A photoacoustic soot spectrometer (PASS-3, Droplet Measurement Techniques, Boulder, CO) was used to measure aerosol absorption (babs) and scattering (babs) coefficients (Mm-1) at 405 and 781 nm. A 532 nm laser is not installed in this particular unit. The PASS determines aerosol absorption (Mm-1) in a cavity which acts as an acoustic resonator. The absorption of incoming radiation heats the particles, which in turn heat the surrounding air in the cavity . The aerosol-laden air thus expands, resulting in a pressure disturbance. By modulating the laser power at the resonance frequency of the cavity, the pressure disturbance is amplified and the resulting acoustic wave is measured using a microphone. Light scattering at both wavelengths is concurrently measured using reciprocal nephelometry . Scattering signals were not corrected for truncation; however, since mass-based particle size distributions at the roadside site generally peaked near or below 100 nm a negative bias in the scattering measurement is unlikely. Since a 532 nm laser was not present in this unit an NO2 calibration was not possible, and the instrument was calibrated using a propane soot generator (miniCAST, 6203A, Jing). PASS measurements of the bulk single scattering albedo at 405 nm (selected due to superior signal-to-noise ratio for scattering relative to the 781 nm channel) are used here only to illustrate differences in optical properties in vehicle plumes with varying composition.

We used the stochastic particle-resolved box model PartMC-MOSAIC (Particle Monte Carlo – Model for Simulating Aerosol Interactions and Chemistry) to quantify the importance of the observed mixing state information for the calculation of cloud condensation nuclei (CCN) and aerosol optical properties. PartMC-MOSAIC is suited for this task, as it explicitly tracks the composition of individual aerosol particles (in our case about 105 particles) in a population of different particle types within a well-mixed computational volume. Particle emissions, dilution with the background, and Brownian coagulation are simulated stochastically with PartMC, by generating a realization of a Poisson process using weighted particles in the sense of and an accelerated binned sampling strategy . Coupled to PartMC is the MOSAIC chemistry code, which simulates gas chemistry , particle-phase thermodynamics , and dynamic gas-particle mass transfer in a deterministic manner.

Here we compare two simulations that differ in the way the mixing state of the aerosol initial conditions and the aerosol emissions are prescribed. The setup of the particle-resolved simulations is similar to the urban plume scenarios in and . Common to both simulations are the following specifics. The number of computational particles used in the simulation is about 105. The total simulation time is 24 h, with a simulation start of 06:00 local standard time. The initial gas-phase concentrations are the same as in . In contrast to , we prescribe a constant mixing height (400 m), relative humidity (70 %), and temperature (298.15 K) to simplify the interpretation of the results. Since the entrainment of background aerosol can modify the aerosol mixing state substantially , we include constant dilution with the background at a rate of 1.5×10-5 s-1. The background aerosol is non-absorbing and consists of ammonium sulfate mixed with biogenic secondary organic aerosol. This dilution rate corresponds to about 75 % of the aerosol being replaced in a 24 h period, comparable to a diurnal mixing height increase of 500 to 2000 m e.g.,, although imposed uniformly over the day for simplicity. We also reduced the gas-phase emissions by a factor of 2 compared to to create more moderately polluted conditions. The initial aerosol population was sampled from log-normal size distributions fitted from the measurement data, as shown in Table S1 in the Supplement. The derivation of model inputs from measurement data is described in Supplement Sect. S3.

To fully exploit the information supplied by the observations, we introduced a new method of sampling the aerosol composition for the aerosol initial conditions and emissions. We now allow for stochastic composition variation at each diameter, with a prescribed standard deviation around a mean value. The new composition-sampling method proceeds as follows. For each aerosol particle, the diameter is first sampled, and then the composition is sampled as a vector of mass fractions w=[wBC,wHOA]⊤. Although we only sample two species for the simulations in this paper, we specify the sampling algorithm for any number of species. We use bold italic to denote vectors, so mf is the mean mass fraction vector from Table S1 in the Supplement. We write Σ for the diagonal covariance matrix with diagonal entries (σi)2, 1 for the vector of ones, and x⊤ for the transpose of a vector x. We sample the composition vector w from a multivariate normal distribution on the affine hyperplane of vectors that sum to 1, truncated to the positive closed orthant (and thus to the probability or standard simplex). This is done as shown in Algorithm 1 using an accept–reject procedure.

