Estimation of Source-Based Aerosol Optical Properties for Polydisperse Aerosols from Receptor Models

We estimated source-based aerosol optical properties for polydisperse aerosols according to a chemical-species-resolved mass contribution method based on source apportionment. We investigated the sensitivity of aerosol optical properties based on PM2.5 (particulate matter that have a diameter of less than 2.5 micrometers) monitoring results. These aerosols were composed of ions, metals, elemental carbon, and water-soluble organic carbon which includes humic-like carbon substances and water-soluble organic carbon. We calculated aerosols’ extinction coefficients based on the PM2.5 composition data and the results of a multivariate receptor model (Solver for Mixture Problem model, SMP). Based on the mass concentration of chemical composition and nine sources calculated with the SMP receptor model, we estimated the size-resolved mass extinction efficiencies for each aerosol source using a multilinear regression model. Consequently, this study quantitatively determined the size resolved sources contributing to the apportionment-based aerosol optical properties and calculated their respective contributions. The results show that source-resolved mass concentrations and extinction coefficients had varying contributions. This discrepancy between the source-based mass concentration and extinction coefficient was mainly due to differences between the source-dependent aerosol size distribution and the aerosol optical properties from different sources.


Introduction
Atmospheric aerosols originate from a wide variety of natural and anthropogenic sources.A combination of various sources and physical and chemical processes generates these atmospheric aerosols.The optical properties of atmospheric aerosols play a key role in earth's radiation budget.They depend on size distribution, chemical composition, mass concentration, density, and wavelength.These optical properties are represented by the refractive index.For example, aerosol scattering is in Seoul, Korea, we calculated the sensitivity of the total aerosol extinction coefficient (b ext ) using Mie theory for polydisperse aerosol by modifying size distribution assumptions.Here, OM was composed of water-soluble organic matter (WSOM), humic-like carbon substances (HULIS-C), and water-insoluble organic matter (WISOM).Subsequently, we estimated the size-resolved source-based MEEs using their source-based mass concentrations and contributions from the SMP receptor model [14].We used the multilinear regression (MLR)-and Mie theory-based model to estimate and calculate the optical properties of polydisperse aerosols in relation to their source.To estimate the absorption properties of HULIS-C, we also tested the sensitivity of size-resolved, source-based HULIS-C MEEs by changing the imaginary refractive index of HULIS-C.

Data
We analyzed the one-year PM2.5 sampling data from a previous study [14], in which a detailed description of the sampling measurements can be found.In order to determine PM2.5 total mass and ion concentrations, 24 h PM2.5 data were collected on pre-weighted 47 mm Teflon filters (Zefluor TM , Pall Corp., Port Washington, NY) using a low-volume (flow rate, 16.7 L min −1 ) sampler.This sampler was equipped with Teflon-coated aluminum cyclone on the rooftop of the Korea Institute of Science and Technology, located northeast of downtown Seoul, Korea (37.603 • N, 127.047 • E, at 58 m above sea level).The PM2.5 was measured daily during a one-year period from October 2012 to September 2013.The PM2.5 mass concentrations, inorganic ions, EC, OM (composed of WSOC, WISOC, and HULIS-C), NaCl, and crustal components were chemically analyzed.
On the basis of PM2.5 chemical species, composed of inorganic matter (ammonium, sulfate, and nitrate), carbonaceous organic matter, NaCl, and crustal components, we applied the SMP model.The PM2.5 source apportionment results reported in Kim et al. [14] indicate the source-based mass concentration and their mass contributions.
As Figure S1a shows, the PM2.5 measurement data and SMP estimated data have good agreement without significant loss of accuracy, which confirms that the data are reliable.Supplementary Figure S1b also shows the comparison of the PM2.5 mass concentration with the extinction coefficient with geometric mean diameter (d g ) of 0.1 µm at geometric standard deviation (GSD) of 1.5.Generally, also these data are in good agreement, as shown in Supplementary Figure S1.A more detailed explanation and comparison of source-based mass contribution with source-based extinction coefficient (b ext ) contribution will be given at Section 3.

