Mass absorption cross section of black carbon for Aethalometer in the Arctic

Abstract Long-term measurements of the mass concentration of black carbon (BC) in the atmosphere (MBC) with well-constrained accuracy are indispensable to quantify its emission, transport, and deposition. The aerosol light absorption coefficient (babs), usually measured by a filter-based absorption photometer, including an Aethalometer (AE), is often used to estimate MBC. The measured babs is converted to MBC by assuming a value for the mass absorption cross section (MAC). Previously, we derived the MAC for AE (MAC (AE)) from measured babs and independently measured MBC values at two sites in the Arctic. MBC was measured with a filter-based absorption photometer with a heated inlet (COSMOS). The accuracy of the COSMOS-derived MBC (MBC (COSMOS)) was within about 15%. Here, we obtained additional MAC (AE) measurements to improve understanding of its variability and uncertainty. We measured babs (AE) and MBC (COSMOS) at Alert (2018–2020), Barrow (2012–2022), Ny-Ålesund (2012–2019), and Pallas (2019–2022). At Pallas, we also obtained four-wavelength photoacoustic aerosol absorption spectrometer (PAAS-4λ) measurements of babs. babs (AE) and MBC (COSMOS) were tightly correlated; the average MAC (AE) at the four sites was 11.4 ± 1.2 m2 g−1 (mean ± 1σ) at 590 nm and 7.76 ± 0.73 m2 g−1 at 880 nm. The spatial variability of MAC (AE) was about 11% (1σ), and its year-to-year variability was about 18%. We compared MAC (AE) in the Arctic with values at mid-latitudes, measured by previous studies, and with values obtained by using other types of filter-based absorption photometer, and PAAS-4λ. Copyright © 2024 American Association for Aerosol Research


Introduction
Black carbon (BC) particles, which are emitted by incomplete combustion of carbon-based fuels, impact the radiation budget in the Arctic and globally (AMAP 2021;Bond et al. 2013;Oshima et al. 2020;Sand et al. 2016).Long-term measurements of the mass concentration of BC in the atmosphere (M BC ) with well-constrained accuracy are useful for quantifying its emission, transport, and deposition (e.g., Matsui et al. 2022).Usually, the aerosol absorption coefficient (b abs ) is used to estimate M BC .The measured b abs is converted to M BC by assuming a value for the mass absorption cross section (MAC).Most ground-based measurements of b abs in the Arctic have been made by using one of the following filter-based absorption photometers: Aethalometer (AE) (Bodhaine 1995;Sharma et al. 2006Sharma et al. , 2013)), continuous soot monitoring system (COSMOS) (Asmi et al. 2021;Kondo et al. 2009;Ohata et al. 2019Ohata et al. , 2021a;;Sinha et al. 2017;Zanatta et al. 2018), multi-angle absorption photometer (MAAP) (Asmi et al. 2021;Backman et al. 2017;Petzold and Sch€ onlinner 2004), particle soot absorption photometer (PSAP) (Bond, Anderson, and Campbell 1999;Collaud Coen et al. 2013;Delene and Ogren 2002;Hirdman et al. 2010;Sharma et al. 2017), or continuous light absorption photometer (CLAP) (Collaud Coen et al. 2020;Ogren et al. 2017;Schmeisser et al. 2017).In contrast, b abs of airborne particles has been measured by using a four-wavelength photoacoustic aerosol absorption spectrometer (PAAS-4k), without particle collection on filters (Schnaiter et al. 2023).
Except for COSMOS measurements, filter-based photometer measurements of b abs are influenced not only by BC, but also by co-existing light-scattering particles and other light-absorbing aerosols, such as brown carbon (BrC) and mineral dust, that are deposited on the filters.In addition to such interference, variations in the mixing state of BC due to atmospheric aging can contribute to variations in the MAC (Kondo 2015;Petzold et al. 2013;Schnaiter et al. 2005;Sharma et al. 2017;Slowik et al. 2007;Zanatta et al. 2018).In general, MAC at wavelength k is defined as, (1) If MAC k ð Þ of BC is known, then M BC can be derived from b abs as follows: However, MAC (k) can show natural variation, which significantly depends on the mixing state of BC, and MAC (k) variation directly affects the value M BC estimated from b abs .If a constant MAC (k) value is used to derive M BC , then, to assess M BC uncertainty, the effects of interference and of MAC (k) variability must be understood.
Unlike other filter-based instruments, COSMOS is equipped with an inlet heated to 300 � C to remove non-refractory light-scattering components from the aerosol particle phase; thus, only bare (uncoated) BC particles are measured (Kondo et al. 2011).The accuracy of M BC measured by COSMOS (M BC (COSMOS)) has been demonstrated to be within about 15% by comparing COSMOS and single-particle soot photometer measurements in Asia and the Arctic (Ohata et al. 2019).Thus, b abs (COSMOS) is more representative of the actual BC mass concentration than b abs measured by the other filter-based absorption photometers described in this section, and M BC (COSMOS) is different from "equivalent" BC mass concentrations estimated by using b abs measurements obtained with unheated instruments (Petzold et al. 2013).The physical parameters related to absorption by BC particles, as derived by different instruments, are summarized in Table 1.
In previous studies, M BC was estimated from b abs (AE, k), measured by using an Aethalometer and assuming fixed but different values of MAC of BC for Aethalometer (MAC (AE, k)) at different sites (Eleftheriadis, Vratolis, and Nyeki 2009;Hirdmann et al. 2010;Sharma et al. 2013) as follows: However, the uncertainties of the MAC (AE, k) values were poorly constrained.In addition, except for Ohata et al. (2021a), none of the previous studies evaluated year-to-year spatial and spectral variations of b abs (AE, k).Ohata et al. (2021a) estimated MAC (AE) in the Arctic by simultaneous measurements of  Additional reliable estimates of MAC (AE, k) in the Arctic are highly desirable to assess its temporal and spatial variations.In this study, we measured b abs (AE, k) for particle diameters less than 10 lm (PM 10 ) or total suspended particles (TSP) simultaneously with M BC (COSMOS)) (PM 1 ) at Alert (2018-2020), Barrow (2012Barrow ( -2021)), Ny-Ålesund (2012-2019), and Pallas (2019-2022).We derived MAC (AE, k) by using the b abs (AE, k)-M BC (COSMOS) correlation and the b abs (AE, k)/M BC (COSMOS) ratio.We then analyzed the spatial and year-to-year variations of MAC (AE, k).We compared our results with MAC (AE, k) derived by previous studies conducted in the Arctic and at mid-latitude locations.We carried out similar comparisons with MAAP, PSAP (CLAP), and PAAS-4k data.

