In order to study the relevance of aerosol dynamics on the fate of PN emitted from traffic in urban areas, the evolution of the particle size distribution with increasing distance from the roadside was modeled using the multicomponent aerosol dynamics model MAFOR . MAFOR uses a fixed sectional grid to represent the particle size distribution with size bins evenly distributed on a logarithmic scale. MAFOR has been evaluated against laboratory chamber data  and PN measurements at a motorway ; it has also been shown to compare well with the sectional aerosol dynamics model AEROFOR .

Aerosol processes considered in this study were condensation and evaporation of organic vapors, coagulation of particles due to Brownian motion, and dry deposition (particle deposition in contact with the street surface and other urban structures). In this study 120 size bins were used in the MAFOR model, to represent the aerosol size distribution ranging from particle diameters from 1 nm to 1 µm.

In the default configuration of the model, particles were assumed to be spherical and the enhancement of coagulation by van der Waals forces and viscous interactions was not taken into account. Additional sensitivity tests were performed to study the respective effects of fractal geometry and of van der Waals forces combined with viscous interactions on the model results. Further, effects of turbulent shear on coagulation between exhaust particles can be neglected for the timescale from roadside to ambient .

The various aerosol dynamical processes were treated by calculation of the temporal variation of the particle number concentration and the mass concentrations of each chemical component within each size section. Mass transfer of gas molecules to particles was calculated using the Analytical Predictor of Condensation scheme .

Dry deposition of particles was modeled according to , which accounts for the physical properties of both the air flow and the surface, as well as the physical properties of the particle size. In this approach rough surfaces are characterized by two length scales: the aerodynamic roughness and the so-called collection scale, which incorporates the effective size of collectors and a ratio of the airflow velocity at the top of the roughness elements to the friction velocity. Alternatively, MAFOR provides a treatment to calculate size-dependent deposition rates according to and .

The concept regarding condensation and evaporation between roadside and ambient environment applied in this study is based on the work of Zhang and Wexler (, ; , ). The effective behavior of condensable organic vapors from vehicular exhaust with respect to changes of the particle number concentration and the particle size distribution was modeled by introducing two different volatility classes: the n-alkane C22H46 (abbreviated as C22) representing semi-volatile vapors and the n-alkane C28H58 (abbreviated as C28) representing low-volatile vapors. Both organic compounds can condense or evaporate to or from particles during their transport downwind from the road. Vapor pressure of n-alkanes as function of temperature was adopted from the work by .

Carbonaceous aerosol in MAFOR is separated into (i) elemental carbon (ECp) from primary emissions, treated as a non-volatile substance, and (ii) organic carbon (OCp), treated as a volatile substance. In this study, organic carbon is assumed to be composed of organic acid (for background OCp) and the two n-alkanes (originated from vehicles). The organic fraction in the nucleation mode below 10 nm diameter was composed by 100 % of C28 in the roadside aerosol. A density of 1200 kgm-3  was used for ECp. The density of OCp was calculated as the weighted average of the densities of the organic compounds.

MAFOR is a one-dimensional model with downwind distance as spatial dimension; it is therefore necessary to couple it to a dispersion model, to simulate combined atmospheric dispersion and transformation processes. In order to approximate atmospheric dispersion, we used a simplified treatment of dilution of particle numbers. This procedure implies the assumption of a well-mixed state within each cross-wind cross-section of the plume. The assumption of a well-mixed state may overestimate the influence of the processes responsible for the temporal decrease of the PN, due to the non-linear nature of the involved processes (condensation and coagulation). Model runs were performed with different dispersion conditions to address the influence of aerosol processes for a wide range of meteorological dispersion regimes.

Emissions from traffic sources commonly contribute to particle size distributions with distinct modes, i.e., nucleation, Aitken, accumulation, and coarse mode. Formation of new liquid particles in the exhaust by nucleation of gases, such as sulfuric acid and semi-volatile organic substances, occurs during the first milliseconds  after release of the exhaust into the ambient air. On-road measurements by confirmed that the nucleation mode was already present after 0.7 s residence time in the atmosphere. Thus, it is practical to regard nucleation as a process that has already occurred, when one considers roadside concentrations. The evolution of vehicular emissions from the engine to the roadside concentrations was not considered in this study, as we used the particle size distributions measured at the roadside locations as a starting point.

Idealized scenarios were set up for the study of relevant aerosol processes (i.e., the dry deposition, the growth by condensation of gases and the coagulation of particles) and dilution by background air (see Fig. ).

We used a simple horizontal particle dilution parameterization, following the numerical power function y=a×x-b=a×(Ut)-b, where x (in m) is the distance from the roadside and U is the horizontal wind speed perpendicular to the road. The height of the air parcel (plume height), Hm (in m), containing the exhaust emissions, as function of time t (in s) during its travel away from the roadside at a specific wind speed was defined by Hm(t)=Hm,02+a×10-3×Utb2, where Hm,0 is the initial plume (or air parcel) height at the roadside. The particle dilution rate for use in the aerosol model was obtained by derivation of the above mentioned numerical power function as function of time. The change of particle number concentration, N (in particlescm-3), in size section i due to dilution with background air is dNidt|dilution=-btNi-Nbg,i, where Nbg,i is the number concentration of background particles in the same size bin. No additional emissions of particles or vapors are collected during transport from roadside to ambient in this idealized scenario.

