# Radiative absorption enhancements by black carbon controlled by particle-to-particle heterogeneity in composition

^{a}Department of Environmental and Climate Sciences, Brookhaven National Laboratory, Upton, NY 11961;^{b}Center for Aerosol and Cloud Chemistry, Aerodyne Research, Inc., Billerica, MA 02467;^{c}Department of Chemistry, Boston College, Chestnut Hill, MA 01821;^{d}Department of Civil and Environmental Engineering, University of California, Davis, CA 95616;^{e}Department of Physics and Atmospheric Sciences Program, Michigan Technological University, Houghton, MI 49931;^{f}Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA 99352;^{g}Department of Chemistry, University of Georgia, Athens, GA 30602

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Edited by Ravi R. Ravishankara, Colorado State University, Fort Collins, CO, and approved January 27, 2020 (received for review November 9, 2019)

## Significance

Absorption by black carbon strongly affects regional and global climate. Yet, large discrepancies between standard model predictions and regionally specific observations—often with observed absorption lower than expected—raise questions about current understanding of black carbon absorption and its atmospheric impacts. Through a combination of measurement and modeling, our analysis resolves the discrepancy by showing that particular laboratory designs or atmospheric conditions engender distinct compositional heterogeneity among particles containing black carbon. Lower-than-expected absorption results largely from increased heterogeneity, although slightly lowered absorption occurs even in a purely homogeneous system. This work provides a framework that explains globally disparate observations and that can be used to improve estimates of black carbon’s global impact.

## Abstract

Black carbon (BC) absorbs solar radiation, leading to a strong but uncertain warming effect on climate. A key challenge in modeling and quantifying BC’s radiative effect on climate is predicting enhancements in light absorption that result from internal mixing between BC and other aerosol components. Modeling and laboratory studies show that BC, when mixed with other aerosol components, absorbs more strongly than pure, uncoated BC; however, some ambient observations suggest more variable and weaker absorption enhancement. We show that the lower-than-expected enhancements in ambient measurements result from a combination of two factors. First, the often used spherical, concentric core-shell approximation generally overestimates the absorption by BC. Second, and more importantly, inadequate consideration of heterogeneity in particle-to-particle composition engenders substantial overestimation in absorption by the total particle population, with greater heterogeneity associated with larger model–measurement differences. We show that accounting for these two effects—variability in per-particle composition and deviations from the core-shell approximation—reconciles absorption enhancement predictions with laboratory and field observations and resolves the apparent discrepancy. Furthermore, our consistent model framework provides a path forward for improving predictions of BC’s radiative effect on climate.

Black carbon (BC) absorbs solar radiation and has a strong warming effect on climate, estimated as second only to

BC in the atmosphere is distributed among complex particles of varied size, shape, and chemical composition. However, atmospheric models necessarily approximate the full complexity and diversity of BC-containing particle composition and internal morphology, which we show affects model predictions of the associated absorption, typically leading to overestimates. First, while ambient BC exists as a fractal-like structure that may be embedded within or attached to other aerosol components in a variety of ways (12⇓⇓⇓–16) (Fig. 1 *A*–*C*), BC is typically approximated in models as a spherical core surrounded by a uniform coating, referred to as the core-shell approximation. This core-shell approximation yields greater enhancements in per-particle absorption with the accumulation of coating material than for calculations using more realistic treatments of particle internal morphology (7, 15, 17, 18). Here, we experimentally establish that the core-shell approximation indeed overestimates BC absorption and develop a robust, empirical correction for use in models. Second, and of particular importance, is how the distribution of BC and non-BC material across the particle population is treated. Ambient BC is distributed among diverse particles of varied composition (19, 20). Models, however, often apply the simplifying approximation that particles within the same population or class contain identical mass fractions of constituent aerosol species (21⇓⇓–24), which we refer to as the uniform composition approximation. Previous studies using the Particle Monte Carlo Model for Simulating Aerosol Interactions and Chemistry (PartMC-MOSAIC) have suggested that this uniform composition approximation artificially redistributes the coating material relative to the true, heterogeneous population and leads to an overestimation in modeled absorption enhancements (25⇓–27). In this study, we extend the particle-resolved modeling with PartMC-MOSAIC from ref. 26 using an experimentally determined parameterization for per-particle absorption enhancement and apply a Bayesian framework to estimate absorption enhancements under different model assumptions. We show that, by representing both heterogeneity in per-particle composition and deviations from the core-shell approximation, the improved model reconciles the disparity between modeled and observed light absorption enhancements.

## Inadequacy of the Core-Shell Approximation

Potential biases in modeled absorption enhancement (denoted *Methods*) (28). The BC4 measurements provide a process-level understanding of the response in BC absorption to internal mixing, made possible through improved methods for generating realistically complex primary BC particles and for mixing the BC with other aerosol components (e.g., secondary organic aerosol and sulfuric acid coatings). The observed enhancement for size- and mass-selected particles tends to increase with the volume ratio of non-BC components relative to BC (denoted *D*). Corresponding electron microscope images reveal that, for particles containing very little coating, the non-BC components tend to accumulate in voids within the fractal BC structure and are, therefore, unlikely to strongly enhance BC absorption. After all voids in the fractal BC particles are filled by non-BC material, which occurs at *A* and *B*. Our observations show that continued accumulation of non-BC material coincident with the collapse of the BC core engenders an increase in absorption, although the enhancement remains lower than predicted by the core-shell approximation (Fig. 1*D*). To account for these morphological effects on absorption cross-sections, we developed an empirical parameterization based on the BC4 data that can be applied to models that use the core-shell approximation (Eqs. **1** and **2** in *Methods*). The degree of disagreement between the core-shell model and the BC4 measurements shows some variation with BC core size, although these differences are typically within the **1** and **2**, which depends only on per-particle

Although the BC4 measurements, consistent with previous laboratory studies (6, 7), indicate that inadequacies of the core-shell approximation contribute to the overestimation in modeled *D*) (10). Thus, the differences in per-particle

## Importance of Compositional Heterogeneity

Enhancements in light absorption by a population of BC-containing particles depend not only on the response of per-particle absorption to the accumulation of coatings but, also, on the particle-to-particle variation in coating amount. The expected dependence of

By accounting for heterogeneity among BC-containing particles along with deviations from the core-shell approximation, our modeling framework reconciles the previously reported gap between modeled and observed *A*). For diverse particle populations, such as those considered here, most of the coating material tends to be mixed with particles containing the smallest amounts of BC mass (25, 26, 32), an effect resulting from the size dependence of the condensation and coagulation processes by which BC accumulates coatings. For a population of differently sized BC cores, the uniform composition approximation leads to an artificial, unrealistic redistribution of coating material from the particles containing small BC cores onto particles containing large BC cores. Importantly, because the particles containing large amounts of BC mass dominate absorption, the redistribution in coating material resulting from the uniform composition approximation leads to overestimation in overall absorption enhancement by populations of BC-containing particles. This is true whether or not deviations from the core-shell approximation are considered.

The ability of the improved model framework to resolve the model–measurement discrepancy is demonstrated by comparing the model predictions with observations of *Methods*). We find general consistency between the improved model predictions and the observations. Specifically, both the modeled and observed *A*), especially at large *B*).

## Reconciling Disparate Absorption Enhancement Measurements

We generalize the above findings by calculating *A* were determined. While the average modeled *C*–*E*)—greater heterogeneity results in smaller absorption enhancement. The variability within a population is quantified here as the standard deviation (SD) of the logarithm of per-particle *C*–*E*). The impact of particle heterogeneity generally increases with the overall amount of coating material, with larger differences in

For example, the particle-resolved simulations suggest that BC sampled in urban outflow exhibits tremendous particle-to-particle variability in *C*–*E*). Alternatively, in laboratory studies in which polydisperse BC is coated via condensation, the population of BC-containing particles will exhibit some variability in per-particle

## Discussion and Conclusion

This study provides a bottom-up modeling framework that reproduces measured absorption enhancements by BC-containing particles across field and laboratory measurements. Previous studies have typically implicated inaccurate representation of particle internal morphology and thus misapplication of the core-shell approximation as the reason for model–measurement differences (7, 15, 17, 34, 35). However, here we demonstrate that neglect of heterogeneity in particle composition is the dominant cause of previously reported discrepancies between models and observations, with failure of the core-shell approximation for less thickly coated BC being a secondary effect. Differences in

To facilitate comparison with measurements, the analysis presented here focuses on enhancements in BC’s light absorption due to dry, nonabsorbing coatings and, therefore, results in relatively small

## Methods

### BC4 Experiments.

The BC4 experiments quantified the dependence of absorption on coating amount for size-selected BC mass with uniform coating, which is used to derive the relationship between per-particle

### Empirical Relationship for Per-Particle E a b s .

As discussed in the text, comparison between *D*) and for the same volume-equivalent BC core diameter, *D*) shows that the core-shell model overestimates the observed

Similar in form to the parameterization given in equations 4 and 5 of ref. 7, the central estimate for

