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Predicting the soiling of modern glass in urban environments: A newphysically-based model

S.C. Alfaro*, A. Chabas, T. Lombardo, A. Verney-Carron, P. AussetLaboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), UMR-CNRS 7583, Université Paris-Est Créteil, Créteil, France

h i g h l i g h t s

< We analyze the soiling of glass exposed to a variety of polluted environments.< Mass deposition and optical impairment do not increase linearly with time.< A physical model allowing prediction of this increase is proposed and validated.< In the model, site category (Roadside, Urban Background, or Suburban) is a critical factor.

a r t i c l e i n f o

Article history:Received 4 January 2012Received in revised form11 May 2012Accepted 18 June 2012

Keywords:Glass soilingHazeMultiple scatteringBCPOMDeposition rate

a b s t r a c t

This study revisits the measurements of the MULTI-ASSESS and Long Term Soiling programs forunderstanding physically, and modeling, the processes controlling the soiling of modern glass in pollutedconditions. The results show a strong correlation between the size distribution of particles and theevolution of the mass deposited at the surface of the glass. Over observation periods covering more than2 years, the mass deposition on glass panels sheltered from the rain is observed to accelerate regularlywith time at the sites closest to the sources of particulate matter (Roadside sites). At these sites thedeposit is also richer in coarse (supermicron) mineral particles than at more distant (Urban Backgroundand Suburban) sites, where the contribution of submicron particles (among which a significant fractionof particulate organic matter) is larger. This size and compositional segregation probably explains thatthe mass accumulation tends to slow down with time and finally saturate after an estimated duration ofmore than 10 years at the Suburban sites.

The analysis of the correlation between the measured accumulated mass and haze shows that thehaze-creating mass efficiency of the deposit decreases progressively as the density of particles increaseson the glass panels. This is interpreted as being a consequence of the increasing influence of multiplescattering. A steady-state is eventually obtained when layers of closely packed particles are formed,which occurs for surface masses of the order of a few tens of mg cm�2. After this stage is reached, the hazeincreases linearly with further mass deposition at a pace conditioned by the size-distribution of thedeposit. The parameterization of the evolution of the deposited mass with time, and of the correlationlinking this mass to the haze allows proposing a new physically-based model able to predict thedevelopment of the haze on sheltered glass. Finally, a comparison of the model predictions with theindependent measurements performed at the experimental sites of the AERO program shows that themodel is able to simulate correctly the development of the haze at a variety of urban sites ranging fromthe Suburban to Roadside categories. This predictive tool should help developing conservation strategiesadapted to the real environmental conditions of the historical and modern buildings.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The action of gaseous and particulate pollutants on modern andhistorical buildings can lead to serious deterioration of their surface

properties. For instance, in the case of corrosion or dissolutiondamages resulting from chemical interactions between thepollutants and the building material induce more or less profoundstructural modifications of the support. With less reactive materialsthe damage is only due to the accumulation of particles pre-existing in the atmosphere or formed directly at the surface, butthis causes a visual impairment generally referred to as ‘soiling’. In

* Corresponding author.E-mail address: alfaro@lisa.univ-paris12.fr (S.C. Alfaro).

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urban areas where the problem is usually more acute, thefrequency and therefore the cost of the cleaning operationsnecessary to restore the initial visual aspect of historical monu-ments and modern buildings can be quite high (Newby et al., 1991;Rabl, 1999; Watt et al., 2008).

For opaque surfaces, modifications of surface gloss, lightness,and more generally any quantity directly related to the surfacereflectance can be used to quantify the visual deterioration inducedby the soiling, (Beloin and Haynie, 1975; Mansfield and Hamilton,1989; Creighton et al., 1990; Hamilton and Mansfield, 1993; Pioet al., 1998; Watt and Hamilton, 2003; Watt et al., 2008;Brimblecombe and Grossi, 2004, 2005, 2009). In the case oftransparent materials such as modern glass panes to which thepresent study is dedicated, the reference parameter can be the lossof light transmittance (Sharples et al., 2001), the reduction ofsurface gloss (Adams et al., 2002; Schwar, 1998) or the haze (H)(Lombardo et al., 2005a,b, 2010; Favez et al., 2006; Ionescu et al.,2006; Chabas et al., 2008, 2010; Verney-Carron et al., 2012)defined as the ratio of the light transmitted by diffusion (Td) to theone transmitted directly (TL) in the initial direction of the assum-edly normal incident light. Note that for H > 1%, a visual nuisancecan be detected by the naked eye. In order to study the building upof Hwith time, the last authors measured the soiling of glass panesexposed to a variety of European urban environments for morethan 2 years and used the results to propose multi-linear(Lombardo et al., 2010) or non-linear neural network (Verney-Carron et al., 2012) statistical models linking this increase toenvironmental factors such as the atmospheric concentrations oftrace gases (NO2, SO2) and particulate matter<10 mm (PM10).

In the present work we favor a more physical and thereforemore explanative approach. In particular we intend to addresssuccessively two different questions: 1) what are the factorsconditioning the rate at which mass accumulates? and 2) how doesH increase with the accumulated mass?

The first point is theoretically quite complex because the aerosolmass concentration at the experimental site, its more or lesssporadic time fluctuations, the size-distribution of the particles,their reactivity.must all be key factors ruling the accumulation ofparticulate matter on the glass surface. In order to simplify theproblem and simulate the increase of mass measured on glasssurfaces exposed to urban pollution but sheltered from the rain,several authors (Lombardo et al., 2005a,b, 2010; Ionescu et al.,2006; Chabas et al., 2010) have proposed to use an empiricalfunction of the Hill’s type (Birch,1999; Motulsky and Christopoulos,2004). This mathematical model predicts an initially weak depo-sition rate which subsequently increases with time, and finallydecreases again to tend toward nil. In fact, the proposition of theHill function is mainly based on the preliminary assumption thata saturation effect must appear after some time of accumulation,which is not always supported by the measurements, at least whenthey are performed over durations of the order of 2 years (seebelow).

