Long‐term measurements of the light absorption coefficient (*b*_{abs}) obtained with a particle soot absorption photometer (PSAP), *b*_{abs} (PSAP), have been previously reported for Barrow, Alaska, and Ny‐Ålesund, Spitsbergen, in the Arctic. However, the effects on *b*_{abs} of other aerosol chemical species coexisting with black carbon (BC) have not been critically evaluated. Furthermore, different mass absorption cross section (MAC) values have been used to convert *b*_{abs} to BC mass concentration (*M*_{BC} = *b*_{abs}/MAC). We used a continuous soot monitoring system (COSMOS), which uses a heated inlet to remove volatile aerosol compounds, to measure *b*_{abs} (*b*_{abs} (COSMOS)) at these sites during 2012–2015. Field measurements and laboratory experiments have suggested that *b*_{abs} (COSMOS) is affected by about 9% on average by sea‐salt aerosols. *M*_{BC} values derived by COSMOS (*M*_{BC} (COSMOS)) using a MAC value obtained by our previous studies agreed to within 9% with elemental carbon concentrations at Barrow measured over 11 months. *b*_{abs} (PSAP) was higher than *b*_{abs} (COSMOS), by 22% at Barrow (PM_{1}) and by 43% at Ny‐Ålesund (PM_{10}), presumably due to the contribution of volatile aerosol species to *b*_{abs} (PSAP). Using *b*_{abs} (COSMOS) as a reference, we derived *M*_{BC} (PSAP) from *b*_{abs} (PSAP) measured since 1998. We also established the seasonal variations of *M*_{BC} at these sites. Seasonally averaged *M*_{BC} (PSAP) decreased at a rate of about 0.55 ± 0.30 ng m^{−3} yr^{−1}. We also compared *M*_{BC} (COSMOS) and scaled *M*_{BC} (PSAP) values with previously reported data and evaluated the degree of inconsistency in the previous data.

^{−3} yr^{−1} during 1998–2015

Black carbon (BC) particles are emitted as a result of incomplete combustion of both natural and anthropogenic carbon‐based fuels. BC particles influence the radiation budget of the Earth's atmosphere by strongly absorbing solar radiation [*Bond et al.*, ; *Kondo*, ]. Warming is occurring in the Arctic at about twice the global average rate [*Shindell and Faluvegi*, ] owing to a combination of climate feedbacks, including radiation feedback [*Sand et al.*, ]. Light‐absorbing particles such as BC likely contribute to radiative forcing in the Arctic also by changing the albedo of snow through the deposition of BC [*Bond et al.*, ; *Flanner et al.*, ; *Shindell and Faluvegi*, ]. However, estimates by climate models of the effects of BC on Arctic warming are still highly uncertain, in part because measurements of the spatiotemporal distribution of the mass concentration of BC (*M*_{BC}) in the atmosphere are limited and not sufficiently accurate.

To better understand the distribution of *M*_{BC} and the processes controlling *M*_{BC} in the Arctic, both aircraft measurements [*Kondo et al.*, ; *Liu et al.*, ; *Matsui et al.*, ; *McNaughton et al.*, ; *Spackman et al.*, ; *Warneke et al.*, , ] and ground‐based measurements [*Bodhaine*, ; *Delene and Ogren*, ; *Eleftheriadis et al.*, ; *Hirdman et al.*, ; *Sharma et al.*, ] have been conducted. We summarize the nomenclature of physical parameters related to absorption and scattering by aerosol particles and the mass concentration of BC particles derived by different instruments in Table .

Detailed studies of emissions of BC from different sources (e.g., Asia, Europe, and North America) and its subsequent transport in the planetary boundary layer and free troposphere have been made by using aircraft measurements [*Brock et al.*, ; *Kondo et al.*, ; *Liu et al.*, ; *Sahu et al.*, ; *Spackman et al.*, ; *Warneke et al.*, , ]. These studies used a single particle soot photometer (SP2) and obtained accurate measurements of BC size distributions [e.g., *Schwarz et al.*, ; *Moteki and Kondo*, ]. However, aircraft measurements are limited both spatially and temporally.

To date, most autonomous and continuous measurements of *M*_{BC} in the Arctic region have been made by a filter‐based optical technique, mainly with a particle soot absorption photometer (PSAP; Radiance Research, Seattle, WA) or an aethalometer (Magee Scientific, Berkeley, CA, USA) [*Bodhaine*, ; *Delene and Ogren*, ; *Eleftheriadis et al.*, ; *Sharma et al.*, ]. However, these studies did not perform detailed error analyses, so the accuracy of the *M*_{BC} values derived from those measurements is uncertain.

Measurements obtained by filter‐based absorption techniques need to be corrected for the effects of coexisting non‐BC aerosol particles in the filter medium because ambient aerosols comprise a complex mixture of light‐absorbing and nonabsorbing particles which optically interact [*Bond et al.*, , ]. We have deployed a continuous soot monitoring system called continuous soot monitoring system (COSMOS) (Kanomax, Osaka, Japan) [*Miyazaki et al.*, ; *Kondo et al.*, , ], which is a filter‐based instrument equipped with an inlet heated at 300°C to remove nonrefractory components from the aerosol phase.

However, light transmission through the filter matrix is reduced not only due to refractory absorbing particles but also due to the presence of embedded light‐scattering particles that do not evaporate during sampling through the heated inlet. As a result, *M*_{BC} determined by COSMOS (*M*_{BC} (COSMOS)) may be overestimated, though *Verma et al.* [] found this effect to be small in Asia. Near the surface in the Arctic, however, *M*_{BC} is often lower by an order of magnitude than it is in midlatitudes [e.g., *Liu et al.*, ; *Spackman et al.*, ]. Therefore, nonvolatile aerosol components such as sea salt and mineral dust particles may substantially interfere with the *M*_{BC} (COSMOS) measurements, depending on their concentrations relative to those of BC. Thus, there is a strong need to evaluate the uncertainties of *M*_{BC} (COSMOS), especially in remote regions such as the Arctic.

For this purpose, we conducted laboratory experiments to estimate how the presence of sea‐salt particles affected *M*_{BC} (COSMOS). For overall evaluation of the accuracy of *M*_{BC} (COSMOS), we compared *M*_{BC} (COSMOS) with measurements of the mass concentration of elemental carbon (EC) (*M*_{EC}) made by the thermal‐optical transmittance (TOT) technique at Barrow. We also compared *M*_{BC} (COSMOS) with *M*_{BC} measured near Ny‐Ålesund by an SP2 onboard aircraft, although the available aircraft data are limited. We used the results of these comparisons to investigate the correlation of the *M*_{BC} (COSMOS) values with absorption coefficients measured by a PSAP (*b*_{abs} (PSAP)) operated at Barrow, Alaska (71.32°N, 156.61°E, 10 m above sea level), by the National Oceanic and Atmospheric Administration (NOAA) Earth System Research Laboratory, Global Monitoring Division and at Zeppelin Station (78.92°N, 11.93°E, 474 m above sea level), Ny‐Ålesund, Spitsbergen, operated by the Norwegian Polar Institute. We then scaled *b*_{abs} (PSAP) measured at Barrow and Ny‐Ålesund by comparing them with *M*_{BC} (COSMOS) based on high correlations between PSAP and COSMOS measurements. Finally, we used the scaled PSAP measurements to derive the long‐term variations of *M*_{BC} (PSAP) at these sites.

The principles of operation of PSAP and COSMOS are identical; the attenuation of light at a given wavelength *λ*, *b*_{0}(*λ*), in a filter‐based absorption photometer, is determined by the following equation:*A* is the area of the sample spot, *V*_{a} is the air sample volume during a given time period between (*t* − Δ*t*) and *t*, and *I*_{t − Δt} and *I _{t}* are the average transmittances at (

In the case of a PSAP, absorption coefficients of aerosol particles collected on filters (*b*_{abs}) are derived from the measured attenuation *b*_{0}. Because the *b*_{0} values measured by this instrument are influenced by light scattering by aerosols, these contributions are corrected by applying the empirical relation of *Bond et al.* []:*f*_{sca}*b*_{sca}, represents a correction for light scattering by aerosol particles collected on filters. *b*_{sca} is obtained by independent measurements, such as with a nephelometer. For PSAPs, *f*_{sca} has been estimated to be 0.016 ± 0.016 [*Bond et al.*, ]. In equation , *f*_{fil} represents the increase in absorption by multiple scattering in the filter medium. In this study, the following equation, which was derived by using polydisperse nigrosine particles, is used for *f*_{fil} [*Bond et al.*, ]:*I _{t}*/

For COSMOS, *b*_{sca} is very close to zero for most aerosols, owing to the use of the heated inlet to remove volatile non‐BC species [*Kondo et al.*, ]. In fact, the contribution of the *f*_{sca}*b*_{sca} term of equation to *b*_{abs} (COSMOS) values has been estimated to be about 2% at midlatitudes [*Kondo*, ]. Hence, we used the following equation for COSMOS:

Equation was used to account for the effect of multiple scattering for COSMOS. As a result of the removal of volatile non‐BC species, errors associated with non‐BC LSPs are small and COSMOS measures *b*_{abs} of bare BC particles (core BC particles) accurately when all scattering particles are volatile. In contrast, a PSAP measures the light absorption of all particles, which is possibly enhanced by volatile coatings on the BC particles (discussed below) and by scattering from nonrefractory particles within the PSAP filter matrix.

