In this study we used the SP2 and COSMOS as standard instruments to measure MBC. Detailed descriptions of the SP2, including calibration methods, are given elsewhere (Schwarz et al., 2006; Moteki and Kondo, 2010). Briefly, the SP2 uses the laser-induced incandescence technique and detects BC on a single-particle basis. We used two SP2s in this study: the one installed at Fukue was maintained and calibrated by the University of Tokyo (UT-SP2, hereafter), and the other one at Alert was maintained and calibrated by Environmental and Climate Change Canada (EC-SP2, hereafter). The configuration of the UT-SP2 is identical to that described by Moteki and Kondo (2010). The model designation of the EC-SP2 was “SP2-D” with eight channels. The UT-SP2 and EC-SP2 measured BC size distributions in the mass-equivalent diameter (Dm) range 70–850 and 60–600 nm, respectively. The void-free density of BC was assumed to be 1.8 g cm-3. These SP2s were calibrated using fullerene soot particles (Alfa Aesar, stock no. 40971, lot no. FS12S011; Moteki and Kondo, 2010; Kondo et al., 2011). The laser-induced incandescence signal intensity of the UT-SP2 for the specific mass of ambient BC particles in Tokyo agrees with that of fullerene soot particles to within about 10 % (Kondo et al., 2011). Laborde et al. (2012) reported similar SP2 calibration curves for fullerene soot particles, diesel exhaust, and ambient BC particles in Switzerland. The accuracy of MBC (SP2) estimated from the uncertainty of the calibration and operational conditions of SP2 was about 10 %. No particle size cut was used for the inlet of the UT-SP2, whereas a PM1 cyclone was used for the EC-SP2.

The principles of operation of the COSMOS apparatus are detailed in previous papers (Miyazaki et al., 2008; Kondo et al., 2011; Kondo, 2015; Ohata et al., 2019). Briefly, the COSMOS measures the attenuation coefficient (b0) of aerosols collected on a quartz-fiber filter at a given wavelength (λ= 565 nm). Most previous studies used filters from Pallflex (E70-2075W, Pall, Port Washington, NY, USA), which are no longer available. Consequently, high-efficiency particulate air (HEPA) filters (L-371M) have been used for more recent observations (Irwin et al., 2015), including this study. An important difference between the COSMOS and the other types of filter-based absorption photometer is that the inlet of the COSMOS is heated to 300 ∘C to remove volatile light-scattering particles (LSPs) and coatings of BC from the aerosol phase. Therefore, the effect on b0 of co-existing volatile components externally or internally mixed with BC particles can be ignored. The COSMOS is equipped with a PM1 cyclone to minimize the effect in coarse mode of refractory non-BC particles, such as dust and sea-salt particles. Consequently, the absorption coefficient for the COSMOS is given as 1babsCOSMOS=ffilb0. Here, ffil is a factor used to correct for the increase in absorption caused by multiple scattering in the filter medium. It is given by 2ffilTr=1[1.0796Tr+0.71]BwithTr≥0.7, where Tr is the filter transmission and B is a scaling factor (Bond et al., 1999; Ogren, 2010; Ohata et al., 2019). The MAC for the COSMOS [m2 g-1] is operationally defined as 3MACCOSMOS,SP2≡babsCOSMOSMBCSP2, where the numerator and denominator, respectively, are simultaneous measurements of babs [Mm-1] by COSMOS and MBC [µg m-3] by SP2 for ambient air. The MAC value for a Pallflex filter at λ= 565 nm was previously set at 8.73 [m2 g-1] with B= 1.397 (Sinha et al., 2017). For a HEPA filter, the value of B is about 6 % lower (Irwin et al., 2015). Depending on the filters used (Pallflex or HEPA), the appropriate B value was used in this study.