M BC (COSMOS) and b abs (AE, k)
COSMOS and Aethalometer work on identical principles of operation.The attenuation coefficient of light (b 0 (k)) at a given wavelength k for a filter-based absorption photometer is determined as follows: where A is the sample spot area, V a is the air sample volume at a given time between (t -Dt) and t, T t − Dt ð Þ and T t ð Þ are the average transmittance at (t -Dt) and t, respectively, and the change in attenuation DATN is defined as,   in filter-based absorption photometers is multiple scattering enhancement of absorption, as the BC-containing particles are deposited on the filter.The multiple scattering enhancement factor changes, as loading of the filter with aerosol particles increases, and this change is called the filter-loading effect.Furthermore, b abs (AE, k) can also be influenced by aerosol light scattering.The aerosol light-scattering artifact is corrected for by subtracting from b 0 (AE, k) the contributions from multiple light scattering within the filter matrix and by non-BC aerosol particles to the filter attenuation.These contributions are determined by independent measurements made with, for example, a nephelometer (Arnott et al. 2005;Collaud Coen et al. 2010).In the absence of simultaneous light-scattering measurements, as was the case for some sites, b abs (AE, k) is derived simply by dividing b 0 (AE, k) by the multiple scattering effect of the light beam within the fiber matrix of the filter (C 0 ) and the filter loading (R) (Collaud Coen et al. 2010;Schmid et al. 2006;Weingartner et al. 2003).Weingartner et al. (2003) and Collaud Coen et al. (2010) used the formula, to derive b abs (AE, k).
A wide range of C 0 values have been reported in the literature for different filter types and Aethalometer models (AE 31 and AE 33), along with their spectral and spatio-temporal variations.However, there is no consensus about C 0 variability (Backman et al. 2017;Drinovec et al. 2015;Luoma et al. 2021;Weingartner et al. 2003;Yus-D� ıez et al. 2021).A C 0 ¼ 3.5 for AE 31 has been recommended based on detailed comparisons between AE and MAAP measurements at several observatories (WMO/ GAW 2016), and the uncertainty of C 0 has been reported to be approximately 25% (WMO/GAW 2016).
Despite several previous studies, the uncertainty of the methodology represented by Equations ( 2) and ( 6) has not been quantitatively estimated.In fact, different values of C 0 have been used, depending on environmental conditions, as described above.For more systematic investigation of this problem, we used a fixed C 0 ¼ 3.5 for both AE 31 and AE 33 instruments to ensure homogeneity of the data set from the four sites in the Arctic.In addition to the recommendation of WMO/GAW (2016), the consistency of a fixed C 0 value close to 3.5 was shown in this study (see Section 10) by comparing AE data with data from the PAAS-4k instrument at Pallas (Schnaiter et al. 2023).
The filter-loading effect is insignificant in the Arctic (Backman et al. 2017); thus, we assumed R ¼ 1 for the present study.Furthermore, model AE 33 adjusts the loading compensation parameter (k) (Virkkula et al. 2007)) in real time; this adjustment is calculated by measuring attenuation at two different filter spots with different loading rates.A more detailed explanation of k is given in Supplementary Information (SI) Section 1.
In practice, it is difficult to evaluate the absolute accuracy of b abs (AE, k).Instead, we evaluate its relative reliability in the form of MAC (AE, k) (Equation ( 2)).In this case, MAC (AE, k) is expressed as, Here, b 0 (AE, k) is normalized by M BC ; this normalization makes comparisons easier, provided that M BC is measured accurately.First, we investigated the variability of MAC (AE, k) in the Arctic.Then, we compared MAC (AE, k) in the Arctic with values obtained at mid-latitudes by previous studies.

