Black carbon absorption at the global scale is affected by particle-scale diversity in composition

Atmospheric black carbon (BC) exerts a strong, but uncertain, warming effect on the climate. BC that is coated with non-absorbing material absorbs more strongly than the same amount of BC in an uncoated particle, but the magnitude of this absorption enhancement (Eabs) is not well constrained. Modelling studies and laboratory measurements have found stronger absorption enhancement than has been observed in the atmosphere. Here, using a particle-resolved aerosol model to simulate diverse BC populations, we show that absorption is overestimated by as much as a factor of two if diversity is neglected and population-averaged composition is assumed across all BC-containing particles. If, instead, composition diversity is resolved, we find Eabs=1−1.5 at low relative humidity, consistent with ambient observations. This study offers not only an explanation for the discrepancy between modelled and observed absorption enhancement, but also demonstrates how particle-scale simulations can be used to develop relationships for global-scale models.

Demonstrates that the range of BC concentrations from simulations covers variation in observed BC concentrations. [28], [29], [30], [31], [32], [33], [34] Figure 5: Procedure for applying nonparametric regression to particle-resolved model data in order to derive a relationship for absorption enhancement as a function of population-level variables.
Supplementary Table 1: Properties assigned to aerosol species. Values for density and refractive index are the same as those assumed in [36]. The range in values for κ were varied dynamically to cover the range in the effective hygroscopicity parameter of coating material expected in the atmosphere, based on [38]   Supplementary Note 1: Particle-resolved model PartMC-MOSAIC simulates the evolution of trace gases and aerosol particles in a Lagrangian air parcel. In each simulation, the model tracks the mass composition of each simulated particle as particle populations evolve through emissions, dilution with background air, coagulation between particles, and gas-particle mass transfer. Emissions, dilution, and coagulation are simulated stochastically with PartMC, while gas-and particle-phase chemistry and gas-particle mass transfer are simulated deterministically with MOSAIC. The position of each particle is not tracked and, instead, the parcel is assumed to be well-mixed. MOSAIC includes modules for gas-phase photochemistry [1], particle-phase thermodynamics [2,3], and gas-particle mass transfer [4]. Secondary organic aerosol formation is simulated in MOSAIC using the SORGAM scheme [5].
The coupled model includes all relevant aerosol species, including SO 2− 4 , NO − 3 , NH + 4 , Na, Ca, other inorganic mass (including species such as SiO 2 , metal oxides, and other unmeasured or unknown inorganic species present in aerosols), black carbon, primary organic carbon, and secondary organic carbon. Sulfate formation through aqueous-phase chemistry of cloud droplets is not included in the simulations; neglecting this process could affect the distribution in coating material between large and small particles (e.g. Figures 1a and 2 of the main text) and, thereby, the population-averaged absorption enhancement E abs (Figures 1d and 3 of the main text). PartMC version 2.1.5 was used for the simulations in this study, which is available at: http://lagrange.mechse.illinois.edu/partmc/. MOSAIC is available upon request from R. A. Zaveri.
Supplementary Note 2: Scenarios simulated with PartMC-MOSAIC This study describes a series of 100 scenarios, representing a variety of particle populations that have aged to varying degree under a range to atmospheric conditions. Each simulation included approximately 5000 computational particles and was one week in duration. Although the simulation settings differed, the structure of the scenarios was the same. In all scenarios, we assumed the air parcels represent a slice of a well-mixed boundary layer during the day and a slice of the residual layer at night. All simulations started at 6:00 am, at which time the air parcel contained only background air. From 6:00 am until 6:00 pm on the first day particles and gases were emitted into the air parcel. All emissions were discontinued at 6:00 pm, at which time the parcel was assumed to enter the residual layer and was decoupled from fresh emissions, but all other processes continued until the simulations ended.
The first part of the manuscript describes a baseline population, sampled from a single simulation at 6:00 pm on the first day (t = 12 hours). The input parameters for this scenario are outlined in Table 2. In the sensitivity scenarios, thirty input parameters were varied, including environmental conditions, the magnitude and characteristics of aerosol emissions, the background aerosol concentration, and the emission rates of gas-phase species. The range in each of these input parameters is given in Table 3. Latin hypercube sampling [37] was used to select 100 scenarios from the infinite possible combinations. These 100 scenarios represent a range of atmospheric aging conditions, causing the evolution of particle sizes and composition by condensation and coagulation to proceed at different rates. Input files required to run all 100 scenarios are available from the authors.
SI Figure 1 shows that the 100 scenarios cover the observed variation in surface concentrations of key aerosol species. The distribution in aerosol mass concentration within these simulations is shown for selected species by the black curve in Figure 1, which includes all time steps in all 100 scenarios. Surface observations of these aerosol species are indicated by the colored vertical lines in Figure 1. Similarly, Figure 2 shows the distribution in BC mass concentrations across the simulations (black line) and the corresponding observations (colored vertical lines). Figures 1 and 2 illustrate that aerosol concentrations simulated in the sampled scenarios cover the observed variation in surface aerosol concentrations.
Supplementary Note 3: Offline modeling of particle optical properties Absorption enhancement by BC in each population was computed offline from per-particle composition data. Each particle's absorption cross section is computed using a combination of models. Computing the absorption cross section of an individual particle from the mass composition provided by PartMC-MOSAIC requires the density, hygroscopicity parameter, and refractive index for each aerosol species. The value of the hygroscopicity parameter κ is uncertain for various aerosol species, so we considered a range in the value of κ for each species. The density, range in κ, and refractive index at λ = 550 nm is given in Table 1.
To explore particle absorption across a range of relative humidity levels, we used the κ-Köhler model [38] to find the volume of water contained in each particle. The overall particle wet volume is determined through solution of Equation 3 of the main text, which depends on particle's dry volume, its effective hygroscopicity parameter, and the environmental relative humidity. The value of A given in Equation 3 of the main text depends on the temperature (T ), the universal gas constant (R), the molecular weight of water M W , the density of water ρ w , and the surface tension of the air-water interface (σ w ), and is given by: The Dynamic Effective Medium Approximation (Equation 5 of the main text) [39,40] is used to determine the effective relative permittivity i of each BC-containing particle, where BC is contained in one or more randomlydistributed inclusions within an otherwise homogeneous particle. Each particle's wet size and effective permittivity varies as particles take up water with relative humidity, causing absorption to also vary with relative humidity. The absorption cross section of each particle is modeled as a function of its wet volume V d and its effective relative permittivity i with the Lorenz-Mie solution to Maxwell's equations. The same procedure is applied to compute absorption enhancement by each particle under the uniform composition approximation, but using the volume composition corresponding to the averaged population (v i ).
The particle-level and population-level absorption enhancement factors given Equations 6-8 of the main text indicate the ratio between absorption by BC in particles mixed with other components, including water, relative to absorption by uncoated BC. The absorption cross section of uncoated BC inclusions is computed using the Mie-Lorentz model, assuming the BC in each particle forms a single homogeneous sphere. As described in Equations 7 and 8 of the main text, the population-levels absorption enhancement under the particle-resolved composition and uniform composition representations, respectively, is given by the sum over the absorption cross section of coated BC relative to the sum over the absorption cross section of uncoated BC.
For the population of BC-containing particles shown in in Figures 1 and 2 of the main text, supplemental Figure 3a shows the distribution in particle number with respect to the mass of BC contained in each particle (horizontal axis) and the volume fraction of coating contained in each particle (vertical axis), whereas Figure 3b shows the distribution with respect to per-particle BC mass (horizontal axis) and per-particle absorption enhancement (vertical axis). For this same population, Figure 4 shows that the effective hygroscopicity parameter κ of BC coatings varies widely across BC-containing particles, even for particles within the same population.