Once the MAC (COSMOS, SP2) is determined, MBC (COSMOS) [g m-3] at standard temperature and pressure (0 ∘C, 1013 hPa) can be estimated as 4MBCCOSMOS=babsCOSMOSMACCOSMOS,SP2. One particular purpose of the heating of sampled air to 300 ∘C is to make the MAC (COSMOS, SP2) stable and independent of original mixing states of BC particles. In other words, the heating treatment makes babs (COSMOS) more proportional to BC mass concentrations, compared to the other filter-based absorption photometers described in Sect. 2.2.3. As a consequence, unlike the other filter-based absorption photometers, the absorption coefficient of unheated original aerosols is not provided by COSMOS. Thus, COSMOS has been developed to measure MBC, not babs. In this sense, MBC (COSMOS) is different from “equivalent” BC mass concentrations estimated from the unheated babs measurements (Petzold et al., 2013).

We call the COSMOS that was calibrated by comparison with the SP2 in Tokyo the “standard COSMOS”, described hereafter as Std-COSMOS. Because the MAC of the Std-COSMOS was determined by comparison with SP2 (Eq. 2), it acts as a transfer standard for the SP2. The babs (COSMOS) of each COSMOS manufactured is compared with the Std-COSMOS by sampling ambient BC particles in Osaka, Japan, typically for 1–2 weeks. The comparisons during these periods were statistically reliable partly due to relatively high BC concentrations in Osaka. The babs (COSMOS) of 28 COSMOS instruments manufactured thus far agrees with that of Std-COSMOS to within about ± 7 %, indicating reliable quality control in manufacturing. The small differences originating from the uncertainty of the filter sampling spot size of each unit are corrected for in deriving MBC (COSMOS).

It is important to compare MBC (COSMOS) and MBC (SP2) outside Tokyo and Osaka, to confirm both the strong correlation between MBC (COSMOS) and MBC (SP2) and the long-term stability of the MAC (COSMOS) value. Ohata et al. (2019) made these comparisons at two remote sites: at Cape Hedo (26.9∘ N, 128.3∘ E), Japan, and at Ny-Ålesund. At each of these locations, the concentrations of BC and LSP and the mixing states of BC were considerably different from those in Tokyo and Osaka. MBC (COSMOS) and MBC (SP2) agree to within about 10 % at these sites, thus demonstrating the validity of using the Std-COSMOS to calibrate each of the COSMOS instruments to be used for field observations. Ohata et al. (2019) also showed that the dependencies of MAC (COSMOS) on the thickness of coatings of BC particles, MBC, and volume concentrations of the co-existing LSPs were small. Although the MAC (COSMOS) showed a slight dependence on the mass size distributions of BC, the sensitivity of the MAC (COSMOS) to such variations in microphysical properties of BC was generally less than 10 % (Kondo et al., 2011; Ohata et al., 2019).

Previously estimated uncertainties of MBC (COSMOS) were about 10 % based on the range of agreement between MBC measurements by COSMOS and UT-SP2 (Kondo et al., 2011; Ohata et al., 2019). It may be more appropriate to estimate the absolute accuracy of MBC (COSMOS) to be about 15 %, including the abovementioned 10 % uncertainty of MBC (SP2). This 15 % uncertainty also covers the range of agreement between MBC (COSMOS) and MBC (SP2) previously reported by other groups at Ny-Ålesund (Zanatta et al., 2018) and at Fukue (Miyakawa et al., 2017).

Although we used the SP2 and COSMOS as standard instruments to measure MBC in this study, thermal–optical analysis, which quantifies elemental carbon (EC) mass concentrations (MEC), has also been a traditional standard method to measure BC. Measurements of MEC can depend on the temperature protocol and optical charring correction method used (e.g., Bond et al., 2013). Agreements within 10 % of MBC (SP2), MBC (COSMOS), and MEC were reported by Kondo et al. (2011), whereas systematic differences between MBC (SP2) and MEC up to a factor of 2 were found by Pileci et al. (2021). Although the difference between MBC (COSMOS) and MEC was generally lower than 5 ng m-3 at the Arctic site Barrow (Sinha et al., 2017), this difference can be important for pristine summer Arctic conditions (MBC (COSMOS) <20 ng m-3). Considering these previously reported agreements and discrepancies between MBC (SP2 or COSMOS) and MEC, in some cases the MAC values determined by babs and MBC measurements (this study) can differ from those determined by babs and MEC measurements (Zanatta et al., 2016).

