Transportation Research Part D: Transport and Environment
Volume 56, October 2017, pages 33–42
A novel approach for the modelling of air quality dynamics in underground
E. Walther∗, M. Bogdan∗
AREP, 16 avenue d’Ivry, 75013 Paris, FRANCE
Indoor air quality in subterranean train stations is a concern in many places around the globe. However, due
to the speciﬁcity of each case, numerous parameters of the problem remain unknown, such as the braking discs
particle emission rate, the ventilation rate of the station or the complete particle size distribution of the emitted
particles. In this study the problem of modelling PM10 concentration evolution in relation with train trafﬁc is
hence addressed with a particle-mass conservation model which parameters are ﬁtted using a genetic algorithm.
The parameters of the model allow to reproduce the dynamics and amplitude of four ﬁeld data sets from the
French and Swedish underground contexts and comply with realistic bounds in terms of emissions, deposition
and ventilation rate.
Keywords: PM10, conservation model, underground air quality
Indoor air quality in subterranean railway station is
an increasing public health concern. Numerous mea-
surement campaigns and simulations have been un-
dertaken worldwide, e.g.  in the Netherlands, 
in Japan, in Korea  or  in Mexico City, as they
help to understand the mechanisms that create such
indoor/outdoor pollution, with the aim to reduce it.
However, these studies mainly measure pollution lev-
els and provide design or operation guidelines with-
out a quantitative analysis of the link between train
trafﬁc and particulate matter concentration.
The clear weekly pattern of PM10 concentration
in subterranean railway stations and the similar be-
haviour of particle concentration evolution and train
movement frequency observed for instance in  as
well as in the measurement data exhibited on Figure
1, led us to investigate the modelling of this relation-
Email addresses: (E. Walther),
The difﬁculty of this enterprise resides in the un-
knowns around the two key phenomena:
- the source of particles, divided in direct emission
by abrasion and resuspension of deposited parti-
cles, is unsufﬁciently characterized,
- the dilution mechanism, which in underground
stations strongly depends on the piston effect
and comfort ventilation. The piston effect is in-
deed responsible for sporadic, violent drafts in
the tunnels  and complex, sometimes coun-
terintuitive, air ﬂows on the platforms, with gen-
erated dynamic pressures reaching about thou-
sand Pascal upon arrival in the station  and
air velocities of about 1/5th of the train velocity
Different sources have shown that iron is the domi-
nant element in underground stations . In the re-
view by  of eight suburban stations over the globe,
particle mass concentration in iron is superior by one
order of magnitude to all other elements. Determin-
ing a value for the direct emission term, i.e. how many
particles are emitted by the components of the trains
Preprint submitted to Elsevier July 27, 2017
that are subject to abrasion (braking system, wheels,
pantograph and catenary) can be achieved by exploit-
ing the maintainer’s parts wearing.
In the underground context, resuspension is more
complicated to evaluate independently of direct emis-
sion, especially without using a tracer such as .
However, an attempt was undertaken by  for a
Parisian subterranean station. A recent and de-
tailed literature review of progress in experimental
and modeling particle resuspension is presented in
Regarding the ventilation phenomenon, it appears
that it is strongly inﬂuenced by wind pressure, air
transfer between tunnels, and the piston effect. The
latter has been studied by , whose approach allows
for an estimation of the amount of ventilation due
to train movement. Piston effect is however largely
driven by the pressure drop between the underground
and the exterior environment, which depends on the
geometry of the stations.  observed for instance
that the lower the station, the higher the PM concen-
tration. This can be related to the inhibition of ventila-
tion by higher pressure drops in the subway corridors.
An attempt of classiﬁcation of the stations relating ge-
ometry and air quality was led by  for Barcelona’s
Airborne particle dynamics is also inﬂuenced by the
particle size distribution. A difference of one order of
magnitude between the particles diameter may result
in more than two orders of magnitude discrepancy of
deposition rates [22, 33]. For the underground con-
text, large particles above 2.5 µm may represent 70% of
the mass concentration [31, 5, 35]. Metallic elements
were found to be dominant during peak hours  or
to exhibit a relative abundance depending on the con-
Based on these elements, it appears that the mod-
elling options are limited in the subterranean railway
environment. CFD is impeded by the lack of informa-
tion about particle size and distribution as well as the
orders of magnitude of the key phenomena such as re-
suspension and deposition. It is also unclear where
the resuspension occurs, although  have observed
that the extremities of platforms exhibit higher PM
concentration levels in comparison with the centre.