Changes in soot morphology during heating do not substantially affect *b*_{abs} measurements by the COSMOS instrument. Laboratory experiments with an SP2 have shown that the change in the diameter of fullerene soot with initial diameters of 150 and 320 nm caused by heating the soot to 300°C is about 3% [*Irwin et al.*, ]. Characteristics of fullerene soot were found to be representative of the ambient BC in Tokyo [*Moteki and Kondo*, ]. A PSAP measures the light absorption of all particles, which is possibly enhanced by coatings on BC particles, as discussed below.

With both PSAPs and COSMOS, *M*_{BC} (g m^{−3}) can be estimated by dividing *b*_{abs} (m^{−1}) by the mass absorption cross section of BC (MAC) (m^{2} g^{−1}), if the effects of LSPs are corrected for with sufficient accuracy and the effect of light‐absorbing particles other than BC is neglected. Namely,

Under the assumptions mentioned above, *b*_{abs} (COSMOS) corresponds to the absorption of bare BC particles, so MAC (COSMOS) depends only (and slightly) on the size distribution of bare BC particles [*Kondo et al.*, ]. On the other hand, *b*_{abs} values obtained by PSAP potentially depend on the mixing state of BC and are also sensitive to absorption by non‐BC species, such as brown carbon, which COSMOS does not sense. They also depend on the BC size distribution.

Light absorption by BC particles is enhanced by coatings of non‐BC compounds, the so‐called lens effect [e.g., *Shiraiwa et al.*, ; *Bond et al.*, ]. Therefore, the MAC (PSAP) value used to calculate *M*_{BC} (PSAP) should be varied according to the mixing state of BC. In other words, the use of a constant MAC (PSAP) value to derive *M*_{BC} (PSAP) under varying atmospheric environmental conditions will introduce additional uncertainties into *M*_{BC} (PSAP) estimates.

To summarize, in principle, COSMOS measures *b*_{abs} of bare BC particles accurately, whereas PSAP measures *b*_{abs} of all particles, and the measured value is enhanced by coatings on BC particles. Furthermore, the MAC value used with COSMOS (MAC of bare BC particles) has less uncertainty than that used with PSAPs (MAC of various BC mixing states). Therefore, *M*_{BC} (COSMOS) is considered to be more accurate than *M*_{BC} (PSAP).

We note that *M*_{BC} (COSMOS) can be influenced not only by the uncertainty of MAC (COSMOS) due to variability of the BC size distribution but also by refractory LSPs (such as sea‐salt and dust particles). These uncertainties are examined individually in the following sections. We then compare *M*_{BC} (COSMOS) values with *M*_{BC} (PSAP) values and discuss the overall uncertainty of *M*_{BC} measurement in detail.

COSMOS measures *b*_{abs} of BC particles deposited on quartz filters (Pallflex, E70‐2075W) at a wavelength (*λ*) of 565 nm. In Asia, the uncertainty of *b*_{abs} (COSMOS) has been found to be better than 10% for an integration time of 1 h [*Kondo et al.*, ]. COSMOS was operated at Barrow from August 2012 to December 2015 and at Ny‐Ålesund from April 2012 to December 2015 (Figure ). The measurements of *b*_{abs} by COSMOS (*b*_{abs} (COSMOS)) and the derived *M*_{BC} (COSMOS) values were made by using a PM_{1} impactor inlet (i.e., with a size cutoff at an aerodynamic diameter *D _{p}* of about 1 µm). COSMOS aspirates ambient air at a flow rate of 0.7 L min

*Kondo et al.* [] and *Miyakawa et al.* [] showed that the accuracy of *M*_{BC} (COSMOS) measurements is approximately 10% through extensive comparisons with *M*_{BC} measurements made by SP2 and EC measurements made by the TOT technique at several sites in Asia. They demonstrated that SP2, TOT (EC), and COSMOS measurements are consistent in the Asian region. By this comparison, MAC was determined to be about 10.0 m^{2} g^{−1} by using *B* = 1.22 in equation . In the present study, we used *B* = 1.397 for the comparison of *b*_{abs} (COSMOS) with *b*_{abs} (PSAP). With a *B* value of 1.397, MAC (COSMOS) must be 10.0 × (1.22/1.397) = 8.73 m^{2} g^{−1}. Different (*B*, MAC) combinations, for example, (1.22, 10.0 m^{2} g^{−1}) and (1.397, 8.73 m^{2} g^{−1}), result in an identical *M*_{BC} (COSMOS) value.

The *M*_{BC} (COSMOS)/*M*_{BC} (SP2) ratio was observed to decrease by about 7% with an increase in the mass median diameter (MMD) of 50 nm (from 130 to 180 nm) in Tokyo, possibly owing to the size dependence between MAC (COSMOS) and *f*_{fil} [*Kondo et al.*, ; *Kondo*, ]. In Tokyo, the mean MMD was 146 ± 12 nm, with a mean geometrical standard deviation (*σ*_{gm}) of 1.82 ± 0.14. Considering the variability of the observed size distribution in Asia and the Arctic (MMD mostly up to about 200 nm) [*Kondo*, ], we estimated the typical uncertainty in *M*_{BC} (COSMOS) in the Arctic associated with the variability in BC size distribution to be about 10%. *M*_{BC} (PSAP) should also be influenced by this effect, although the degree of influence may be different owing to internal mixing of BC particles.

In this study, we also used *b*_{abs} data obtained with a PSAP and a continuous light absorption photometer (CLAP) [*Lack et al.*, ]. The CLAP is conceptually similar to PSAP but uses a solenoid valve to cycle through eight sample filter spots. Brief descriptions of the PSAP and CLAP measurements at Barrow and Ny‐Ålesund are given here, and more details are provided in section A1. At these sites, all three instruments (PSAP, CLAP, and COSMOS) collected aerosol particles containing BC on the same type of fiber filter (Pallflex, type E70‐2075W). The PSAP and CLAP measured *b*_{abs} of aerosol particles collected on the filter at *λ* = 529 nm and 522 nm, respectively, and both the PSAP and CLAP aspirated ambient air at a volumetric flow rate of 1 L min^{−1} (about 0.9 L min^{−1} at STP) using PM_{1} and PM_{10} (*D _{p}* < 10 µm) impactors alternately for 30 min of each hour. The values of

The uncertainty of the 1 h average *b*_{abs} (PSAP) was estimated to be about 20% at midlatitudes (35°N–45°N), considering instrumental noise and calibration following *Bond et al.* [], and unit‐to‐unit variability [*Sherman et al.*, ]. In this study, we used CLAP data obtained at Barrow between August 2012 and December 2015. The daily mean *b*_{abs} (PSAP) and *b*_{abs} (CLAP) values agreed to within 2% during 2012–2015. Therefore, for simplicity, we consider the instruments to be equivalent and refer to CLAP data as PSAP data hereafter.

Similarly, at Ny‐Ålesund, measurements of *b*_{abs} at 532 nm were also carried out at about 10 m above the ground by using a custom‐built PSAP [*Krecl et al.*, ]. No cyclone or impactor was used, so there was no particle size cutoff for the PSAP data obtained at Ny‐Ålesund. However, it is unlikely that a substantial number of particles with *D _{p}* > 10 µm were included in the PSAP measurements, given the particle losses in the inlet system. Therefore, for simplicity, we refer to these data as PM

The Arctic has basically two seasons. Therefore, for the analyses, the *M*_{BC} (COSMOS) and *M*_{BC} (PSAP) data were classified into winter (November–April) and summer (May–October) seasons.

As discussed in section 3, in COSMOS measurements, light transmittance through a filter matrix is reduced by light scattering by refractory aerosol particles such as sea salt (predominantly NaCl) and mineral dust. Sea‐salt particles are reported to constitute about 20% of the mass concentration of aerosols with diameters less than 1 µm at Barrow [*Quinn et al.*, ].