The question of how the deposited material alters the opticalproperties of the surface is also a challenge. The electromagnetictheory states that the scattering and absorption of light by airsuspended particles (Mie,1908; Van de Hulst, 1957) depends on thesize/wavelength ratio, composition, and to a lesser extent shape, ofthe particles. Several experimental studies have confirmed quali-tatively the validity of these theoretical predictions for particlesdeposited on solid surfaces. For instance, Brooks and Schwar (1987)showed that the modification of reflectance of glossy surfaces issensitive to the size of the dust particles deposited on them. Morerecently, Favez et al. (2006) showed that absorption is mainlycontrolled by the strongly absorbing Black Carbon component ofthe deposited material whereas diffusion is controlled by the

soluble-ions fraction of the deposit. However, the role of the surfaceon which the particles accumulate has never been assessed. Inparticular, multiple scattering must significantly alter absorptionand scattering in the case of more or less closely packed particlessuch as those accumulated on the surface of materials. Our aim is topropose a new operational, more physically-based model of theevolution of the haze which could be used in a variety of envi-ronments of the urban type to predict soiling of glass surfaces.

2. Material and methods

2.1. Available data

The database upon which this study is based was built upthrough different field exposure campaigns conducted within tworesearch projects: the MULTI-ASSESS and the Long Term Soiling(LTS) programs. Basically, samples were exposed at 6 sites (London,Krakow, Prague, Athens, Paris e Saint-Eustache, Rome-MonteLibretti) characterized by different environments ranging from theSuburban to the urban types. In addition, the data collected at 5urban (Gonesse), suburban (Paray-Vieille-Poste, Issy-les-Moulineaux, Bobigny) and rural (Fontainebleau) sites of the AEROprogram are also used here as an independent dataset to test thequality of the proposed model. Further details about these expo-sures can be found in Favez et al. (2006) and in Lombardo et al.(2005b, 2010).

For each campaign 10� 10� 0.2 cm glass panes silico-soda-limein composition (Planilux�) were exposed in two contrastedconditions: sheltered and unsheltered (except for the LTS program)from the rain. According to the ISO8565 standard (Kucera et al.,2007), sheltered samples were exposed vertically in a ventilatedbox or under awindshield upon awall whereas unsheltered samplewere positioned on a wooden rack, with an inclination of 45� andfacing South. The exposed glass panes were withdrawn regularlyafter durations ranging from 3 months to more than 5 years(according to the program).

The analysis of data begins with the long-term series collectedin the frames of Multi ASSESS and LTS programs. Data are used forreanalyzing, characterizing, and understanding the increase withtime of the mass deposited on glass panes exposed to pollutedenvironments. The data is then used for analyzing the correlationbetween the characteristics of the deposit and the haze, which isnecessary for understanding the impact of mass deposition on theglass optical properties. Note that in order to cover a range ofexposures representative of the variety of real outdoor conditions,samples exposed under shelters and samples exposed to rain areboth, when available, considered in this part of the study. Then,after having explained the variability of the mass deposition inurban environments and the implications of the characteristics ofthe particle-deposit for the haze we develop a new physically-based parameterization of the increase of haze with time valid forsheltered conditions. Finally, the quality of the proposed parame-terization is tested by comparing its prediction with a completelyindependent set of haze values measured in the frame of the AEROprogram. Note that the corresponding experimental data werecollected at 6 different locations of the Greater Paris area and can befound in the final report of the study available online (in French) athttp://www.airparif.asso.fr/_pdf/publications/Rsuies.pdf.

2.2. Sample characterization

2.2.1. Mass and bulk composition of the depositAfter cleaning with dust-free paper impregnated with de-

ionized water the face opposite to the one exposed to ambientpollution, the glass panes were analyzed in order to access themass

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and the composition of the deposit. Assuming that the mass of theglass panels remained constant, the mass of the deposit per surfaceunit (M, in mg cm�2) was simply obtained by weighing them beforeand after exposure with a Mettler AE240 Balance (accu-racy � 100 mg). The chemical characterization of the deposit wascarried out on separate aliquots of the sheltered sample to quantifythe soluble, the insoluble, and the carbonaceous (Black Carbon (BC)and Particulate Organic Matter (POM)) fractions of the deposit.Practically, the major soluble ion concentrations were quantified byIon Chromatography analysis (using a Dionex DX-600) of thesolution obtained by rinsing the glass deposit. Note that theprotocol used allows the detection of inorganic ions only. Followingthe method of Cachier et al. (1989), carbon analysis comprised theevaluation of the total carbonaceous (TC) and organic carbon (OC)contents of the aerosol by Thermocoulometric measurementsapplied to two glass portions submitted to different thermictreatments. The particulate organic matter (POM) is then estimatedby multiplying the OC value by a conversion factor (1.6). Finally, theinsoluble fraction was obtained by deducting the soluble andcarbonaceous fractions from the total mass. Except for theunsheltered exposure, whose original data are presented for thefirst time in this paper, results reproduced here were previouslypublished in Favez et al. (2006) for the MULTI-ASSESS and inLombardo et al. (2010) for the LTS and AERO programs. Therefore,we refer the reader to these papers for further details on theanalytical methodology.

2.2.2. Size-distributionIn this study, a newmethod has been designed for assessing the

size-distribution of the deposit present on the glass surface. One ofthe advantages of this method based on the analysis of profilesacquired with a Veeco NT1100 profilometer is that it is non-destructive and relatively fast. It also allows detection of submi-cron particles which are too small to be observed with opticalmicroscopes.

The original purpose of the profilometer is to scan the surface ofa sample in the vertical direction. It uses interferometric methodsfor scanning precisely the elevation of the surface above a flatreference plane with a vertical resolution around 5 nm.

In the horizontal (xy) plane, the instrument field of viewcorresponds to 120 � 120 mm square fields in which individualsegments of length 120 mm can be scanned. The step of the hori-zontal displacement (also hereinafter referred to as ‘the pixel’)along these segments is fixed (0.16 mm).

Basically, the sizing method assumes that the presence ofa particle on the glass surface creates a detectable local enhance-ment of its elevation. Practically, a threshold correspondingapproximately to the dimension of the underlying surface irregu-larities is selected. In the analysis of the profiles, all the consecutivepixels above this threshold are considered as belonging to a uniqueparticle which supposes that the individual particles are wellseparated. Note that the size of a particle is measured in the hori-zontal plane and that this size is necessarily a multiple of the ‘pixel’.