Light-absorbing iron oxide (FeOx) aerosols such as magnetite, which the SP2 can distinguish from BC (Yoshida et al., 2016; Lamb, 2019), can affect MBC measured by filter-based absorption photometers. FeOx aerosols are emitted from both anthropogenic sources (e.g., motor vehicle exhaust) and natural sources (e.g., windblown mineral dust). Within the detectable diameter range of the UT-SP2 (Dm= 70–850 nm for BC and Dm = 170–2100 nm for FeOx), the mass concentration ratios of FeOx to BC were typically ∼ 0.4 in East Asia and ∼ 0.2 in the Arctic; they were mainly of anthropogenic origin in the form of aggregated magnetite nanoparticles in both regions (Moteki et al., 2017; Ohata et al., 2018; Yoshida et al., 2018, 2020). FeOx aerosols contribute at least 4 %–7 % of the short-wave absorbing powers of BC in Asian continental outflows (Moteki et al., 2017), and their direct radiative forcing has been estimated to be 0.22 W m-2 over East Asia (Matsui et al., 2018). Here, we estimate the effect of light absorption by FeOx on MBC measured by the COSMOS. The ratio of light absorbed by FeOx to that absorbed by BC at a wavelength λ (ε(λ)) is given by 5ελ=∫DLDUdMFeOxdlogDmMACMie_FeOxDm,λdlogDm∫DLDUdMBCdlogDmMACMie_BCDm,λdlogDm, where Dm is mass-equivalent diameter of bare BC or FeOx; DL and DU are the lower and upper limits, respectively, of the diameter for the integral calculus; dMBC/ dlogDm and dMFeOx/ dlogDm are the mass size distributions of BC and FeOx, respectively; and MACMie_BC (Dm, λ) and MACMie_FeOx (Dm, λ) are the MAC values of bare BC and FeOx, respectively, for Dm and λ calculated by Mie theory.

The mass size distributions of BC and FeOx at Fukue and Ny-Ålesund (Fig. 2) were obtained by fitting monomodal and bimodal lognormal functions to the average mass size distributions measured by the SP2 during each observation campaign (Yoshida et al., 2020). The measurements at Fukue were made in April 2019 and those at Ny-Ålesund in March 2017. The MACMie_BC (Dm, λ) and MACMie_FeOx (Dm, λ) data (Fig. 2) were calculated by Mie theory for λ= 565 nm (wavelength used for COSMOS). For this calculation, we assumed BC and FeOx to be in the form of bare spheres with void-free densities of 1.80 g cm-3 and 5.17 g cm-3, respectively. The refractive index of BC we used was 1.99 + 0.64i, which is the value for BC at λ= 600 nm (Bergstrom, 1972). The refractive index of FeOx we used was 2.56 + 0.57i, which is the value for magnetite at λ= 600 nm (Huffman and Stapp, 1973).

From Eq. (4), the ε values at Fukue and Ny-Ålesund were calculated to be 3.6 % and 1.9 %, respectively, for (DL, DU)= (30, 1000 nm). These ε values became 4.6 % and 2.6 % for (DL, DU)= (30, 2500 nm). Because COSMOS is equipped with a PM1 cyclone, we estimated the effect of light absorption by FeOx on MBC measured by COSMOS to be <4 % in East Asia and <2 % in the Arctic. Note that these estimates are upper limits of the effect of FeOx because the PM1 cyclone is designed to remove particles of >1 µm aerodynamic diameter (Da). Due to the fractal shape and high density of FeOx particles (Moteki et al., 2017), Dm is considerably smaller than Da for FeOx particles, and thus DU in Eq. (4) should be less than 1 µm.

The effect of FeOx on MBC (COSMOS) should be even smaller considering that the mass concentration of anthropogenic FeOx is correlated with MBC, as mentioned above. Even if babs (COSMOS) is enhanced by FeOx by a few percent, this effect is already incorporated to some extent, by operationally defining MAC (COSMOS, SP2) by Eq. (2).

