A New Method for Eliminating Dust Effects When Quantifying the Light Absorption Properties of Brown Carbon

Accurate quantification of the absorption properties of brown carbon (BrC) aerosols is crucial to assess the Earth‐atmosphere radiative impacts of BrC. However, the BrC absorption properties were often misestimated in field observations, due to neglecting the contribution of dust absorption. This study solved this problem by coupling a method for calculating the dust concentration into the traditional model for quantifying BrC absorption. The results show that dust absorption was up to 16.8% of the sum of BrC and dust absorption in northwestern China. The potential contribution of dust to the sum of BrC and dust absorption was significantly higher in the Asia‐located studies (0.4%–16.8%) than in the Americas‐located (<1.2%) and Europe‐located (<2.3%) studies. This work underscores the necessity of eliminating the negative effect of dust in BrC quantitative model. It prompts us to revisit the BrC absorption properties resolved by previous studies, especially in dust‐influenced areas such as Asia.


Introduction
Brown carbon (BrC) aerosols are organic aerosols (OA) with light absorbing properties (Cappa et al., 2020;Laskin et al., 2015).BrC can perturb the energy balance of the atmospheric column by absorbing solar radiation, affecting atmospheric stability, cloud properties, precipitation, and more (Jacobson, 2001;Ramanathan & Carmichael, 2008;Shrivastava et al., 2017;Y. Wang et al., 2022).The estimation of aerosol effects on the Earth's radiation balance relies on the aerosol optical parameters in models (Bond et al., 2013;Ghan & Schwartz, 2007).The radiative effects of BrC remain highly variable in models due to the current difficulties in accurately quantifying BrC optical parameters, especially absorption properties (Saleh, 2020).Therefore, a method to accurately quantify the BrC absorption properties is urgent at present (Laskin et al., 2015;Samset et al., 2018).
Only total aerosol absorption is usually observed in field observations, due to the fact that absorbing aerosol species, including black carbon (BC), BrC, and dust, are mixed in the real atmosphere.Quantifying the BrC absorption properties means separating the fraction belonging to BrC from the total aerosol absorption properties.The absorption Ångström exponent of BC (AAE BC ) method is the most widely used method to separate out BrC absorption (Pani et al., 2021; Y. J. Zhang et al., 2020).A constant AAE BC is used to separate the total aerosol absorption coefficients into BC and non-BC (NBC) in this method.The NBC absorption coefficients is considered as the BrC absorption coefficients after neglecting dust absorption.Aerosol chemistry measurement techniques have driven the subsequent development of the method.Qin et al. (2018) considered three BrC components as the contributing sources to the NBC absorption coefficients and separated the NBC absorption coefficients into three BrC components via the multiple linear regression (MLR) method.This algorithm proposed by Qin et al. (2018) has now been widely used worldwide because of its advantages in separating the absorption coefficients of individual BrC components (Cappa et al., 2019;de Sá et al., 2019;Kaskaoutis et al., 2021;Kasthuriarachchi et al., 2020;Singh et al., 2021; Q. Y. Wang et al., 2019; J. F. Wang et al., 2021; Y. J. Zhang et al., 2020;X. H. Zhang et al., 2021).The studies applying this algorithm (Figure 1 and Text S1 in Supporting Information S1) reveal that biomass combustion-related OA and secondary OA (SOA) are the most significant contributors to NBC absorption at 370 nm worldwide.The algorithm effectively advances the understanding of BrC absorption properties in the academic community, and it has much room for advancement in the future as well.However, the algorithm still suffers from an unresolved but important problem, which is the difficulty in separating dust and BrC absorption.Ignoring possible dust absorption and treating NBC absorption coefficients as BrC absorption coefficients is the response in almost all studies, even though they mostly acknowledge the presence of dust (Text S2 in Supporting Information S1).This may assign the absorption caused by dust to BrC, thus incorrectly assessing the radiative effects of BrC.
This study aims to optimize this algorithm by solving the problem of separating between BrC and dust absorption, thus achieving an accurate quantification of the BrC absorption properties.We first presented a method to calculate the dust mass concentrations using aerosol size distributions, then the dust mass concentrations were introduced into MLR analysis, thus solving the challenge of separating the absorption properties of dust and BrC components.Our findings underscore the necessity of including dust in NBC absorption modeling, particularly in northwestern Chinese regions where dust presence is notable.Therefore, it is necessary to revisit the BrC absorption properties quantified in previous observations.
northwest China (Figure S1 in Supporting Information S1) (Huang et al., 2008).The SACOL site suffers from anthropogenic aerosol pollution (e.g., BC and BrC), which is most severe during the winter (Guan et al., 2022;Tang et al., 2022).The dust aerosols emitted from desert sources, such as the Taklamakan and Gobi deserts, are frequently transported to the SACOL site during the spring and winter (Tian et al., 2015).It can be found that the SACOL site during the winter is a natural experimental field for studying BrC and dust absorption.