Dilution parameters a and b that are used in Eqs. () and () for moderate dispersion conditions were derived from a fit of the modeled total number concentration to measured number concentration in different distances (below 100 m) from a major highway in Helsinki (LIPIKA campaign, case 10; Fig. 5 in , ). It was assured that the PN change in the distance up to 100 m was solely due to dilution with background air. Best fit was obtained with parameter values a=40 and b=0.5. For neutral conditions, the values a=86.49 and b=0.923 were reported for dispersion downwind of a motorway . Similar values were adopted for efficient dispersion conditions in this study (a=80.0 and b=0.90). For inefficient dispersion conditions, a and b were chosen to be typical for atmospheric situations with inversion and stagnant air. Details on the approximation of initial plume height, Hm,0, at the roadside are provided in Sect. S1 of the Supplement. Table  provides an overview of the set of meteorological and dilution parameters that were tested in sensitivity studies. Model simulations were forced by the applied dilution scheme to relax towards the size-binned particle concentrations of the background air, where the time constant of the relaxation was controlled by the respective dilution parameters.

The model simulations were started by assuming an initial chemical composition of the aerosol at the respective roadside traffic site and urban background site. Chemical composition of the urban background aerosol was estimated based on the measured PM2.5 and the mass fractions of the chemical components in PM2.5. Composition of the nucleation, Aitken, accumulation and coarse modes was estimated based on mass fractions for the urban background of Helsinki . Then mass concentrations of the respective lognormal modes were distributed over the discrete size sections of the model. The aerosol composition of the traffic-influenced aerosol at the traffic station was approximated by adding mass concentrations of OCp and ECp (from vehicle exhaust emissions) to the mass concentrations of the background aerosol. Fixed modal OCp : ECp ratios were used (nucleation mode: 100:0, Aitken mode: 80:20, accumulation mode 1: 40:60, accumulation mode 2: 60:40) based on the mass composition of vehicle exhaust particle emissions . Finally, the initial model number size distribution was fitted to the observed number size distribution at the traffic site for each of the campaigns, by variation of the geometric-mean mass diameter (by ±30 %) and the geometric standard deviation (within the range 1.5–2.0) in each lognormal mode.

The applied aerosol dynamics model makes no assumption regarding the equilibrium between organic vapor and the condensed phase at the roadside. If the gas-phase concentration of an organic compound is below the saturation concentration, the compound will evaporate from the particles, if it is above the saturation concentration, the compound will condense to the particles. During the road-to-ambient process, some compounds may continue condensing, while others begin evaporating, depending on the relative magnitude of their vapor pressures. In addition, the vapor pressure of the model compounds C22 and C28 is further modified by their molar fraction in the particle phase, according to Raoult's law, and by their molar volume and surface tension according to the Kelvin effect.

For the included campaigns, gas-phase concentration of n-alkanes and other condensable organic compounds have not been measured at the roadside locations. Measurements of n-alkane vapor concentrations in urban environments indicate typical concentrations of 5 ppt for the sum of the n-alkanes, but higher concentrations may occur (for more details see Sect. S2). obtained best fit between modeled and measured particle size distribution on a distance scale of 125 m near a major road in Helsinki when using roadside concentrations of one condensable organic vapor of the order of 1010 moleculescm-3 (ca. 0.4 ppb). Based on this, initial concentrations of 0.25 ppb C22 and 0.25 ppb C28 were used in the reference case (all campaigns and dispersion conditions). The background concentration of C22 and C28 was set to zero, forcing maximum dilution of the condensable organic vapors during travel of the air parcel away from the roadside.

Additional sensitivity tests were carried out to address uncertainties in the modeling with respect to (i) dry deposition of particles to urban surfaces, (ii) assumptions about the roadside concentrations of condensable organic vapors (represented as n-alkanes), (iii) the fractal geometry of soot particles and (iv) the enhancement of coagulation through van der Waals and viscous forces.

As the air parcel containing vehicle exhaust leaves street scale, it can be assumed to be advected through a network of streets, and over and around buildings, defined as the neighborhood scale with a characteristic length scale of 1–2 km. On the neighborhood scale, geometrical features dominate mean flow and mixing. Effects caused by buildings and other structures are disregarded in this study. Instead the flow was assumed to have a long fetch over a statistically homogeneous surface. However, different average surface types may have an impact on dry deposition of particles. In a series of tests the sensitivity of PN changes were studied, caused by dry deposition on various surface types and roughness conditions. Table  provides a summary of relevant parameters for dry deposition used in the reference case (all campaigns and dispersion conditions) and in the sensitivity tests (selected campaigns).

The parameterization used in the reference runs is thought to represent dry deposition to typical urban surfaces, i.e. streets and buildings (urban case). Values for friction velocity near surface, u*, and roughness height, z0, used in the urban case were adopted from the work of . Sensitivity tests for dry deposition were performed for the campaigns in Rotterdam and Oslo using the dilution parameters for moderate dispersion conditions.

The methodology by considers Brownian diffusion, interception, inertial impaction and gravitational settling as mechanisms for dry deposition to rough surfaces. They define a collection length scale to characterize the properties of rough surfaces. This collection length depends on the ratio Utop/u* (Utop is the wind speed at top of the canopy, i.e. at height zC) and to the effective collector size, dcol, of the canopy. The methodology by is a three-layer deposition model formulation with Brownian and turbulent diffusion, turbophoresis and gravitational settling as the main particle transport mechanisms to rough surfaces. introduced the effective surface roughness length F+ to relate roughness height and the peak-to-peak distance between its roughness elements. For a hydraulically smooth surface, F+ approaches zero. Parameters z0, zC and dcol are only used in the concept of while F+ is only used in the concept of . Size-dependent dry deposition velocities of particles were calculated with two different methodologies: the methodology of (short: KS2012) was applied in the reference case for all simulations. In addition the methodology of (short: H2012) was applied for all cases in the sensitivity test.