The effect of FeOx on babs may be somewhat higher for the other filter-based absorption photometers than for COSMOS if they are equipped with a larger particle size cut (PM2.5 or PM10). For accurate measurements of MBC, the use of a PM1 cyclone or impactor is recommended to minimize the effects of FeOx, as well as other refractory particles such as natural dust and sea-salt particles.

The principle of operation of the PSAP is similar to those of COSMOS (Bond et al., 1999; Sinha et al., 2017). In this study, we also used babs data obtained with a CLAP (Ogren et al., 2017). The CLAP is conceptually similar to the PSAP but uses solenoid valves to cycle through eight sample filter spots. The PSAP and CLAP both utilize the Pallflex filters. The unit-to-unit variations in the PSAP and CLAP were reported to be within 6 % (Bond et al.,1999) and 4 % (Ogren et al., 2017), respectively. The wavelengths of the light absorption measured by either PSAP or CLAP at Barrow, Ny-Ålesund, and Alert were about 467, 530, and 660 nm. The major difference of PSAP and CLAP from COSMOS is that the sample air inlets of PSAP and CLAP are not heated to 300 ∘C. Therefore, the effect of the attenuation of light by LSPs is corrected for by using the aerosol light-scattering coefficient simultaneously measured by an integrating nephelometer (Bond et al., 1999; Ogren, 2010). This correction adjusts for measurement artifacts but introduces uncertainties in the estimate of babs (PSAP or CLAP). At the above three sites, light-scattering coefficients measured by nephelometers at wavelengths of 450, 550, and 700 nm were used for this correction. The babs for the PSAP or CLAP (hereafter, babs (PSAP–CLAP)) at λ= 550 nm was obtained by adjusting measured absorption at 530 to 550 nm by using the λ-1 relationship (Sinha et al., 2017; Sharma et al., 2017). Schmeisser et al. (2017) reported that the median value of the absorption Ångström exponent at Arctic sites was 1.04, which supports our assumption of the λ-1 relationship. The accuracy of the babs measured by PSAP ranges between 20 % and 30 % (Bond et al., 2013). Note that a custom-built PSAP (Krecl et al., 2007) was used at Ny-Ålesund, and commercial ones were used at Alert and Barrow.

An AE-31 Aethalometer (Hansen et al., 1984) has been used for measurements of babs at Alert without any particle size cut (Sharma et al., 2017). This Aethalometer measures the attenuation (ATN) of light transmitted through particles accumulating on a quartz fiber filter at seven wavelengths (370, 470, 520, 590, 660, 880, and 950 nm). In deriving babs (Aethalometer) from ATN data, the correction factor Cf= 3.45 (Backman et al., 2017) was applied. This correction factor is very close to the correction factor C0= 3.5 recommended by the World Meteorological Organization/Global Atmosphere Watch (WMO/GAW, 2016). The uncertainty of C0 is approximately 25 % (WMO/GAW, 2016).

Another AE-31 Aethalometer has also been used at Ny-Ålesund (Zeppelin station) (Eleftheriadis et al., 2009), where the sampling inlet was equipped with a calculated PM10 size cut. Data post-processing included flagging based on Zeppelin station logs, Ny-Ålesund harbor logs, and diagnostics reported by the instrument (flow rate, raw attenuation, zero signal, etc). A correction factor C0= 3.5 was used to compensate for the multiple-scattering effect.

The filter loading effect is not significant for Arctic aerosol, as reported by Backman et al. (2017). For Alert, the slope of the correction factor Cf to ATN is k = 0.00074, indicating a 5 % difference at an ATN value of 80. For Zeppelin, the loading effect causes a 2 % difference in Cf at an attenuation value of 80. These uncertainties are considered small compared to the overall babs uncertainty, which is 20 %–30 % (Bond et al., 2013). Therefore, the loading correction is not applied to the AE31 measurements. Corrections for light scattering by using nephelometer data were also not applied. One of the manufacturer's suggested values of MAC (Aethalometer) is given by 14625/ (λ [nm] ×C0) [m2 g-1], which corresponds to 7.1 m2 g-1 for λ = 590 nm and C0= 3.5.