Measurements of b abs (AE, k) and b abs (COSMOS) in the Arctic
COSMOS and Aethalometer measure b abs of BC particles deposited on filters at k ¼ 565 nm and k ¼ 370-950 nm, respectively.Measurements of b abs by COSMOS (b abs (COSMOS)) were made by using a PM 1 impactor inlet (i.e., with a cutoff size at an aerodynamic diameter D p of about 1 lm).COSMOS aspirates ambient air at a flow rate of about 0.7 L min −1 at standard temperature and pressure (STP: 273.15 K, 1013 hPa).The time resolution of the measurement was maintained at 1 min.M BC (COSMOS) was then derived from the measured b abs (COSMOS) by using a constant MAC value.It is 8.73 m 2 g −1 for a Pallflex filter (Sinha et al. 2017).The characteristics of models AE 31, and AE 33 used at the Arctic sites are summarized in Table 2.The relative uncertainty of b 0 (AE) is expressed as ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi where A, V a , and DATN are as defined in Section 3.1.The uncertainties in A, V a , and DATN were estimated to be about 1.5%, 2%, and 2.5% (for DATN � 2%), respectively.The upper bound of relative uncertainty of b abs (AE, k) was estimated following Backman et al. (2017) to be about 36% at very low BC concentrations.In this study, C 0 was held constant, as discussed in Section 3.1.Even using this constant C 0 , the uncertainty of b abs (AE, k) should be about 36% at low BC concentrations, given that the errors in b abs (AE, k) mentioned above were for a non-constant C 0 (Backman et al. 2017).For our analysis, we used 1-h and 24-h averaged data for M BC (COSMOS) and b abs (AE, k).

MAC cor (AE, k)
Variations of M BC (COSMOS) and b abs (AE, k) were highly correlated at the four sites because these parameters are related by Equation ( 3), as already shown by Ohata et al. (2021a).We thus describe only the observed features of M BC (COSMOS) (Figure 2).We define the year-to-year variation as the ratio of the yearly mean M BC (COSMOS) to the mean M BC (COSMOS) over the whole observation period.At Alert, Barrow, Ny-Ålesund, and Pallas, the ratio varied from year to year by a factor of up to 1.1, 2.2, 1.3, and 1.5, respectively.
Unless otherwise stated, b abs from both models AE 31 and AE 33 is designated as "b abs (AE, k)".For each correlation, we used the data obtained during each entire year.Considering the inherent uncertainties in Equation ( 6), as discussed in Section 3, we did not analyze the variations of the correlation over shorter periods.Therefore, the slope of the correlation, namely MAC (AE, k), is strongly influenced by high-M BC data, which are typical in winter and early spring (Figure 2).
The observed contributions of BC particles larger than 1 lm to M BC in the Arctic and Asia were less than 10% (Ohata et al. 2019;Sinha et al. 2017).Thus, the uncertainty associated with the difference in the size cut for M BC (COSMOS) (PM 1 ) should be less than 10%.TSP and PM 10 inlets have been used for the long-term observations of b abs by Aethalometer at various sites in the Arctic.The C 0 value of 3.5 in Equation ( 6) was determined by comparison with MAAP (see Section 2) using the same size cut.Therefore, the Aethalometer's TSP and PM 10 size cut is consistent with C 0 ¼ 3.5.
Generally, 1-h and 24-h averaged b abs (AE, 590 nm) and b abs (AE, 880 nm) for TSP, and PM 10 were well correlated with M BC (COSMOS) for PM 1 over wide ranges of values throughout the measurement periods (Figure 3).These results suggest that the contribution of BC particles with diameters larger than 1 lm to b abs (AE, k) was not significant at these sites.The high correlations between b abs (AE, k) and M BC (COSMOS) at 590 nm (r 2 ¼ 0.80-0.96)and 880 nm (r 2 ¼ 0.83-0.95)for 24-h averaged data during the study period (Figures 3a and b) enabled the statistically reliable estimation of MAC (AE, k), as described below.MAC (AE, k) for each site was derived by two methods.The first method was linear regression of 1-h and 24-h averaged M BC (COSMOS) and b abs (AE, k).MAC (AE, k) derived by this method is denoted as MAC cor (AE, k).The slope was determined from the least-squares regression line forced through the origin (intercept ¼ 0).The intercept of the regression line was, on average, smaller than 3 times its standard deviation for all sites (Table S1 in SI Section 2).Also, the slope variations of the regression lines calculated with and without forcing to the origin were about 6 ± 2% at all sites.
The MAC cor (AE, k) values, calculated for the 1-h and 24-h averaged data for k ¼ 590 and k ¼ 880 nm, are shown in Table 3.We estimated the uncertainty of MAC cor (AE, k) to be about 39%, taking into account the M BC (COSMOS) accuracy of 15% (Ohata et al. 2021a), and the relative uncertainty of b abs (AE, k) to be about 36% (Backman et al. 2017).

MAC med (AE)
The second method used the ratios of the 1-h and 24h median M BC (COSMOS) values to b abs (AE, k).MAC (AE, k) derived by this method consists of median values of b abs (AE, k)/M BC ratios and is denoted as MAC med (AE, k).Figures 4a and 4b present the frequency distributions of b abs (AE, k)/M BC (COSMOS) at k ¼ 590 nm and k ¼ 880 nm for the 24h averaged data.In all regions, b abs (AE, k)/M BC exhibited a skewed distribution with modes at �13 m 2 g −1 at 590 nm and at �9 m 2 g −1 at k ¼ 880 nm, with the occurrence frequency showing a sharp decrease at lower values and a gradual decrease at higher values.b abs (AE, k)/M BC (COSMOS) ratios tended to be unstable with low BC; thus, we set a threshold M BC (COSMOS) value of > 5 ng m −3 in this analysis (Figures 4a and b).The error associated with b abs (AE) became large for low BC concentrations, leading to a large error in MAC, consistent with the error analysis in Backman et al. (2017).
The MAC med (AE, k) values calculated for the 1-h and 24-h averaged data for k ¼ 590 and k ¼ 880 nm are shown in Table 3. MAC med (AE) was higher than MAC cor (AE) by about 10% and 16% for the 1-h and 24-h averaged data, respectively (Table 3).We use only MAC cor (AE) for subsequent analyses and denote it as MAC (AE) for simplicity.

Spectral MAC (AE)
MAC (AE, k) values for k ¼ 370-950 nm at each site are shown in Figure 5 and summarized in Table S2.
In addition, AAE depends on various microphysical properties of BC-containing particles, including their size distribution, refractive index, shape, and mixing state (e.g., Liu et al. 2018;Virkkula 2021).In the Arctic, BC has been observed to be thickly coated, with a shell/core ratio of about 1.4, and the median diameter in number size distributions is about 0.1 lm (Ohata et al. 2019(Ohata et al. , 2021b)).For coated BC, AAE was calculated to decrease as the geometric mean diameter (GMD) increased.The calculated AAE of about 1.0 at a GMD of 0.1 lm (Fig. 6 of Liu et al. 2018) is in reasonable agreement with the average AAE observed at the four sites.There may be several explanations for the different AAE at Pallas.The aerosol optical properties at Pallas differ from those at other Arctic sites, especially during summer, when the amount of biogenic aerosol is greater there than at the other sites (Schmeisser et al. 2017); these different properties would certainly affect the AAE in a variety of ways (Virkkula 2021).More quantitative interpretation of the higher AAE at Pallas requires measurements of the size distribution and mixing state of BC there.

Spatial and temporal variations of MAC (AE)
The average MAC (AE, 590 nm) and MAC (AE, 880 nm) at the four sites over the whole study period were 11.4 ± 1.2 m 2 g −1 (mean ± 1r) and 7.76 ± 0.73 m 2 g −1 , respectively, and they exhibited a weak spatial variability of about 11%.Annual mean MAC (AE, 590 nm) and MAC (AE, 880 nm) were stable, varying from 10.1 to 12.8 m 2 g −1 and from 7.2 to 9.0 m 2 g −1 , respectively (Figure 7 and Table 3).The year-to-year variability of MAC (AE) was about 15% (1r) except at Barrow, where it was up to 18% (Figure 7; Table S4).Furthermore, the relative year-to-year variability of MAC (AE, 590 nm) was 2%, 11%, 18%, 14%, and 8.7% (1r) at Alert, Barrow 31, Barrow 33, Ny-Ålesund, and Pallas, respectively, over the entire period (Figure 7, and Table S4 in SI).The relatively uniform MAC (AE) values among these sites are partly due to the correspondingly uniform mixing state of BC in the Arctic, which is distant from BC sources.BC aerosols have been observed to be thickly coated in the Arctic (Kodros et al. 2018;Ohata et al. 2021b;Sharma et al. 2017;Zanatta et al. 2018) with shell-core ratios of BC in spring of 1.4-1.5 at 0-5 km (Kodros et al. 2018;Ohata et al. 2021b).These results suggest that, on average, BC is thickly coated in the Arctic in spring, which leads to a decrease in AAE (see Section 5).Interestingly, MAC (AE 31) and MAC (AE 33) values at Barrow derived by using C 0 ¼ 3.5 were similar (Figure 7), suggesting that C 0 is independent of the AE model.This result is in contrast to results previously reported by Weingartner et al. (2003) and Drinovec et al. (2015).

Comparison of MAC (AE) with other studies in the Arctic and mid-latitudes
Figure 8 and Table 4 compare the MAC (AE) values obtained by this study with those reported by previous studies conducted in the mid-latitudes and the Arctic, with corrected and uncorrected Aethalometer data for C 0 .However, these previous studies, except Ohata et al. (2021a), measured M BC with elemental carbon/ organic carbon (EC/OC) aerosol analyzers instead of COSMOS.
The MAC values reported in the literature have been adjusted to 590 nm by assuming AAE ¼ 1 (i.e., a k −1 relationship) (Table 4).The spatial average of the previously measured MAC (AE, 590 nm) values at mid-latitude and mid-latitude to Arctic sites were 12.4 ± 2.0 m 2 g −1 and 11.7 ± 1.8 m 2 g −1 , respectively; these values agree to within 10% with the MAC (AE, 590 nm) of 11.4 ± 1.2 m 2 g −1 obtained by this study in the Arctic for a wide range of M BC values.For this comparison, we used only those previous studies that reported C 0 values.This agreement is unexpected considering the differences in aerosol characteristics between the mid-latitudes and the Arctic (Radke et al. 1989;Yang et al. 2021) and also considering the potential uncertainties contained in the approximated Equation ( 6).This Equation ( 6) does not account for any concrete physical light scattering and absorption processes occurring on the filter surface.It should be noted that in this comparison, we used temporally averaged MAC (AE, 590 nm) values in the Arctic.Nevertheless, this result is very important when the spatial variability of MAC (AE, 590 nm), extending to the mid-latitudes, is considered.
The MAC (AE, k) values at mid-latitudes and in the Arctic are reported in other published work based on different Aethalometer models, and data uncorrected for C 0 show large variability, up to a factor of about 3.7 (7.7 to 28.3 m 2 g −1 ) in MAC (AE, 590 nm), depending on the site (Table 4).It is difficult to quantify possible causes of the large range of the reported MAC (AE, k) because of the lack of key parameters for these studies, including C 0 and the uncertainty of M BC .

Comparison of MAC (MAAP) in the Arctic and at mid-latitudes
The procedures for deriving b abs (MAAP) and b abs (PSAP) are different from those used for AE.Therefore, it is also essential to investigate the spatial variations of MAC obtained with the filter-based MAAP, PSAP, and CLAP instruments in the mid-latitudes and the Arctic.
The MAC values for MAAP and PSAP/CLAP, denoted as MAC (MAAP) and MAC (PSAP/CLAP), respectively, were calculated using the b abs -M BC correlation.
The MAC (MAAP) values obtained from various locations and reported in the literature are shown in Figure 9a and summarized in Table S5.The MAC (MAAP, 637 nm) value of 11.8 ± 1.7 m 2 g −1 (mean ± 1r) reported at two sites in the Arctic by Ohata et al. (2021a) is comparable (agrees to within 9%) to the spatial mean value of 10.4 ± 3.0 m 2 g −1 for mid-latitude sites (Figure 9a and Table S5).MAC (MAAP) at 637 nm at mid-latitude sites varied from 4.6 to 17.3 m 2 g −1 with a spatial variation of about 29%  (1r), which is higher than the estimated uncertainty of 12% in measured b abs by MAAP (Petzold and Sch€ onlinner 2004).The MAC (MAAP, 590 nm) value of 11.2 ± 3.3 m 2 g −1 (Table S5 in SI) agreed with the latitudinally averaged MAC (AE, k ¼ 590 nm) value of 11.7 ± 1.8 m 2 g −1 (Table 4 and Figure 8) to within 4%.MAAP corrects the effect of light-scattering particles on the particle-loaded filter by concurrent measurement of the back-scattering signal from the filter tape at multiple angles.For this reason, MAAP is generally considered the most sophisticated and reliable filter-based instrument for measuring b abs (Petzold and Sch€ onlinner 2004).The somewhat larger variability of MAC (MAAP, 637 nm) compared with MAC (AE, k) may reflect the actual variability of MAC, which is not represented by MAC (AE, k).Or M BC used to derive MAC (MAAP, 637 nm) might simply have larger errors.Still, the latitudinal dependence of MAC (MAAP, 637 nm) and MAC (AE, k) is weak.It is possible that the measurements at mid-latitudes were made in remote areas, far from BC sources.If so, BC aging processes might have increased their shell-core ratios (Kondo 2015), leading to reduced latitudinal dependence of both MAC (MAAP, 637 nm) and MAC (AE, k).

Comparison of MAC (PSAP) in the Arctic and at mid-latitudes
MAC (PSAP, 550 nm) of 13.0 ± 2.0 m 2 g −1 reported at three sites in the Arctic by Ohata et al. (2021a) agrees to within 10% of the value at mid-latitude sites (Figure 9b, Table S6 in SI).However, MAC (PSAP, 550 nm) values in the mid-latitudes exhibit a large variation from 8.6 to 26.2 m 2 g −1 , for a site-to-site variation of about 44% (1r).This is much larger than the estimated uncertainty following Bond, Anderson, and Campbell (1999) of about 20% in the measurement of b abs by PSAP at mid-latitudes (35 � N-45 � N), which includes the unit-to-unit variability of PSAP of about 6% (Sherman et al. 2015).
The b abs (PSAP, 550 nm) value used to calculate MAC (PSAP, 550 nm) is influenced by the correction for light-scattering particles (Sinha et al. 2017).This correction is made by using the scattering coefficient (b scat ) measured with a nephelometer.This procedure is different from those used for AE and MAAP.The larger variability in MAC (PSAP, 550 nm) is likely due to the variability in b abs (PSAP, 550 nm).The accuracy of the correction using b scat has not been extensively assessed thus far.The methodology for this evaluation can be very complicated, considering the complexity of light scattering by the filter fibers.Nevertheless, the present comparison of MAC (PSAP, 550 nm) gives some measure of the uncertainty associated with the correction process.The larger variability of MAC (PSAP, 550 nm) compared with that of MAC (MAAP, 637 nm) suggests that the precision and absolute accuracy of b abs (PSAP) are lower than those of b abs (MAAP).

Comparison of MAC (AE) with MAC (PAAS-4k) at Pallas
To evaluate the overall accuracy of MAC (AE), we carried out a detailed intercomparison between MAC (AE) and the MAC of BC derived by using the PAAS-4k instrument, MAC (PAAS-4k), at Pallas.MAC (PAAS-4k) was derived by using the M BC (COSMOS)-b abs (PAAS-4k) linear regression using 3h averaged M BC (COSMOS) and b abs (PAAS-4k) data (Schnaiter et al. 2023).For a detailed description of the design, characterization, and calibration of PAAS-4k, see Schnaiter et al. (2023).In brief, light-absorbing aerosol particles are periodically heated in a modulated laser beam, which translates into a periodic pressure variation in the surrounding air, and consequently in a sound wave with the same frequency as the modulation frequency.This photoacoustic signal is then amplified, digitized and calibrated with a standard sample of known absorption cross section (e.g., premixed NO 2 /air samples) to determine b abs (PAAS-4k).Because the photoacoustic effect is specific to absorption only, the measured b abs, (PAAS-4k) is not influenced by particle light scattering even in situations where the aerosol light extinction is dominated by light scattering.PAAS-4k serves as a reliable instrument for validating the widely used filter-based instruments for measuring b abs (Schnaiter et al. 2023).The performance of PAAS-4k has been demonstrated in the Arctic by comparing b abs (PAAS-4k) with b abs (MAAP); these values agreed to within 14% (slope ¼ 0.86) that is within the combined accuracy of about 20% of both instruments (10% for PAAS-4k and 12% for MAAP, Schnaiter et al. 2023).Spectral MAC (PAAS-4k) values at four wavelengths in the 405-660 nm range were derived by using b abs (PAAS-4k) obtained from December 2021 to November 2022 (Schnaiter et al. 2023).The MAC values reported by Schnaiter et al. (2023) were adjusted to match the corresponding Aethalometer wavelengths by assuming a k −1 dependence.MAC (AE, k) and MAC (PAAS-4k) exhibited very good agreement (Figure 10).This agreement was improved to some extent when the whole period of AE observations (2019-2022) at Pallas was used for the comparison.Importantly, MAC (AE) and MAC (PAAS-4k) agreed to within 6%, which strongly supports the choice of C 0 ¼ 3.5 for the model AE 33 instrument at this site (Figure 11).

Comparison of MAC of BC among different instruments
In this section, we compared MAC values of BC among Aethalometer, MAAP, PAAS-4k, and PSAP deployed in the Arctic (Table 5).MAC values at the operating wavelengths of the instruments were adjusted to 590 nm.The mean ± 1r MAC value of all instruments was 11.8 ± 0.5 m 2 g −1 , and the median value was 11.7 m 2 g −1 at 590 nm.Thus, the variation (1r) among all instruments was very weak, about 4%.This result also supports the choice of C 0 ¼ 3.5 as reasonable for AE in the Arctic.
In addition, MAC (AE) agreed to be within 4% with MAC (MAAP) at 590 nm in the latitude range of 35-83 � N (see Section 8).This agreement in the Arctic and at mid-latitudes, in addition to the agreement of MAC (AE) with MAC (PAAS-4k) in the Arctic, strongly suggests that these MAC (AE) values represent the yearly averaged MAC for airborne BC particles to within about 18% uncertainty, which includes the uncertainty of M BC (COSMOS).

Recommendations
The MAC for AE 31 recommended by the manufacturer is 14625/(k � C 0 ), which corresponds to 7.1 m 2 g −1 at k ¼ 590 and C 0 ¼ 3.5, whereas the estimated MAC (AE, 590 nm) derived by this study was 11.4 ± 1.2 m 2 g −1 , or about 1.6 times the recommended value.Therefore, the use of the default value to convert b abs (AE) to M BC (AE) at these sites would result in overestimation of M BC (AE) by a factor of 1.6.The MAC (AE, k) obtained by the present study showed weak spatial and temporal variations of about 11% and 18%, respectively, among the four Arctic sites.The MAC (AE) values estimated in this study for Arctic sites agreed to within 10% with MAC (AE) values obtained by previous studies for several sites in the mid-latitudes and the Arctic.We recommend scaling M BC (AE) with the MAC (AE, k) (Table 3, and Table S2 in the SI), and C 0 ¼ 3.5 values reported in this study to obtain an improved, error-constrained approximation of M BC (AE) by using Equation ( 10 We first derived b abs (AE) by using Equation ( 6) with C 0 ¼ 3.5.We showed that b abs (AE) and M BC (COSMOS) were correlated (r 2 ¼ 0.82-0.95)throughout the study period at all four sites.This result suggests that BC is the dominant light-absorbing particles with diameters smaller than 1 lm.The high correlations indicated that MAC (AE) estimation by the b abs (AE)-M BC (COSMOS) correlation method is reliable.We derived MAC (AE) by using Equation ( 7) with C 0 ¼ 3.5.At Barrow, MAC (AE 31) and MAC (AE 33) values were similar, suggesting that C 0 did not depend on the AE model.At the four sites, MAC (AE) estimated by this method at 590 nm varied from 10.2 to 12.9 m 2 g −1 in 1-h data and from 10.1 to 12.8 m 2 g −1 in 24-h data.
b abs was also measured concurrently by the fourwavelength photoacoustic aerosol absorption spectrometer (PAAS-4k) at Pallas from December 2021 to November 2022.This b abs value was not influenced by light-scattering particles.MAC (PAAS-4k) agreed with the simultaneously measured MAC (AE) to within 6%.This result strongly supports the use of C 0 ¼ 3.5 in deriving b abs (AE).
The absorption Ångstr€ om exponent (AAE) was calculated by a power law fit to spectral MAC (AE, k) values for k ¼ 370-950 nm for the whole study period at each site.In addition, AAE (MAC) was also determined coefficient measured by Aethalometer, also denoted as r ap in the literature b abs (COSMOS) b abs measured by a continuous soot monitoring system (COSMOS) MAC Mass absorption cross section M BC (COSMOS) Mass concentration of black carbon derived from measurements of the light absorption coefficient (b abs ) with COSMOS using a MAC of 8.73 m 2 g −1 for a Pallflex filter.C 0 Multiple scattering factor due to the scattering effect of the light beam by the filter fibers R Filter-loading correction factor MAC (AE) Mass absorption cross section of BC for Aethalometer (AE) MAC (PSAP) Mass absorption cross section of BC for particle soot absorption photometer (PSAP) MAC (MAAP) Mass absorption cross section of BC for multi-angle absorption photometer (MAAP) MAC (PAAS-4k) Mass absorption cross section of BC for four-wavelength photoacoustic aerosol absorption spectrometer (PAAS-4k) MAC cor (AE) Mass absorption cross section of BC for Aethalometer derived from the correlation between b abs (AE) and M BC (COSMOS) MAC med (AE) Mass absorption cross section of BC for Aethalometer derived from the ratio of b abs (AE) to M BC (COSMOS) AAE Absorption Ångstr€ om exponent AAE (MAC) Absorption Ångstr€ om exponent derived from a power law fit to the spectral MAC (AE) BC Black carbon BrC Brown carbon b abs (AE, k) and M BC measured by COSMOS (M BC (COSMOS)).They estimated MAC (AE, 590 nm) to be 12.5 m 2 g −1 at Alert (2018-2019) and 10.2 m 2 g −1 at Ny-Ålesund (2012-2019).
) With Aethalometer models AE 31 and AE 33, b abs (AE, k) is derived from the measured b 0 (k).The b 0 (k) values measured by models AE 31 and AE 33 are also influenced by light scattering by non-BC aerosols, multiple scattering enhancements by the filter, and filter-loading effects.These effects introduce systematic errors to b abs (AE, k) that need to be corrected.Five different correction schemes have been proposed to derive b abs (AE, k) from b 0 (k): the Weingartner (Weingartner et al. 2003), Arnott (Arnott et al. 2005), Schmid (Schmid et al. 2006), Virkkula filter-loading (Virkkula et al. 2007), and Collaud Coen corrections (Collaud Coen et al. 2010).In brief, the largest artifact

Figure 1 .
Figure 1.Location map of the sites in the Arctic where M BC (COSMOS) and b abs (AE) were measured for this study: Alert, Barrow, Ny-Ålesund, and Pallas.