To assess the interference from sea‐salt particles on *M*_{BC} (COSMOS), we performed laboratory experiments, as shown schematically in Figure . The aim of the experiments was to estimate the decrease in transmittance per unit scattering coefficient or volume (mass) of sea‐salt particles. The refractive indices of NaCl are 1.54 and 1.55 at *λ* = 589 nm and 565 nm, respectively, whereas the refractive indices of polystyrene latex (PSL) are 1.59 and 1.60 at *λ* = 589 nm and 486 nm, respectively. Given that NaCl constitutes the major fraction of sea‐salt particles [*Barrie and Barrie*, ], it is likely that sea‐salt particles and PSL have similar optical effects on *M*_{BC} (COSMOS). Thus, in our experiments, we used PSL, which does not evaporate at 300°C, as a surrogate for sea‐salt particles, which are not accurately sized by our calibration system because they are not spherical.

Water samples containing PSL particles were introduced by a peristaltic pump into a nebulizer at a constant flow rate (Figure a). The nebulizer then aerosolized PSL particles from the water suspension and passed them to a differential mobility analyzer (Model 3081, TSI Inc., MN, USA) for size segregation according to their mobility diameters. Monomodal PSL particles with diameters of 254 nm, 506 nm, and 814 nm were then sampled by COSMOS and SP2. The light‐scattering data from the SP2 were used to derive the number concentration of PSL particles from the light‐scattering data.

The scattering coefficient (Mm^{−1}) of the PSL particles at *λ* = 565 nm (*b*_{sca} (PSL)) was calculated from their number concentration as measured by the SP2 on the basis of Mie theory. The volume concentration (*V*_{PSL}, µm^{3} cm^{−3}) of the extracted PSL particles was also calculated from their number concentration and known diameter. The measured transmittance change of COSMOS due to PSL particles deposited on the filter was converted to the apparent BC mass concentration, denoted as Δ*M*_{BC} (µg m^{−3}).

Δ*M*_{BC} correlated well with *b*_{sca} (PSL) (Figure ). As expected, Δ*M*_{BC} also correlated well with *V*_{PSL} (not shown). The Δ*M*_{BC}/*b*_{sca} (PSL) ratios, which showed only small dependence on the PSL diameters, were found to be about 0.0021 µg m^{−3}/Mm^{−1}. The Δ*M*_{BC}/*V*_{PSL} ratios, which also showed little dependence on the PSL diameters, were found to be about 0.022 µg m^{−3}/10^{−6} cm^{3} m^{−3}. The observed size dependence on PSL diameter was significantly smaller than that calculated on the basis of Mie theory for airborne PSL particles [*Moteki et al.*, ].

Considering these results, we used an average Δ*M*_{BC}/*b*_{sca} (PSL) ratio of 0.0021 µg m^{−3}/Mm^{−1} for the subsequent analysis as follows:

Using this relationship, we also estimated *f*_{sca} in equation as *f*_{sca} = 0.0021 (g m^{−3}/m^{−1}) × MAC (COSMOS) (m^{2} g^{−1}) = 0.0021 × 8.73 = 0.018. This value is very similar to the value of 0.016 derived by *Bond et al.* [] by using polydisperse LSPs ((NH_{4})_{2}SO_{4} and NaCl) (section 2). This agreement indicates that equation is consistent with their measurement of the effect of LSPs on *b*_{abs} (PSAP).

To further ascertain whether the relationship represented by equation is valid for ambient *M*_{BC} measurements, we conducted an additional experiment with a different configuration (Figure b). In the second experiment, ambient air containing BC particles was mixed with air containing PSL particles with a diameter of 506 nm and subsequently heated to 300°C. An SP2 was used to measure the BC mass concentration and the PSL number concentration, and then we derived the scattering coefficient of PSL from these measurements.

Δ*M*_{BC}/*b*_{sca} (PSL) was approximately 0.0025 µg m^{−3}/Mm^{−1} (correlations not shown). This value is similar to that obtained in the first experiment, indicating that interference from a mixture of BC and sea‐salt particles is very similar to interference from sea‐salt particles alone. We used equation to estimate the error due to sea‐salt aerosol particles, as described in section 4.2.

For the measurements of the sea‐salt mass concentration (*M*_{s‐s}) at Barrow, ambient air samples were collected through an inlet mounted 10 m above the ground onto filters by using PM_{1} and PM_{10} impactors at 1 to 4 day intervals between October 1997 and December 2009. At Ny‐Ålesund, air samples containing sea‐salt particles were collected daily from January 2012 to December 2014 without use of an impactor. For simplicity, we also designated these data as PM_{10}. More detailed descriptions of the *M*_{s‐s} measurements are presented in section A2.

*M*_{s‐s} was calculated from measured Na^{+} and Cl^{–} with equation [*Holland*, ].

The factor 1.47 is the (Na + K + Mg + Ca + SO_{4} + HCO_{3})/Na seawater ratio. The uncertainty arising from the use of equation to estimate *M*_{s‐s} is described in section A2.

At both sites, *M*_{s‐s} showed similar and notable seasonal variations; values were about an order of magnitude higher in winter (about 1 µg m^{−3}) than in summer (about 0.1 µg m^{−3}) (Figure a). The seasonality and magnitude of *M*_{s‐s} at Barrow during 1997–2009 were very similar to those from October 1997 to December 2000 [*Quinn et al.*, ]. This similarity suggests that the interannual variability of *M*_{s‐s} is relatively small.

To estimate Δ*M*_{BC} we first calculated the contribution of sea‐salt aerosols to *b*_{sca} for PM_{1} aerosols (*b*_{sca} (PM_{1})) measured at Barrow. For this calculation, we used mass concentrations and the scattering coefficient for PM_{1} aerosols measured at Barrow between 1997 and 2000 [*Quinn et al.*, ]. The scattering coefficient of sea salt (*b*_{sca} (*s‐s*)) and *b*_{sca} (PM_{1}) can be calculated with equations and . The monthly averaged values of these parameters, (*b*_{sca} (s‐s))_{av} and (*b*_{sca} (PM_{1}))_{av}, were obtained from *Quinn et al.* [, Tables 2 and 4].*M*_{s‐s}]_{av} and [*M*_{PM1}]_{av} are monthly averaged mass concentrations of sea‐salt and PM_{1} aerosols, respectively, and *α*_{s‐s} and *α*_{PM1} are the mass‐scattering efficiencies (m^{2} g^{−1}) of sea‐salt and total aerosols, respectively, for PM_{1}.

The [*f*_{s‐s}]_{av} = [*b*_{sca} (*s‐s*)]_{av}/[*b*_{sca} (PM_{1})]_{av} ratio ranged between 0.06 and 0.38 with an annual average of 0.24. We used monthly averaged *b*_{sca} (PM_{1}) observed from August 2012 to December 2015 to estimate the monthly averaged *b*_{sca} (*s‐s*) by the following equation:

Finally, we calculated monthly mean Δ*M*_{BC} by replacing *b*_{sca} (PSL) in equation with *b*_{sca} (*s‐s*) (Figure b). At Barrow, Δ*M*_{BC} varied from about 0.19 to 4.3 ng m^{−3}, with a mean value of about 2.2 ng m^{−3}, which corresponds to about 9% of the annual mean *M*_{BC} (COSMOS).

Data similar to those used to derive Δ*M*_{BC} at Barrow were not available at Ny‐Ålesund. However, Δ*M*_{BC} should be proportional to *M*_{s‐s}, as shown by our laboratory experiments (section 4.1). At Ny‐Ålesund, the *M*_{s‐s} values were about 30% lower than at Barrow (Figure a) and the yearly average Δ*M*_{BC} was estimated to be about 1.6 ng m^{−3}.

In addition to sea‐salt particles, mineral dust particles may contribute to Δ*M*_{BC}, although reported mass concentrations of dust particles in the Arctic are much less than those of sea‐salt particles [*Brock et al.*, ; *Quinn et al.*, ]. The variability in BC size distribution may cause an additional uncertainty. Therefore, comparisons of *M*_{BC} (COSMOS) with the measurements of *M*_{BC} by other reliable techniques, such as the comparisons we did in Asia, are critically important for evaluating the overall accuracy of *M*_{BC} (COSMOS) in the Arctic.