Algorithm 1 has five important properties, as follows. (1) It is clear that if the algorithm terminates then w lies in the positive closed orthant, so every species has a non-negative mass fraction. (2) The sum of the sampled mass fractions w is one, as can be seen from 1⊤w=1⊤x+(1-1⊤x)1⊤mf=1⊤x+1-1⊤x=1, assuming that the mean mass fractions sum to one and so 1⊤mf=1. (3) The distribution of w is a truncated multivariate normal, which follows from the fact that x has a multivariate normal distribution, w is an affine function of x, and the accept–reject procedure samples from the truncation of the per-iteration distribution. Note, however, that the resulting marginal distributions for each single-species mass fraction will not in general have mean and standard deviation given by mfi and σi, respectively. (4) Adding additional species with 0 mean mass fraction and 0 standard deviation will not change the distribution of the other sampled mass fractions, as the additional species will have 0 components in both x and w and will not alter the calculation of any other components. (5) Finally, the algorithm will terminate with probability 1, under the conditions that the mean mass fractions sum to 1 and each σi is non-negative and 0 only if the corresponding mfi is non-negative. This last property can be seen by first considering the set A of x that will result in a w in the positive closed orthant, terminating the algorithm. This set A is exactly the direct sum of the probability simplex with the span of {mf}, as can be seen by checking that x=p+αmf for p in the probability simplex and any scalar α results in w=p, so that the entire probability simplex is thus obtained from A. The conditions on mf and the σi imply that x has non-zero probability of lying in A, and hence the algorithm has non-zero probability of terminating on each iteration. Because each iteration is an independent and identically distributed Bernoulli trial, the algorithm thus terminates with probability 1.

The two simulations differ in the assigned mixing state of the initial aerosol populations and the aerosol emissions. For the measurement-constrained case we distinguish between rBC-rich and HOA-rich particle classes, as the observations indicate. Both classes consist of two modes, which amounts to four modes in total, as listed in Table S1 in the Supplement. Note that the modes BC1 and HOA1 have the same geometric mean diameter and geometric standard deviation, but they differ in their abundance and their emission rate, respectively. The same applies to modes BC2 and HOA2. This specific choice is guided by the observations as shown in Table S1.

For the uniform case only two modes are prescribed, with the same geometric mean diameter and standard deviation as modes BC1/HOA1 and BC2/HOA2, respectively (Table S2). The mass fractions of BC and HOA in these two modes are identical, and they are equal to the mass fractions of the bulk concentrations for the measurement constrained case. Hence the uniform case represents conditions for which the bulk mass concentrations and the size distribution are the same as for the measurement-constrained case, but for which the detailed mixing state information is not available. A comparison of the two cases therefore quantifies the importance of mixing state information at emission for properties of interest, such as optical properties and CCN activation properties.

Figure S10 shows the temporal evolution of the bulk aerosol species over the course of the 24 h simulation. The primary species black carbon and organic carbon increase initially owing to emissions and then decrease after emissions are discontinued at t=12 h as a result of dilution with the background. The model simulations also show the production of inorganic and organic secondary aerosol species, which condense on the primary particles, continuously modifying the composition of each particle in the aerosol population. Not shown in this figure is the aerosol water content. While the particles start out dry, they take up water around t=6 h when nitrate formation begins.

We calculate the optical properties for ambient conditions (including aerosol water content) at a wavelength of 550 nm and the critical supersaturations of each particle in a post-processing step according to . For the optical properties we assume spherical particles with a “core-and-shell” configuration in which BC forms the particle core and the other substances compose the shell. We then use Mie calculations to determine the extinction and scattering cross sections for each particle in the population. From these values, the volume extinction, scattering, and absorption coefficients can be reconstructed. Note that we assume all primary and secondary organic substances to be non-absorbing; hence we do not consider any effects due to brown carbon.

To determine the critical supersaturations, we employ κ Köhler theory (see for details). Based on the critical supersaturation values of each particle in the population, we construct CCN spectra, as shown in Fig. S11 for different times throughout the simulation. As the simulation progresses, the CCN/CN fraction at low values of critical supersaturation increases, since the particles become more hygroscopic due to the condensation of secondary aerosol material. Since both primary organic carbon (κ=0.001) and black carbon (κ=0) are model species with similar and low hygroscopicity parameters, the differences between the uniform case and the measurement-constrained case are expected to be small, and the two CCN spectra are almost indistinguishable, as we will show in Sect. 3.3.