Calculation of Dust Mass Concentration in PM 2.5
The root cause for the difficulty in separating BrC and dust absorption is the lack of dust information.Therefore, a method for calculating dust mass concentration using APS data was proposed in this study.First, the number PSD observed by APS was converted to mass PSD with the spherical particle assumption.Note that APS is good at capturing the PSD shape but is not designed for fully quantitative measurements, so the mass PSD needs to be corrected.Therefore, the mass PSD was corrected using the TEOM-observed PM 2.5 mass concentration.The strong correlation (R 2 = 0.72) between the TEOM-observed PM 2.5 and the corrected APS-reconstructed PM 2.5 proved the reliability of the APS data (Figure 2a).Finally, the corrected mass PSD was decomposed into two modes using multi-modal fitting (Figure 2b).The mode 1 was the mass PSD of anthropogenic aerosol and the mode 2 was the mass PSD of dust aerosol (The contribution of sea salt aerosol does not need to be considered because the SACOL site is far from the ocean.).The dust mass PSD in the size range of 0-2.5 μm was integrated to obtain the dust mass concentration in PM 2.5 .The detailed processing of the APS data is in Text S3 in Supporting Information S1.

Calculation of BC and NBC Absorption Coefficients
The aethalometer data processor (https://zenodo.org/record/832403)with Weingartner's algorithm was applied to correct the AE31 data (Weingartner et al., 2003;C. Wu et al., 2018).The following equation is used in the Weingartner's algorithm to convert the aerosol light attenuation coefficient (b ATN ) collected at the filter fiber to the aerosol light absorption coefficient (b abs ) in the atmosphere: where C ref is a parameter to correct multiple scattering of the light beam at the filter fiber, R(ATN) is a function of attenuation to correct the particle loading effect.R(ATN) is used to adjust the continuity of b abs and has little effect on b abs , but C ref , which depends on the filter material and aerosol composition (Drinovec et al., 2015;Weingartner et al., 2003) where b abs (λ) is the b abs at the wavelength of λ. λ 1 = 370 nm and λ 2 = 880 nm were taken for AAE of total aerosol and BC, λ 1 = 370 nm and λ 2 = 660 nm were taken for AAE of BrC.
BC has a strong absorption at all wavelengths, whereas NBC absorption is negligible at near-infrared wavelengths.Therefore, it is assumed that b abs at 880 nm, which is abbreviated as b abs (880), was only contributed by BC and that AAE BC was a constant (Qin et al., 2018).The NBC absorption coefficient (b abs,NBC ) at the wavelength of λ was obtained as follows: (3) AAE BC = 1 was taken in most studies, but recent studies have suggested that there may be significant uncertainty in the AAE BC (Lack & Cappa, 2010;Tasoglou et al., 2020).To estimate the effect of AAE BC , the results with AAE BC from 0.8 to 1.2 were calculated.

