Source-Based Size-Resolved Optical Properties of Carbonaceous Aerosols

: In this study, the source-based optical properties of polydisperse carbonaceous aerosols were determined from PM 2.5 concentrations measured at a Global Atmospheric Watch station in South Korea. The extinction and absorption coefﬁcients of carbonaceous aerosols were calculated using the Mie theory and assuming a lognormal size distribution. Based on the mass concentration from the EPA’s Positive Matrix Factorization (PMF) receptor model, which considers ﬁve source identiﬁcation and apportionment factors (biogenic source, local biomass burning, secondary organic aerosol, transported biomass burning, and mixed sources), the source-based size-resolved mass extinction and absorption efﬁciencies were estimated for each source using a multilinear regression model. The results show that the source-based optical properties depend on the aerosol size and physicochemical characteristics of the chemical compounds. The long-range transport of biomass burning (LBB) aerosol, which has a mass concentration of 20%, holds a 12.1–23.1% total extinction efﬁciency—depending on the size and refractive index—in the range of 0.1–0.5 µ m in geometric mean diameter and humic-like substances (HULIS) imaginary refractive index of 0.006–0.3. Biogenic sources of aerosols with small diameters have higher mass absorption efﬁciencies (MAE) than other sources, depending on the size and refractive index.


Introduction
Carbonaceous aerosols are composed of organic aerosols and refractory light-absorbing components, generally referred to as elemental carbon or black carbon [1]. Organic aerosols contain thousands of organic compounds and account for 20-50% of the total fine aerosol mass at mid-latitudes [2,3]. The organic aerosols originate from both anthropogenic sources, such as fossil fuel combustion, and biogenic sources. In addition, an organic aerosol is either directly emitted in particulate form (primary organic aerosol) or generated in the air (secondary organic aerosol) [4]. Organic aerosols can be divided into water-soluble organic carbon and water-insoluble organic carbon. Humic-like substances account for a substantial fraction of the water-soluble organic carbon. In general, humic-like substances are weak absorbers. However, the results of several studies have showed that the imaginary refractive index of absorbing aerosols, such as humic-like substances and brown carbon, is much higher and its contribution to absorption may therefore be important [5][6][7][8][9][10]. Receptor models are used to infer source contributions by determining the linear combination of emission source chemical compositions that best fits the chemical composition of ambient samples [11]. A regional Global Atmospheric Watch (GAW, 36 • 32 N; 126 • 19 E, 45.7 m above sea level) station was established by the Korean Meteorological Administration on Anmyeon Island on the midwestern coast of South Korea. One of the goals of the GAW station is to monitor the variations in components that might affect climate change.
Many studies have been conducted to understand the effects of aerosols on the climate. For example, optical properties, such as radiative forcing, have been characterized using direct measurements [12,13]. Chemical composition-based optical properties are also important for understanding the contribution of aerosol species and their effects on climate [7,14,15]. In addition, source-based aerosol optical properties can provide information about their effects on the climate [16]. Han et al. [17] measured the carbonaceous aerosol compounds in PM 2.5 samples and determined the major factors affecting the carbonaceous organic compounds at the Anmyeon GAW station using a receptor model. In this study, the source-based mass extinction efficiency of polydisperse aerosols was estimated from source apportionment-based chemical species-resolved mass contribution results [17]. The size-resolved extinction and absorption coefficients of carbonaceous aerosols were calculated using the Mie theory and the mass extinction and absorption efficiencies of each of the five sources of the EPA's Positive Matrix Factorization (PMF) model were estimated using a multilinear regression model.

Data
The study site was the GAW station on Anmyeon Island (36.32 • N, 126.19 • E, altitude: 45.7 m) on the western coast of Korea ( Figure 1). A total of 34 Samples from Anmyeon Island were measured every 6 days from 2 July 2015, to 2 April 2016, on the rooftop of the GAW station. A total of 34 samples were analyzed after quality control. A high-volume air sampler with a flow rate of 1000 L min −1 was used. The PM 2.5 samples were collected using quartz fiber filters (203 mm × 254 mm, Whatman Inc., Maidstone, UK). The organic carbon, elemental carbon (EC), water-soluble organic carbon (WSOC), and humic-like substances (HULIS) concentrations were measured. A detailed description of the data and sampling methodology can be found in previous studies [14,17]. Figure A1 shows the composition-based mass concentrations and contributions of carbonaceous aerosols.