To evaluate the overall accuracy of *M*_{BC} (COSMOS), we carried out a detailed intercomparison between *M*_{BC} (COSMOS) and the mass concentration of EC measured by the TOT technique at Barrow. For each *M*_{EC} measurement, air samples were collected at Barrow between August 2012 and June 2013 on a quartz fiber filter (Tissuquartz Filters 2500 QAT‐UP; 20 × 25 cm Pall Corporation) by using a Tisch high‐volume sampler (TE‐6070; Tisch Environmental Cleves, Ohio, USA) with a PM_{10} cutoff and a flow rate of about 1.2 m^{3} min^{−1} at 10 m above ground level. The particle‐laden filters were analyzed with a TOT carbon analyzer (Sunset Laboratories, Tigard, OR, USA), and *M*_{EC} was quantified following the temperature protocol recommended by the National Institute for Occupational Safety and Health (NIOSH 5040) [*Birch and Cary*, ]. The *M*_{EC} values are given in units of ng m^{−3} STP. We estimated the uncertainty of *M*_{EC} associated with the uncertainty of the flow rate of the filter sampling to be about 10%. We estimated the overall uncertainty of the *M*_{EC} measurement to be about 17% (excluding the uncertainty of the flow rate). More details of the EC measurements are given in section A3.

In Tokyo, the contributions of BC particles with diameters (*D*_{BC}) larger than 1 µm to *M*_{BC} of particles with diameters less than about 4 µm (PM_{4}) were observed to be less than 10%, based on SP2 measurements. At the remote site of Hedo (26.9°N, 128.3°E) on Okinawa Island, Japan, the contribution was about 8% in spring 2016 (section A4, Figure a). BC particles become more active as cloud condensation nuclei as their diameters increase, and larger BC particles have been observed to be removed more efficiently by wet deposition than BC particles with smaller diameters [*Ohata et al.*, ; *Moteki et al*., ; *Kondo et al.*, ]. BC particles larger than 1 µm should be scavenged more efficiently during long‐range transport to the Arctic from lower latitudes. Therefore, it is unlikely that the contribution of BC particles larger than 1 µm to *M*_{BC} (i.e., PM_{10} minus PM_{1}) exceeds about 10% at Barrow; thus, the uncertainty in the comparison between *M*_{BC} (COSMOS) (PM_{1}) and *M*_{EC} (PM_{10}) should be similar at Barrow.

We averaged the 1 min *M*_{BC} (COSMOS) data over the same periods as the individual *M*_{EC} observations and compared the *M*_{EC} and *M*_{BC} (COSMOS) time series (Figure ). The two measurements agreed very well throughout the year, and the monthly mean of the difference between *M*_{BC} (COSMOS) and *M*_{EC} did not show any clear seasonal variation (section A5, Figure ). In most months, *M*_{BC} (COSMOS)‐*M*_{EC} was less than 5 ng m^{−3}; this result is consistent with Δ*M*_{BC} estimated in section 4.2. Overall, this comparison indicates that the effect of sea‐salt or mineral dust particles on *M*_{BC} (COSMOS) was less than 5 ng m^{−3}.

Moreover, *M*_{EC} and *M*_{BC} (COSMOS) were highly correlated (*r*^{2} = 0.92) and the slope of the *M*_{EC}‐*M*_{BC} (COSMOS) correlation was 0.99 (Figure ). Because the COSMOS measurement is based on light absorption, the good agreement between *M*_{BC} (COSMOS) and *M*_{EC} indicates that BC is the dominant light‐absorbing component of aerosols with diameters smaller than 1 µm at Barrow. It should be noted here that in Asia, MAC (COSMOS) was determined to be 8.73 m^{2} g^{−1} (or 10.0 m^{2} g^{−1} for *B* = 1.22) by comparing *M*_{BC} (COSMOS) with *M*_{BC} (SP2) and *M*_{EC} [*Kondo et al.*, ]. The present results indicate that the same MAC (COSMOS) value can be applied to the BC measurements in the Arctic and they demonstrate the consistency and lack of regional dependence of MAC (COSMOS).

We compared *M*_{BC} (COSMOS) at Ny‐Ålesund with aircraft *M*_{BC} (SP2) measurements conducted near Zeppelin station, Ny‐Ålesund, for 3 days in March 2013, during the Aerosol‐Cloud Coupling and Climate Interactions in the Arctic (ACCACIA) campaign [*Liu et al.*, ]. Detailed descriptions of the aircraft *M*_{BC} (SP2) measurements and calibration procedures are provided elsewhere [*Liu et al.*, ; *McMeeking et al.*, ]. In brief, BC size distributions were measured in the diameter range *D*_{BC} = 69–478 nm and *M*_{BC} (SP2) was obtained by integrating the BC mass size distributions with an accuracy of about 10% [*Liu et al.*, ].

We estimated BC mass concentrations between 478 nm and 1000 nm by fitting a lognormal function to the SP2 data (section A4, Figure b) and found that the mean contribution of BC mass concentrations between 478 nm and 1000 nm to *M*_{BC} (SP2) for PM_{1} was about 15%. In the comparison with *M*_{BC} (COSMOS), we corrected the *M*_{BC} (SP2) data for this additional contribution.

Daily mean *M*_{BC} (COSMOS) at Ny‐Ålesund agreed well to within about 3% (*r*^{2} = 0.96) with the vertical profiles of *M*_{BC} (SP2), in units of ng m^{−3} STP, obtained on 20, 21, and 23 March 2013 with an uncertainty of 15% (Figure and section A6). The absolute difference between *M*_{BC} (COSMOS) and *M*_{BC} (SP2) was less than 4 ng m^{−3}, despite the temporal and spatial differences of these data (Figure ).

Although in this paper we do not present a detailed interpretation of the variability in *b*_{sca}, it is useful to examine temporal variations of *b*_{sca}, which is used in equation to derive *b*_{abs} (PSAP) at Barrow and Ny‐Ålesund. At Barrow, daily *b*_{sca} values varied between about 1 and 20 Mm^{−1}, with an annual mean of 4.1 ± 3.5 Mm^{−1} (Figure a); wintertime *b*_{abs}/b_{sca} ratios were higher by a factor of about 1.5 than the summertime ratios, and, as a result, the wintertime single scattering albedo, defined as SSA = *b*_{sca}/(*b*_{abs} (PSAP) + *b*_{sca}), of 0.94 ± 0.03, was lower than the summertime value (0.96 ± 0.04) (section A7). At Ny‐Ålesund, daily *b*_{sca} values ranged between about 0.1 and 18 Mm^{−1}, with an annual mean of 4.0 ± 3.5 Mm^{−1} (Figure b), and wintertime *b*_{abs}/*b*_{sca} ratios were higher by a factor of about 1.3 than the summertime ratios. The corresponding SSA values were 0.95 ± 0.05 and 0.96 ± 0.04 in winter and summer, respectively (section A7). These results suggest that the contribution of absorbing particles to the total aerosol extinction coefficient was larger during winter at both sites.

We also compared *b*_{abs} (COSMOS) and *b*_{abs} (PSAP) at Barrow and Ny‐Ålesund. At Barrow, about 36% of the daily *b*_{abs} (PSAP) values were less than 0.1 Mm^{−1} and *b*_{abs} (PSAP) rarely exceeded 1 Mm^{−1} (Figure a), whereas at Ny‐Ålesund, about 60% of *b*_{abs} values were less than 0.1 Mm^{−1} and higher values (*b*_{abs} > 1 Mm^{−1}) were seldom observed (Figure b).

*b*_{abs} (PSAP) (PM_{1}) was highly correlated with *b*_{abs} (PSAP) (PM_{10}) (*r*^{2} = 0.97) at Barrow (Figure a). The slope of the correlation, denoted as *β*, was 0.85. Even when the symmetrical least squares fit was computed, *β* was little changed owing to the relatively high correlation between the parameters (*r*^{2} > 0.82).

Light‐absorbing particles with diameters larger than 1 µm, including mineral dust particles and BC, likely contribute to *b*_{abs} (PSAP) for PM_{10}. In addition, correction of the scattering effects may be size‐dependent, which is not fully taken into account by the correction made with equation . As discussed in section 5.1, it is unlikely that the BC mass concentration fraction with particle diameters larger than 1 µm exceeds 10%. Moreover, the MAC for BC particles larger than 1 µm is considerably smaller than that for BC particles smaller than 1 µm [*Schwarz et al.*, ]. Therefore, it is likely that the contribution of BC particles larger than 1 µm is limited. It is difficult to identify the reason for the slope being less than 1, owing to the lack of sufficient data necessary to quantify these effects.

*b*_{abs} (COSMOS) was highly correlated with both *b*_{abs} (PSAP) for PM_{1} (*r*^{2} = 0.87; *β* = 0.82) and PM_{10} (*r*^{2} = 0.88; *β* = 0.72) at Barrow, although some data points deviated significantly from the least squares fitted line (Figures b and c). The *β* value of 0.72 is largely explained by the product of the slopes = 0.85 (PSAP (PM_{10}) − PSAP (PM_{1})) × 0.82 (COSMOS − PSAP (PM_{1})) = 0.70.