Figure 3 .
Figure 3. (a) Scatter plots of M BC (COSMOS) and b abs (AE) at 590 nm in 24-h averaged data for the entire study period at Alert, Barrow, Ny-Ålesund, and Pallas.The solid black line is the least-squares regression line forced through the origin (intercept ¼ 0).(b) Same as (a) but at 880 nm.

Figure 4 .
Figure 4. (a) Histograms of b abs (AE)/M BC (COSMOS) ratios for all data and data with M BC (COSMOS) > 5 ng m −3 at 590 nm for the whole study period at Alert, Barrow, Ny-Ålesund, and Pallas.(b) Same as (a) but at 880 nm.

Figure 5 .
Figure 5. Spectral variations of MAC (AE) during the whole observation period at Alert, Barrow, Ny-Ålesund, and Pallas.

Figure 6 .
Figure 6.(a) Time series of yearly averaged AAE (MAC) (470 and 950 nm) and its (b) site-to-site variation at the four sites in the Arctic during the entire observation period.The black open circle corresponds to AAE (MAC) for AE 33 at Barrow.The AAE (MAC) (470 and 950 nm) value of 1 is shown by a thin horizontal line.Station name abbreviations: PAL, Pallas; BRW, Barrow; ZEP, Zeppelin (Ny-Ålesund); and ALT, Alert.

Figure 7 .
Figure 7. Time series of yearly averaged MAC (AE, 590 nm) for the four sites in the Arctic.The solid horizontal line indicates the mean and dashed lines ±1r values of the MAC (AE, 590 nm) at the four sites over the study period.

Figure 8 .
Figure 8. MAC (AE) values from published work at mid-latitude (FKL, MAG, PAY, and HRL), and Arctic sites (black circles).The MAC values reported in the original literature have been adjusted to 590 nm by assuming an absorption Ångstr€ om exponent of 1.0.The MAC (AE) values at the four sites derived from this study (red circles) are also shown for comparison.The mean ± 1r value is shown by the thin horizontal line.Station name abbreviations, following Global Atmosphere Watch (GAW) station code numbers: FKL, Finokalia; MAG, Magadino; PAY, Payerne; HRL, Harwell; PAL, Pallas; BRW, Barrow; ZEP, Zeppelin (Ny-Ålesund); and ALT, Alert.The solid horizontal line indicates the mean and dashed lines ±1r values of the MAC (AE, 590 nm) at mid-latitude and Arctic sites.

Figure 10 .
Figure 10.Spectral variations of MAC (AE 33) and MAC (PAAS-4k) at Pallas derived from the concurrent measurement of AE 33 and PAAS-4k from December 2021 to November 2022.Spectral variations of MAC (AE 33) during the whole observation period (March 2019 to November 2022) are also shown for comparison.
Several previous studies have derived black carbon mass concentrations (M BC ) in the Arctic solely from the absorption coefficient (b abs ) measured by Aethalometer (AE).For this purpose, a predefined, fixed mass absorption cross section (MAC (AE)) has been widely used.However, these studies, with the exception ofOhata et al. (2021a), did not evaluate the uncertainty associated with MAC (AE) or year-to-year, spatial, and spectral variations of MAC (AE).We measured b abs by Aethalometer (b abs (AE)) using variable particle size cutoffs (PM 10 , TSP), and for reference, we measured M BC with COSMOS (M BC (COSMOS)) for PM 1 at Alert (2018-2020),Barrow  (2012Barrow  ( -2022)),Ny-Ålesund (2012-2019), and Pallas (2019- 2022).

Figure 11 .
Figure 11.Scatter plot of MAC (AE) and MAC (PAAS-4k) at Pallas from December 2021 to November 2022.The solid black line is the least-squares regression line forced through the origin (intercept ¼ 0).

Table 1 .
Summary of the symbols and acronyms used for variables in this study.

Table 2 .
Overview of Aethalometer measurement locations, periods, and instruments, flow rates, and sampling inlet (size cutoff; cyclone) used in this study.

Table 3 .
MAC cor (AE) and MAC med (AE) at 590 nm and 880 nm in 1-h and 24-h data at the four study locations.

Table 5 .
Comparison of MAC values from various instruments deployed in the Arctic.The table shows the MAC values at the operating wavelengths (k) of the instruments and those adjusted to 590 nm by assuming AAE ¼ 1.0.The MAC (AE, 590 nm) values correspond to those studies in the Arctic that reported C 0 values (see Table4).The MAC (PAAS-4k, 660 nm) was derived by using 24-h average data.Climate Observatory.E. Andrews and the aerosol measurements at NOAA's Barrow Atmospheric Baseline Observatory were supported by a Department of Energy/ Atmospheric Radiation Measurement User grant (ANL award no.0F-60239).