Calculation of Multiple Linear Regression
The R 2 between BBOA, CCOA, and dust and b abs,NBC (370) were approximately 0.4, 0.8, and 0.2 (Figure S6 in Supporting Information S1), respectively, suggesting that they were potential contributors to NBC absorption.Note that OOA had no light-absorbing capacity and was not added to the MLR analysis because there was no correlation between OOA and b abs,NBC (370).
MLR method was used to resolve the mass absorption coefficient (MAC) of each absorbing species (m 2 • g 1 ).
Three MLR schemes (called T1, T2, and T3 schemes, respectively) were established.T1 scheme is an optimized MLR scheme with dust added.BBOA, CCOA, and dust were potential contributors to NBC absorption in T1 scheme.T2 scheme is a traditional MLR scheme without an intercept.Only BBOA and CCOA were potential contributors to NBC absorption in T2 scheme.T3 scheme is a traditional MLR scheme with an intercept.BBOA, CCOA, and intercept were considered potential contributors to NBC absorption in T3 scheme.The regression models of three MLR schemes were as follows: In the above equations, [BBOA], [CCOA], and [Dust] indicate the mass concentrations of BBOA, CCOA, and dust, respectively.a, b, and c are regression coefficients and their physical significance is the MACs of BBOA, CCOA, and dust, respectively, at the wavelength of λ.The physical significance of intercept is the unconsidered NBC absorption contributor.The intercept can be considered as dust absorption coefficient if the dust and OA components are completely decoupled in the MLR calculation, which will be discussed in Section 3.3.The MLR results of T1, T2, and T3 schemes have been examined and are considered robust (Figure S7 in Supporting Information S1).
Notably, the particle sizes for b abs,NBC and dust mass concentration were PM 2.5 , whereas the particle sizes for BBOA and CCOA mass concentrations were PM 1 .Although the organic matter is usually mainly present in PM 1 , there is still a little organic matter in range of 1-2.5 μm (Cappa et al., 2016;Elser et al., 2016).Therefore, the mass concentrations of BBOA and CCOA in PM 1 might be slightly lower than those in PM 2.5 , which might lead to a slight overestimation of the MACs of BBOA and CCOA in the MLR analysis.

Overview of BC and NBC Absorption
This study focused on aerosol absorption at 370 nm because of its high signal-to-noise ratio.The average total b abs (370) was 61.2 (37.5)Mm 1 for C ref = 2.80 (4.57) (Figure S8 in Supporting Information S1).AAE of total aerosols was mainly distributed in the range of 1.0-2.2, and the highest frequency was found in the range of 1.4-1.5.The AAE BC is usually around 1, so the AAE much greater than 1 indicated the presence of both NBC and BC aerosol.The contributions of the NBC to b abs (370) were 49%, 39%, and 29%, which were higher than the results at most sites worldwide (Figure S9 in Supporting Information S1), when AAE BC = 0.8, 1.0, and 1.2, respectively.It highlighted the importance of NBC absorption on the radiation balance of the Earth-atmosphere system at the SACOL site.It also implied that the SACOL site was well suited for conducting studies on BrC and dust absorption.

Overview of Absorbing Species
The average mass concentrations of BBOA and CCOA were 1.6 and 3.8 μg • m 3 , respectively.The average mass concentration of dust was 11.7 μg • m 3 , which was ∼8 and ∼3 times higher than those of BBOA and CCOA, respectively.Three average trajectories clusters (i.e., C1, C2, and C3) were calculated by the 72-hr backward trajectories at 500 m (Text S4 and Figure S10 in Supporting Information S1).C1, which accounted for 62% of the trajectories, came from the Tengger Desert.C2 passed through the northeastern Tibetan Plateau and explained 28% of the trajectories.C3, which accounted for 10% of the trajectories, originated from the southern Taklamakan Desert and passed through the northern Tibetan Plateau.The relative mass contribution of CCOA, BBOA, and dust corresponding to C1, C2, and C3 were similar, indicating that there was almost no long-range transported CCOA, BBOA, and dust during the observation period.Bivariate polar plots (Figure S11 in Supporting Information S1) showed that there were significant regional transported CCOA from the west and south and BBOA from the southeast, which were emitted from Lanzhou and Dingxi city (Tang et al., 2022).The distribution of dust was homogeneous in the bivariate polar plots, indicating the dust was a regional background aerosol.