In order to achieve representative size-distributions,a minimum of ten 120 � 120 mm square fields are chosen atrandom on the surface of the exposed glass samples and from 4 to6 equidistant lines parallel to one of the sides are scanned in eachof these fields. In all, more than 40 profiles are examined, whichcorresponds to between a few hundreds and more than 1000individual particles (see Section 3.1.3). The relative size-distribution of the deposits is obtained by distributing theseparticles in seven diameter classes of equal logarithmic widthsbetween 0.2 and 25.6 mm. In order to check whether the numberof counted particles is large enough to yield statistically repre-sentative size-distributions, it is also possible to study the

evolution of the size-distribution versus the number of scannedprofiles. It is observed (results not shown) that the particle size-distribution becomes fairly stable above 25 profiles, approxi-mately. The variability of the fraction represented by each sizeclass for a number of profiles between 25 and themaximum is alsouseful for quantifying the accuracy of the method. For all sizeclasses, the uncertainty on the results lies between 1 and 5%.

2.2.3. Optical propertiesThe accumulation of particulate matter on the surface of

transparent materials such as glass panels modifies light trans-mittance and reflectance. These optical alterations can be quanti-fied using a VIS Spectrometer (Lambda 9 and 650, PerkineElmer,accuracy respectively 0.2 and 0.1 units). In this instrument cali-brated with a D65 standard illuminant, the light produced bya halogen lamp illuminates the glass samples normally and severaloptical parameters are measured between 380 and 780 nm witha step of 10 nm. These parameters, expressed in % of the incidentlight, include the total reflectance (R(l)) and the total (TL(l)) anddiffuse (Td(l)) transmittances. The spectral haze (H(l)) can bederived from these measurements as the ratio of Td(l) to TL(l).

HðlÞ ¼ TdðlÞ=TLðlÞ (1)

The integration of H(l) between 380 and 780 nm yields thevalue of the haze (H) used as a standard quantification of the opticaldegradation of glass panels in the industry.

H ¼�

1780� 380

� Z780

380

HðlÞdl (2)

3. Results and discussion

3.1. Characterization of the mass deposit

3.1.1. Mass accumulation with time

a) Sheltered conditions

As already stated above, exposition durations of several yearswere achieved in the frame of theMULTI-ASSESS and LTS programs.The corresponding results allow determination of the particleaccumulation flux over periods of more than 2 years at 5completely different European locations (Athens, London, Krakow,Prague, and Rome), and for more than 5 years at the Paris experi-mental site.

As can be seen in the results reported in Table 1, for comparableexposure durations the order of magnitude of the deposited masscan differ notably from one site to the other. The average accu-mulation flux (Fd,mean in mg cm�2 day�1) calculated over the wholeexposure duration is much larger at the Roadside than at theBackground sites. For instance, the absolute maximum of Fd,mean isobtained in Athens (0.81 mg cm�2 day�1) followed by London,Krakow, and Prague (0.52, 0.38, and 0.10 mg cm�2 day�1, respec-tively) but deposition is slower by one order of magnitude at therural site of Rome (0.039 mg cm�2 day�1) or at the Paris one(0.033 mg cm�2 day�1). In this last case, a possible explanation forthe low Fd,mean value is that, though exposed in a downtownlocation, the glass panels were positioned at the top of a 40 m-hightower surrounded by a pedestrian area. The evolution of thedeposited mass also varies according to the site. At the Suburbansite of Rome where the deposition flux is small and the exposureduration limited to 826 days, the deposited mass does not exceed

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32 mg cm�2. In this case the accumulation of mass with time is alsoalmost perfectly linear (M ¼ 0.04t, r2 ¼ 0.96, n ¼ 8) (Fig. 1). In Paris,the deposition flux is in the same order of magnitude as in Romebut because the exposure duration was much longer (2102 days), itbecomes possible to detect a departure of the mass accumulationfrom the linear trend (Fig.1). Indeed, accumulation at this site tendsto slow downwith time. At the sites of Athens, Krakow, and LondonM also increases regularly with time but faster than just linearly.This shows that in spite of the probable high-frequency temporal

fluctuations, typical of the atmospheric gas and particle concen-trations in urban environments, the averaging of the depositionover long time periods generally results in a regular and smoothincrease of the mass. With its sudden increase of the accumulatedmass observed between 300 and 400 days of exposure, Krakowseems to be the only exception to this rule. The reason for thisdiscontinuity is probably due to a sudden increase in the atmo-spheric particulate concentration, but because aerosol concentra-tion and chemical composition were not monitored in real time atthe experimental site this point cannot be further elaborated on.Notwithstanding this exception, the fact that the accumulatedmassdoes not seem to have reached an upper limit even after severalyears could question the assumption that mass deposition shouldsystematically saturate after some time. In any case, the observa-tions show that the removal processes acting in dry conditions arenot efficient enough to counterbalance the accumulation ofparticulate matter on the glass panels during the first years ofexposure.

At sites like Athens and London, the fact that M increases withtime faster than linearly (Fig. 1) suggests that the first depositedparticles could modify the panel surface properties in such a waythat deposition of the following particles is facilitated. Conversely,in the case of Paris the first particles seem to hinder deposition offurther ones which results in M increasing with time less rapidlythan the linear trend. The reasons for these different behaviorsmust probably be sought in the different environmental conditionsprevailing at the various experimental sites and their impact on thephysical characteristics of the particulate matter accumulating atthe glass surface.

Fig. 1. Examples of increase with time of the mass deposited on the surface of glasspanels exposed in sheltered conditions. Results were obtained in the frame of theMULTI-ASSESS and LTS programs.

Table 1Mass of the deposit accumulated per surface unit (M, in mg cm�2) and the corresponding haze (H, in %) measured on the glass panels after an exposition of duration t (in days).At the 5 sites of the MULTI-ASSESS program both sheltered (shelt.) and unsheltered (unshelt.) expositions were considered whereas only sheltered conditions were used at theParis Saint-Eustache (Paris SE) site. The type of the environment characterizing each site is also indicated.

