Scaling Laws for Light Absorption Enhancement Due to Nonrefractory Coating of Atmospheric Black Carbon Aerosol

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Scaling Laws for Light Absorption Enhancement Due to Nonrefractory Coating of Atmospheric Black Carbon Aerosol

Rajan K. Chakrabarty and William R. Heinson

Phys. Rev. Lett. 121, 218701 – Published 19 November 2018

Abstract

Black carbon (BC) aerosol, the strongest absorber of visible solar radiation in the atmosphere, contributes to a large uncertainty in direct radiative forcing estimates. A primary reason for this uncertainty is inaccurate parametrizations of the BC mass absorption cross section ( ${MAC}_{BC}$ ) and its enhancement factor ( $E_{{MAC}_{BC}}$ )—resulting from internal mixing with nonrefractory and nonlight absorbing materials—in climate models. Here, applying scaling theory to numerically exact electromagnetic calculations of simulated BC particles and observational data on BC light absorption, we show that ${MAC}_{BC}$ and $E_{{MAC}_{BC}}$ evolve with increasing internal mixing ratios in simple power-law exponents of $1 / 3$ . Remarkably, ${MAC}_{BC}$ remains inversely proportional to the wavelength of light at any mixing ratio. When mixing states are represented using mass-equivalent core-shell spheres, as is done in current climate models, it results in significant underprediction of ${MAC}_{BC}$ . We elucidate the responsible mechanism based on shielding of photons by a sphere’s skin depth and establish a correction factor that scales with a $¾$ power-law exponent.

Received 19 January 2018
Revised 8 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.218701

Physics Subject Headings (PhySH)

Atmospheric science Scaling laws of complex systems

Interdisciplinary Physics

Authors & Affiliations

Rajan K. Chakrabarty^1,2,* and William R. Heinson¹

¹Center for Aerosol Science and Engineering, Department of Energy, Environmental and Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
²McDonnell Center for the Space Sciences, Washington University in St. Louis, St. Louis, Missouri 63130, USA

^*Corresponding author. chakrabarty@wustl.edu

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Vol. 121, Iss. 21 — 23 November 2018

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Figure 1
Morphologies of internally mixed black carbon aggregates. Three simulated aggregates from this study that were “cherry picked” (shown in right column) demonstrate their close resemblance with real-world BC aerosol (left panel) corresponding to the three categories of internal mixing states as observed by China et al. [8]. The first-row particles represent bare BC aggregate with point contacting monomers and an open fractal morphology; partially coated aggregates are shown in the second row; and thickly coated or embedded aggregates are displayed in the third row. The total particle mass to BC mass ratio is shown in the center for each class of particle.
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Figure 2
The $1 / 3$ scaling laws for BC mass absorption cross section ( ${MAC}_{BC}$ ) and enhancement of ${MAC}_{BC}$ ( $E_{{MAC}_{BC}}$ ). The ${MAC}_{BC}$ vs total coated aggregate mass divided by its bare BC mass ( $M_{total} / M_{BC}$ ) at wavelengths $λ = 405$ , 532, and 880 nm is shown in (A). At all $λ$ , ${MAC}_{BC}$ scales with a power-law exponent of $0.33 \pm 0.05$ . Our work compares well with observational findings on cook stove emissions done by Saliba et al. [23], while data from Liu et al. [13] have smaller prefactors owing to integrated absorption measurements as opposed to the single particle, yet their trends are parallel to the other data sets. (b). The enhancement of the absorption $E_{{MAC}_{BC}}$ of internally mixed BC is plotted versus $(M_{total} / M_{BC})$ . The “Meta Data” set of points represent the mean values of all observational data sets; the error bars represent 2 standard deviations. Independent of $λ$ , $E_{{MAC}_{BC}}$ for all data sets follows the same upward increasing trend with a power-law exponent of $0.32 \pm 0.05$ . The $E_{{MAC}_{BC}}$ estimates from our simulation agree very well (regression coefficient $R^{2} = 0.89$ ) with findings from past observational field studies carried out globally [9, 10, 11, 13]. This agreement suggests a universal behavior for $E_{{MAC}_{BC}}$ for internally mixed BC at visible and near infrared wavelengths.
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Figure 3
Inverse wavelength scaling of BC mass absorption cross section ( ${MAC}_{BC}$ ). The spectral response of MAC values for BC aggregates with varying degrees of mixing states are shown to follow an inverse functionality in wavelength (power law with exponent of $- 1$ ). The fractal prefactor $B_{λ}$ ranges from 3.5 (bare) to 5.2 (partially coated) to 7.8 (embedded), and denotes the enhancement in ${MAC}_{BC}$ through the phenomenological “lensing effect.” Observational data sets collected over California, USA (Gyawali et al. [40]) and Manchester, UK (Liu et al. [13]) follow the scaling trends. Error bars indicate the standard deviation in the reported measurements.
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Figure 4
Role of particle morphology in light absorption. The strength of internal light absorption is shown for BC particles in their bare and heavily coated states [panels (a)–(f)]. The coating material is nonabsorbing and is therefore invisible in this representation. The incident light impacts the particles from the left. (a) BC sphere of diameter of $D = 80 nm$ ; (b) same sphere as (a) but having a 90 nm thick layer of coating; (c) BC sphere of $D = 300 nm$ ; (d) same sphere as (c) but with a 260 nm coating; and (e) and (f) represent BC aggregates having volume equivalence to spheres in (c) and (d), respectively. Particles in (b), (d), and (f) are heavily coated which results in stronger absorption due to the lensing effect. The diameter of spherical BC cores in (c) and (d) is larger than the absorption skin depth resulting in the interior of the particle being excluded from contributing to light absorption. The BC aggregate is porous in structure and therefore light penetrates completely into it, allowing the entire volume to add to the total absorption [panels (e)–(f)]. (g) The ${MAC}_{BC}$ ratios for coated aggregates to core shell is plotted versus the mass equivalent sphere diameter $D_{eq, BC}$ divided by absorption skin depth. Significant disagreement is seen between the fractal and core-shell approximation models as $D_{eq, BC}$ becomes greater than the skin depth. As the equivalent spheres become larger than the absorption skin depth, the core-shell model underpredicts the ${MAC}_{BC}$ of the aggregates. The shaded region scales as $({MAC}_{BC} / {MAC}_{BC, core shell}) \propto {(D_{eq, BC} / skin depth)}^{0.75}$ .
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