It is possible that the *b*_{abs} (PSAP)‐*b*_{abs} (COSMOS) correlation with *β* less than 1 and the occasional large scatter between *b*_{abs} (PSAP) and *b*_{abs} (COSMOS) for PM_{1} at Barrow are partly due to differences in the methodology used to derive *b*_{abs}: equation for PSAP data, whereas equation for COSMOS data. The subtraction of the effect of scattering by non‐BC aerosols in equation may add uncertainty to the absolute accuracy and precision of *b*_{abs} (PSAP). In addition, light absorption of internally mixed BC particles collected on filters is enhanced by the lens effect in a PSAP, whereas this effect is negligibly small for COSMOS, as discussed in section 2. Further, there may exist volatile light‐absorbing aerosol species that affect *b*_{abs} (PSAP) but not *b*_{abs} (COSMOS). The combined effect of these factors is that nonabsorbing coatings or non‐BC absorbers may contribute to an enhancement of up to 22% (1/0.82) of the absorption of uncoated BC particles. It should be noted that differences in the absolute value of *b*_{abs} do not influence the *M*_{BC} values derived from PSAP data, as discussed below.

At Ny‐Ålesund, *b*_{abs} (COSMOS) and *b*_{abs} (PSAP) for PM_{10} were also correlated (*r*^{2} = 0.82; *β* = 0.70) (Figure d). *b*_{abs} (PSAP) was higher than *b*_{abs} (COSMOS) by 43% (1/0.70) at Ny‐Ålesund (PM_{10}). The slope (0.70) agrees with that obtained at Barrow to within 3%. Because *β* for PM_{10} was similar between the two sites, we used *b*_{abs} (PSAP) for PM_{10} to derive *M*_{BC} at Ny‐Ålesund.

Finally, it is possible to derive the mass concentration of BC by using the *b*_{abs} (PSAP) data and applying these empirically determined relationships. Equation is the condition of scaling of *M*_{BC} (PSAP) by *M*_{BC} (COSMOS):*β* = 0.82 ± 0.01 (±1*σ*)_{,} and MAC (COSMOS) = 8.73 m^{2} g^{−1}.

MAC (PSAP) is expressed as follows:^{2} g^{−1} for PM_{1}. At Ny‐Ålesund, *β* = 0.70 ± 0.01 and MAC (PSAP) = 12.5 ± 0.2 m^{2} g^{−1} for PM_{10}.

MAC (PSAP) values were also derived for each year by using the corresponding comparison between COSMOS and PSAP measurements at Barrow and Ny‐Ålesund. The derived MAC (PSAP) values varied between 8.5 and 11.8 m^{2} g^{−1} (PM_{1}) during 2012–2015 at Barrow and between 9.5 and 13.4 m^{2} g^{−1} (PM_{10}) during 2012–2014 at Ny‐Ålesund (Table ). At Barrow, we estimated the MAC (PSAP) accuracy to be about 18%, taking into account the slope determination accuracy of about 2%, the *M*_{BC} (COSMOS) accuracy of 10%, and the year‐to‐year variability in MAC (PSAP) of about 15% (1*σ*). Similarly, at Ny‐Ålesund, we estimated the accuracy of MAC (PSAP) to be about 20%, taking into account the year‐to‐year variability in MAC (PSAP) of about 18% (1*σ*).

We examined time series of daily mean *M*_{BC} (COSMOS) and *M*_{BC} (PSAP) for the entire period (2012–2015) of COSMOS measurements at both sites to evaluate the consistency of these two instruments (Figure ). The temporal variations of *M*_{BC} (COSMOS) and those of *M*_{BC} (PSAP) were generally well correlated over wide ranges of values, as expected from the high correlation between *b*_{abs} (PSAP) and *b*_{abs} (COSMOS) (Figure ) and the scaling of *b*_{abs} (PSAP) in equation . The time series qualitatively show the degree of the differences between individual daily mean values of *M*_{BC} (COSMOS) and *M*_{BC} (PSAP). The difference between monthly mean *M*_{BC} (COSMOS) and *M*_{BC} (PSAP) values was generally less than 10 ng m^{−3} (section A8.1, Figure ) and agreed to within 5% (*r*^{2} = 0.96) and 2% (*r*^{2} = 0.95) at Barrow and Ny‐Ålesund, respectively (section A8.2, Figure ). It is not known whether the relationship between the PSAP and COSMOS measurements observed in the Arctic holds at other latitudes.

*M*_{BC} (COSMOS) did not show well‐defined diurnal variations (monthly mean diurnal variation <10% of the daily mean) at these sites during any part of the year (section A9), suggesting that localized BC emissions from anthropogenic activities had little influence on the measured *M*_{BC}.

It is important to investigate year‐to‐year variations of *M*_{BC} in the Arctic with reliable data sets because year‐to‐year variations in BC emissions and transport pathways can be reflected in *M*_{BC} changes. As we showed in section 6, it is possible to use *M*_{BC} (PSAP) for this purpose. We examined time series of monthly mean *M*_{BC} (PSAP) from January 1998 to July 2012 at Barrow and from April 2006 to March 2012 at Ny‐Ålesund. Monthly mean *M*_{BC} (COSMOS) values at these sites also partly overlap these time series and extend them up to December 2015 (Figure ). PSAP data are missing at Barrow from January 2010 to April 2011 because of an instrument malfunction.

In winter, *M*_{BC} showed year‐to‐year variations of up to a factor of two with a relative variability of about 22% (1*σ*). In summer, *M*_{BC} was much lower than it was in winter and year‐to‐year variability in *M*_{BC} was correspondingly lower; the relative variability in *M*_{BC} was about 36% (1*σ*) in summer. Year‐to‐year variability can be caused by variations in BC emissions, especially those due to biomass burning, as well as by differences in the transport pathway and the degree of the wet deposition of BC during transport.

Relatively high *M*_{BC} values were observed in winter 2008 at Barrow (Figure ). During winter 2008, the BC profiles observed by the Aerosol, Radiation, and Cloud Processes affecting Arctic Climate aircraft observations indicated downward transport of BC from the free troposphere to the planetary boundary layer over the Alaskan Arctic [*Spackman et al.*, ; *Brock et al.*, ]; these findings suggest that biomass burning events in Siberia (Russia) and Kazakhstan influenced the surface‐measured *M*_{BC} at Barrow in winter 2008. More detailed studies of the effects of the temporal variations of the emission and transport of BC on the surface *M*_{BC} in the Arctic require simulations with sophisticated numerical models, which are beyond the scope of this study.

At Barrow, *Quinn et al.* [] showed that there was a significant decreasing trend in *b*_{abs} (PSAP) (PM_{10}) at 550 nm in the months of March and April between 1998 and 2006. Here we extended the period of the measurements to 1998–2015 and investigated the long‐term changes of *M*_{BC} (PSAP) in winter and summer.

We applied the least squares (LS) method to time series of *M*_{BC} (PSAP) averaged over winter and summer seasons from 1998 to 2015 to obtain regression lines (Figure ). The slopes derived by the LS method were −0.56 ± 0.45 ng m^{−3} yr^{−1} (−1.3% yr^{−1}) with *r*^{2} = 0.10 for winter and −0.53 ± 0.17 ng m^{−3} yr^{−1} (−4.7% yr^{−1}) with *r*^{2} = 0.50 for summer (Table ).

It is noteworthy that after 2001, the changes in *M*_{BC} (PSAP) were small in summer (Figure ). We therefore excluded the data for the initial 3 years and recalculated the slopes, obtaining values of −0.43 ± 0.56 ng m^{−3} yr^{−1} (−1.3% yr^{−1}) with *r*^{2} = 0.05 for winter and −0.23 ± 0.13 ng m^{−3} yr^{−1} (−1.7% yr^{−1}) with *r*^{2} = 0.20 for summer (Table ). We also derived the *M*_{BC} (PSAP) trends for 3 month periods between 1998 and 2015, but *r*^{2} values were not substantially improved (section A10).

We also estimated the trends by a regression analysis of *M*_{BC} (PSAP) at Barrow against time based on the Bayesian statistical method [e.g., *Hoff*, ] (section A10). The expected value of the slope and its uncertainty were evaluated as the mean and standard deviation, respectively, of ~2 × 10^{5} sampling points over the slope‐intercept space obtained by the Markov chain Monte Carlo (MCMC) method. The trends derived by the MCMC method were statistically insignificant (not shown), although slopes were obtained for 3 month periods between 1998 and 2015 (Table ). Both the LS and MCMC results indicate that it is difficult to derive the slopes of long‐term *M*_{BC} (PSAP) changes accurately for the period 1998–2015. The lack of statistical reliability is due to the large year‐to‐year variability in *M*_{BC} (PSAP), which potentially includes the year‐to‐year variability of MAC (PSAP) (maximum about 20%; section A8.1).