Detailed descriptions of the MAAP are given elsewhere (Petzold et al., 2002, 2005; Petzold and Schönlinner, 2004; Kanaya et al., 2013). In brief, the MAAP monitors the transmittance of light through a glass-fiber tape and measures reflectance at two angles. To remove the influence of LSPs, babs (MAAP) from particles deposited on the filter is derived by radiative transfer calculations. The uncertainty of babs (MAAP) was estimated by Petzold and Schönlinner (2004) to be 12 %. The unit-to-unit variation in the MAAP was reported to be within 5 % (Müller et al., 2011). The MAC values for the MAAP (MAC (MAAP)) for λ= 637 nm were determined by comparing babs (MAAP) and MBC measured at four sites in Germany by the German reference method VDI2465 Part 1 (GRM; Schmid et al., 2001), represented by 6MACMAAP,GRM≡babsMAAPMBCGRM. For the measurements of MBC (GRM), organic carbon was removed by solvent extraction and the residual BC particles on the filters were oxidized to CO2 and quantified by coulometric titration. The measurement uncertainty of MBC (GRM) was about 25 % (Petzold and Schönlinner, 2004). The MAC of 6.6 m2 g-1 is the default setting by the manufacturer based on their study. In determining MAC (MAAP, GRM), an SP2 was not used to measure MBC, and this is a potential source of discrepancy in this value of MAC, as discussed in Sect. 3.4.1 and 3.5.2. A correction factor of 1.05 due to the wavelength shift from the nominal value (Müller et al., 2011) was applied in this study. Note that the measured peak wavelength of the light source of the MAAP at Fukue was 639 nm (Kanaya et al., 2013), which is very slightly different from the previously reported value (637 nm; Müller et al., 2011).

Long-term measurements of BC using different model versions of SP2s have been conducted at Alert since 2011 (Sharma et al., 2017). In this study, we used the data obtained by an EC-SP2 (model “SP2-D” with eight channels; see Sect. 2.2.1) from January to May 2018 for comparison with the COSMOS data. The EC-SP2 and COSMOS aspired sample air from a common inlet with a PM1 size cut. Figure 3a shows the number and mass size distributions of BC averaged over the observation period. The mode diameter of the average mass size distribution of BC was ∼ 210 nm in mass-equivalent diameter, which is similar to that previously reported at Alert (Sharma et al., 2017) and to that observed by aircraft-based measurements over Alert (Schulz et al., 2019). Because the upper limit of the detectable diameter range of BC was ∼ 600 nm for the EC-SP2, we have estimated MBC (SP2) over the range up to 1000 nm by fitting lognormal functions to the measured mass size distributions. The time series of hourly values of MBC (COSMOS) and MBC (SP2) (Fig. 3b) were strongly correlated (r2= 0.92; r2 is the square of the correlation coefficient), and the slope of the regression forced through the origin was 1.02 (Fig. 3c). Based on the slope value of the regression for all MBC ranges observed, the agreement between MBC (COSMOS) and MBC (SP2) at Alert was generally within 10 %. The degree of agreement between MBC (COSMOS) and MBC (SP2) was also examined on a logarithmic scale in Fig. S1a in the Supplement. When MBC (SP2) is relatively low (MBC <10 ng m-3), which corresponds to the monthly-averaged MBC ranges in summer at Arctic sites (Sinha et al., 2017), MBC (COSMOS) tended to be higher than MBC (SP2) by about 1–2 ng m-3. This small absolute difference is consistent with the previously reported difference between MBC (COSMOS) and MEC at Barrow (Sinha et al., 2017).