The current computing capacity is also a drawback as
it reduces the computable duration of particle disper-
sion to a narrow span that does not allow for the siz-
ing of air quality equipment (for instance ventilation
or ﬁltration), which rely on the daily values of concen-
Given the previous observations, this study is an
attempt of coarse modelling of the PM10dynamics in
underground stations using the approach suggested
by , based on the well-mixed volume hypothesis,
with an adaptation to the subterranean railway con-
text. Recently,  led a similar study aiming at the
prediction of CO2concentration in the platform and
concourse of a station, linking the measurements of
CO2concentration in the tunnel and an estimation of
the train-induced wind after measurements per .
It seems however that no study couples the analy-
sis of train trafﬁc and PM10 distribution, as underlined
by . The originality of this work hence relies in the
relation of the PM10 concentration with piston effect,
particle emission and resuspension with train move-
ments. An ordinary differential equation with vari-
able coefﬁcients describes the phenomena. The few
parameters of the equation are then identiﬁed versus
available four data sets from the French and Swedish
2. Measurement data
2.1. Underground PM10 measurements
The experimental data in this work originates from
two main sources :
- Three of Paris subterranean stations, namely
Saint-Michel Notre-Dame, Gare du Nord and La
Défense were part of an air quality measurement
campaign by the French national railway com-
pany SNCF lead in 2005. TEOM devices recorded
the underground air quality over a year. The data
presented here show the year-averaged weekly
- The eight-weeks averaged TEOM measurements
from Arlanda C station in Stockholm retrieved
from  were also used.
Despite the numerous unknowns of the under-
ground context, the measurement data on Figure 1
exhibit a strong correlation between train movement
frequency and PM10 concentration: from Monday to
Friday the daily concentration has a similar shape and
decreases during week-end, as does the train move-
ment frequency (see also Figures 6 and 7 for Gare du
Nord and La Défense and the study by  for two
Additional information may be deduced from the
data: for instance, the overnight peaks circled in red
on Figure 1 stand for the emission of a diesel engine
train passing through the station for overnight work
that occurred during the year of the measurement.
Figure 1: Comparison between PM10 concentrations and train traf-
ﬁc - Saint-Michel station (average 2005 week, SNCF data)
The concentration decrease every night at the end
of service also allows for an estimation of the natural
Interestingly, the daily minima on a yearly average
are not only dependent on the train trafﬁc and exhibit
a bell-shaped behaviour (see dotted line on Figure 1).
The same phenomenon can be observed in the mea-
surement campaign done by , however, to the best
of the authors’ knowledge, this feature has not been
described previously, and is related to the exterior par-
ticle concentration: on the average Friday early morn-
ing, the minimum PM10 concentration is smaller than
the previous morning, whereas train trafﬁc has the
2.2. Outdoor air PM10 concentration
The average week of outdoor air PM10 concen-
tration for the year corresponding to the measure-
ments was calculated from the hourly air quality open
database  at the station of Paris-Centre in 1st dis-
trict, which is about 1 km from Saint-Michel’s under-
ground (the outcome is plotted on Figure 2). On the
2005 average week, one can see by the dotted line on
Figure 2 that the PM10 concentration minima also ex-
hibit a bell-curve behaviour. Concentrations levels are
nevertheless lower than the minima of the concentra-
tion for station Saint-Michel plotted Figure 1.
For Arlanda C station as the outdoor air data was
not available an average outdoor air concentration of
15 [µg/m3] was chosen after the yearly average value
speciﬁed in the World Health Organization report .