*Collaud Coen et al.* [] derived *b*_{abs} (PSAP) (PM_{10}) trends at Barrow for the periods 1998–2010 and 2001–2010 by a different method and obtained slopes of −1.3% yr^{−1} (1998–2010) and −6.5% yr^{−1} (2001–2010). The much smaller slope for 1998–2009 than for 2001–2010 is qualitatively consistent with our analysis. However, they used different parameters. First, they used PM_{10} data, whereas we used PM_{1} data, and second, they did not exclude the 2010 data, whereas we excluded anomalously low 2010 PM_{1} values caused by a malfunction of the PSAP (section 7.1, Figure ).

We could not perform a similar trend analysis of the Ny‐Ålesund data owing to the lack of *M*_{BC} (PSAP) data with sufficient reliability prior to 2006.

At Barrow, the monthly mean *M*_{BC} (COSMOS) averaged over the 3 year period from 2012 to 2015 agreed with the *M*_{BC} (PSAP) values averaged over the 10 year period from January 2005 to December 2015 to within 10% (Figure a), as expected from the trend analysis discussed in section 7.2. At Ny‐Ålesund, monthly mean *M*_{BC} (COSMOS) averaged over the 3 year period agreed with the *M*_{BC} (PSAP) values averaged over the 8 year period from April 2006 to December 2014 to within 15% (Figure b).

*M*_{BC} reached a maximum in winter and a minimum in summer, as shown by previous studies, although these studies did not critically evaluate the absolute values of *M*_{BC} [*Hirdman et al.*, , ; *Eleftheriadis et al.*, ; *Sharma et al.*, ]. At Barrow, mean *M*_{BC} (COSMOS) was 38.4 ± 26.0 ng m^{−3} in winter and 9.3 ± 12.0 ng m^{−3} in summer between 2012 and 2015, whereas at Ny‐Ålesund during those years, mean *M*_{BC} (COSMOS) was 22.3 ± 21.0 ng m^{−3} in winter and 6.2 ± 7.9 ng m^{−3} in summer.

During winter, daily *M*_{BC} (COSMOS) values between 20 and 30 ng m^{−3} were more frequent at Barrow than at Ny‐Ålesund, where the distribution shifted to lower *M*_{BC} (COSMOS) values (section A11). In summer, the *M*_{BC} (COSMOS) distribution shifted to lower values with a mode of 5 ng m^{−3}, indicating more frequent occurrence of low BC loading. These seasonal variabilities in *M*_{BC} (COSMOS) have been attributed mainly to changes in air mass transport pathways from potential source regions, along with wet scavenging [*Browse et al.*, ; *Hirdman et al.*, ; *Liu et al.*, ; *Sharma et al.*, ].

To date, aethalometer and PSAP instruments have been widely used for continuous measurements of *M*_{BC} in the Arctic. *Hirdman et al.* [, ] reported *M*_{BC} values at Barrow and Ny‐Ålesund based on measurements made by PSAP instruments, but they used different methods to derive *M*_{BC}. Because of the methodological differences, we denote *M*_{BC} values derived by these previous studies as *M*_{BC}^{*} (PSAP‐PM_{1}) for Barrow and *M*_{BC}^{*} (PSAP‐PM_{10}) for Ny‐Ålesund in comparisons with our *M*_{BC} (PSAP) values, which were scaled by *M*_{BC} (COSMOS). The values of *M*_{BC}^{*} (PSAP‐PM_{1}) and *M*_{BC}^{*} (PSAP‐PM_{10}) were obtained from *Hirdman et al.* [, Figure 2].

We compared monthly mean *M*_{BC}^{*} (PSAP‐PM_{1}), *M*_{BC}^{*} (PSAP‐PM_{10}), and *M*_{BC} (aethalometer) variations with monthly mean *M*_{BC} (COSMOS) and *M*_{BC} (PSAP) variations (Figure ). The values of *M*_{BC} (aethalometer) at Barrow were obtained from *Sharma et al.* [, Figure 6b]. The results for winter and summer are summarized in Table . At Barrow, in *M*_{BC}^{*} (PSAP‐PM_{1}) and *M*_{BC} (PSAP) data collected during the same period (2002–2007), *M*_{BC}^{*} (PSAP‐PM_{1})/*M*_{BC} (PSAP) ratios were about 1.3 in both winter and summer (Figure a and Table ). A MAC value of 10.0 m^{2} g^{−1} was used to derive *M*_{BC}^{*} (PSAP‐PM_{1}) [*Hirdman et al.*, , ], whereas we calculated MAC to be 10.6 m^{2} g^{−1} in this study. Thus, we estimate the difference between *M*_{BC}^{*} (PSAP‐PM_{1}) and *M*_{BC} (PSAP) to be about 10–20%. In winter and summer, *M*_{BC} (aethalometer) differed from *M*_{BC} (PSAP) by a factor of about 1.3 and 1.2, respectively. This difference is much larger than the uncertainty of *M*_{BC} (PSAP).

At Ny‐Ålesund, the *M*_{BC}^{*} (PSAP‐PM_{10})/*M*_{BC} (PSAP) ratios were about 3.2 and 3.6 in winter and summer, respectively (Figure b and Table ). The *M*_{BC}^{*} (PSAP‐PM_{10}) data were obtained during 2002–2007, whereas the *M*_{BC} (PSAP) data were obtained during 2006–2014, but the difference between *M*_{BC}^{*} (PSAP‐PM_{10}) and *M*_{BC} (PSAP) far exceeds the temporal change in *M*_{BC} (PSAP) that would be expected from the long‐term trend of about −0.56 ± 0.45 ng m^{−3} yr^{−1} derived at Barrow. A MAC value of 10.0 m^{2} g^{−1} was used to derive *M*_{BC}^{*} (PSAP‐PM_{10}), whereas in the present analysis, we obtained a MAC value of 12.5 m^{2} g^{−1} (PM_{10}) for Ny‐Ålesund. The large difference between *M*_{BC}^{*} (PSAP‐PM_{10}) and *M*_{BC} (PSAP) cannot be explained only by the difference in the MAC values because they differ by a factor of only about 1.25. Thus, there must be other unidentified problems with the derivation of the PM_{10} absorption coefficient at Ny‐Ålesund prior to 2006.

The *M*_{BC} (aethalometer)/*M*_{BC} (PSAP) ratio was about 3.0 in winter and about 3.1 in summer. The values of *M*_{BC} (aethalometer) at Ny‐Ålesund were taken from *Sharma et al.* [, Figure 6c]. The period of the *M*_{BC} (aethalometer) measurements (2002–2005) does not overlap the period of the *M*_{BC} (PSAP) measurements (2007–2014), but it is unlikely that these large ratios can be explained by the long‐term trend in *M*_{BC} (PSAP), as discussed above.

The ratio of the *M*_{BC} (COSMOS) at Barrow to that at Ny‐Ålesund in winter was about 1.77 ± 0.42. The corresponding *M*_{BC} (aethalometer) and *M*_{BC}^{*} (PSAP‐PM_{1}) ratios were 0.81 ± 0.13 and 0.52 ± 0.23, respectively. Reliable ratios, such as those obtained by the present study, are important for improving our understanding of the spatial variability in *M*_{BC} in the Arctic.

Although long‐term particle soot absorption photometer (PSAP) measurements of the light absorption coefficient (*b*_{abs}) (*b*_{abs} (PSAP)) have been reported by previous studies at Barrow, Alaska, and Ny‐Ålesund, Spitsbergen, in the Arctic, those studies did not critically evaluate the effects on *b*_{abs} (PSAP) of aerosols coexisting with BC. Furthermore, they used different mass absorption cross section (MAC) values to convert *b*_{abs} to BC mass concentrations. We measured *b*_{abs} at these sites for about 3 years by using COSMOS (*b*_{abs} (COSMOS)), which uses a heated inlet to remove non‐BC compounds, and then evaluated the performance of COSMOS for the measurement of BC mass concentrations (*M*_{BC} (COSMOS)) with particle diameters less than 1 µm (PM_{1}) at these sites.

We also showed by laboratory experiments with PSL particles that sea‐salt aerosols caused *M*_{BC} (COSMOS) to be overestimated by about 2 ng m^{−3} on average under the conditions at Barrow and Ny‐Ålesund. *M*_{BC} (COSMOS) derived by using MAC (COSMOS) obtained by our previous studies in Asia agreed to within 9%, with an uncertainty of 17%, with *M*_{EC} values measured by the thermal‐optical transmittance technique at Barrow for 11 months (August 2012 to June 2013). Further, *M*_{BC} (COSMOS) values agreed to within 3%, with an uncertainty of 15%, with *M*_{BC} measured by a single particle soot photometer (SP2) near Ny‐Ålesund for 3 days in winter 2013 during the ACCACIA aircraft campaign. These results indicate that at both sites, *M*_{BC} (COSMOS) was consistent and reliable.