Receptor Modeling
The source-based mass concentrations were obtained from a receptor model (US EPA PMF v5.0) [18]. The PMF is a multivariate factor analysis tool that decomposes a matrix of speciated sample data into two matrices: source profile and source contribution [18,19].
The concentrations were used as measured data, and the error fractions and 1/2 of

Receptor Modeling
The source-based mass concentrations were obtained from a receptor model (US EPA PMF v5.0) [18]. The PMF is a multivariate factor analysis tool that decomposes a matrix of speciated sample data into two matrices: source profile and source contribution [18,19].
The concentrations were used as measured data, and the error fractions and 1/2 of the method detection limit values were used as the overall uncertainty assigned to each observation [17].
Based on the study by Han et al. [17], the profiles and relative contributions of five factors were used: (1) secondary organic aerosols (SOA); (2) biogenic sources, identified based on the characteristics of the profile and seasonal trend of the relative contribution; (3) long-range transport of biomass burning (LBB); (4) local biomass burning (local BB); and (5) various sources, including vehicular and other combustion sources, such as biomass burning, based on the mixed characteristics.

Size-Resolved Aerosol Optical Properties
Aerosol optical properties play important roles in regulating the Earth's radiation budget. The light scattering and absorption properties of atmospheric aerosols depend on the aerosol size distribution, chemical composition, and refractive index, which means that the contribution of aerosol optical properties differs from the mass contribution.
The aerosol extinction coefficient (b ext ) can be calculated using the Mie theory based on the mass concentration, chemical composition, and size distribution [7,14]. Figure A2 shows the composition-based extinction coefficients (b ext ) of carbonaceous aerosols with different geometric mean diameters (d g0 ) and imaginary refractive indices (IRIs) of HULIS of 0.006 and 0.3. The refractive indices are 1.9-0.66i for EC, 1.595-IRIi (i.e., 1.595-0.006i and 1.595-0.3i) for HULIS and 1.53-0.006i for WSOC and WISOC (water-insoluble organic carbon) [14]. It should be noted that there uncertainty exists in calculating aerosol optical properties by the Mie theory. The Mie theory assumes aerosols are spherical particles, and so does not consider the morphology of non-spherical aerosols, or their aggregation. The model of homogeneous compact particles results in a systematic underestimation of the scattering phase function for almost all angles, but most typically, in the backscatter zone [20]. The impact of material mixing on the absorption efficiency of carbonaceous particles increases with the particle size and for particles with high carbon content [21]. More rigorous studies should be conducted that consider the non-spherical shape and aggregation of particles in order to accurately estimate aerosol optical properties.