We applied a Bayesian approach to find the expected value of the parameter set

The expected value of

We found a threshold of **1** and **2** with these coefficients accurately reproduces the BC4 laboratory measurements independent of wavelength. Only results at 532 nm are presented in the text. All core-shell model calculations in this study were performed using PyMieScatt (44). The parameterization in Eqs. **1** and **2** is suitable for any model using the core-shell approximation, including reduced aerosol schemes used in global models. However, as we have shown in the main text, application of this parameterization for per-particle absorption is not sufficient to improve modeled absorption; models must also account for particle-to-particle heterogeneity in

### Predicting E a b s , b u l k from Particle-Resolved Model.

The population-level _{4}^{+}, Na^{+}, Ca^{2+}, other inorganic mass (including species such as

The absorption enhancement

The per-particle absorption enhancement is computed for each of the thousands of particles simulated by PartMC-MOSAIC using either the core-shell approximation or the empirical parameterization given in Eqs. **1** and **2**. At each model time step, PartMC-MOSAIC provides the mass of each aerosol species contained in each particle. Taking as inputs the volume-equivalent diameter of the BC core, the volume or thickness of the coating, and the wavelength-dependent refractive indices for the BC core and coating, the absorption enhancement under the core-shell approximation, **1** and **2** then predicts the adjusted

In order to assess the impact of the uniform composition approximation, we compared the enhancements from the particle-resolved simulations,

### Ensembles of Urban Scenarios.

To quantify the general dependence of

### Conditional Probability of E a b s , b u l k Given R B C , b u l k .

For a known

Similarly, the bivariate density function,

For the most realistic model approximation,

The trivariate density function

### Observations of E a b s by BC in Urban Outflow.

Model predictions of

### Bayes Factor for Evaluating Models.

The strength of the observational evidence in support of one model over another was quantified using the Bayes factor, K. In our case, the Bayes factor quantifies the likelihood given the observational evidence of an improved model,

### Data Availability.

PartMC version 2.1.5 was used for the simulations in this paper, which is available at http://lagrange.mechse.illinois.edu/partmc/. MOSAIC is available from Rahul A. Zaveri. The core-shell optical calculations were performed with PyMieScatt, which is available at https://github.com/bsumlin/PyMieScatt. The input files for the PartMC-MOSAIC simulations, the field and laboratory data shown in the figures, and the Python script used to analyze data and make figures are available at https://github.com/lfierce2/fierce2020_BC-abs-mixing.

## Acknowledgments

We acknowledge all participants of the BC4 laboratory study, including Leah Williams, Jesse Kroll, Ellie Browne, Gabriel Isaacman-Wertz, Yatish Parmar, James Brogan, Sara Forestieri, and Noopur Sharma. Parts of this study were completed using Michigan Technological University’s Applied Chemical and Morphological Analysis Laboratory. The BC4 study was supported by US Department of Energy (DOE) Grant DE-SC0011935 and National Science Foundation Grants AGS-1244918 (to Boston College) and AGS-1244999 (to Aerodyne). The participation of the single-particle soot photometer was made possible by a DOE Atmospheric Radiation Measurement Climate Research Facility small campaign grant. S.C. is supported by the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the DOE’s Office of Biological and Environmental Research at Pacific Northwest National Laboratory. L.F. was supported under the DOE Atmospheric System Research program at Brookhaven National Laboratory, a multiprogram national laboratory supported by DOE Contract DE-SC0012704.

## Footnotes

- ↵
^{1}To whom correspondence may be addressed. Email: lfierce{at}bnl.gov. ↵

^{2}Present address: Department of Chemistry and Physics, Western Carolina University, Cullowhee, NC 28723.↵

^{3}Present address: Air Quality Planning and Science Division, California Air Resources Board, Sacramento, CA 95814.

Author contributions: L.F., T.B.O., and C.D.C. designed research; L.F., T.B.O., C.D.C., C.M., S.C., J.B., P.D., D.A.F., T.H., A.T.L., A.J.S., G.D.S., and L.W. performed research; L.F. analyzed data; and L.F., T.B.O., C.D.C., and C.M. wrote the paper.

The authors declare no competing interest.

This article is a PNAS Direct Submission.

Data deposition: The input files for the PartMC-MOSAIC simulations, the field and laboratory data shown in the figures, and the Python script used to analyze data and make figures are available in GitHub, https://github.com/lfierce2/fierce2020_BC-abs-mixing.

- Copyright © 2020 the Author(s). Published by PNAS.

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

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