We found that *b*_{abs} (PSAP) was highly correlated with *b*_{abs} (COSMOS). The high correlations enabled reliable estimation of *M*_{BC} (PSAP) from *b*_{abs} (PSAP). *b*_{abs} (PSAP) was systematically higher than *b*_{abs} (COSMOS) by 22% at Barrow (PM_{1}) and by 43% at Ny‐Ålesund (PM_{10}). The higher *b*_{abs} (PSAP) than *b*_{abs} (COSMOS) is attributable to enhanced absorption by internal mixing of BC and additional light absorption by volatile light‐absorbing aerosol species.

At Barrow, monthly mean *M*_{BC} (COSMOS) averaged over 3 years agreed to within 10% with *M*_{BC} (PSAP) averaged over 10 years. At Ny‐Ålesund, the 3 year monthly mean *M*_{BC} (COSMOS) values agreed with *M*_{BC} (PSAP) values averaged over 8 years to within 15%. At Barrow, *M*_{BC} (COSMOS) reached a maximum of 38.4 ± 26.0 ng m^{−3} in winter and a minimum of 9.3 ± 12.0 ng m^{−3} in summer. At Ny‐Ålesund, *M*_{BC} (COSMOS) was 22.3 ± 21.0 ng m^{−3} in winter and 6.2 ± 7.9 ng m^{−3} in summer during 2012–2015.

We estimated the linear trend of *M*_{BC} (PSAP) values obtained at Barrow during 1998–2015 by linear regression and the Markov chain Monte Carlo methods. The seasonally averaged *M*_{BC} (PSAP) generally decreased in winter and summer at a rate of about 0.55 ± 0.30 ng m^{−3} yr^{−1}. However, the absolute values of the rates are highly uncertain, partly owing to the large year‐to‐year variability of *M*_{BC} (PSAP) values.

At Ny‐Ålesund, *M*_{BC}^{*} (PSAP‐PM_{10}) values were systematically greater than *M*_{BC} (PSAP) values by a factor of 3.2 and 3.6 in winter and summer, respectively. *M*_{BC} (aethalometer) values were greater than *M*_{BC} (PSAP) values by a factor of 1.3 at Barrow in both winter and summer and of about 3.0 and 3.1 at Ny‐Ålesund in winter and summer, respectively. We analyzed the causes of the inconsistency in the previously reported *M*_{BC} values in the Arctic.

The accuracy of *M*_{BC} (COSMOS) has been critically assessed by this study, and we anticipate that *M*_{BC} (COSMOS) will continue to be a reliable reference value for *M*_{BC} at Barrow and Ny‐Ålesund in the Arctic.

In this Appendix, we describe the measurement method of *b*_{abs} by using PSAP and CLAP at Barrow and Ny‐Ålesund. The ambient air was aspirated at a flow rate of about 0.9 L min^{−1} at STP to measure *b*_{abs}. Unlike the PSAP, the CLAP uses a solenoid valve to cycle through eight sample filter spots and two reference spots, which facilitates field observations, particularly in remote locations.

*b*_{sca} at *λ* = 550 nm was measured with integrating nephelometers at Barrow (PM_{1} and PM_{10}) and Ny‐Ålesund. Detailed descriptions of the measurements, instrument calibration, and uncertainty analysis are presented elsewhere [*Anderson and Ogren*, ; *Anderson et al.*, ; *Sheridan et al.*, ]. The overall uncertainty of *b*_{sca} averaged over 1 min, accounting for instrumental noise, drift in calibration, Rayleigh scattering of air, and blocking of near‐forward scattering light (truncation), was less than 10% [*Sheridan et al.*, ]. The uncertainty of *b*_{abs} (PSAP) was estimated to be about 20% for the 1 h average at midlatitudes (35°N–45°N), taking account of instrumental noise, calibration of PSAP following *Bond et al.* [], and unit‐to‐unit variability [*Sherman et al.*, ].

The PSAP and nephelometers at Barrow were equipped with switchable PM_{1} and PM_{10} impactors for particle size selection. The PM_{1} and PM_{10} size ranges were alternated every 30 min (twice each hour). We therefore used *b*_{abs} values obtained by the PSAP during the last 30 min of each hour for the comparison with the COSMOS measurements at Barrow in this study. Data were further screened to avoid any local contamination; only data collected when the wind direction was from the clean air sector, from 0 to 130°, were included.

At Ny‐Ålesund, measurements of *b*_{abs} at 532 nm were also carried out at about 10 m above the ground by using a custom‐built PSAP until November 2012. The custom‐built PSAP was replaced with a new PSAP in December 2012. The *b*_{abs} values obtained by the new PSAP were larger than those obtained by the custom‐built PSAP by a factor of about 1.52 on average. The *b*_{abs} (PSAP) data obtained after December 2012 were corrected for this bias. These *b*_{abs} (PSAP) values were also adjusted to 550 nm as described in section 3.

For measurement of the *M*_{s‐s} at Barrow, ambient air samples were collected onto filters after particle‐size selection by PM_{1} and PM_{10} impactors through an inlet mounted 10 m above the ground from October 1997 to December 2009. The chemical composition of the collected aerosols, including Na^{+} and Cl^{−}, was analyzed by ion chromatography. Depending on the season and the aerosol loading, filter samples were collected at 1 to 4 day intervals at Barrow. *Quinn et al.* [] have described the sampling and measurement analysis at Barrow in detail. We estimated *M*_{s‐s} from the Na^{+} concentration, and we also took into account the Cl^{−} concentration to minimize the effect of the loss of Cl^{−} owing to the release of HCl from the sea‐salt aerosol. Other components such as sulfate that are not always present in sea‐salt aerosols at the standard seawater ratio also add to the uncertainty in the estimation of *M*_{s‐s} with equation .

At Ny‐Ålesund, ambient air samples containing sea‐salt particles were collected daily from January 2012 to December 2014 as part of a cooperative program for monitoring and evaluation of long‐range transmission of air pollutants in Europe (European Monitoring and Evaluation Programme) by using a filter pack sampler mounted 2 m above the ground. No impactor was used to restrict the size of the particles for *M*_{s‐s} measurement at Ny‐Ålesund, but for simplicity, we refer to these data as PM_{10} in our comparison, despite the fact that the resulting *M*_{s‐s} values might be larger than *M*_{s‐s} (PM_{10}) values.

*Hjellbrekke and Fjæraa* [] have described the detailed sample collection and analysis procedures. *M*_{s‐s} in the submicrometer size range at Ny‐Ålesund was deduced by assuming the value of *f*_{PM1} (=PM_{1}/PM_{10} ratio) of *M*_{s‐s} measured at Barrow. At Barrow, *f*_{PM1} varied between 0.08 and 0.77 during 1997–2009. The use of the measured values of *M*_{s‐s} may result in the overestimation of *M*_{s‐s} (PM_{1}) at Ny‐Ålesund. Such overestimation would have little influence on the conclusion derived from this analysis, however.

The samples were collected outdoors on a sampling platform 10 m above ground level at the North Slope of Alaska Atmospheric Radiation Measurement Facility at Barrow. Filters were heated to 500°C for 12 h prior to the sampling and stored in aluminum foil packets; they were kept in a freezer both before and after sampling. Each filter sampling period was approximately 7 days long during the entire observation period between August 2012 and June 2013. Measurements of *M*_{EC} were made in two combustion phases. In the first phase, each quartz fiber filter containing samples of particulate matter was heated to 870°C in an oxygen‐free helium atmosphere and then heated to 900°C in the presence of 2% oxygen. In the second heating phase, EC and carbon produced by pyrolysis of organic carbon (OC) were converted to CO_{2}. CO_{2} was then converted to methane and measured by a flame ionization detector. To correct for the pyrolytic conversion of OC to EC, the transmittance of a pulsed diode laser beam at 670 nm through a quartz fiber filter was monitored during the sample analysis. Calibration of the TOT analyzer was carried out with a sucrose standard after every 10 samples. The blank value (0.18 µg cm^{−2} of OC) was subtracted from all sample measurements. The *M*_{EC} values were not affected by the blank subtraction [*Barrett et al.*, ]. The *M*_{EC} values are given in units of ng m^{−3} STP.