Although the particle-resolved results reveal variability in coating thickness, even for particles of the same size, Figures 1 and 2 of the main text show that the mass of coating material associated with BC-containing particles tends to vary according with per-particle BC mass, such that most of the coating mass tends to be contained in particles containing small amounts of BC. This variation in the volume fraction of coating material between particles containing small and large amounts of BC is the result of two processes: condensation and coagulation. PartMC-MOSAIC simulates Brownian coagulation, such that the smallest BC-containing particles frequently coagulate with large background particles and, thereby, accumulate thick coatings, as described for the evolution of particle CCN properties in [41]. Condensation of semi-volatile substances also causes the volume fraction of coating material to be greater for particles with small mass-equivalent BC core diameter. Particles with small BC cores will tend to contain a greater volume fraction of coating material even in a limiting case in which the thickness of dry coating is the same across the particle population, an oversimplification that is not applied in this study but is discussed here only for illustration. For example, a particle with a mass-equivalent BC core diameter of 10 nm coated with a coating thickness of 20 nm corresponds to 99% coating by mass. On the other hand, a particle with BC core diameter of 200 nm with the same 20 nm coating thickness will contain 42% coating by mass.
Supplementary Note 4: Nonparametric regression to find relationship for population-level absorption enhancement We applied a kernel density regression [42,43] on model data from PartMC-MOSAIC to find the relationship for absorption enhancement shown in Figure 3 of the main text. To develop this relationship, we first applied the regression to identify the independent variables that best explain variance in absorption enhancement through a similar procedure as the one described in [44]. We found that the nonparametric relationship defined in terms of the average volume fraction of dry coating, the hygroscopicity of that coating, and the environmental relative humidity, which is shown in Figure 3 of the main text, explains 85% of variance in population-level absorption enhancement.
The procedure for applying the kernel regression to construct the nonparametric relationship is illustrated in Figure 5a, and the procedure for applying this nonparametric relationship to global model fields is illustrated in Figure 5b. For each of N particle-resolved composition distributions simulated by PartMC-MOSAIC, we determined population-level absorption enhancement by BC using the procedure described in the previous section. The composition distribution was also used to find the average volume fraction of dry coating (f coat ) on BC-containing particles and the average hygroscopicity of this coating (κ coat ). The kernel regression combines all of this population-level data to find the expected value of absorption enhancement,Ê abs , for a population of BC-containing particles given their bulk composition and the relative humidity to which they are exposed: wheref coat ,κ coat , andR w are the target values for f coat , κ coat , and R w at which the regression is performed and K f , K κ , and K R are the kernel functions with respect to f coat , κ coat , and R w , respectively. Here, we apply a Gaussian kernel in each dimension. For example, the kernel function with respect to K f is given by: where the standard deviation h f is the kernel bandwidth. The bandwidth h in each dimension was estimated using Silverman's rule of thumb [35], such that h depends on the number of independent variables, the standard deviation of each independent variable, and the total number of data points. Refer to [44] for further details on the application of nonparametric regression to PartMC-MOSAIC data. The nonparametric relationship developed from the regression on many particle-resolved populations was used to estimate the value of E abs using global model fields for the independent variables, given byf coat ,κ coat , andR w in Equation 2, using the procedure shown in Figure 5b. For each of 7 BC modes simulated by the global aerosol scheme GISS-MATRIX, we estimated population-level absorption enhancement E abs . Values for f coat and κ coat for each mode in each location and R w in each location were extracted directly from GISS-MATRIX. Supplementary Figure 6 shows mean values for f coat and κ coat , weighted by BC mass and R w , for surface-level grid cells. Values for κ coat are computed using the composition of each MARIX mode, assuming κ of 0.6, , and 0 for sulfate, dust, and organic aerosol, respectively. The representation of aerosol chemistry and dynamics varies between global models, leading to differences in f coat and κ coat , and thereby E abs , depending on the modeled species and treatments of particle size distributions and mixing state.