Based on single particle SP-AMS measurements in both roadside and non-roadside studies, we identified two types of particles originating from vehicle exhaust, which are primarily composed of rBC and hydrocarbon-like organic aerosol (Fig. a–d). One type is dominated by HOA mass (referred to as the “HOA-rich” particle class) and the other is dominated by rBC (“rBC-rich” particle class). The mass spectra of HOA-rich particles (Fig. a and c) exhibit fragmentation patterns associated with hydrocarbon structures (e.g., m/z 43 (C3H7+), 57 (C4H9+), 71 (C5H11+)) and are consistent with previous aerosol mass spectrometer observations of gasoline/diesel vehicle exhaust and unburned lubricating oil . In conjunction with differences in mass spectra, clear differences in particle size distributions (Fig. c and d) demonstrate that the division of traffic-related rBC-containing particles into HOA-rich and rBC-rich classes is physically meaningful.

The average mass fractions of rBC (mfrBC) in HOA-rich particles during the non-roadside and roadside studies are low: 0.03 and 0.05, respectively. The narrow distribution of mfrBC (Fig. a) suggests that most of the HOA-rich particles are either mixed with a small amount of rBC or do not contain detectable rBC mass, while a very small number of particles contain larger mfrBC (Fig. , split axis). Mass spectra of rBC-rich particles are dominated by Cx+ fragments (i.e., m/z 12, 24, 36, 48, and 60 in Fig. b and d) arising from black carbon. Smaller signals associated with HOA-like material in these particles are similar to the primary organic materials derived from diesel engine exhaust observed in laboratory studies . In contrast to the HOA-rich particles, Fig. c illustrates a wider range of mfrBC values in rBC-rich particles. In the non-roadside and roadside environments the average mfrBC values (±1 standard deviation) in this particle class are 0.72 (±0.18) and 0.86 (±0.14), respectively, highlighting the possibility that condensation and/or coagulation of HOA material on rBC particles might occur within a short time of emission.

The mass fraction of rBC derived from SP-AMS measurements may be best regarded as a lower limit. For the reasons detailed in Sect. 2.1.2, including the potential for incomplete vaporization and uncertainty in SP-AMS sensitivity to rBC coating materials, mfrBC values presented here may be underestimated. A 50 % overestimation in the mass of HOA would increase mfrBC in rBC-rich particles to 0.85 (±0.16) and 0.92 (±0.10) in the non-roadside and roadside studies, respectively (Fig. c, dashed lines). In addition to these uncertainties, in the roadside study only rBC-containing particles are detected by the SP-AMS, while in the non-roadside study it is possible that the HOA-rich class includes HOA particles that do not contain rBC (i.e., “externally mixed” HOA).

Single particle measurements provide direct insight into mixing state at an individual particle level; however, single particle detection has an inherent bias towards large particle sizes because light scattering triggers particle detection . Ensemble size distributions of rBC peaked at ∼100 nm in both roadside and non-roadside studies indicating that fresh rBC-containing particles emitted from vehicle exhaust are small (Fig. a and b). Smaller rBC-containing particles fall below the lower size limit of single particle detection (Fig. c and d). Therefore, single particle observations do not necessarily quantify mixing state at the population level. To provide a complementary view of rBC mixing state we turn to ensemble measurements from the roadside study where only rBC-containing particles were detected in the SP-AMS. Ensemble measurements better represent mixing state on a population basis compared to single particle observations, because they cover a wider range of particle size (i.e., 80–1000 nm vacuum aerodynamic diameter, dva).

By measuring very close to a busy road, ensemble SP-AMS observations of rBC and organic aerosol enabled the analysis of more than 100 vehicle exhaust plumes over the course of the roadside study (Fig. a and b). PMF indicates three major sources of rBC-containing aerosol in the roadside environment: transported BBOA, regional background (OOA), and traffic emissions comprised of two PMF factors (HOA-rich and rBC-rich factors; Fig. c–f). Inorganic species evident in the bulk aerosol size distributions (Fig. a and b) are largely associated with OOA and BBOA factors, while the traffic-related factors contain the majority of rBC and HOA . Mass spectra of all four PMF factors and a discussion of selection of the number of factors are presented in Supplement Sect. 2. Not previously observed with an AMS, the HOA-rich and rBC-rich factors represent two types of vehicle exhaust plumes with different amounts of rBC and HOA (Fig. e and f). The mfrBC of HOA-rich and rBC-rich factors are 0.16 and 0.75, respectively. High-time-resolution SP-AMS measurements (Fig. ) also demonstrated varying organic and rBC levels in vehicle plumes (Fig. g and h), with corresponding differences in optical properties (SSA at 405 nm) indicating that rBC-rich plumes were more highly absorbing. The origin of different plume types at this site has been characterized through long-term measurements and is related to a variety of engine types, operating conditions, and pollution control features .