To determine the contribution of BC aerosol particles with diameters larger than 1 µm to total *M*_{BC}, we used the BC mass size distribution measured by an SP2 at the remote site of Hedo (26.9°N, 128.3°E) on Okinawa Island, Japan, during 17 days in March 2016 (Figure a). Hedo is located downstream of China [*Kondo et al.*, ]. BC mass concentrations below the detection limit of the SP2 (around 75 nm) were estimated by extrapolating a lognormal function fitted to the BC mass size distribution. Mean *M*_{BC} was 128.8 ng m^{−3} between 0 and 4000 nm (PM_{4}) and 10.0 ng m^{−3} between 1000 and 4000 nm. On average, the ratio of *M*_{BC} above 1 µm in diameter to total *M*_{BC} was 0.08 (8%).

The BC mass size distribution in airborne SP2 measurements at an altitude of about 500 m near Zeppelin station, Ny‐Ålesund, on 20 March 2013, is shown in Figure b. BC mass concentrations above the detection range of the SP2 measurements of 477 nm were estimated from a lognormal function fitted to the BC mass size distribution up to 1000 nm. The contributions of BC mass concentrations between 478 nm and 1000 nm to *M*_{BC} (SP2) for PM_{1} were estimated to be in the range of 8.7–17.7% between 20 and 23 March 2013 with a mean contribution of about 15%.

Figure presents the monthly mean values of the difference between *M*_{BC} (COSMOS) and *M*_{EC} at Barrow from August 2012 to June 2013. The *M*_{BC} (COSMOS)‐*M*_{EC} difference was generally lower than 5 ng m^{−3} for most months except April and May 2013. However, no distinct seasonal variation in the monthly mean difference between *M*_{BC} (COSMOS) and *M*_{EC} is apparent.

We compared the daily mean *M*_{BC} (COSMOS) with *M*_{BC} (SP2) values linearly interpolated to 474 m altitude and present the results in Figure . The daily mean *M*_{BC} (COSMOS) and *M*_{BC} (SP2) agreed to within about 3% (slope = 1.03, *r*^{2} = 0.96) with an uncertainty of about 15%, although the statistical reliability is limited owing to the small number of *M*_{BC} (SP2) measurements.

Time series plots of daily and monthly mean variations of the single scattering albedo (SSA) from hourly data at Barrow (PM_{1}) and Ny‐Ålesund (PM_{10}) are shown Figure . At Barrow, SSA showed considerable day‐to‐day variability, particularly during winter, whereas at Ny‐Ålesund, conspicuous variability was not seen, although episodically low SSA values were observed there in both winter and summer.

The amplitude of the seasonal variation of SSA was stronger at Barrow than at Ny‐Ålesund. At Barrow, the mean wintertime SSA value (0.94 ± 0.03) in winter was lower than the summertime mean (0.96 ± 0.04). This wintertime SSA value is very similar to the value of 0.94 derived by *Delene and Ogren* [] for March–May during 1997–2000. At Ny‐Ålesund, the mean wintertime SSA value of 0.95 ± 0.05 was higher than the wintertime mean at Barrow, but the summertime mean (0.96 ± 0.04) was similar to that at Barrow.

Time series of the difference between monthly mean *M*_{BC} (COSMOS) and *M*_{BC} (PSAP) at Barrow (2012–2015) and at Ny‐Ålesund (2012–2014) are presented in Figure . Although this difference, *M*_{BC} (COSMOS)‐*M*_{BC} (PSAP), varied greatly from year to year, the variation was not systematic at these sites during the study period. The difference was generally less than 10 ng m^{−3} at both sites, and the standard deviation of the difference was about 4.7 ng m^{−3} at Barrow and 3.8 ng m^{−3} at Ny‐Ålesund. The maximum year‐to‐year variability of MAC (PSAP) was about ±20% at Barrow. This value is a measure of the year‐to‐year stability of the *M*_{BC} (PSAP) measurements in the Arctic and partly accounts for the difference between the monthly mean values of *M*_{BC} (COSMOS) and *M*_{BC} (PSAP).

We examined the correlation between monthly mean *M*_{BC} (COSMOS) and *M*_{BC} (PSAP) values at Barrow and Ny‐Ålesund to visualize the degree to which individual data points deviated from the average correlation, as shown in Figure . Monthly mean *M*_{BC} (COSMOS) and *M*_{BC} (PSAP) values were well correlated (*r*^{2} = 0.96 at Barrow and 0.95 at Ny‐Ålesund), as expected given the correlations between *b*_{abs} (PSAP) and *b*_{abs} (COSMOS). The average slope was 1.05 at Barrow and 0.98 at Ny‐Ålesund, as a result of the scaling.

Monthly mean diurnal variations of *M*_{BC} (COSMOS) at Barrow and Ny‐Ålesund in February and July 2013 are shown in Figure . These months were chosen as representative of the winter and summer seasons, respectively. At both sites, the amplitude of the diurnal variation in *M*_{BC} (COSMOS) was generally smaller in July than in February, partly reflecting the seasonal variation in *M*_{BC} (COSMOS). Overall, the monthly mean diurnal variation of *M*_{BC} (COSMOS) was generally less than 10% of the daily mean in all months. Similarly, *Sharma et al.* [] and *Eleftheriadis et al.* [] reported weak diurnal variability in *M*_{BC} at Ny‐Ålesund. The absence of diurnal variability in *M*_{BC} (COSMOS) suggests that the influence of localized BC emissions on the measured *M*_{BC} was small; however, anthropogenic activities have been observed to vary diurnally in more populated areas [e.g., *Sahu et al.*, ]. In addition, if very high concentrations of BC are confined within the relatively shallow atmosphere near the measurement sites, diurnal variations of BC might be associated with variations in the thickness of the planetary boundary layer.

We also estimated long‐term trends by performing a regression analysis of *M*_{BC} (PSAP) at Barrow against time by the Bayesian statistical method [e.g., *Hoff*, ] in addition to the LS method. Under this mathematical formulation, the probability distribution of the linear trend (slope) was evaluated as a posterior distribution of *M*_{BC} (PSAP). The expected value of the slope and its uncertainty were evaluated as the mean and standard deviation, respectively, of ~2 × 10^{5} sampling points over the slope‐intercept space obtained by the Markov chain Monte Carlo (MCMC) method.

We applied this method to time series of *M*_{BC} (PSAP) values obtained during 1998–2015 at Barrow and averaged over 3 month periods. The resulting slopes and their ±1*σ* values are summarized in Table . For comparison, the results obtained by the LS method are also summarized in Table . In general, the slopes obtained by least squares fitting were similar to those obtained by the MCMC method, but the slopes for March–May differed between the two methods.

The frequency distributions of the daily mean *M*_{BC} (COSMOS) values during winter and summer at Barrow and Ny‐Ålesund are presented in Figure . During winter, values of *M*_{BC} (COSMOS) of 20–30 ng m^{−3} were more frequent at Barrow than at Ny‐Ålesund, where the distribution was shifted to lower *M*_{BC} (COSMOS) values. The frequency distributions of *M*_{BC} (COSMOS) at the two sites had long thin tails, which extended to more than 100 ng m^{−3}, in winter. During summer, the frequency distributions of *M*_{BC} (COSMOS) were similar at the two sites. The *M*_{BC} (COSMOS) distribution was skewed toward lower values, with a mode at 5 ng m^{−3}, indicating more frequent occurrence of low BC loadings. The frequency distributions of *M*_{BC} (COSMOS) were much narrower at lower *M*_{BC} values in summer compared with those in winter. The seasonal variation in *M*_{BC} (COSMOS) is mainly attributable to changes in transport pathways and the degree of wet deposition of BC during transport. It is often difficult for transport models to predict precisely trajectories of individual air parcels reaching the observation sites at given times. Comparison of the occurrence frequencies observed by this study and those calculated by numerical models would be useful for statistical evaluation of the transport processes included in the models. Such a comparison was made for Asia by *Kondo et al.* [].

We thank NOAA personnel for reliably carrying out the observations by PSAP, nephelometer, and COSMOS instruments at Barrow. We also thank the staff of the Norwegian Polar Institute for reliably performing the COSMOS measurements at Zeppelin station, Ny‐Ålesund. This work was supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), the Global Environment Research Fund of the Japanese Ministry of the Environment (A‐1101, 2‐1403, and 2‐1703), the Japan Society for the Promotion of Science (JSPS) KAKENHI grants (JP12J06736, JP23221001, and JP16H01770), the GRENE Arctic Climate Change Research Project, and the Arctic Challenge for Sustainability (ArCS) project. This is Pacific Marine Environmental Laboratory (PMEL) contribution number 4552. We thank the anonymous reviewers for their constructive comments and suggestions. The data used in this study are available upon request from the authors. (