Figure  shows size-dependent dry deposition velocity of particles for the different cases listed in Table  for the two methodologies. The curve “KS2012 Urban” (thick black line) represents the parameterization used in the reference runs of this study. Dry deposition velocities calculated by H2012 for the urban case (“H2012 Urban”) agree with “KS2012 Urban” within a factor of 3 as a function of particle diameter. Results from the KS2012 methodology were not sensitive to changes of friction velocity within a range (0.27–1.33 ms-1) typical for the urban environment.

A large discrepancy between the two methodologies was found for deciduous forest (green area with forest). H2012 closely matches measured dry deposition velocities over a beech forest by when using F+=2.25. state that their parameterization offsets measured data for broad-leaf forests by 2–3 orders, unless using a very small collector size (dcol<0.2 cm). However, their parameterization is in close agreement with one wind tunnel measurement for 1 µm particle deposition on natural oak branches by . It should be kept in mind that “KS2012 Forest” does not necessarily represent realistic dry deposition rates to forests and was rather included as lower limit for particle deposition from the KS2012 method in urban environments.

We have used the measured particle number size distributions at a traffic station and at an urban background (UB) station, during campaigns in the cities of Oslo, Rotterdam and Helsinki. The included campaign data sets were the following:

Rotterdam 2011, TRANSPHORM. Traffic site Bentinckplein and urban background location Zwartewaalstraat (6–19 May 2011) at Rotterdam, and the regional background station at Cabauw in the Netherlands (February–November 2011).

The measured data for roadside and urban background in the TRANSPHORM campaign at Rotterdam, in the UFP-Oslo (“Measurements of ultrafine particles in Oslo”) campaign at Oslo, and in the SAPPHIRE campaigns in Helsinki were obtained simultaneously. Whereas in the LIPIKA and the MMEA campaigns in Helsinki the measured data were obtained with the mobile laboratory “Sniffer” e.g., at various locations during each measurement day. Quality control (QC) procedures in the measurement campaigns at Helsinki are described in the cited literature. Table  compiles the information on the size distribution data from the different campaigns in Rotterdam, Oslo, and Helsinki. In order to obtain an average size distribution for the respective traffic station and urban background station, either median or mean of measured time series of size distributions (dN/dlog⁡(Dp)) were calculated, as specified in Table . A comparison of measured total PN concentrations between campaigns is shown in Supplement Fig. S1.

In Rotterdam, particle measurements were performed at the regional background station at Cabauw near Rotterdam and a traffic location at less than 5 m from the roadside (Bentinckplein) by two scanning mobility particle sizer (SMPS) instruments: one SMPS 3080 covering size diameters (Dp) 10–480 nm and a CPC 3775 (TSI Inc.)  with a 50 % cut-off at 4 nm, and one SMPS 3034 with Dp 10–470 nm and a CPC 3010 (TSI Inc.) with a 50 % cut-off at 7 nm. The comparability of both SMPS was tested by parallel measurements. The Pearson correlation (r) between the parallel SMPS measurements was 0.96, hence R2=0.92. The absolute mean bias was 5400 particlescm-3 between both instruments, corresponding to a relative bias of 16 %. The results of the PNC measurements were corrected for the difference in comparability between both instruments. Hourly averaged wind direction was used to select campaign data that were directly influenced by the traffic emissions in the street. The traffic volume at Bentinckplein, which is a street canyon (width: 50 m; height: 12 m) was 35 000 vehicles per 24 h with 4 % trucks and buses. The urban background location Zwartewaalstraat in Rotterdam total PN concentrations were measured by a condensation particle counter (TSI 3007). The entire monitoring period at the regional background site was from February until December 2011. QC procedures were derived from the European Supersites for Atmospheric Aerosol Research (EUSAAR) project . These involved inter-comparison studies of monitoring instruments, biweekly checking of the sampling flow and annual calibration of the PN monitors by the manufacturer.

In Oslo, PN concentration and particle size distributions were measured at two stations in the municipality of Oslo for a 4-month period in winter 2008, using a Grimm 565 Environmental Wide Range Aerosol Spectrometer system (http://www.GRIMM-Aerosol.com). This system combines a Grimm 190 aerosol spectrometer OPC (optical particle counter), and a scanning mobility particle sizer with a condensation particle counter (SMPS+C). The entire system in principle covers the range from 5 nm to 30 µm. Instruments were calibrated by the manufacturer prior to installation on site. Weekly zero filter test and other maintenance was carried out according to the manufacturers guide. In addition to automatic QC in the Grimm software, data from the two sites were compared and aligned with other air quality data from the respective sites. For the analysis of the Oslo campaign, only data from the SMPS were used and the smallest size bin was discarded. The traffic station (Smestad) was at a busy road with an average daily traffic (ADT) of around 50 000 vehicles. The traffic signal at the urban background station (Sofienberg park) showed a continuous shift of the size distribution peak towards larger sizes with decreasing air temperature, i.e., the maximum of the size distribution is shifted from 16 nm at 6 ∘C to 26 nm at -10 ∘C. Size distribution data measured at -8 to -12 ∘C were used as a separate data set, UFP-Oslo Winter. The complete data set from the period December 2007 to April 2008 is referred to as UFP-Oslo Tav.