Source-Based Aerosol Optical Properties of Polydisperse Carbonaceous Aerosols
The source-based receptor model provides information about the aerosol sources. The receptor model can be used to estimate the contribution of each source to the compositionbased mass concentration.
In this study, source-based optical properties were obtained from the source-based mass concentration, size distribution, and refractive index. Figure 2 shows the schematic diagram for calculating the source-based optical properties of polydisperse carbonaceous aerosols.
For the mass concentration of a given species, the extinction coefficient (b ext,i ) and mass extinction efficiency of carbonaceous aerosols can be simplified as follows [16,22,23]: where MEE i is the mass extinction efficiency in m 2 /g and C i is the mass concentration of the ith carbonaceous composition (µg/m 3 ). The receptor model can be used to estimate the contribution of each source to the composition-based mass concentration. In this study, source-based optical properties were obtained from the source-based mass concentration, size distribution, and refractive index. Figure 2 shows the schematic diagram for calculating the source-based optical properties of polydisperse carbonaceous aerosols. For the mass concentration of a given species, the extinction coefficient (bext,i) and mass extinction efficiency of carbonaceous aerosols can be simplified as follows [16,22,23]: where MEEi is the mass extinction efficiency in m 2 /g and Ci is the mass concentration of the ith carbonaceous composition (μg/m 3 ). The bext value can be calculated using the Mie theory based on the refractive index and size distribution of the carbonaceous aerosol. A lognormal size distribution was assumed in this study. The lognormal size distribution for mass concentration ( ) can be expressed as a function of the dg0 and geometric standard deviation ( ) as follows.
where, is the geometric standard deviation and is particle diameter. From bext and the mass concentration, the mass extinction efficiency (MEE) can be obtained using Equation (1). Table A1 shows the MEE, mass absorption efficiency (MAE), The b ext value can be calculated using the Mie theory based on the refractive index and size distribution of the carbonaceous aerosol. A lognormal size distribution was assumed in this study. The lognormal size distribution for mass concentration (n M lnd p ) can be expressed as a function of the d g0 and geometric standard deviation (σ g ) as follows.
where, σ g is the geometric standard deviation and d p is particle diameter. From b ext and the mass concentration, the mass extinction efficiency (MEE) can be obtained using Equation (1). Table A1 shows the MEE, mass absorption efficiency (MAE), and refractive index of the carbonaceous species based on different size distributions and refractive indices of HULISs.
Based on the b ext value and source-based mass concentration from the receptor model (C s ), the source-resolved optical properties can be obtained. The total mass concentration of the carbonaceous aerosol comprises each carbonaceous aerosol species. In addition, the receptor model can be used to express the mass concentration as a combination of each source (Jung et al., 2018). In this study, we used source-based mass concentrations (C s ) from the PMF receptor model. Subsequently, the source-based MEEs and MAEs were obtained from the source-based mass concentration from the PMF receptor model and b ext values calculated using the Mie theory [16,[22][23][24]: where MEE s and MAE s are the mass extinction and absorption efficiencies in m 2 /g, respectively, and C s is the mass concentration of the sth source-based on the PMF model (µg/m 3 ). In this study, the MEEs of each source were obtained using multilinear regression, where the mass concentration of each source from the PMF model is the dependent variable and the aerosol extinction coefficient is the independent variable. Subsequently, source-based mass extinction coefficients for source s were calculated as follows: The obtained extinction coefficient is statistically significant at the 99% confidence level. A more detailed methodological description for obtaining the source-based size-dependent optical properties can be found in a previous publication [16]. Table 1 shows the source-based MAEs and MEEs for different d g0 and IRIs of HULIS. The σ g is assumed to be 1.5. The d g0 of 0.1 and 0.5 µm and IRIs of 0.006 and 0.3 are compared. Table 1 shows that the MEEs of biogenic sources are relatively higher than that of other sources at a d g0 of 0.1 compared with that at 0.5 µm. This means that the biogenic source is closely related to EC. Figure A3 shows the size-resolved MEE of each carbonaceous aerosol. As shown in Figure A3, the 0.3 for MEE of EC and for HULIS for IRI is higher for small particles and decreases as d g0 increases. Because of the size dependency of source aerosol, the MEEs of LBB and local BB are higher at a d g0 of 0.5 µm compared with those at a d g0 of 0.1 µm. The MAE of the biogenic source is higher at a d g0 of 0.1 µm compared with that at a d g0 of 0.5 µm. The MAEs become higher for all sources as the IRI of HULIS increases. Table 1 also shows that the single scattering albedo (SSA) differs depending on the d g0 . The SSA for smaller biogenic source particles was lower than other sources. The influence of the HULIS imaginary refractive index on SSA is greater at smaller particle sizes. This is because the MEE and MAE is more sensitive to small particles than large particles.  Figure 3 shows the source-based extinction (b ext,s ) and absorption coefficient (b abs,s ) of carbonaceous aerosols with different d g0 and IRIs of HULISs. In this study, d g0 values of 0.1 and 0.5 µm and IRIs of 0.006 and 0.3 were considered. The source-based extinction (b ext,s ) and absorption (b abs,s ) coefficients can be calculated from the source-based MEEs and MAEs using Equation (4) and the source-based mass concentration from the PMF model. Figure 3 shows that the source-based extinction (b ext,s ) and absorption coefficient (b abs,s ) depend on d g and IRI. Overall b ext is larger at a d g0 of 0.5 µm than at 0.1 µm for IRIs of 0.006. On the contrary, b abs is larger at a d g0 value of 0.1 µm than at 0.5 µm. The IRI of the HULIS significantly affects b abs , which means that b abs at an IRI of 0.3 is larger than at 0.006.       Because of the lack of information regarding the source-based size distribution, we evaluated the contribution of extinction coefficients with different size. Figure 6 shows the comparison of the average source-based extinction coefficients for different dg0. A dg0 value of 0.5 μm and IRI of 0.006 represent the background condition. The sources with different dg0 (0.1 μm) were compared with the background conditions of other sources. Note that the mass concentration of each source did not change with dg0. Figure 6 shows that the contribution of bext differs depending on the dg0 value of the source. Generally, the contribution of sources decreases with decreasing dg0 value (dg0 of 0.1 μm in this study). However, the magnitude of the decrease depends on the source. Based on the source-based mass concentration, the contributions can be ordered as follows: LBB > mixed > SOA > biogenic > local BB. However, Figure 6 shows that the contributions of the source-based extinction coefficients differ depending on the size distribution of the sources. Although Figure 6 shows the size dependency of source-based aerosol optical properties, this study assumed that the size distribution of each species was conserved without aggregation and this assumption may lead to potential errors as discussed in Section 2 and conclusions [20,21]. Because of the lack of information regarding the source-based size distribution, we evaluated the contribution of extinction coefficients with different size. Figure 6 shows the comparison of the average source-based extinction coefficients for different d g0 . A d g0 value of 0.5 µm and IRI of 0.006 represent the background condition. The sources with different d g0 (0.1 µm) were compared with the background conditions of other sources. Note that the mass concentration of each source did not change with d g0 . Figure 6 shows that the contribution of b ext differs depending on the d g0 value of the source. Generally, the contribution of sources decreases with decreasing d g0 value (d g0 of 0.1 µm in this study). However, the magnitude of the decrease depends on the source. Based on the source-based mass concentration, the contributions can be ordered as follows: LBB > mixed > SOA > biogenic > local BB. However, Figure 6 shows that the contributions of the source-based extinction coefficients differ depending on the size distribution of the sources. Although Figure 6 shows the size dependency of source-based aerosol optical properties, this study assumed that the size distribution of each species was conserved without aggregation and this assumption may lead to potential errors as discussed in Section 2 and conclusions [20,21]