Extinction Coefficient (b ext ) Calculations for Polydisperse Aerosols
Generally, the contribution of aerosol optical properties (scattering and absorption) differ owing to the characteristics of each chemical compound.Figure 1 shows a schematic diagram of how to obtain source-based aerosol optical properties of polydisperse aerosol particles from the SMP model and Mie theory [15].Three steps are required.First, size-resolved aerosol optical properties (aerosol extinction and the scattering and absorption coefficients) can be obtained on the basis of input variables such as the chemical-species-based mass concentration of the PM2.5 measurement, lognormally assumed aerosol size distribution, aerosol densities, and wavelength (550 nm in this study) using Mie theory.Second, the SMP receptor model can derive source-based mass concentrations.Third, from size-resolved aerosol mass extinction coefficients using Mie theory and source-based mass concentrations, sourceand size-resolved mass extinction efficiencies can be estimated using the MLR model [10].As outlined above, the b ext value at a given size distribution was calculated with Mie theory, and the source-based MEE was calculated from the size-resolved b ext and source-based mass concentration.To calculate the aerosol extinction coefficient (b ext ), the mass concentrations of inorganic ions, EC, OM (WSOM, HULIS, WISOM), NaCl, and crustal component, as well as aerosol properties (size distributions, densities, refractive index) are necessary as input data.Here, we basically used the same refractive index for OM; only the HULIS refractive index was sensitively investigated.Table 1 lists the refractive indices at a wavelength of 550 nm and the densities of the various aerosol components used in this study [16][17][18][19][20][21].We assumed a log-normal aerosol size distribution.An organic aerosol can be divided into water-soluble (HULIS and WSOC) and water-insoluble components.With these assumptions and initial data, we calculated the total aerosol extinction coefficient based on Mie theory.From the total b ext and total mass concentration, the MEE, MSE, and MAE were obtained under the assumption that the aerosol was internally mixed.Figure 2 shows the sensitivities of mass efficiencies (MEE, MSE, and MAE) as a function of the d g and the GSD of internally mixed aerosols.The d g of 0.1-2.5 µm and the GSD of 1.5-2.5 were considered.As shown in Figure 2, the calculated scattering, absorption, and extinction efficiencies had different values for the different GSDs and d g .Generally, the mass efficiencies had a peak value around d g = 0.3 µm for a GSD of 1.5.However, the d g at which mass efficiencies had their maximum value decreased as the GSD increased.(Supplementary Figure S2 shows the sensitivity of the MEE for EC, inorganic ion, OM, NaCl, and crustal aerosol.)A physical relationship between light extinction and atmospheric particle composition for externally mixed aerosol can be expressed by the following equations with respect to a given particle concentration, size distribution, refractive indices, and densities of each chemical species [3,16,21]: where bext,i is the extinction coefficient associated with the ith species; n(dp) is the number distribution; ,  , ,  is the extinction efficiency of a particle with a diameter, dp and a refractive index, m, at a specific wavelength, λ, for the ith species.It should be noted that bext can be expressed as a function of particle size.For a given mass concentration, the overall extinction coefficient expressed in Equations ( 1) and ( 2) can be simplified as follows: where MEEi is the mass extinction efficiency in m 2 g −1 , and Ci is the mass concentration of the ith chemical species (in µg m −3 ).In this study, the resultant expression of bext and babs for a dry aerosol can be expressed as follows: where the MEE for each species is usually considered constant.However, for polydisperse aerosols, we must use size-dependent MEEs.We obtained the MEE using Equation ( 5) from the bext and mass concentration.The MEE is defined as the ratio between the aerosol extinction coefficient and the aerosol mass concentration in a unit volume of air [7,22].A physical relationship between light extinction and atmospheric particle composition for externally mixed aerosol can be expressed by the following equations with respect to a given particle concentration, size distribution, refractive indices, and densities of each chemical species [3,16,21]: where b ext,i is the extinction coefficient associated with the ith species; n(d p ) is the number distribution; Q ext,i d p , λ, m is the extinction efficiency of a particle with a diameter, d p and a refractive index, m, at a specific wavelength, λ, for the ith species.It should be noted that b ext can be expressed as a function of particle size.For a given mass concentration, the overall extinction coefficient expressed in Equations ( 1) and (2) can be simplified as follows: where MEE i is the mass extinction efficiency in m 2 g −1 , and C i is the mass concentration of the ith chemical species (in µg m −3 ).In this study, the resultant expression of b ext and b abs for a dry aerosol can be expressed as follows: where the MEE for each species is usually considered constant.However, for polydisperse aerosols, we must use size-dependent MEEs.We obtained the MEE using Equation ( 5) from the b ext and mass concentration.The MEE is defined as the ratio between the aerosol extinction coefficient and the aerosol mass concentration in a unit volume of air [7,22].
We assumed that aerosols follow a log-normal size distribution, which is expressed as a function of d g and the GSD. Figure 3 shows the size-resolved MEEs for different chemical species and GSDs.A d g range of 0.1-2.5 µm was considered, and GSDs of 1.5, 2.1, and 2.5 were compared.As shown in Figure 3, the MEEs had different distributions that depended on the chemical species, which were characterized by different size distributions.According to Malm et al. [23], the MEE values for inorganic ion, OM, NaCl, crust, and EC are 3.0, 4.0, 1.7, 1.0, and 10.0 m 2 g −1 , which represent constants at specific conditions among the widely distributed MEEs.We assumed that aerosols follow a log-normal size distribution, which is expressed as a function of dg and the GSD.
Figure 3 shows the size-resolved MEEs for different chemical species and GSDs.A dg range of 0.1-2.5 µm was considered, and GSDs of 1.5, 2.1, and 2.5 were compared.As shown in Figure 3, the MEEs had different distributions that depended on the chemical species, which were characterized by different size distributions.According to Malm et al. [23], the MEE values for inorganic ion, OM, NaCl, crust, and EC are 3.0, 4.0, 1.7, 1.0, and 10.0 m 2 g −1 , which represent constants at specific conditions among the widely distributed MEEs. Figure 3 implies that the MEEs for polydisperse aerosols are influenced by many factors, including emissions, chemical signature, and meteorology.This suggests that we must pay careful attention when applying MEEs from previous studies that may have used different spatiotemporal conditions.Figure 3 implies that the MEEs for polydisperse aerosols are influenced by many factors, including emissions, chemical signature, and meteorology.This suggests that we must pay careful attention when applying MEEs from previous studies that may have used different spatiotemporal conditions.

Source-Based Aerosol Mass Extinction Efficiency for Polydisperse Aerosol Particles
Based on the size-resolved b ext and source-resolved mass concentrations, we could estimate the size-resolved and the source-resolved MEEs.The total aerosol b ext can also be expressed as a combination of each source-based extinction coefficient.Here, we obtained the source-based MEEs from the source-based mass concentration in the SMP receptor model, and the total aerosol extinction coefficient from Mie theory.We estimated MEEs by applying the MLR method [24]: where MEE s is the mass extinction efficiency of sth source (in m 2 g −1 ), and C s is the mass concentration of the sth source from the SMP results (in µg m −3 ).Multilinear regression is a useful tool for estimating aerosol optical parameters, such as MEE [10][11][12].For example, a previous study [11] investigated aerosol optical properties, mass concentrations, and chemical compositions over a one-year period and obtained the total scattering coefficient using MLR analysis.The authors calculated the total scattering coefficient as the independent variable, and the sulfate ion, nitrate ion, mineral matter, organic and elemental carbon, and residual fraction mass concentrations as the dependent variables.
Using Equation ( 6), we obtained the total aerosol b ext in Equation ( 3) based on the mass concentration of the sources.As explained, the SMP model can provide the mass concentration of each source.Subsequently, the MLR method can provide the MEE of each source.All the derived MEEs from MLR were within the 95% confidence interval and significance at the 0.05 level.It should be also noted that all b ext and MEE values are size-dependent [25].We carefully estimated the MEEs for polydisperse aerosols as a function of d g and GSD.Among the nine sources based on the SMP results [14], contributions from WB were very low, except for four days when the WB contribution was high.For this reason, WB was not considered, and we excluded the optical contribution from WB when estimating b ext and MEEs.
As the properties (MEE, MAE, and MSE) are size-dependent for each chemical compound and source, there are many ranges depending on GSD and d g .Table 2 shows the ranges of MEE, MAE, and MSE for each source for GDS of 1.5-2.5 and d g of 0.1-2.5 µm.The values extended over a wide range.Taking TS as an example, the maximum MEE, MAE, and MSE ranged from 0.098 to 4.471, 0.000 to 0.112, and 0.061 to 4.471 m 2 g −1 , respectively.Figure 4 shows the size-resolved MEE for each different source based on the results of Equation (6).A dg of 0.1-2.5 µm and GSDs of 1.5, 2.1, and 2.5 were considered.For a GSD of 1.5, maximum MEEs were 4.471 m 2 g −1 for TS (dg of 0.3 µm), 3.802 m 2 g −1 for LS (dg of 0.4 µm), 5.064 m 2 g −1 for LN (dg of 0.3 µm), 3.418 m 2 g −1 for G (dg of 0.3 µm), 11.004 m 2 g −1 for D (dg of 0.2 µm), 10.229 m 2 g −1 for TBB (dg of 0.3 µm), 6.335 m 2 g −1 for LBB (dg of 0.3 µm), and 1.655 m 2 g −1 for FSD (dg of 0.3 µm).As the properties (MEE, MAE, and MSE) are size-dependent for each chemical compound and source, there are many ranges depending on GSD and dg.Table 2 shows the ranges of MEE, MAE, and MSE for each source for GDS of 1.5-2.5 and dg of 0.1-2.5 µm.The values extended over a wide range.Taking TS as an example, the maximum MEE, MAE, and MSE ranged from 0.098 to 4.471, 0.000 to 0.112, and 0.061 to 4.471m 2 g −1 , respectively.
Table 2. Ranges of MEE, MAE, and MSE for each source in the GSD range of 1.5-2.5 and the dg range of 0.1-2.5 µm.As shown in Figure 4, the MEEs peaked at a d g of ~0.3 µm for a GSD of 1.5 for all sources and showed a declining trend as d g increased.The d g at which MEEs had peak values decreased as GSD increased.However, detailed MEE values differed depending on the sources.Figure 4 shows that D and TBB sources had relatively higher MEE values compared with the other sources.They had Appl.Sci.2019, 9, 1443 9 of 15 maximum values higher than 10 m 2 g −1 in submicron sizes for a GSD value of 1.5.Meanwhile, the FSD and the G sources were characterized by relatively lower MEEs with maximum values of less than 2 and 3 m 2 g −1 , respectively, for a GSD of 1.5.Thus, assuming size-dependent MEEs as constant variables may result in significant errors in estimating aerosol optical properties.

Source Range MEE MAE MSE
Another important parameter in estimating aerosol optical properties is the aerosol light-absorbing property.This light absorption property is mainly determined by EC.As shown in Table 1, the imaginary refractive index was 0.44, which means that EC was the main light-absorbing compound.In this study, we assumed OM to be a non-absorbing compound.However, some OM (e.g., HULIS) is known to have weakly to moderate light-absorbing ability depending on its characteristics [8,9].In order to identify the effects of the source-resolved MEEs on HULIS light-absorbing property, HULIS imaginary refractive index was tested.Figure 5 compares the size-resolved MEE for each source with the various HULIS imaginary refractive indices.The HULIS imaginary refractive indices of 0.006 and 0.1 with a GSD value of 1.5 were compared.As shown in Figure 5, the TS, LS, and FSD sources had an insignificant impact on the variation of HULIS imaginary refractive index.However, biomass burning sources (D, TBB, and LBB) showed discrepancies at a d g value of 1.5 µm, which indicates that the HULIS imaginary refractive index had a stronger influence on these sources than on other sources.
Figure 6 shows the trends of the source-resolved total extinction coefficient (b ext ) and their contributions.The d g values of 0.1 and 0.5 µm were compared, with a GSD of 1.5 during the sampling period.The source-resolved mass concentration is also displayed in Figure 6 [14].In general, the trends of the source-based optical property were similar to those of the source-based mass concentrations [14] (see also contribution of mass in Supplementary Figure S3).However, the specific contributions to b ext and mass were different according to the sources.Total b ext values were generally high during winter and spring and low during summer.In the source-based analysis, the b ext associated with some sources such as G and LBB did not show significant seasonal variation.The contributions of G and LBB were relatively consistent regardless of the season.However, the contributions of transported sources (TS and TBB) showed relatively distinct seasonal characteristics: they were high during winter and low during summer.For LN, the contribution increased during winter and spring but remained low in summer.The contribution of LS was great in summer and low in winter.
Figure 6 also shows that b ext increased as d g increased from 0.1 to 0.5 µm.This was due to the MEE with a GSD of 1.5, which increased as d g increased from 0.1 to 0.5 µm (except for EC), as shown in Figure 3.Although there were differences in the b ext values, the contributions of each source were similar.
Table 3 shows the source-based extinction coefficients across the whole sampling period with different geometric mean diameters (GSD = 1.5).The b ext will have different values for different GSDs.As Table 3 clearly shows, size distributions can influence source-based b ext values.resolved MEE for each source with the various HULIS imaginary refractive indices.The HULIS imaginary refractive indices of 0.006 and 0.1 with a GSD value of 1.5 were compared.As shown in Figure 5, the TS, LS, and FSD sources had an insignificant impact on the variation of HULIS imaginary refractive index.However, biomass burning sources (D, TBB, and LBB) showed discrepancies at a dg value of 1.5 µm, which indicates that the HULIS imaginary refractive index had a stronger influence on these sources than on other sources.Figure 6 shows the trends of the source-resolved total extinction coefficient (bext) and their contributions.The dg values of 0.1 and 0.5 µm were compared, with a GSD of 1.5 during the sampling period.The source-resolved mass concentration is also displayed in Figure 6 [14].In general, the trends of the source-based optical property were similar to those of the source-based mass concentrations [14] (see also contribution of mass in Supplementary Figure S3).However, the specific contributions to bext and mass were different according to the sources.Total bext values were generally high during winter and spring and low during summer.In the source-based analysis, the bext associated with some sources such as G and LBB did not show significant seasonal variation.The contributions of G and LBB were relatively consistent regardless of the season.However, the contributions of transported sources (TS and TBB) showed relatively distinct seasonal characteristics:   Figure 7 compares the source-based mass contributions with the source-based bext contributions for different dg values.The average values were based on the whole sampling period.In this study, several size distributions with geometric mean diameters of 0.1, 0.3, 0.5, and 1.0 µm for a GSD of 1.5 were considered.Supplementary Figure S3 shows detailed mass concentrations and their contributions based on chemical compounds and sources.The mass contributions of each source are shown in Figure 7. Figure 7 shows contributions of 20.3%, 21.2%, 22.8%, 8.2%, 6.3%, 7.9%, 5.2%, and 8.2% by TS, LS, LN, G, D, TBB, LBB, and FSD, respectively.The contribution of b ext depended on the size distribution.For example, for d g of 0.1 µm and a GSD of 1.5, the contributions made by D, TBB, and LBB to mass and to b ext increased from 6.3%, 7.9%, and 5.2% for mass to 22.6%, 15.5%, and 7.3% for b ext , respectively.Meanwhile, the contributions of TS, LS, LN, G, and FSD decreased from 20.3% (TS), 21.2% (LS), 22.8% (LN), 8.2% (G), 8.2% (FSD) for mass to 13% (TS), 14% (LS), 17.8% (LN), 6.5% (G), and 3.4% (FSD) for b ext , respectively.
Theoretically, the MEE for each source is the extinction coefficient to mass ratio in m 2 /g, which is shown in Figure 4.This means that sources with large MEE values (D, TBB) had higher contributions to the extinction coefficient compared with other sources.
Under the condition of a GSD of 1.5 and d g of 0.1 µm, the ratio of total b ext to PM2.5 mass concentration was 1.7 m 2 /g.Sources with MEE higher than 1.7 m 2 /g will make larger contributions to b ext than to mass, and sources with MEE lower than 1.7 m 2 /g will make smaller contributions to b ext than to mass.As shown in Figure 7 Figure 8 shows a comparison of the daily averaged AOD in Seoul from the AERONET Seoul-SNU station (37.458N, 126.951E) with the obtained extinction coefficient (b ext ) based on daily mass concentration data of species [27].The comparison yielded R 2 of 0.60 to 0.68 for the d g range of 0.1-2.5 µm at a GSD of 1.5.A more direct measurement comparison, such as of in situ aerosol scattering coefficient values from nephelometer scattering, was not possible because of data unavailability.However, the comparison between AOD from AERONET and our calculated b ext showed a comparable correlation and regression.
Figure 8 shows a comparison of the daily averaged AOD in Seoul from the AERONET Seoul-SNU station (37.458N, 126.951E) with the obtained extinction coefficient (bext) based on daily mass concentration data of species [27].The comparison yielded R 2 of 0.60 to 0.68 for the dg range of 0.1-2.5 µm at a GSD of 1.5.A more direct measurement comparison, such as of in situ aerosol scattering coefficient values from nephelometer scattering, was not possible because of data unavailability.However, the comparison between AOD from AERONET and our calculated bext showed a comparable correlation and regression.

Conclusions
In this study, the source-based MEE for polydisperse aerosols was estimated according to the results of the source apportionment-based chemical-species-resolved mass contribution.The aerosol extinction coefficient was calculated on the basis of the chemical composition mass concentrations of

Figure 1 .
Figure 1.Schematic diagram showing the steps to calculate the source-based aerosol optical properties of polydisperse aerosols using the Solver for Mixture Problem (SMP) model and Mie theory.

Figure 2 .
Figure 2. Sensitivity of (a) the mass extinction efficiency (MEE), (b) mass scattering efficiency (MSE), and (c) mass absorption efficiency (MAE) for internally mixed aerosol as a function of the geometric mean diameters (dg) in the range of 0.1-2.5 µm and geometric standard deviations (GSD) in the range of 1.5-2.5.

Figure 2 .
Figure 2. Sensitivity of (a) the mass extinction efficiency (MEE), (b) mass scattering efficiency (MSE), and (c) mass absorption efficiency (MAE) for internally mixed aerosol as a function of the geometric mean diameters (d g ) in the range of 0.1-2.5 µm and geometric standard deviations (GSD) in the range of 1.5-2.5.

Figure 3 .
Figure 3. Composition-based mass extinction efficiency as a function of the geometric mean diameter for different geometric standard deviations for (a) elemental carbon (EC), (b) inorganic ions, (c) organic matter (OM), (d) NaCl, and (e) Crust.

Figure 3 .
Figure 3. Composition-based mass extinction efficiency as a function of the geometric mean diameter for different geometric standard deviations for (a) elemental carbon (EC), (b) inorganic ions, (c) organic matter (OM), (d) NaCl, and (e) Crust.

Figure 7
Figure 7 compares the source-based mass contributions with the source-based b ext contributions for different d g values.The average values were based on the whole sampling period.In this study, several size distributions with geometric mean diameters of 0.1, 0.3, 0.5, and 1.0 µm for a GSD of 1.5 were considered.Supplementary Figure S3 shows detailed mass concentrations and their contributions based on chemical compounds and sources.

Figure 7 .
Figure 7. Comparisons of the average source-based mass contribution with the source-based bext contributions (GSD = 1.5).

Figure 7 .
Figure 7. Comparisons of the average source-based mass contribution with the source-based b ext contributions (GSD = 1.5).
, the contributions of b ext for TS (MEE = 1.2 for a GSD of 1.5 and d g of 0.1 µm), LS (MEE = 1.234),LN (MEE = 1.463),G (MEE = 1.478), and FSD (MEE = 0.775) to total b ext became smaller as compared to the mass contribution.In contrast, the contributions of b ext for D (MEE = 6.735),TBB (MEE = 3.679), and LBB (MEE = 2.634) to total b ext became larger as compared to the contribution based on chemical compound mass concentration.It should also be noted that sources containing EC increased the MEE, and this made the contribution of sources containing EC to b ext increase compared with the contribution to mass.
Figure 7 shows how the size distribution and refractive index influenced the source-based b ext contribution.As discussed, the optical properties depend on chemical species mass concentration.It was important to validate the reliability of the obtained b ext .In this study, we compared our b ext with AOD (Aerosol Optical Depth) from the Aerosol Robotic Network (AERONET) network.The AOD is the integration of b ext over the height (z) of the atmospheric column between sensor and sun[26]: Appl.Sci.2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsciAOD =

Table 2 .
Ranges of MEE, MAE, and MSE for each source in the GSD range of 1.5-2.5 and the d g range of 0.1-2.5 µm.