Multiple Linear Regression Analysis
The MLR results for three schemes are shown in Figure 3.The results of T1 scheme with AAE BC = 1 were discussed in this paragraph.CCOA was the strongest light-absorbing NBC species with a MAC of 2.67-4.36m 2 • g 1 at 370 nm (The lower and upper limits of MAC indicated C ref = 4.57 and 2.80, respectively.).CCOA was the largest contributor to b abs,NBC (69.7% at 370 nm).Strong CCOA absorption was also found at the Chinese Xianghe site in winter 2017-2018 (Q.Y. Wang et al., 2019), implying that the radiative effects of absorbing aerosols emitted from winter coal combustion need special attention in China.BBOA had the second highest MAC (1.24-2.03m 2 • g 1 ) at 370 nm and contributed to 13.4% of b abs,NBC (370).The MAC of dust at 370 nm (0.21-0.34 m 2 • g 1 ) in this study was very close to the MAC of PM 2.5 dust at 375 nm (0.20 ± 0.03 m 2 • g 1 ) in the Chinese Gobi Desert (Caponi et al., 2017).Although the MAC of dust is much lower than the MAC of BBOA, the contribution of dust to b abs,NBC (370) (16.8%) was slightly higher than that of BBOA because of the high dust concentration.X. Q. Wu et al. (2018) quantified a dust MAC of 0.014 m 2 • g 1 at 637 nm at the Zhangye site, which was dominated by fresh dust (X.Wang et al., 2018), much lower than the dust MAC of 0.05-0.08m 2 • g 1 at 637 nm in this study.This difference is attributed to the enhanced dust absorption capacity at the SACOL site due to the mixing of dust with anthropogenic pollutants (Tian et al., 2018).C ref did not affect the contribution of absorbing species to NBC absorption, but AAE BC significantly affected the assignment of b abs,NBC (370) to absorbing species.An increase in the contribution of CCOA to b abs,NBC (370) from 62.9% to 80.5% when AAE BC increased from 0.8 to 1.2 was found.The contribution of BBOA and dust to b abs,NBC (370) decreased from 14.4% and 22.7% to 11.0% and 8.5% when AAE BC increased from 0.8 to 1.2.Therefore, caution should be maintained when selecting AAE BC .
The results of T1 scheme were taken as a baseline to assess the estimation biases in the results of the other schemes.In the T2 scheme (Figure 3d), the absorption coefficients of CCOA and BBOA at 370 nm were all overestimated due to the dust absorption was forced to be assigned to CCOA and BBOA.The evaluation biases of CCOA and BBOA decreased from 20.3% and 69.2% to 6.0% and 32.9% when AAE BC increased from 0.8 to 1.2.
In the T3 scheme (Figure 3e), the estimation biases of CCOA and BBOA were not sensitive to AAE BC and were stable at approximately 3% and 4%, respectively.It suggested an improvement in the results for the BrC components with the addition of the intercept.
Theoretically, the intercept can be equated to dust absorption coefficient if the absorption of the dust and BrC components are completely decoupled.However, this does not hold true in practical calculations because the intercept in the T3 scheme was always greater than the dust absorption coefficient in the T1 scheme (Figure 3e).The bias of intercept increased continuously with the increase of AAE BC when AAE BC ≤ 1.14; after AAE BC > 1.14, the bias of intercept decreased slightly with increasing AAE BC and then increased again.It is deduced that the main reason is the lack of constraints from the dust mass concentration in T3 scheme, resulting in the absorption of dust and BrC components not being completely decoupled, so that a part of the absorption coefficients belonging to the BrC component was also included in the intercept.Another possible explanation is that there were still some absorptive aerosol components that cannot be measured by current observation methods, and the absorption coefficients of these unknown components were classified in the intercept by the MLR method.Based on the above analysis, the intercept cannot be simply equated to the dust absorption coefficient.The physical significance of the intercept may include the dust absorption coefficient, the noise generated by the incomplete decoupling, and the absorption coefficients of unknown components.This was also supported by the calculation result in Section 3.4 that the potential contribution of dust to the b abs,NBC was lower than the contribution of the intercept in the studies at the Delhi (16% vs. 1.6%-3.3%)and Amazonia (2.8% vs. 0.6%-1.2%)sites, as well as at the SACOL site.
In summary, the MAC of the BrC components resolved by the MLR with an intercept (i.e., T3 scheme) is closer to that resolved by the T1 scheme.Therefore, it is recommended to add an intercept to the MLR analysis if dust concentration information cannot be obtained due to limited observations.In addition, not only the research data in this study can be applied to this optimized MLR algorithm.For example, the organic components observed by an HR-ToF-AMS can be replaced by the organic matter measured by an organic carbon/elemental carbon analyzer (Du et al., 2020).The dust mass concentration can also be reconstructed using the mass concentration of aerosol metal elements (M.Wang et al., 2021;L. Zhang et al., 2021).It is believed that the radiative effects of global BC, BrC, and dust aerosols can be better constrained if the algorithm in this study is extended and applied to globally accumulated aerosol chemistry and absorption data.