Summary and Discussions
In this study, the source-based optical properties of polydisperse carbonaceous aerosols were investigated based on the measurements of PM2.5 concentrations at the GAW station, Anmyeon Island, on the western coast of Korea. The PM2.5 samples were collected every six days from July 2015 to April 2016. The optical properties, such as the extinction and absorption coefficient, of carbonaceous aerosols were calculated using the WSOC, WISOC, HULIS, and EC contents. The source-identified mass extinction and absorption efficiencies and optical properties were obtained based on the source-based mass concentration from the PMF model.
The results show that the source-based aerosol optical properties (MEE, MAE and SSA) depend on the size distribution and the refractive index of the absorbing aerosol, which is related to the chemical composition. Compared to MEE, MAE was higher for aerosols with small diameters because of the absorption properties of EC and HULIS. The biogenic source of aerosols with small diameters has a higher MAE than other sources. The MAE for biogenic sources at a of 0.01 is 0.89 m 2 /g, which is higher than 0.38 m 2 /g at a of 0.5 μm ( of 1.5, HULIS IRI of 0.006). On the contrary, MAE for large particles

Summary and Discussions
In this study, the source-based optical properties of polydisperse carbonaceous aerosols were investigated based on the measurements of PM 2.5 concentrations at the GAW station, Anmyeon Island, on the western coast of Korea. The PM 2.5 samples were collected every six days from July 2015 to April 2016. The optical properties, such as the extinction and absorption coefficient, of carbonaceous aerosols were calculated using the WSOC, WISOC, HULIS, and EC contents. The source-identified mass extinction and absorption efficiencies and optical properties were obtained based on the source-based mass concentration from the PMF model.
The results show that the source-based aerosol optical properties (MEE, MAE and SSA) depend on the size distribution and the refractive index of the absorbing aerosol, which is related to the chemical composition. Compared to MEE, MAE was higher for aerosols with small diameters because of the absorption properties of EC and HULIS. The biogenic source of aerosols with small diameters has a higher MAE than other sources. The MAE for biogenic sources at a d g0 of 0.01 is 0.89 m 2 /g, which is higher than 0.38 m 2 /g at a d g0 of 0.5 µm (σ g of 1.5, HULIS IRI of 0.006). On the contrary, MAE for large particles was relatively consistent regardless of the source. This study also shows that the source-based SSA (single scattering albedo) depends on the source-based size distribution and refractive index of HULIS under the condition of the same mass special concentration. The SSA for smaller biogenic source particles was lower than for other sources. The influence of the HULIS imaginary refractive index on SSA is greater at smaller particle sizes. This is because the MEE and MAE is more sensitive to small particles than large particles. Consequently, the source-based contribution of total extinction coefficient depends on the source-based mass concentration and corresponding MEE and size distribution. LBB aerosol, which has a mass concentration of 20%, for example, holds a 12.1~23.1% total extinction efficiency-depending on the size and refractive index-in the range of 0.1~0.5 µm in d g0 and a HULIS IRI of 0.006~0.3. In conclusion, the aerosol optical properties depend on the physico-chemical characteristics of the aerosol source. These characteristics are important for estimating source-based optical properties and the related climate effects of aerosols. More combinations of different aerosol sources with different sizes and refractive indices for absorbing aerosols may result in a wider range of optical properties and related climate effects.
In this study, we made the simple polydisperse aerosol assumption, which assumes that aerosols retain a lognormal size distribution. This assumption does not consider the aggregation of individual particles which can lead to discrepancies and error. Thus, alternative methods, such as the Rayleigh-Debye-Gans theory for aggregates [25] and the T-matrix method for non-spherical particles [26], should be utilized. However, most aerosol retrieval algorithms are based on the Mie theory, although there is sufficient theoretical evidence that the non-sphericity of dust particles can cause scattering properties different from those predicted by the Mie theory [27]. It should be also noted that, despite these deficiencies, the Mie theory usually calculates MEE with high accuracy based on the known mass-size distribution of chemical components [28,29]. The relation between the mass concentration of the sampled chemical species and their source-based mass concentration with individual particles behavior is complex and should be considered under the simple assumption when detailed experimental data are unavailable. This absence of detailed measurement data for the validation of accurate simulations is one of the main reasons that many studies, including our study, assume simple physico-chemical characteristics despite the limitations. By considering all these points of view, in this study, the Mie theory was used under confined conditions. More rigorous methods are required for further study to overcome the limitations of the Mie theory.

Conflicts of Interest:
The authors declare no conflict of interest.