Site t Shelt. Unshelt. Site t Shelt. Unshelt.

M H M H M H M H

Athens Roadside 0 0.0 0.8 0 0.8 Krakow Urban Background 0 0.0 0.8 0 0.892 e 5.2 3.67 5.2 86 0.83 1.2 e 5.6

182 96.7 8.5 37 5.4 178 16.5 2.7 3.0 4.1276 170.0 8.6 43 7.4 273 29.5 3.3 e 7.1373 217.3 13.4 e 6.6 367 e 7.3 e 4.6464 343.7 22.2 40 13.3 435 195.7 12.2 18.2 3.9548 444.7 22.9 28 9.8 519 e 13.0 e 3.7853 e 31.7 e e 616 266.7 15.7 28.7 6.3

738 281.8 15.9 18.0 7.7London Roadside 0 0.0 0.8 0.0 0.8 Rome-Monte Libretti Suburban 0 0.0 0.8 0 0.8

91 44.0 5.5 0.3 2.3 90 1.0 1.0 78.3 12.8186 58.7 7.2 e 1.5 182 4.3 1.7 46.7 7.0272 122.3 11.0 17.3 3.3 274 13.0 2.9 15.3 5.0368 152.3 14.1 e 4.0 369 12.0 3.3 7.0 4.2453 178.7 15.0 e 1.7 460 18.0 2.3 34.7 0.7560 248.3 19.1 4.0 2.2 552 22.7 3.7 12.7 5.7748 356.0 33.7 5.3 12.0 644 29.0 4.4 83.3 5.4840 439.0 36.1 0.0 0.8 826 32.0 6.2 64.0 9.0

Prague Urban Background 0 0.0 0.8 0.0 0.8 Paris SE Suburban 0 0 0.4 e e

88 5.3 2.3 15.7 7.1 14 4.3 2.1 e e

180 44.2 5.0 e 3.5 25 4.1 3.6 e e

276 45.8 4.4 e 3.0 56 7.3 1.6 e e

364 66.7 7.1 6.8 5.2 88 7.7 2.7 e e

452 79.7 7.5 11.2 4.5 135 7.2 3.2 e e

560 e 9.8 e 3.6 193 10.8 3.5 e e

732 81.7 9.5 17.7 4.9 273 9.2 4.8 e e

842 85.7 10.6 31.3 5.9 357 20.0 5.3 e e

597 25.7 5.4 e e

877 35.4 6.3 e e

1087 40.3 6.1 e e

1354 33.6 7.5 e e

1638 48.7 7.6 e e

2102 68.7 10.1 e e

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Independently of the type of mass accumulation behavior thedeposition velocity (V) appears generally to be a function ofM. If weadopt the simplest possible (linear) expression for V, this leads to:

V ¼ V0ð1� aMÞ (3)

In this equation, V0 is the deposition velocity of particles on aninitially perfectly clean glass, and a reflects the effect of particledeposition on the capacity of the surface to retain more particulatematter. This last parameter cannot be determined precisely in thecase of Rome because of the small accumulated mass, but it ispositive in the case of Paris and negative for the other sites.

Based on the definition of the deposition velocity, the massdeposition flux (Fd) at the glass surface can be written as theproduct of V and the atmospheric mass concentration (C), whichyields:

Fd ¼ dMdt

¼ CV0ð1� aMÞ (4)

Note that in this equation CV0 represents the initial depositionflux, which is to say the flux on the clean surface.

As already explained above, the smooth increase ofMwith timeshows that the rapid fluctuations of C can be neglected when tryingto derive an expression of the increase of M with time. In theseconditions, integrating Equation (4) is straightforward. With thecondition that M is initially nil, one obtains:

M ¼ 1a½1� expð�aCV0tÞ� (5)

When a is positive, M tends toward 1/a after an infinite expo-sure. Practically, 90% of this final value is obtained after:

t90 ¼ ln10aCV0

(6)

In contrast, Equation (5) predicts no upper limit for the massaccumulation when a is negative. The numerical values of theunknown quantities (a and CV0) appearing in Equation (5) can alsobe determined for each site by application of a least square iterativeroutine. Generally, the obtained fit is excellent as demonstrated bythe values of the correlation coefficient quite close to 1 (Table 2).Note that Paris is the only case for which mass deposition is pre-dicted to saturate but only after more than 14 years of exposure insheltered conditions (t90 ¼ 5420 days).

b) Unsheltered conditions

The risk of breaking at least partially the glass samples inunprotected conditions is larger than in sheltered conditions.Combinedwith the fact that no samples were exposed to the rain atthe Paris site, this explains the number of missing mass values inTable 1. However, the examination of the results reported in thistable reveals that the mass accumulated over the panes exposed to

the rain at any of the 5 sites of the MULTI-ASSESS program neverexceeds 90 mg cm�2, which is to say 5 times less than the maximummeasured in sheltered conditions. Contrary to what was observedwith the panels exposed under shelters, the accumulation of masswith time is also erratic. This shows not only that rainwashes awaya significant part of the deposits, thus limiting their importance, butalso that the sporadic occurrence of the rain events destroys anypossibility of observing a significant correlation between theaccumulated mass and time.

3.1.2. Chemical compositionThe main results on the chemical composition of the deposit

(insoluble, soluble, BC, and POM fractions) performed by Favez et al.(2006) on the samples collected at the 5 sites of the MULTI-ASSESSprograms are summarized in Table 3. They show that the inter-sitevariability is primarily due to differences in the shares of theinsoluble mineral fraction on the one side, and of the particulateorganic matter on the other side. At the rural site of Rome, theemission of organic compounds by local vegetation probablyexplains that the POM fraction is maximal (23%). This interpreta-tion is supported by the large value of the POM/BC ratio (3.8)(Table 3) typical of the carbonaceous species emitted by biogenicprocesses (Cachier et al., 1991; Alfaro et al., 2003). The contributionof the insoluble minerals is also minimal (50%) at this Suburban siteand maximal at the two Urban Background and Roadside exposuresites (66 and 63% for Krakow and Athens, respectively) due to theremobilization of coarse mineral particles by local traffic. Theseconsiderations suggest that the POM/Mineral ratio could beconsidered as an indicator of the remoteness of an experimentalsite, with values increasing from 0.13 for the location most affectedby urban activities (Athens) to 0.46 for the rural case (Rome).

3.1.3. Surface distribution and size-distributionOne glass sample exposed in sheltered conditions at each site

(Athens, Prague, Krakow, Rome, London, and Paris) was chosen forbeing analyzed with the Veeco NT1100 profilometer. For the sake ofcomparison one sample exposed to the rain in Athens was alsoselected. Beside that they had been exposed in contrasted envi-ronments, the first criterion used for the selection of the sampleswas that their surface load should not be too large (between 28 and46 mg cm�2). Indeed, this is necessary for avoiding situations inwhich the individual particles would be so closely packed that theprofilometer would no longer be able to separate them. The secondselection criterionwas that themasses accumulated on the samplesshould be in the same order of magnitude for simplifying subse-quent comparison of the results. The exposure durations andsurface loads for the 7 samples finally retained are reported inTable 4.

Results show that the total number of counted particles withdiameters larger than 0.2 mm ranges from approximately 300(London) to more than 1200 (Athens in unsheltered conditions).The average number of particles counted per line is in the order of

Table 2Initial deposition flux (CV0) and mass accumulation parameter (a) retrieved byfitting Equation (5) to the mass measurements performed on samples exposed at 6different European urban sites. The correlation coefficient (r2) is also reported toshow the quality of the adjustment.

Athens London Krakow Rome Prague Paris

CV0 (mg cm�2

day�1)0.41 0.34 0.24 0.04 0.19 0.04

a (mg cm�2) �5.5810�3

�2.7910�3

�5.1910�3

e �1.610�3

9.610�3

r2 0.99 0.99 0.92 0.96 0.95 0.95

Table 3Fractional composition of the mass accumulated (in %) at the surface of glass panelsexposed under shelters at the 5 sites of the MULTI-ASSESS program, (adapted fromFavez et al., 2006). BC stands for black carbon and POM for particulate organicmatter.

Rome London Krakow Prague Athens

Insol. Mineral 50 52 66 59 63Soluble ions 21 27 18 23 24BC 6 6 4 4 5POM 23 15 12 12 8POM/Mineral 0.46 0.29 0.18 0.20 0.13

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5e30, which means that at these relatively low surface densitiesthe individual particles are still well separated and that closelypacked layers of particles are still not formed for this range ofmasses as requested by the profilometer sizing method.

The relative size-distributions reported in Table 4 all displayamaximum in the 0.8e1.6 mm size-range but on closer examinationthe deposits appear to be generally richer in fine particles (particleswith a diameter <0.8 mm) at the background sites (Paris and Rome)than at the other sites. The ratio of these fine particles to the coarseones (defined as those with d > 1.6 mm) can be used for quantifyingthis difference more precisely. For sheltered conditions, the fine/coarse ratio decreases from approximately 2.5 at the backgroundlocations of Paris and Rome to 0.5 at the Roadside site of Athens. Inthis range of variability, London, Prague, and Krakow are interme-diate cases. Also noteworthy is that for the 5 sites for which thechemical composition of the deposit was previously determined,the POM/insoluble mineral ratio is found to be strongly, and posi-tively, correlated to the fine/coarse ratio (Fig. 2). This is consistentwith the fact that carbonaceous species such as POM belong mostlyto the submicron range of diameters whereas insoluble minerals

are essentially associated with supermicron sizes (e.g. Seinfeld andPandis, 1998).

The results of Athens also reveal the influence of the type ofexposure (sheltered versus unsheltered) on the size characteristicsof the deposit (Table 4). For a mass deposit of 28 mg cm�2 inunsheltered conditions, the average number of particles countedper line (30) is 2.5 larger than in sheltered conditions (12), and thiseven though the deposited mass (42 mg cm�2) is larger in this lastcase. At the same time, the proportion of particles with diameters>1.6 mm decreases from 44.8% to 20.8%. This suggests that the raindoes not just suppress efficiently the coarsest particles from thesurface; it also enhances the number of the finest particles. Theprocess leading to this enrichment in fine particles is most probablya combination of 1) the aqueous dislocation of preexisting coarseaggregates of fine particles previously deposited at the surface indry conditions, 2) a preferential detachment of coarse particles(corresponding mostly to mineral particles), consistent with thesize of particles scavenged by precipitation (e.g. Andronache, 2003)and 3) formation of fine particles directly at the surface of the glassby the heterogeneous chemistry reactions taking place in presenceof liquid water (Lombardo et al., 2005a; Chabas et al., 2008).

3.2. Impact of particle deposition on the haze

Results of the haze measurements performed on the glasssamples exposed at the MULTI-ASSESS and Paris sites are reportedin Table 1. In the following study, we will focus first on the resultsobtained in sheltered conditions because the mass of the materialaccumulated at the surface of the glass panels protected from therain covers a wider range of values than in unsheltered conditions.In a second stage, wewill try to detect the changes due to the actionof rain by comparing the results obtained in unsheltered conditionswith the previous ones.

3.2.1. Mass haze-efficiency in sheltered conditions

a) Observations and interpretation

As expected, it is observed that the haze generally tends toincrease at each site with the deposited mass. However, a closerexamination suggests that the correlation between H and M is notsimply linear. In order to document this pointmore precisely, theH/M ratio can be plotted against M (Fig. 3). Then, it becomes obviousthat H/M decreases first rapidly before tending eventually towarda constant for M > 100 mg cm�2, approximately. This suggests 1)

Table 4Results of the profilometer size-analysis of the deposits present at the surface of glass panels exposed in sheltered (6 samples) and unsheltered (1 sample) conditions. In eachcase, the exposure duration, the mass of particles (M) per surface unit, the number of analyzed lines, the total number of counted particles (N), and their distribution in the 7diameter classes defined between 0.2 and 25.6 mm are reported. The ratio of the number of particles with diameters <0.8 mm (Fine) to those with diameters >1.6 mm (Coarse)has also been calculated.

Paris (shelt.) Rome (shelt.) London (shelt.) Krakow (shelt.) Prague (shelt.) Athens (shelt.) Athens (unshelt.)

Duration (days) 1347 644 91 273 276 92 548M (mg cm�2) 33.6 29 44 29.5 45.8 42 28Lines 57 46 47 54 41 49 41

N (%) N (%) N (%) N (%) N (%) N (%) N (%)

0.2e0.4 122 (14.9) 121 (15.5) 52 (16.9) 61 (15.1) 113 (15.0) 52 (9.0) 136 (11.1)0.4e0.8 256 (31.3) 199 (25.5) 77 (25.0) 88 (21.8) 150 (19.9) 84 (14.6) 306 (25.0)0.8e1.6 292 (35.7) 329 (42.2) 100 (32.5) 138 (34.2) 215 (28.5) 182 (31.6) 526 (43.0)1.6e3.2 91 (11.1) 79 (10.1) 46 (14.9) 73 (18.1) 173 (22.9) 135 (23.4) 185 (15.1)3.2e6.4 40 (4.9) 26 (3.3) 25 (8.1) 35 (8.7) 69 (9.1) 81 (14.1) 51 (4.2)6.4e12.8 14 (1.7) 16 (2.1) 5 (1.6) 7 (1.7) 24 (3.2) 36 (6.3) 13 (1.1)12.8e25.6 4 (0.5) 10 (1.3) 3 (1.0) 1 (0.2) 11 (1.5) 6 (1.0) 5 (0.4)Total 819 780 308 403 755 576 1222Fine/Coarse 2.54 2.44 1.63 1.28 0.95 0.53 1.74

Fig. 2. Correlation between the particulate organic matter (POM) to insoluble mineralfraction (Insol. Miner.) ratio in the deposit and the fine (d > 0.8 mm) to coarse(d > 1.6 mm) particles ratio for the 5 sites of the MultiAssess programs.

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that the first deposited particles are more efficient at creating hazethan the following ones, and 2) that after deposition of a certaininitial amount of particles (around 100 mg cm�2), the haze increaseslinearly with further particle deposition. This behavior could beexplained by the fact that for the smallest values of M the averageinter-particles distance is still large and that in these conditions theparticles behave as individual light-scatterers. Then, with inter-particle distances decreasing the effects of multiple-scatteringbecome more strongly felt. These effects include a reduction ofthe mass haze-efficiency until the particles become so numerousthat they finally form densely-packed layers. As suggested previ-ously, this likely occurs for M larger than a few tens of mg cm�2,approximately. After this stage is reached, the continuing accu-mulation of particles only increases the thickness of the particlelayer and H increases linearly with M at a rate conditioned in greatpart by the size-distribution of the deposited particles. This inter-pretation is supported by the evolution of the spectral dependenceof the Haze when M increases. From this point of view, the case ofParis is particularly illustrative (Fig. 4a). Indeed, as predicted byMietheory for well separated particles of submicron sizes, the spectralhaze measured on the glass panels exposed at the Paris site isgenerally a decreasing power function of wavelength in the solarspectrum:

HðlÞ=H380 ¼ ðl=380Þ�a (7)

However, the exponent a involved in this equation decreasesprogressively from around 0.77 for an exposure of less than 3months (88 days) to stabilize eventually around 0.33 after anexposure of more than 1000 days. This suggests that the increas-ingly smaller distances separating the particles as they accumulateat the glass surface induces effects similar to those of multiplescattering in 3D media. In particular, scattering at the largerwavelengths of the solar spectrum is preferentially enhanced ascompared to the smaller wavelengths (Ben-David, 1993;Mishchenko et al., 2007), which finally results in a smootherspectral dependence of the haze.

According to the electromagnetic theory, the final value of thespectral dependence of the haze achieved for packed layers shouldalso be sensitive to the size-distribution of the individual particlesforming them. More precisely, the coarser the particles, the smallera should be. This is confirmed by the normalized spectral depen-dence of the haze measured on samples exposed for at least 18months at the MULTI-ASSESS and LST sites (Fig. 4b). In the case ofLondon, H(l) is practically independent of the wavelength

(a ¼ 0.03) but increases with it in Krakow, Prague, and especiallyAthens (a ¼ �0.14). At these 3 sites, the reversal of the spectralbehavior as compared to the cases of Paris and Rome can beexplained by the large proportion of coarse particles in the deposits(see Table 4). The comparison of the haze measured on the samplesexposed for 18 and 21 months in sheltered and unshelteredconditions, respectively, at the Prague site, suggests that theenhancement of the relative proportion of fine particles by the raingreatly increases the spectral dependency of H(l).

b) Parameterization of the mass haze efficiency

The evolution of the mass haze-efficiency with M can bedescribed by the simple sum of the limit, (H/M)lim, toward whichthe ratio H/M tends at large M and of a decreasing function (g(M)):

HM

¼�HM

�lim

þ gðMÞ (8a)

As can be seen also on Fig. 3, (H/Mlim) is significantly lower in thecases of the Athens and Krakow sites (0.05 � 0.01% mg cm�2) thanfor the London site (0.08 � 0.01% mg cm�2), or for the Paris site(0.12� 0.01% mg cm�2). Note that at sites such as Athens or London,the mass accumulated after the shortest (3 months) exposure isalready too large for the decreasing trend to be easily distinguishedby the naked eye, and that the asymptotic behavior only can beobserved (Fig. 3). Conversely, for Paris where themass deposition ismuch slower, (H/M)lim is approached only after an exposure ofseveral years.

In order to document the exact shape of g(M), the difference H/M e H/Mlim, can be plotted againstM. On a LneLn scale the scatter-plot is almost perfectly linear (y ¼ �0.898$ln M þ 0.203; r2 ¼ 0.87;

Fig. 3. Evolution of the haze creating efficiency (H/M) of the deposit with massaccumulation (M) at the surface of the glass samples exposed in 6 European urbanenvironments.

Fig. 4. Spectral dependency of the haze normalized to the 380 nm value for glasssamples exposed at the Paris site (a) and at 6 different European locations (b). Theexposure durations are given in days.