Potential Dust Absorption Contributions From Previous Studies
We used the results resolved at the SACOL site to reassess the results at the other studies in Figure 1 in order to provide suggestions for future studies.We used the dust MACs of 0.21-0.34m 2 • g 1 at 370 nm from this study as the upper and lower limits of the dust MACs, and used in situ observation data and Modern-Era Retrospective analysis for Research and Applications Version 2 (MERRA-2) reanalysis data to acquire the surface dust mass concentrations, and finally quantified the potential contributions of the dust to the NBC absorption coefficient in these studies (Figure 4).The detailed calculation is shown in Text S5 in Supporting Information S1.
The ratio of dust to organic aerosol mass concentrations (abbreviated as dust/OA) in PM 2.5 was used as an indicator of the degree of dust dominance.Most of the Americas-located and Europe-located studies had dust/OA values below 0.1, except for the study at the Athens site (0.27), which is close to the African dust region, indicating that the influence of dust was weaker in the Americas and Europe.The studies at the SACOL, Everest, Xianghe, and Delhi sites had dust/OA values as high as 0.28-1.04because of the frequent exposure to Asian dust (Sun et al., 2010;Tian et al., 2018;T. H. Wang et al., 2021;Z. D. Zhang et al., 2024), and these four sites are categorized as Asian dust influenced sites.The contributions of dust to the b abs,NBC were below 1.2% in the studies at the Fresno (405 nm) and Amazonia (370 nm) sites.The contributions of dust to the b abs,NBC at 370 nm were 1.4%-2.3%and 1.2%-1.9%,respectively, in the studies at the Athens and Greater Paris sites.Overall, there was almost no contribution of dust to the b abs,NBC in the Americas-located and Europe-located studies.The contributions of dust to the b abs,NBC at 370 nm were much higher in almost all Asia-located studies than in the Americaslocated and Europe-located studies, while the contributions at the Asian-located studies were highly correlated with the observed particle sizes.The PM 2.5 particle sizes used in the studies at the SACOL, Qomolangma, Guangzhou, and Singapore sites corresponded to high contributions.Among the Asia-located studies, the contribution at the SACOL site (16.8% at AAE BC = 1.0) was the highest, followed by the Qomolangma site (8.1%-13.1%).The studies at the Guangzhou site (5.6%-9.1%)and Singapore site (3.8%-6.1%)also exhibited high dust absorption contributions, although they were weakly affected by Asian dust.D. W. Wang et al. (2022) quantified the contribution of dust to methanol-soluble BrC absorption in Guangzhou in the winter to be 10.9%, which was similar to the results in this study (5.6%-9.1%).Meanwhile, The PM 1 particle sizes in the studies at the Xianghe site and Delhi site were used.The contributions of dust to the b abs,NBC at the Xianghe site (0.4%-0.8%) and Delhi site (1.6%-3.3%)were the lowest among the Asia-located studies, even though they are located in the Asian dust influenced areas.This phenomenon is attributed to the selection of the observed particle size.The ratio of organic concentration in PM 1 and PM 2.5 is usually approximately 60%-80% (Lim et al., 2012;Y. F. Wu et al., 2022), much higher than the ratio of dust concentration in PM 1 and PM 2.5 (0.16-0.20 in Text S5 in Supporting Information S1).PM 1 particle size can retain BrC particles and remove dust particles as much as possible, thus minimizing the effect of dust absorption.
In summary, the contribution of dust to the NBC absorption are much higher in the Asia-located studies (except at the Xianghe site) than in the Americas-located and Europe-located studies.The natural reason for this situation is the high background dust concentration in Asia.The technical reason is the use of PM 2.5 particle size at most Asia-located studies.These two reasons together lead to the non-negligible contribution of dust to NBC absorption in the Asia-located studies.Considering that dust aerosols are important not only in the Asian dust influenced areas but also in the Middle East, Northern Africa, and Central Australia (Figure 4a), it is necessary to revisit the BrC absorption properties at these dust-influenced areas resolved by previous studies.It should also be TANG ET AL.
realized that the impact of dust absorption in the Americas, Europe, the Pacific Islands, and Southern Africa may be limited because of low background dust concentrations.We strongly suggest that BrC absorption studies in these dust-influenced areas should apply the improved algorithm in this study or select PM 1 particle size to exclude dust absorption as much as possible.