For Helsinki, two cases from the SAPPHIRE campaign, one case from the LIPIKA campaign (both at Herttoniemi), and one case at the city center from the MMEA campaign  were included. The roadside station near the highway Itäväylä at Herttoniemi is located about 6 km east of the center of Helsinki in a suburban area, with substantial local traffic. Particle measurements were performed with a differential mobility particle sizer (DMPS) at the background station and with a twin SMPS at the traffic site. Particle measurements during the LIPIKA campaign were conducted by Sniffer at various locations near the highway Itäväylä . The highway consists of six lanes, three lanes to both directions (total width of three lanes: 12 m), and a 6 m wide central grass area between the lanes to both directions, with a speed limit of 80 kmh-1. Particle size distributions in the range of 7 nm to 10 µm (aerodynamic diameter) were measured by an electrical low-pressure impactor (ELPI, Dekati Ltd.; 12 channels). Nucleation mode particles were measured with high size resolution by a Hauke type SMPS (20 channels); measured size range was 3–50 nm (mobility diameter). The study period included 14 cases of measurements downwind of the highway Itäväylä from wind sector 1 (northwestern wind; , ). The daily traffic density varied between 32 000–54 000 vehicles per day. Based on the traffic density information for the year 2001, the vehicle fleet on the highway was composed of 85 % light-duty vehicles (of which 11 % were diesel), 12 % vans (of which about 84 % diesel), and 4 % heavy-duty vehicles .

During the MMEA campaign  the mobile laboratory “Sniffer” was driving along the main street Mannerheimintie (MA) at the city center of Helsinki. MA is about 40 m wide and surrounded by 21 m tall buildings at both sides. The daily traffic flow was 36 300 vehiclesday-1 (of which ca. 10 % were heavy duty diesel vehicles). On 13–14 December 2010, the northeastern wind was perpendicular to MA, allowing traffic exhaust to be diluted freely between the buildings as in open environments. During rush hours, “Sniffer” was stopping around 10 min at 8, 28 and 56 m distances from the driving lane of MA downwind. Particle size distribution was measured by two SMPS (size ranges: 3–60 and 10–420 nm). The urban background particles were measured while Sniffer was standing at Lääkärinkatu, 300 m north from the measurement sites at MA.

A summary of the meteorological and dispersion conditions for the different campaigns is given in Table S1 in the Supplement. Measured meteorological data were not directly used in the model study of idealized scenarios, but are considered to be important for discussing the relevance of aerosol dynamical processes compared to dilution under real-world conditions.

Measured PN concentrations based on hourly averages or 10 min averages (in case of the LIPIKA and MMEA campaigns) showed a wide range of PN concentrations (20 000–100 000 particlescm-3) for the traffic sites considered, depending on the season of the year, traffic density, and distance from the road. Size distributions of the measured data sets at the traffic sites from all campaigns were normalized by the measured total PN concentrations (Fig. ). We have also calculated the average values of the size distribution curves for all traffic sites, denoted as “mean of traffic sites” (black curve in Fig. ). This size distribution is considered to be representative for the traffic-influenced roadside aerosol in the considered cities.

The “mean of traffic sites” distribution is characterized by a fraction of ultrafine particles (Dp: 10–100 nm) and accumulation mode (ACC) particles (Dp: 100–500 nm) of 80 and 4%, respectively, while 16 % of the particles were below 10 nm. SAPPHIRE Case I had the highest fraction of <10 nm particles (38 %); in Rotterdam <10 nm particles were not measured. For the other campaigns fraction of <10 nm particles was in the range 6–19 %. The fraction of ultrafine particles was 60 % for SAPPHIRE Case I and 74–87 % for all other campaigns. The fraction of ACC particles was smallest for the SAPPHIRE campaigns (≈1 %), and between 4 and 9% for the other campaigns in Helsinki and Oslo.

From a three-modal fit to the mean traffic-related size distribution with the MAFOR model (following the procedure described in Sect. ), three distinct modes with mean diameter at 17, 85, and 250 nm, respectively, were obtained. The measured average size distributions from the campaigns LIPIKA and MMEA in Helsinki, as well as UFP-Oslo Tav exhibited a similar shape as the mean traffic-related size distribution. The distribution of SAPPHIRE Case II also resembled the constructed distribution but did not show significant particle numbers with diameter >100 nm. Ultrafine particles measured at the traffic sites in the campaigns were most likely from fresh vehicle exhaust emissions. Particles emitted from diesel engines are usually in the size range 20–130 nm e.g.,, somewhat larger than those emitted from gasoline engines, typically being in the range 20–60 nm (, ; , ). Comparing campaigns in Helsinki, MMEA size distribution peaked at 20–40 nm, while LIPIKA and SAPPHIRE size distributions peaked at 8–25 nm. The higher fraction of heavy-duty diesel vehicles at Mannerheimintie (10 %) compared to highway Itäväylä (4 %) could be one possible reason for the peak at relatively larger sizes in MMEA. Different driving conditions may also have contributed to the difference in peaks; at Mannerheimintie rush hour limited the speed to 20–25 kmh-1 with stop-and-go driving, whereas at Itäväylä vehicles could drive 60–80 kmh-1 very fluently.

The peak of the size distribution for UFP-Oslo Winter was below 10 nm and for Helsinki SAPPHIRE Case II the peak was below 20 nm. Both campaigns were during winter in Northern Europe; ambient temperature in UFP-Oslo Winter ranged from -12 to -8 ∘C and SAPPHIRE Case II ranged from -15 to -4 ∘C. The relative increase of nanoparticle numbers in cold conditions may be the result of increased nucleation of semi-volatile compounds post-emission and decreased saturation ratio of the condensing vapors that tend to enhance initial particle growth. It has also been reported that particle emission from light-duty diesel vehicles are influenced by low ambient temperatures during the vehicle cold-start . However, the primary effect of a cold environment on vehicle cold-start is a number increase of semi-volatile nucleation mode particles, not of the solid particles in the exhaust .

Accumulation mode particles have a longer lifetime in the atmosphere, it is therefore likely that they are either a result of ageing processes on the urban timescale or that they are from short-range or long-range transport of aerosols. Since the size distribution measurements were carried out at traffic sites at distances of a few meters from busy roads, the measured aerosols are expected to be mainly influenced by primary traffic emissions. However, for the campaigns at Rotterdam and Oslo, measurements were not always downwind from the traffic emissions, and could be influenced also by other local particle sources and secondary pollution from local traffic.

The number size distribution at Rotterdam showed an exceptionally broad peak mode at 30–70 nm and a large fraction of ACC particles. Other sources, such as emissions from harbor activities and refineries situated in the harbor area, could have contributed to the relatively high fraction of ACC particles at Bentinckplein. Average wind direction during the Rotterdam campaign was from southwest, from the direction of the harbor area “Nieuw Mathenesse”. At an average wind speed of 3.6 ms-1, the travel time of particles from the harbor and refineries to the traffic site was about 15 min. Ships emit large amounts of particles larger than 20 nm, which consist of soot and volatile material (e.g.  ; , ; , ). Number size distributions of ship emissions in the ports of Helsinki and Turku (Finland) measured by “Sniffer” showed peaks at around 20–30 and 80–100 nm .

Truck traffic in the harbor during loading and unloading of ships also leads to increased particle numbers . Measurements downwind of a harbor at Rotterdam showed that 61 % of the PN concentration was in the size range 25–100 nm while it was 48 % downwind of a motorway . Condensation of vapors onto particles emitted from ships during their transport to the traffic site might explain the relatively high number concentration of ACC particles in the Rotterdam campaign. We note that the measured PN concentration of ACC particles in Rotterdam was similar as in Oslo but lower than during the LIPIKA and MMEA campaigns in Helsinki.

The evolution of the particle size distribution as function of time up to 1 h for all the cases, and by definition, following increasing distance from the roadside (idealized scenario, Sect. ), was studied with the one-dimensional aerosol dynamics model MAFOR and compared to measured size distributions data from the respective campaigns. Figures  and S2 show the comparison of modeled number size distributions from the idealized scenarios and the measured number size distribution at the roadside and at the urban background site for campaigns at Oslo, Rotterdam, and Helsinki. As the air parcel containing vehicle exhaust leaves street scale it is assumed to be advected over a homogenous surface in the neighborhood with a length scale of a few kilometers and further to the city scale. In the model, initial particle concentrations in all size bins were diluted with background air containing particles with a size distribution that matched the measured size distribution at the urban background site. In this way, the modeled size distributions were forced by the applied dilution scheme to relax towards the background size distribution, with a time constant dictated by the respective dilution scheme parameters. An in-depth evaluation of the aerosol dynamics model has not been carried out in the frame of this study, as the main focus was on the model's responses to changes in the treatment of aerosol microphysics.

The modeled number size distribution calculated for moderate dispersion conditions after ∼10 min of travel time, corresponding to a distance of 3600 m from the roadside, was generally in good agreement with the size distribution measured at the urban background site. Note that modeled size distributions range from 1 nm (lower bound) to 10 000 nm (upper bound); in Fig.  the relevant size range of 6–1000 nm is shown. Dilution was the dominant process changing the size distribution between roadside and urban background, as shown by the continuous decrease of concentrations with time. For the campaigns Helsinki SAPPHIRE Case I (Fig. c) and Case II (Fig. S2c), as well as Helsinki MMEA (Fig. d) the maximum of the particle size distribution was moved to a larger diameter. For instance, the modeled size distribution in Helsinki SAPPHIRE Case I showed an increase of the nucleation mode peak diameter from 10 to 18 nm within a distance of 3600 m. This behavior can be explained by dilution transforming the shape of the roadside distribution into the (prescribed) shape of the urban background distribution. UFP-Oslo Winter (Fig. a) shows signs of growing small particles by condensation, with peak diameter moving from ca. 5 to 8 nm.

Model simulations using different wind speed and dilution parameters, representative for different dispersion conditions (efficient, moderate, inefficient dispersion; as given in Table ), were performed for each campaign. The contribution of the various aerosol dynamic processes to the change of total PN at a given travel time was derived by switching off the respective aerosol process in the model calculation. The percentage PN change due to a specific aerosol dynamic process was obtained by division of the total PN change with the total PN change when all processes were considered (PN change defined as difference between initial total particle number and total particle number after a certain travel time). Table  summarizes the PN change after 30 min of travel time due to each selected aerosol process, and also to dilution, in each of the campaigns for efficient, moderate and inefficient dispersion conditions. The considered aerosol processes accounted for PN concentration changes of up to 20 % after 10 min and up to ∼30 % after 30 min (Fig. ), respectively.

According to the results shown in Table , coagulation and dry deposition were relevant aerosol dynamic processes for particle removal in the Rotterdam campaign whereas dry deposition was the predominant aerosol process in the Oslo campaign. Due to identical dispersion conditions and wind speeds used in the comparison, the observed difference is attributed to the different shapes of the initial size distribution measured at the roadside station and the background particle size distributions. The larger fraction of particles with diameter >25 nm measured at Rotterdam (accounting for 73 % of total PN) explains the higher relevance of coagulation compared to the Oslo campaign. Particles with larger diameter more efficiently scavenge the small (<25 nm diameter) particles by coagulation.

For the LIPIKA and MMEA campaigns coagulation was the most important aerosol process for particle removal during low wind speed. The size distributions for LIPIKA and MMEA (green and cyan lines in Fig. a) peak in a size range between 10 and 40 nm diameter and show a higher fraction of ACC particles than the SAPPHIRE distributions. Obviously, coagulation becomes a relevant PN loss process once large numbers of particles below 50 nm diameter from vehicle exhaust emissions (e.g. ca. 92 000 particlescm-3 at roadside, LIPIKA) are accompanied by a significant PN fraction of larger particles, which originate either from other local sources or from secondary particle formation within the urban area. These results are in agreement with the ones by who estimated that the lower and upper limits for the inter-modal coagulation timescale during the rush hours were 15–20 and 60–80 min, respectively. During the night, the inter-modal coagulation timescale was 2–3 times that during the rush hours .

The contribution of dry deposition and coagulation to total PN losses is comparable to those determined in previous measurements and model studies. City scale modelling studies with a multi-plume aerosol dynamics and transport model indicated that coagulation and dry deposition can cause total PN losses of 15–30 % between roadside measurement and urban background measurement in Copenhagen . , using an urban dispersion model that included aerosol dynamics in Stockholm, concluded that in terms of time-averaged PN concentration, dry deposition may yield particle number losses of up to 25 % in certain locations, while coagulation contributed little to PN losses. During particle peak episodes the removal by dry deposition and coagulation was more substantial .

Condensation and evaporation of vapors as such is not expected to change the total number concentrations, however this can modify the particle size distributions and particle volume. In this study a significant increase of PN (by up to 8 % after 30 min travel time) was evident under inefficient dispersion conditions, when condensation was considered in addition to coagulation and dry deposition. The reason could be the competition between condensation and coagulation. As the air parcel moves away from the roadside, condensation of condensable organic vapors leads to rapid growth of small particles to larger diameters at which they are less affected by coagulational loss. In addition, dry deposition velocity decreases with increasing diameter between 1 and 100 nm. Hence particles grown by condensation of condensable organic vapors will be less affected by deposition.

Aerosol dynamics are less relevant under conditions with efficient dispersion. When efficient dispersion occurs in the urban canopy, dilution by background air is the only effective process reducing PN concentration with distance from the roadside. In such situations (dilution parameters: a=80, b=0.9) aerosol processes account for PN concentration changes of less than 3 % after 10 min and PN concentration changes of less than 6 % after 30 min, hence modelling of PN as passive tracer is adequate. According to the previously published model study at the Dutch motorway A16; the particle size distribution at Dp>40 nm is not further altered by aerosol processes after a distance of 1000 m from the roadside . The distance where the PN level reaches background concentrations depends on dispersion conditions. Background PN levels were reached approximately (within an accuracy of ±5 %) after 1740, 900, and 160 m in distance from the road for inefficient, moderate, and efficient dispersion conditions, respectively, in box model simulations using the Rotterdam campaign data.

The sensitivity of modeled PN concentrations towards dry deposition of particles on various surface types and roughness conditions were studied in the campaigns Rotterdam TRANSPHORM and UFP-Oslo Tav under moderate dispersion conditions. Two different deposition methodologies, KS2012 and H2012 (detailed description in Sect. ), were applied. Results from the sensitivity tests are summarized in Table S2.

Between different KS2012 cases, calculated dry deposition velocity, νd, spanned about 1 order of magnitude for all particle diameters. Case “KS2012 Urban” corresponded to the surface characteristics of typical urban environments, i.e. streets and buildings, as used for the reference model runs with MAFOR. KS2012 parameterization was not sensitive to changes of friction velocity or roughness length within a typical urban range of values: reducing friction velocity (case “Low friction”) or increasing roughness length (case “High roughness”) resulted in negligible (≤0.1 %) change of PN loss due to dry deposition compared to case “Urban”. Over grassland and forest, modeled PN concentration changes due to dry deposition were smaller by 30 and 50%, respectively, than over urban surfaces.

Using the deposition methodology H2012 for case “Urban” resulted in 40–50 % lower PN losses by dry deposition compared to KS2012. Between different H2012 cases calculated νd spans about 2 orders of magnitude for accumulation mode particles (Dp 100–1000 nm) which can be attributed to the fact that surface roughness becomes a dominant factor in collecting aerosol particles efficiently for that particle size range, where neither diffusion nor inertial processes are significant processes. H2012 parameterization was very sensitive to changes of friction velocity or roughness length. The contribution of dry deposition to PN changes varied by roughly a factor of 5 for Rotterdam and by a factor of 3–4 for Oslo due to changing roughness conditions.

It has been evident in the literature e.g.,, that surface roughness can increase νd by up to 2 orders of magnitudes, in the size range between particle diffusion regime and diffusion-impaction regime, compared to a smooth surface. This behavior is reflected by the H2012 parameterization, but not by the KS2012 parameterization.

Inspection of the modeled evolution of number size distributions in simulations of Helsinki LIPIKA (moderate dispersion) revealed that variation of organic vapor concentration mainly affected the nucleation mode. Compared to a simulation without condensation and evaporation, the reference case with 0.5 ppb condensable organic vapors (sum of C22 and C28 gas-phase concentration with ratio 50 : 50) did not significantly change the number size distribution in a distance of 240 m from the road (Fig. S3a) but doubled the mass of 10 nm particles (Fig. S3b). When the concentration of condensable organic vapors was reduced to 0.05 ppb or below, condensation became completely negligible. Our sensitivity results are qualitatively in line with the study of who, based on measured PN data and the aerosol dynamics model MONO32 , found that the influence of condensation on PN concentrations was negligible on a distance scale of 200 m near a major road in Helsinki. For example, presence of a condensable organic compound with ∼0.4 ppb increased the diameter in the two smallest particle size modes by only 14 and 1.9%, respectively .

An extreme case to test the relevance of condensing n-alkane vapor and its effect on traffic-related size distributions was the Oslo Winter data (Fig. a). Under inefficient dispersion conditions, modeled total PN concentration in UFP-Oslo Winter was 2% higher after a distance of 240 m with 0.5 ppb condensable organic vapors, compared to a simulation without condensation. Growth of particles by condensation caused a shift of the nucleation mode diameter from 5.9 to 8.8 nm (Fig S4a), thus increasing the survival probability of the very small particles. Two factors enhanced the effect of condensation on the changing size distribution: first, the low temperature causing low vapor pressure (a factor of 90 smaller than at 10 ∘C) and second, the high fraction of initially present particle numbers with diameter below 10 nm. For lower concentrations of condensable organic vapors, 0.05 and 0.005 ppb, no significant particle growth was found (mass size distribution in Fig. S4b). Evaporation of particles <10 nm diameter occurred at 0.005 ppb, when changing the organic fraction of nucleation mode particles to 100% C22, i.e., assuming higher volatility of vehicular nanoparticles that formed post-emission. Interestingly, the evaporated material partly re-condensed to particles with diameter >100 nm within 240 m distance from the roadside (blue dashed line in Fig. S4a, b).

The growth of small particles (Dp<10 nm) at 0.5 ppb condensable organic vapors to larger sizes within a distance of 240 m in campaign UFP-Oslo Winter corroborates the finding in a curbside study by at two freeways in Los Angeles, that a large number of emitted sub-6 nm particles can grow substantially 30–90 m downwind. However, it cannot be excluded that downwind emissions of vehicle pollutants or oxidized volatile organic compounds (VOC) contributed to the observed growth.

Model simulations of the idealized scenario suggest that evaporation could be an important process, altering the particle size distribution in urban micro-environments, if the semi-volatile vapor and also the nanoparticles forming post-emission were assumed to have the same or higher volatility as the n-alkane C22. analyzed observations of particle size distributions from London and reported a reduction in the size of nucleation mode particles during advection from a major highway into the cleaner environment of a park, indicating evaporative loss of semi-volatile constituents during travel times of around 5 min. , for the same location, found most rapid evaporation to occur at higher wind speeds, associated with shorter travel times, but cleaner air.

Model calculations for the idealized scenario assumed that all particles are spherical. However, soot particles emitted from diesel vehicles are fractal-like aggregates consisting of nano-sized primary spherules. The effect of fractal geometry on coagulation was taken into account by considering the effect on radius, diffusion coefficient and the Knudsen number in the Brownian collision kernel. In order to test how fractal geometry of soot particles affects the modeled particle size distribution and PN concentrations, the coagulation kernel in MAFOR was modified by assuming that the collision radius is equal to the fractal (outer) radius, rf, defined as rf,i=rs×ns,i1/Df, where ns=υi/υs is the number of primary spherules in the soot aggregate, υi is the volume of the aggregate, treated as if it were spherical, rs is the radius of spherules and υs is the volume of a spherule that makes up the aggregate, and Df is the fractal dimension. Soot particle density was corrected as explained in .

Van der Waals forces and viscous interactions affect the coagulation rate of small particles. It has been shown that van der Waals forces can enhance the coagulation rate of particles with diameter <50 nm by up to a factor of five . To evaluate how neglecting the two forces affected the particle size distribution evolution, a correction factor VE,i,j accounting for van der Waals and viscous forces was applied to the Brownian collision kernel, Ki,jB, for the collision of particle of size bin i with particles of size bin j in the MAFOR model: Ki,jcorr=Ki,jB×VE,i,j.

Refer to Sect. S3 for details of the implementation. The effect of van der Waals forces and viscous interactions as well as fractal geometry on the Brownian collision kernel is shown in Fig. S5. Parameters of the fractal geometry adapted from , rs = 13.5 nm and Df= 1.7, resulted in stronger enhancement of the coagulation rate for collisions with a 10 nm particle than the parameters (rs= 2.5 nm and Df= 2.5) adapted from .

The combination of both effects substantially enhanced the loss of nanoparticles in the simulation of the evolution of the roadside aerosol. For Helsinki MMEA, inefficient dispersion conditions, the enhancement was similar for the two effects separately, i.e., spherical particles with van der Waals and viscous forces versus fractal particles (Fig. S6). The combined effect increased the loss of total PN by 15% compared to the reference simulation (coagulation of spherical particles by Brownian motion) in 600 m distance from the road.

Computation of the aerosol evolution between the roadside station and the neighborhood environment with the idealized scenarios involves several assumptions and uncertain parameters. An uncertainty analysis was performed to quantify the errors associated with the determination of the contribution of the respective atmospheric processes to the change of total PN. Errors were determined based on simulations for the mean traffic-related particle distribution (Sect. ) under inefficient dispersion conditions after 30 min travel time (Fig. ).

Fractal parameters of  were chosen for the evaluation of the uncertainty of the coagulation process. The combined effect of fractal geometry and van der Waals plus viscous interactions was taken into account, resulting in an error of +130%, roughly corresponding to a doubling of the contribution of coagulation to PN losses between roadside station and the neighborhood.

Measurements of dry deposition velocities of particles for one particular surface type generally vary by 1 order of magnitude for a given particle size range of a half logarithmic decade (e.g., for different grassland and forest types; , ). Dry deposition velocities for total PN (0.2–0.9 cms-1), calculated with the reference case parameterization “KS2012 Urban”, correspond to the reported range of measured deposition velocity values. Here, dry deposition velocity was scaled by factor 2 and 1/5 to evaluate the uncertainty of the dry deposition process due to literature span of measured velocities. This resulted in an error margin from -76 to +64% for the contribution from dry deposition.

For the mean traffic-related particle distribution, evaporation contributed 0.3% to PN losses when assuming 0.005 ppb C22 + C28 and 100% C22 in <10 nm particles. Condensation and evaporation are uncertain processes due to the lack of measurements of the gas-phase and particle phase concentrations of condensable compounds at the roadside station. Oxidation of VOC from vehicular emissions may provide an additional source of condensable material on the neighborhood scale. However, oxidized VOC in the background air are expected to condense on the particles of the accumulation mode, increasing their volume, rather than changing PN concentrations.

Additional emissions of particles on the travel path between the roadside station and the background were not considered in the idealized scenario. Since the dilution process in the model simulations was constrained with the measured size distribution at the background, the influence of additional particle emissions has been implicitly taken into account. However, if there are strong emission sources of ultrafine particles on the way, the momentary particle size distribution might be perturbed. The error due to fluctuations of the dilution rate caused by additional emissions was estimated to be -4%.

The main uncertain parameter in the applied dilution scheme (Eqs. , ) is the initial plume height at the roadside, Hm,0. Doubling Hm,0 resulted in a small error (-1%) of the contribution of dilution to PN losses.

It is concluded that errors due to the design of the scenario (dilution scheme, additional emissions) are relatively small compared to the magnitude of the potential contribution of coagulation and dry deposition to total PN losses between roadside station and the neighborhood environment.

As a first step of the implementation of a treatment of aerosol processes in urban air quality models, a separation of PN to various size categories is required. Three particle number concentration (PNC) categories were defined, as follows: PNC1 (8.5 nm <Dp<25 nm; “Nucleation mode”), PNC2 (25 nm <Dp<100 nm; “Aitken mode”), and PNC3 (100 nm <Dp<500 nm; ACC). The upper boundary of 500 nm is justified because the contribution of large particles (defined here as >500 nm) to total PN concentration from vehicular exhaust is negligible.

A first-order rate law for PNC in the three size categories (index k) was derived for number concentration change with time due to dry deposition: ln⁡PNCkPNCk,0=-νd,k‾Hm×t, where PNCk,0 is initial concentration. The average dry deposition velocity νd,k‾ was determined by fitting a linear regression model to the time series of modeled PNC1, PNC2, and PNC3, from a MAFOR run initialized with the size distribution “mean of traffic sites” (see Sect. ) and dry deposition as only process.

In Eulerian models, dry deposition of particles can be implemented according to dPNCkdt|depo=-PNCkνd,k‾Hgrid. Here Hgrid is the depth of the lowest grid level. Table  provides average dry deposition velocity derived from the fit to Eq. (). If applying the parameterization in a Gaussian model then the deposition velocity is usually used to influence the reflection parameter (α) for the reflected plume, e.g., using the following equation : αk(x)=1-2νd,k‾νt+νd,k‾+Uh-νtx×σz-1dσzdx, where h is the effective plume rise and σz is the vertical dispersion coefficient. Gravitational settling velocity νt in Eq. () can be neglected (set to zero) since only particle sizes below 500 nm are relevant for determining PN concentrations.

Coagulation of particles can be implemented, rate according to dPNCkdt|coag=-PNCk×Kcoag,k‾×PNCk0, where Kcoag,k‾ (in units cm3s-1) is the average coagulation coefficient in a size category k derived from MAFOR calculations, provided in Table . The expression in Eq. () neglects the production terms of coagulation. The superscript 0 indicates the number concentration at the start of the time step calculation in Eulerian models. For Gaussian models this is the calculated concentration before the inclusion of the decay rate due to any physical and chemical processes considered for PNC.

Dry deposition and coagulation terms are applied separately for the three PNC classes. This means that coagulation between different size categories is not calculated explicitly with the parameterization. However, inter-modal coagulation is partly taken into account through the average coagulation coefficient derived from a model calculation that included coagulation between all size bins. Since the average coagulation coefficient of a given size category depends on the number concentrations in the other size categories, the predicted coagulational loss for PNC1 and PNC2 of roadside size distributions that differ from the size distribution “mean of traffic sites” will be somewhat inaccurate.

The accuracy of the presented parameterization for aerosol processes for prediction of PN concentrations is limited by three factors: first, by the averaging of process parameters over a certain size range; second by the simplified treatment of coagulation; and third by neglecting condensation and evaporation. The uncertainty of the parameterization was studied by comparison with PN concentrations resulting from a detailed aerosol dynamics calculation with MAFOR as reference. For the case “mean of traffic sites”, calculated total PNC after 10 min travel time deviated from the reference solution by only 1 %, implying that the error introduced by size-averaged process parameters is negligible. When applying the parameterization to campaign data, the deviation of the total PNC to the reference solution was up to 10 %. UFP-Oslo Winter was excluded from the evaluation due to the obvious influence of condensation as shown in Sect. . Increasing the number of PNC size categories is expected to reduce the error due to neglecting coagulation between size categories. A parameterization with six PNC categories resulted in a deviation to the reference solution by only up to 5 % (Table S3). In addition, the parameterization is uncertain due to assumptions about particle shape, neglecting van der Waals forces as well as inaccurate measured dry deposition velocities. It is however not affected by the specific treatment of dilution in the idealized scenarios because the simplified PNC parameterization was derived with only one aerosol process activated.

Results of PN concentration modelling for Oslo using the simplified parameterization for dry deposition and coagulation in the Eulerian urban dispersion model EPISODE are presented in .

The computer code of the MAFOR aerosol dynamics model, version 1.8, can be made available upon request (contact: Matthias Karl on email matthias.karl@hzg.de). The code is written in FORTRAN 90.