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n ¼ 47), showing that g(M) can be approximated by a decreasingpower function. Finally, Equation (8a) can be rewritten as:

HM

¼�HM

�lim

þ pM�q; (8b)

In this equation, the constants p and q are equal to 1.22 and0.898, respectively, when M is expressed in mg cm�2.

In order to visualize the quality of the adjustment, the increase ofthehazewithM aspredictedbyEquation (8b) can be compared to themeasurements. In this comparison,pandqare consideredasfixedbut(H/M)lim is allowed to vary and takes successively the values deter-mined for Athens, London, and Paris (0.05, 0.08, and 0.12, respec-tively). In spite of the scatterof the experimental points, especially forthe smallest deposited masses, Fig. 5a shows that a relatively goodagreement is obtained. In particular, the initial change in the rate ofevolution of the haze withM and the subsequent linear behavior arewell reproduced. This was not the case with the doseeresponsemodels proposed in previous studies. Indeed, although they wereable to capture the final linear trend these models systematicallyunderestimated the haze for the smallest accumulated masses(Lombardo et al., 2010). Furthermore, Verney-Carron et al. (2012)published a new statistical model to predict glass soiling confirm-ing that the exponential function is more adequate to retrieve data,especially for the short term exposures.

3.2.2. Mass Haze-efficiency in unsheltered conditionsThe haze measured on the panels exposed to the rain at the

same six sites than before is plotted against M on Fig. 5b. It can be

seen that the measurements are generally well above the predic-tions of Equation (8b) for any which one of the Athens, London, andParis sites in sheltered conditions. This shows that after undergoingthe action of rain the deposit present at the surface of the panelbecomes more efficient at creating haze. A good example of thisenhancement is given by the case of Prague. In sheltered condi-tions, M went up from 5.3 to 85.7 mg cm�2 between days 88 and842, and the corresponding increase of the haze is well reproducedby Equation (8b) in which H/Mlim is set equal to 0.08. For the sameperiod in unsheltered conditions, M fluctuates between 6.8 and31.3 mg cm�2 and according to Equation (8b) the hazewould remainless than 3% for this range of masses in sheltered conditions. This issignificantly less than the haze (around 5%) really measured on theunsheltered samples. This enhancement of the mass haze-efficiency for the unsheltered panels is most probably due to boththe alteration of the size-distribution and the compositional change(increase in the soluble salt fraction) resulting from the action ofthe rain.

4. Implications for the operational modeling of glass soiling

4.1. Proposition of an operational model

The analysis of the experimental results shows that in shelteredconditions the accumulation of mass at the surface of the glasspanels is regular and well described by Equation (5). The combi-nation of this Equation (5) with Equation (8b) also theoreticallyoffers the possibility of predicting the value of the haze for anylocation but this requires the determination of the 3 parameters(CV0, a, and (H/M)lim) involved in our parameterization of the haze.In fact, these 3 parameters are not independent. Indeed, we haveshown that their values are directly controlled by the environ-mental conditions prevailing at the experimental site. Moreprecisely, 3 main types of locations can be distinguished based onthe magnitude of the mass accumulation flux. The first typecorresponds to Suburban sites such as Paris and Rome whereparticle concentration is low and therefore accumulation slow(small CV0). At sites of this type, the deposit is also particularly richin fine particles, which in turn has an impact on the sign ofa (positive) and on the magnitude of (H/M)lim (relatively largevalues). At the opposite of the previous category, one can define theRoadside locations, such as Athens or London. They are character-ized by a heavy traffic and the largest values of CV0. At these sites,the proportion of coarse particles in the deposit can vary but issignificantly larger than at Suburban sites. This importance of thefraction represented by coarse particles leads to lower values of (H/M)lim and to negative values of a. Finally, a category of UrbanBackground locations, such as Prague and Krakow, can be definedbetween the two previous extremes.

For facilitating the operational prediction of the evolution of Hwith time at a given location, we propose to 1) assume that anyexposure site can be distributed in either one of the 3 previouscategories and 2) adopt for these categories average sets ofparameters derived from our analysis. These parameters arereported in Table 5.

Fig. 5. Increase of the haze (H in %) with the mass of the deposit (M in mg cm�2).Measurements were made in sheltered (a) and unsheltered (b) conditions. Thecontinuous lines correspond to the haze predicted by Equation (8b) for the sites ofAthens (or Krakow), London, and Paris in sheltered conditions. The dotted line isa model assuming that the haze is simply proportional to the accumulated mass (M). Inthis case, the haze is notably underestimated for the short exposure durations.

Table 5Summary of the parameters retained for characterizing in the modeling each of thethree site categories (Suburban, Urban Background, and Roadside) defined in thetext.

Category Roadside Urban Background Suburban

CV0 (mg cm�2 day�1) 0.40 0.18 0.05a (mg cm�2) �4 10�3 �4 10�3 10 10�3

(H/M)lim (% mg cm�2) 0.05 0.08 0.12

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Naturally, adopting one of the pre-fixed sets of parameters ofTable 5 instead of its own CV0, a, and (H/M)lim values for repre-senting any given site of the LTS and MULTI-ASSESS programsconstitutes a simplificationwhich must lead to a degradation of thehaze prediction. In order to test whether this degradation issignificant or not, the haze calculated using the preset parametersand Equations (5) and (8b) are compared to the 52 haze valuesmeasured at the 6 experimental sites. The agreement between thecalculated and measured haze is found to be quite satisfactory(Fig. 6) as indicated by the values of the slope and correlationcoefficient very close to 1 (0.99 and 0.92, respectively) and by theintercept with the vertical axis (0.19) close to 0. The fact that theagreement is correct even for the small values of the haze indicatesthat the proposed model does not suffer from the limitations of thepreviously-developed parameterizations which systematicallyunderestimated those small values of H.