Conclusions
The absorption properties of BrC are critical for the accurate assessment of the impact of BrC on the Earthatmosphere radiation balance in models.However, the quantified BrC absorption properties are subject to large errors due to the current inability to separate BrC and dust absorption in field observations.To solve this problem, we coupled the traditional MLR algorithm and the method of calculating dust mass concentration, and successfully separated the BrC and dust absorption properties at the SACOL site.The dust absorption was up to 16.8% of NBC absorption at the SACOL site, emphasizing the non-negligible influence of dust when quantifying BrC absorption properties.We evaluated the results in other studies around the world and showed that the potential contribution of dust to non-black carbon absorption is much higher in the Asia-located studies (0.4%-16.8%) than in the Americas-located studies (<1.2%) and European studies (<2.3%).It suggests that the BrC absorption properties in the Asia-located studies resolved by previous studies are likely to be overestimated and need to be reexamined.Higher background dust concentrations and more frequent selection of PM 2.5 particle size are both natural and technical reasons for the higher dust absorption contributions in the Asia-located studies.We strongly recommend that future BrC studies in dust-influenced areas, including Asia, the Middle East, North Africa, and Central Australia, use the improved algorithm in this study or select PM 1 particle size to exclude as much as possible the effect of dust absorption.

Figure 2 .
Figure 2. (a) Correlation between the tapered element oscillating microbalance machine (TEOM)-observed PM 2.5 concentration and the corrected aerodynamic particle sizer spectrometer (APS)-reconstructed PM 2.5 concentration.(b) Average corrected mass PSDs.The gray bars indicate the original mass particle size distributions (PSDs) observed by APS.The mode 1 (blue line) and mode 2 (brown line) indicate the fitted mass PSDs of anthropogenic and dust aerosols, respectively.

Figure 3 .
Figure 3. Contributions of different absorbing aerosol species to the b abs,NBC at 370 nm as a function of absorption Ångström exponent of BC (AAE BC ) in (a) T1, (b) T2, and (c) T3 schemes.Estimation bias of absorption contributions as a function of AAE BC for (d) T2 and (e) T3 schemes relative to T1 scheme.

Figure 4 .
Figure 4. (a) Spatial distribution of average surface dust concentration in PM 2.5 (colorbar) during 2017-2021 from MERRA-2 reanalysis data and the positions of sites (yellow dots) where the multiple linear regression method had been applied.(b) Potential contributions of dust to the non-BC absorption coefficient at 370 or 405 nm (brown bar) and the ratio of the dust to organic aerosol mass concentration in PM 2.5 (green dot) at these sites.The upper and lower ends of the brown bars indicate the upper and lower limits of the potential contribution, while the solid and striped bars indicate that the particle sizes are PM 1 and PM 2.5 , respectively.
, can significantly affects the magnitude of b abs .Based on the range of C ref reported by Collaud Coen et al. (2010), we used C ref = 2.80 and 4.57 for quartz filter fiber to represent the upper and lower limits of b abs at all wavelengths in this study.Aerosol absorption Ångström exponent (AAE) reflects the wavelength dependence of b abs , expressed as: