefully.
381
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382
Fig. 10. Comparison of the mean annual concentrations (A) -velocity-range wind distribution and
383
using the intermediate velocity, and (B) based on the optimized sigmoid function and  = 0.01 m/s.
384
4. Discussion
385
This study provides tools to assess wind velocity distributions based 
386
annual air pollutant concentrations based on CFD results. Additional work should be done to
387
improve the methodologies and the major issues are discussed hereafter.
388
The capability of the Weibull and the sigmoid functions to describe wind velocity distribution
389
was assessed based on wind data from four meteorological stations in France. All of these
390
stations were located in peri-urban environments close to large French cities. It is necessary to
391
take into account that the results, and especially the interpolation-related errors, might be
392
different for other types of stations such as urban and rural stations, and for other countries with
393
different wind characteristics. In particular, the optimization suggested for the sigmoid function
394
may not be suitable for different countries or type of station. Further works are therefore
395
required in this direction.
396
The mean annual atmospheric pollutant concentrations can be calculated using a discrete
397
methodology. However, this methodology has two major problems. The first concerns the
398
choice of wind velocity for which the pollutant concentrations will be calculated: choosing an
399
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intermediate velocity is a simple approach which can lead to considerable underestimations of
400
pollutant concentrations, and it is better to use a representative velocity instead, as suggested in
401
this paper. Using the representative velocity requires, however, making a choice for the first
402
velocity range. The second problem concerns the velocity step used to build the wind velocity
403
ranges: the result depends on the velocity step used, especially for the lower wind velocities for
404
which a decrease in the velocity-step leads to higher mean annual concentrations. To avoid
405
these two problems, a continuous methodology has been proposed. This methodology does not
406
have an intrinsic limitation, but dependent on the function describing the evolution of the
407
concentration as a function of wind velocity. If we consider a hyperbolic evolution of the
408
concentration with wind velocity, it is necessary to choose a minimal value of velocity for which
409
it is considered that lower velocities will not increase the concentrations due to compensatory
410
phenomena (traffic-induced turbulence, atmospheric stability, etc.). The value of the minimal
411
velocity is open to discussion and assessing this value is outside the scope of this paper. Further
412
works are required, for example with infield measurement campaigns and comparisons between
413
mean annual concentrations monitored and calculated with the continuous methodology.
414
Finally, it should be noted that the methodologies to assess mean annual concentrations were
415
addressed using CFD results implying a neutral atmosphere, but can be used for any numerical
416
results as long as a function describing the evolution of the concentration with the wind velocity
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is available.
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5. Conclusion
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The objectives of this study were to provide methodologies; (1) to assess wind velocity
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, and (2) to assess mean annual air pollutant concentrations
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based on numerical results. Three approaches for each objective were described and compared
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throughout this paper and the main conclusions are as follows:
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(1.a) The Weibull distribution and the sigmoid function can both accurately reproduce
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detailed 18-velocity-range wind distribution based on basic 4-velocity-range wind
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data with an average error of 12%. These functions can nonetheless underestimate the
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frequencies of low velocities.
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(1.b) The optimized sigmoid function improves the wind distribution results over the
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standard sigmoid function, especially for low wind velocities.
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(2.a) -velocity-range wind data and the discrete methodology can provide an
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estimation of the mean annual concentrations but is not sufficient to achieve high
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precision, leading to a difference of around 19
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18-velocity-
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wind data improves the mean annual concentration results with a global error of less
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than 4%.
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(2.b) When using the discrete methodology to assess mean annual concentrations, it is
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suggested to use a representative velocity of the function describing the evolution of
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pollutant concentrations with the wind velocities instead of an intermediate velocity.
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The intermediate velocity leads to underestimations of mean annual concentrations,
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especially when using CFD results with a neutral case hypothesis where the
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concentration evolves hyperbolically with the wind velocity.
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(2.c) Mean annual concentrations can be assessed using a continuous methodology that does
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not have any of the limitations of discrete methodologies. It is, however, limited by
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the function describing the evolution of the concentrations with the wind velocities,
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which leads to the need to choose a minimal velocity when using the sigmoid function.
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Finally, the methodologies presented in this paper can be used for outdoor air quality study
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purposes, which is a relevant starting point for improving both outdoor and indoor air quality
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and, therefore, a key-point to achieve smart sustainable cities.
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Acknowledgments
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We would like to thank the ANRT (Association Nationale de la Recherche et de la Technologie)
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for their support and Météo-France for allowing us to use their data for this study.
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... However, one of the key open challenge for this type of models is to compute mean annual concentrations that are relevant for the AQD (Thunis et al., 2011) without performing a great number of simulations and, therefore, saving the calculation time and reducing the calculation costs of numerical modelling. Recent works, such as Rivas et al. (2019) and Reiminger et al. (2020), have explored different methodologies to assess mean annual concentrations based on numerical results. However, these studies were only focused on numerical results from CFD models and wind rose data, whereby, further works are required to improve the available approaches, to assess their limits, to test its applicability to other spatial scales and to explore other tools and methods able to assess mean annual concentrations. ...
... The time-effective method based on meteorological data, hereafter referred as M3, is based on the assessment and selection of the predominant meteorological conditions, focused on wind velocity and wind direction at 10 m from the ground, over 1-year period (2010) and Reiminger et al. (2020)) and adapted to the current study objectives. Three steps were performed. ...
... To deal with this last issue, two kind of approaches can be adopted as future work: 1) a hybrid method, which implies the application of M3 for transportation and commercial and residential sectors and run the numerical model (M1) for industrial point sources; this approach will not have an impact on the computational demand (the model run point sources for an entire year in an hourly basis in few minutes) and will solve the overestimation of annual concentrations found in this work; 2) refine the methodology to select the predominant wind conditions. Reiminger et al. (2020) explored different methodologies to assess mean annual concentrations with CFD tools based on wind speed distribution, having concluded that the more detailed is the velocity-range wind distribution the more precise are the results. Further works should explore how the approaches used in CFD applications can be adapted to Gaussian studies over complex urban areas. ...
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... La question de la concaténation de ces résultats et la prise en compte de la fréquence d'apparition des différentes vitesses de vent reste toutefois en suspens. Il est possible de faire le calcul de façon discrète, mais de cette façon, une importante sous-estimation des concentrations moyennes annuelles peut avoir lieu suivant les hypothèses de calcul (Reiminger et al., 2020b). ...
... It is therefore necessary to combine all numerical results in order to obtain concentration values comparable with these standards. It is particularly necessary to have an idea of the annual concentrations.The annual concentrations based on the CFD results were assessed according to the methodology ofReiminger et al. (2020b) described in Chapter 4. Firstly, the wind distribution of each wind direction considered was assessed based on the wind rose data given by Météo-France at the nearest meteorological station from the area of interest (see Section 4.3.1. for further details), the wind rose being proposed inFigure 8.11. ...
... This issue is important in a policy context because annual statistics are relevant for air quality directives. However, post-processing methodologies have been developed and successfully applied to compute high-resolution maps of long-period (e.g., yearly) average concentrations [15,17,22,[26][27][28][29][30]. ...
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... γ is lower incomplete Gamma function. The estimated parameters for GA based on MLE can be obtained using the following equations LG is also a popular model with ubiquitous applications [29,30]. The PDF for LN is given as follows: ...
... Though these machine learning models have better performance than statistical prediction models, but fail to handle huge multidimensional datasets. However, recent studies provided evidence that air pollution is mostly affected by temperature (Kalisa, Fadlallah, Amani, Nahayo, & Habiyaremye, 2018), wind speed (Reiminger et al., 2020;Yang et al., 2020), wind direction, rainfall, and humidity. Therefore researchers must analyze the sensitivity of meteorological factors for air quality modeling. ...
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