Figure 2: PM10 concentration on the average week (2005 - Paris 1st
3. Physical modelling
Most of the particle matter evolution studies use
a “two compartment model” that includes both the
airborne particles and the particles deposited on the
enclosure’s surfaces. For a stringent closure of the
model, the differential equation quantifying the depo-
sition and resuspension rate on surfaces in the station
would be necessary, such as in  or . As esti-
mating the quantity of particles deposited on surfaces
appeared uncertain, surfaces are supposed to be sat-
urated with particles and hence a “one compartment”
model is used, based on the airborne PM10 conser-
vation. Due to the perfect mixing hypothesis, spatial
effects described in  for instance, cannot be ob-
served. Coagulation or agglomeration as well as ther-
mal effects on particles are also ignored.
3.1. Presentation of the model
The conservation model proposed in the next para-
graphs relies on a concentration balance in the spirit
of  and considers only three main phenomena:
- The emission of particles is modelled with an
“apparent emission” term αthat includes emis-
sion by friction (brakes, catenary. . . ) and particle
resuspension due to train movement.
- Ventilation is composed of the apparent ventila-
tion rate τ0and of the outdoor air βinduced by
the train piston effect.
- Deposition δis chosen in the range calculated af-
ter the procedure detailed in  for the settling
of PM10 in the speciﬁc subterranean station en-
Other phenomena occurring in polydisperse
aerosols are neglected, e.g. particle size change
by condensation and coagulation as in [27, 28] or
Cbeing the concentration in PM10, the mass bal-
ance is then expressed as follows:
This ordinary differential equation is solved numer-
ically with a semi-implicit Crank-Nicolson second-
order scheme using a time step of one minute. The
initial condition is the measured initial concentration.
The physcial meaning of all terms are explained in fol-
3.2. Terms of the conservation equation
In the box-model approach, we consider that the
average velocity in the station is proportional to train
movement. The kinetic energy being proportional to
the square of velocity, the mass of resuspended par-
ticles increases with the square of train frequency, as
suggested in . The emission term is then propor-
tional to the apparent emission α[µg/m3] and to the
square of train movement N(t) [1/h] such that the ap-
parent source of particles is α×N2(t). The mixing with
the air pushed into the station from the tunnels is also
included in the apparent emission term.
The ventilation rate τ(t) in air changes per hour
[1/h] is composed of an apparent air change rate τ0in-
cluding mechanical and natural ventilation, plus the
amount of outdoor air brought by the piston effect-
driven ventilation term β×N :
β[-] is the ratio of the volume of outdoor air
brought by train circulation, divided by the station’s
air volume. In the cases presented in this study, the
geometry of the station and the complex interconnec-
tions with other tunnels at different depths makes it
hard to have an a priori a value of the piston effect per
train. Nevertheless, an order of magnitude of β<1
can be derived from  for a station volume of about
10 000 m3. A similar order of magnitude is obtained
from the analytical derivation by .
The physical phenomena driving particle deposi-
tion range from brownian diffusion, turbulent diffu-
sion and gravitational sedimentation, depending on
the particle size. The enclosure overall deposition
loss-rate also depends on its aspect ratio as it is de-
rived from the individual deposition rates of particles
on each type of surface (e.g. vertical walls, ﬂoor or
ceiling). The global deposition rate δfor an enclosure
can be computed for still and stirred environments
[33, 15], depending on the friction velocity at the de-
A comparison of the deposition rate in a still envi-
ronment between a typical room with a volume V=
4×5×3 [m3] as in  and a typical underground
station (V=200 ×20 ×5 [m3]) was done using a fric-
tion velocity of 0.01 [m/s] after the model by . On
Figure 3, one can compare the overall deposition co-
efﬁcient of both enclosures for a particle density of
1 [g/cm3]: with an equal particle density the under-
ground station exhibits a lower deposition rate. This
difference is related to the aspect ratios of the two
spaces: for instance, the relative contribution of the
ceiling surface to the overall deposition coefﬁcient is
higher for the underground than for the typical indoor
(respectively 48 % versus 23 % of the total surface).
In the underground context, the mean density of
particles has been reported to reach 4 [g/cm3] [35, 6,
36]. The overall deposition coefﬁcient δcomputed
with this density presents a shift from ∼0.2 [µm] to
∼0.1 [µm] of the particle diameter yielding the lowest
deposition rate (see Figure 3). As a result of the higher
particle inertia, the overall deposition rate is higher
than in the typical indoor environment for particles
above ∼0.2 [µm].
Figure 3: Comparison of the overall deposition loss rate δfor a typi-
cal indoor room (V=4×5×3 [m3]) and typical underground station
(V=200×20×5 [m3]) after the model by  (friction velocity = 0.01
As underground stations are subject to important
air velocities, a correction of the deposition coefﬁcient
is necessary . In the underground context, air ve-
locities reaching ∼3 [m/s] or more were measured 
(the authors’ data exhibit a maximum of no less than
9.5 [m/s] on the platform of Paris’ Saint-Michel sta-
tion). An estimate of the friction velocity can be ob-
tained using the correlation by , as described in
. With this approach, supposing that the air ve-
locity in the station reaches ∼10 [m/s], the friction
velocity attains ∼0.30 [m/s]. Figure 4 shows the co-
efﬁcient δcomputed for such a high friction velocity
and for a low one, 0.01 [m/s] being considered as a
typical indoor friction velocity . One can observe
that turbulent diffusion drastically increases the de-
position for sub-micrometric particles and shifts the
minimum of δto ∼0.4 [µm] diameter.
Figure 4: Overall deposition loss rate δin a typical underground sta-
tion for two different friction velocities (ρ=4 [g/cm3]).
Neither the composition nor the particle size distri-
bution was available for the stations considered. In
other stations around the globe, the PM2.5/PM10 ra-
tio ranges from 0.23 to 0.88  depending amongst
other parameters on the train material and the sta-
tion conﬁguration. A previous study by  on a sta-
tion of the same railway network has shown that the
PM10 particles prevail in mass during train operation.
Indeed, the ratio PM2.5/PM10 equals 0.3 during daily
train operation and comes back to 1 for the short pe-
riod of absence of circulation over night [32, 5]. A ratio
of 0.28 was also measured by  in a Budapest under-
ground station.  reported the same phenomenon
in Barcelona underground, with a ratio of 0.3.
Based on these results and in absence of a bet-
ter characterisation of the particle size distribution
for the available data sets, we considered in this ﬁrst
approach that the predominant particle size affect-
ing the mass concentration was in the coarse mode
[31, 5, 35] (obviously, in terms of particle numbers, the
ﬁne and ultra-ﬁne particles may prevail ). In the
later identiﬁcation process δwill hence be bounded
between 0.002 and 7.2 [h−1] as per Figure 4.
4. Identiﬁcation procedure
4.1. Method and preliminary identiﬁcation
The model was tested against data sets of three
of Paris underground railway stations (Saint-Michel,
Gare du Nord and La Défense) as well as one station
in Sweden (Arlanda C, Stockholm) with the data from
. Fitting the parameters to the measurement was
not straightforward and three different methods were
tested using the Scilab scientiﬁc computing software:
- The Levenberg-Marquardt algorithm  proved
to be the fastest in terms of computation time but
also to be very dependent on the initial guess. It
sometimes provided unphysical results (e.g. neg-
ative values of the piston ventilation β).
- A least squares method was much slower and in
many cases the algorithm did not converge.
- The method giving the best results in terms of
computational intensity and diversity of the min-
ima proved to be a genetic algorithm .
The genetic algorithm was used with following pa-
rameters: 200 individuals, 50 generations, probability
of crossover of 70 % and mutation rate of 5%. The orig-
inal functions detailed in the documentation  for
coding, selection or mutation of the individuals were
Prior to the identiﬁcation procedure, the correct or-
der of magnitude of natural ventilation has to be es-
timated. This value is computed using the concen-
tration decrease overnight and integrating Equation
1 with N=0 and β=0. The base ventilation rate
τ0[vol/h] that best ﬁts the measurements is then se-
lected. This preliminary calculation also provides an
ﬁrst guess for the deposition phenomena through the
identiﬁcation of δ.