4.2. Validation of the model

The validation of the model must be performed using a datasetnot used previously in the elaboration of the parameterization. Thehaze measurements performed in the frame of the AERO programat 5 different suburban sites of the Paris area constitute such anindependent dataset. Based on the proximity of the experimentalsites to the traffic sources, the 5 locations have been classified asRoadside (Gonesse), Urban Background (Paray, Issy, Bobigny), andSuburban (Fontainebleau) sites. At each of these experimental sitesthe haze had been measured after 90, 180, 270, and 360 days ofexposure (see details in Lombardo et al., 2010). The good agreementobtained when comparing the calculated haze with the measuredone (Fig. 6, slope ¼ 1.03; r2 ¼ 0.79; n ¼ 23) confirms the ability ofthe model to predict the evolution of the haze at a series of 6completely different sites. It is also interesting to note that in sucha geographically-limited area as Paris and its surroundings, thesame variety of exposure sites can be encountered as in the broaderEuropean context of the MULTI-ASSESS program.

5. Summary and conclusion

In thepresent studywehave re-examined thedata collected in theframe of the MULTI-ASSESS and LTS programs whose experimental

sites are thought to be representative of the variety of conditionsencountered in European urban areas. For modeling the soiling ofglass panels in sheltered conditions, the sites can be convenientlysorted into three different categories: Roadside, Urban Background,and Suburban. At the Suburban sites, particulate matter accumulatesslowly on the surface at an initial rate of 0.05 mg cm�2 day�1, which isone order of magnitude lower than at the Roadside sites (about0.3e0.4 mg cm�2 day�1). Probably because coarse particles are lesseasily transported by atmospheric movements, the proportion ofsubmicron particles in the deposit is larger at Suburban sites than atthe Urban Background and Roadside ones. This size segregationexplains at least inpart the enrichment in carbonaceous species, suchas POM or BC which are known to be essentially located in thesubmicron range of sizes. Conversely, the proportion of supermicronmaterial particularly rich in insolublemineral particles is found to belarger at Urban Background and Roadside locations. These size andcompositional differences seem to have a direct impact on the rate atwhich mass accumulates at the surface of the glass panels. Moreprecisely, in the period of two years corresponding to the measure-ments performed at the Roadside and Urban Background sites massdeposition does not show any sign of limitation and even accelerateswith time. Conversely, mass accumulation tends to slow down at thesites of the Suburban type. Extrapolation of the results collected formore than 5 years at the Paris site suggests that saturation will beobtained after an estimated duration of 14 years. Note that except inthe frame of scientific programs specially designed to study thesoiling of glass on the long term, it is highly improbable that a glasspanel would remain exposed for such a long duration without beingcleaned. In consequence, the saturation predicted for the Suburbansites is largely theoretical.

Regarding the increase of the glass haze with the accumulatedmass, two successive phases can be distinguished. In the first phase,the density of the deposited particles increases progressively but isstill not large enough for closely-packed layers to be formed. Theeffects of multiple scattering on the characteristics of the haze arefelt more and more strongly as particulate matter accumulates.These effects include a progressive lowering of the mass haze-creating efficiency and a flattening of the spectral dependence ofthe haze. The second phase corresponds to a stage in which fulllayers of particles are now formed. This occurs for surface massdepositions of a few tens of mg cm�2. From then on, the hazeincreases simply linearly with further mass deposition at a rateconditioned by the size distribution of the deposit. In shelteredconditions, this rate varies from 0.05% mg cm�2 at the Roadsidelocations to 0.12% mg cm�2 at the Suburban ones. Because it greatlyenhances the proportion of fine particles in the deposit, the actionof rain on unsheltered panels results in a significant increase of thehaze-creating efficiency of the deposit.

From the observations of the MULTI-ASSESS and LTS programsa model describing the mass deposition with time in shelteredconditions and the subsequent increase of the haze, has beenproposed. Its application only relies on the possibility of classifyinga priori the experimental sites in one of the 3 pre-defined(Suburban, Urban Background, and Roadside) categories. Ascompared to the previous parameterizations relying solely onmathematical equations of the Hill type, this new model is morephysically explicit. It does not assume that the haze will system-atically reach a saturation state after long exposure durations, anassumption which, except at the Suburban site of Paris and prob-ably Rome, is contradicted by the observations performed overdurations of more than two years. The new model also representsmore accurately the initial stages of the soiling and avoids thesystematic underestimation of the haze in the first months ofexposure. This is a key point because these relatively short dura-tions are more in keeping with the frequency of the periodic

Fig. 6. Comparison of the modeled and measured haze (in %) using on the one handthe data of the MULTI-ASSESS and LTS programs (diamonds) and the data of the AEROprogram on the other hand (squares).

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maintenance (cleaning) operations usually performed in urbanareas.

Furthermore the comparison of the haze predicted by the modelwith the measurements of the AERO program validated the possi-bility of applying it in a variety of sites completely independent ofthose used for the model development. Although more physically-based, the new model also has it shortcomings. In particular, com-plementing it by a statistical module for predicting the occurrenceand intensity of rain events in a given location would be a necessarystep toward applicability in unsheltered conditions. Another impor-tant point is that the classification of a site in one particular categorymight need to be revised if its environmental conditions came tochange dramatically. For instance, the on-goingmeasurements of theParis experimental site suggests that due to the very importantrenovating activities and road works taking place at the very foot ofthe Saint-Eustache tower, the classification of the sitewouldprobablyneed now to be changed from Suburban to Roadside.

In fine, this paper shows that the classification of the experi-mental sites in 3 categories as well as the associated model can beused to predict the soiling incurred by glass surfaces (modernfaçades, protective glazing for stained glass windows.) success-fully. Indeed, one of the possible applications consists in theestablishment of risk maps. These maps, together with the relevantinformation on the chemical composition of the deposit specific toeach type of site, would permit the development of sustainablestrategies for the conservation and the protection of modern andhistorical building adapted to the environment of exposure ofmonuments; which is to say, adapted to the different levels of risk.For instance, the use of restoration products with photocatalyticproperties in order to limit organic pollution would be particularlyadapted to sites characterized by a high proportion of fine carbo-naceous particles.

Acknowledgments

The authors would like to thanks the colleagues of the MULTI-ASSESS project for taking care of the glass exposure at thedifferent sites. They are also grateful to the clergy of the Saint-Eustache Church (Paris) for allowing them to use their platformof the north tower for the exposure of the glass samples.

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