Mass spectra of HOA-rich and rBC-rich PMF factors (Fig. e and f) are strikingly similar to the mass spectra of HOA-rich and rBC-rich particle classes identified in the single particle measurements (Fig. c and d), validating the division of traffic emissions into the two factors observed here. The single particle and ensemble mass spectra show some differences. First, the HOA-rich factor has a larger rBC content compared to the HOA-rich particle class; second, the rBC-rich factor contains higher CO+ and CO2+ signals compared to the rBC-rich particle class (inserts of Figs. d, e, and f). The latter difference arises because highly oxygenated organic fragments (m/z 28 (CO+) and 44 (CO2+)) were excluded in the single particle analysis due to interference of air signals in unit mass resolution spectra . Differences in mfrBC between single particle and ensemble measurements, especially for HOA-rich particles that contain a small amount of rBC, could be due to the probability of rBC detection in a single particle such that single particle mfrBC may be underestimated relative to ensemble mfrBC .

With support of direct measurements of single particle mixing state, this work presents the first interpretation of ensemble AMS results in terms of rBC and HOA mixing state. Using the intensity of the two traffic-related factors in plumes (Fig. e and f), we estimate that rBC-rich particles account for ∼90 % of the observed total traffic-related rBC mass (Fig. d). In a similar manner, we estimate that ∼60 % of the total HOA mass is due to HOA-rich particles (Fig. b). Purple dashed lines shown in Fig. b and d represent the inclusion of all COx+ fragments (due to surface functionality of ambient rBC, ) in the calculation of rBC mass (see Supplement Sect. S1), providing similar results. Dashed lines in Fig. a, b, and c represent the effect of a 50 % overestimation of HOA mass (see Sect. S1), again providing similar results.

These novel single particle and ensemble observations of rBC mixing state were used to initialize the particle-resolved aerosol box model PartMC-MOSAIC (see Sect. 2.3) , which simulates the evolution of aerosol due to condensation and coagulation in an idealized urban setting. As described in Sect. 2.3, we simulate two cases to isolate the impact of mixing state of rBC emissions on aerosol properties: first, a uniform mixing state case in which all particles are assigned identical composition at emission (measured average mfrBC); second, a measurement-constrained mixing state case where mfrBC is prescribed directly from our mixing state observations. The evolution of dry mfrBC over a 24 h period is illustrated in Fig. a and b for the two cases. As ageing proceeds mfrBC shifts to lower values, but in the uniform initial composition case no particles ever have mfrBC larger than ∼45 %. Note that the bulk aerosol composition and number size distributions are identical in the two cases (Fig. S10), and any differences in optical properties arise only due to the distribution of aerosol components amongst the particles.

Optical properties are determined for each particle in the population using Mie calculations and assuming a core-shell structure. We acknowledge that the underlying assumptions of Mie calculations may not be appropriate for rBC-containing aerosol in the real atmosphere e.g.,, which is often not spherical and may not exhibit a core-shell configuration e.g.,. In particular, the enhancement of rBC absorption due to non-absorbing coatings may be overestimated , except in situations where rBC sources and ageing promote extensive coating . However, Mie calculations are commonly applied in regional and global models to estimate optical properties, and we therefore include this comparison to illustrate the sensitivity to mixing state.

Consistent with previous studies e.g.,, we observe a difference in volume absorption and scattering coefficients (Babs and Bscat, Fig. c) and a resulting increase of 0.1 in SSA from the uniform mixing state to the measurement-constrained case that is present during the emission period in the simulation and, notably, persists throughout ageing (Fig. d). Note that a direct comparison between measured and modelled SSA is not valid since we measure SSA of the bulk aerosol population and model it only for a subset of this population (i.e., the rBC-containing particles). No significant differences in calculated cloud condensation nuclei activity were observed in these simulations (Fig. S11), owing to the very similar hygroscopicity of rBC and HOA species. Calculations of aerosol DRF are very sensitive to changes in SSA (e.g., uncertainties in SSA on the order of only 0.02 can result in a DRF uncertainty of 1 Wm-2 for a particular particle type; ), illustrating the importance of accurately measuring and simulating mixing state for calculating climatologically relevant aerosol properties.