After this step, the identiﬁcation procedure is
launched over parameters α,β,δand τ0.δis bound
by the physical principle of deposition, βand τ0are
allowed to vary by ±25% around their pre-identiﬁed
The identiﬁcation procedure for Gare du Nord and
Saint-Michel stations gave a correct representation of
the phenomenon, as presented on Figures 5 and 6.
Figure 5: PM10 model versus measurements for Saint-Michel.
Figure 6: PM10 model versus measurements for Gare du Nord.
For both stations the identiﬁcation allow to repro-
duce the dynamics and amplitude of PM10 concen-
tration related to train trafﬁc. For Saint-Michel sta-
tion, owing to the overnight construction work (see
2.1), this discrepancy is slightly higher: shortly after
service, the concentration decrease is perturbated by
a passing diesel engine train, which sharpens the dif-
ference between the actual and simulated concentra-
Figures 7 and 8 provide a comparison between the
model and the experiment for stations La Défense and
Arlanda C. Although the dynamics are respected, the
model performs noticeably less accurately for station
La Défense (Figure 7), which we believe is caused by
the geometry of the station: it is probable that the
station’s much larger volume and wider openings to-
wards the concourse leads to a different kind of de-
pendance between the average velocity and train traf-
ﬁc. Additionally, these geometric features make the
well-mixed enclosure hypothesis questionable and
may lead to an inappropriate estimation of the piston
The peak hours concentrations of Arlanda C sta-
tion (Figure 8) exhibit a greater discrepancy between
model and measurement. This is probably related to
the fact that the PM10 and train trafﬁc values were av-
eraged over 8 weeks only and thus are less homoge-
neous than measurement data of the three stations in
Paris, for which a yearly average was used.
Figure 7: PM10 model versus measurements for La Défense.
Figure 8: PM10 model versus measurements for Arlanda C.
A summary of the identiﬁed parameters are sum-
marized in table 1 where GDN, SHL, LDF and ARL re-
spectively stand for Gare du Nord, Saint-Michel, La
Défense and Arlanda C stations.
Parameter GDN SHL LDF ARL
α[µg/m3] 2.27 5.30 1.65 9.33
β[-] 0.82 0.54 0.42 0.17
τ0[vol/h] 0.50 0.11 0.48 0.06
δ[h−1] 0.06 0.36 0.26 0.14
Mean error [%] 15.8 27.7 13.8 26.1
Mean diff. [µg/m3] 14.1 52.8 10.2 47.2
Table 1: Summary of the parameters α,β,τ0,δidentiﬁed for each
station and corresponding mean error.
The simulation results are in good accordance with
the measurements in terms of amplitude and dynam-
ics, using parameters within realistic orders of magni-
tude of deposition, ventilation and piston effect. The
outcome of this study is also an “apparent emission”
term αthat mimics the direct emission and the resus-
The relative error between the model and the PM10
measurements is plotted over time and day on Fig-
ures 9,10,11,12, respectively for Gare du Nord, Saint-
Michel, La Défense and Arlanda C stations. The max-
imum relative error varies from about 0.3 up to 1 de-
pending on the station and time of the day. One can
observe on the aforementioned ﬁgures that the daily
values of concentration are generally closer than the
nightly ones. During the night period, ﬁne particles in
the real aerosol settle slower than coarse ones, which
leads to higher concentrations that the model can-
not represent as it has a constant deposition coefﬁ-
cient. Diesel engines passing through the station for
overnight work in the tunnels also affect the results,
as explained 2.1.
Interestingly, calculating the slope of the function
PM10 =PM10(Ntrain ) as in [9, 35] seems to be yielding
an accurate ﬁrst guess of α. However, for all stations,
the model is slightly "ahead" of measurements, which
could imply a delay for example in the mixing process
in the enclosure. Further investigations are to be con-
sidered on this point.
One can notice that the apparent emission term α
of SHL is higher than the one of GDN or LDF stations.
This difference may relate to the fact that SHL station
is much older and hence a higher amount of parti-
cles available for resuspension is deposited on the sur-
faces. Noticeably, the value of αfor Arlanda C is higher
up to a factor ∼5 compared to the apparent emission
term of the three French stations studied. This may be
Figure 9: Relative error between the model and measurements for
Gare Du Nord station
Figure 10: Relative error between the model and measurements for
related to the different rolling stocks or braking ma-
terial used, however too little information about the
Swedish rail context was at the authors’ disposal to
In this paper, a novel approach for the estimation
of the PM10 concentration in underground train sta-
tion is presented. A reduced number of parameters
allow for the representation of the general phenom-
ena driving PM concentration in subterranean railway
context using a mass-conservation model. Consider-
ing that particle emission is proportional to train traf-
ﬁc, the method reproduces the dynamics and ampli-
tude of the PM10 concentration measured in four un-
derground stations in Europe.
Figure 11: Relative error between the model and measurements for
La Défense station
Figure 12: Relative error between the model and measurements for
Arlanda C station
Intrinsically, the model is space and time-averaged,
hence it does not provide an access to the concentra-
tion spatial distribution and requires concentration
measurements prior to being used. The mass con-
centration of other particles size-class was unfortu-
nately not available, which impeded the modeling of
a multi-component aerosol. For instance, having the
PM2.5 concentration measurements would have al-
lowed simulating the difference in dynamics between
the part of the aerosol containing ﬁne-mode particles
(below 2.5 µm) and coarse ones (above 2.5 µm).
This ﬁrst approach has drawbacks, however it could
provide a reasonably simple way to estimate the level
of particle concentration originating from train circu-
lation and the amount of ventilation or ﬁltration that
would be required to reduce air pollution.
It has been shown that the model is tractable to dif-
ferent underground railway stations, which supports
our idea that the number of ﬁtting parameters is suf-
ﬁcient for this type of train stations. We believe it can
be used to generate multiple scenarios with different
ventilation rates, and provide engineers with a way to
quantify the corresponding air quality increase, given
that a new measurement campaign – after implemen-
tation of a solution – can attest the validity of our hy-
potheses and model. Regarding the improvement of
air quality with such technical solutions, the tests lead
by the authors show that ventilation with outdoor air
and ﬁltration of the air inside the station can improve
the underground air quality but only to a limited ex-
tent: the square dependency of the apparent emission
term with train trafﬁc (i.e. air velocity) penalizes the
air quality. For example, a simulated scenario of 10
[vol/h] outdoor air in addition of 2.5 [vol/h] of indoor
air ﬁltration with 90% mass efﬁciency provided ∼30%
reduction of the average PM10 concentration.
Moreover, the model is still dependent on the iden-
tiﬁcation of the parameters: the source term αand
the dilution one τhaving antagonist effects, one can
ﬁnd several sets of parameters with different orders
of magnitude that provide a coherent ﬁt on the mea-
sured data. A measurement campaign of the piston
effect in Saint-Michel’s station realised in early 2017
will give the correct order of magnitude of this param-
Considering only coarse particles is also insufﬁ-
cient for a proper modeling of aerosol behaviour
[33, 22]. Translating the principle of  to the
underground environment, an improvement of the
model would be to model the evolution of concen-
tration in the station as a multi-component aerosol.
A permanent measurement station deployed in Paris
Saint-Michel underground station with commitment
to public availability of the results should make this
possible in a near future (see the online PM10 and
PM2.5 data on ).
Although the model seems to be able to represent
the dynamics and amplitude of the train-related PM
concentration, it fails to catch the overnight low con-
centration, for instance in Gare du Nord and Saint-
Michel (Figures 5 and 6). Indeed, the nightly min-
ima over the average week exhibit a bell curve that the
model does not manage to reproduce faithfully. We
suppose that this is linked to the slower deposition
rate of ﬁne-mode particles (PM<2.5 µm). An attempt
in this direction is under progress.
A concentration delay at peak hours is also to be
noted and still has to be explained.
The authors would like to express their gratitude to
the SNCF for allowing the use of the PM10 normalized
concentrations presented in this paper and especially
to Dr. Cremezi at SNCF-Direction du Développement
Durable for her expert views and advice on the topic,
as well as to Pr. Gustafsson for providing Arlanda C
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