Although this agreement between MBC (COSMOS) and MBC (SP2) at Alert was consistent with those reported in previous studies using UT-SP2 (Kondo et al., 2011; Ohata et al., 2019), note that there were some differences between MBC (SP2) measured by the EC-SP2 and that by the UT-SP2. The EC-SP2 was calibrated using Aquadag samples at Alert during the observation period and also calibrated using fullerene soot samples at the Paul Scherrer Institute in Switzerland after the observation period. Because the sensitivity of the incandescence signals of the SP2 to Aquadag is higher than that to fullerene soot, the calibration curve for Aquadag needs correction to obtain the fullerene-soot-equivalent calibration curve (Baumgardner et al., 2012). Additionally, to make this correction, assumptions of the effective density (ρeff) values of Aquadag (Moteki and Kondo, 2010; Gysel et al., 2011), which depend on the mobility diameter of Aquadag, are needed since a differential mobility analyzer (DMA) is used for the on-site calibration at Alert instead of an aerosol particle mass analyzer (APM) or a centrifugal particle mass analyzer. The ρeff values of Aquadag samples can depend on their batches (Gysel et al., 2011). In the previous study by Sharma et al. (2017), the constant value of ρeff (= 0.7 g cm-3) for Aquadag was assumed in order to derive MBC (SP2) at Alert. However, we have found that MBC (SP2) at Alert was highly dependent on the assumed ρeff values of Aquadag used for the on-site calibration with a DMA. Because of this, we used the calibration curve obtained by fullerene soot with an APM at the Paul Scherrer Institute after the observation period for this study. The conditions of the EC-SP2 might have differed slightly during and after the observation period, which may lead to additional uncertainties for MBC (SP2) at Alert, although the difference between Aquadag calibrations made before and after the campaign was less than about 10 %. In addition, the upper limit of the detectable diameter of BC for the EC-SP2 (Dm ∼ 600 nm) was lower than that for the UT-SP2 (Dm ∼ 850 nm), although the abovementioned extrapolation up to 1000 nm was made to derive MBC (SP2) at Alert. Despite these differences between EC-SP2 and UT-SP2, MBC (COSMOS) and MBC (SP2) agree to within 10 % at Alert, consistent with previous studies that reported the stability of the relationship between MBC (COSMOS) and MBC (SP2) at various sites (Kondo et al., 2011; Ohata et. al., 2019).

Measurements of MBC (COSMOS) at Alert began in January 2018. A PM1 cyclone was used for COSMOS, and a PM1 impactor was used for PSAP and two CLAP instruments (CLAP1, CLAP2). The time series of 1 and 24 h averaged MBC (COSMOS) were strongly correlated with babs (PSAP; λ = 550 nm) for 2018–2019 (r2 ∼ 0.96; Fig. 4a–d). In this study, we define the MAC value, MACcor, as the slope of the least-squares regression forced through the origin in the correlation plot. The values of MACcor (PSAP; λ= 550 nm) for the whole period were 13.9 and 14.0 m2 g-1 for the 1 and 24 h averaged data, respectively, as summarized in Table 2. The results of the same analyses for other wavelengths of the PSAP and the two CLAPs show that the strength of the correlation depended little on wavelength (Table 2). The babs, and therefore the MAC, for the PSAP and the two CLAP instruments (CLAP1, CLAP2) agree to within 13 % at λ= 550 nm, indicating a small difference in the performance of these instruments.

Along with the correlation analysis, variability of the babs (PSAP) / MBC (COSMOS) ratio was also analyzed for the 1 and 24 h data (Fig. 4e and f). This ratio can be interpreted as an hourly or daily MAC value at each time. Because this ratio tends to be unstable when the MBC (COSMOS) values are very low, we set a threshold MBC (COSMOS) value of 2 ng m-3 in this analysis, as shown in these figures. The median ratio, defined as median MAC and denoted as MACmed, was 13.5 m2 g-1 for both 1 and 24 h data, which is very close to MACcor (13.9 and 14.0 m2 g-1 for the 1 and 24 h data, respectively) (Table 3). The difference between MACcor and MACmed was about 4 %, leading to the same difference between the estimated MBC values if these MAC values are used for conversion of babs (PSAP) to MBC. Based on the interquartile ranges of the babs (PSAP) / MBC (COSMOS) ratios (Fig. 4e and f), variations in the ratios (with an MBC threshold of 2 ng m-3), denoted as VMAC, were within 19 % and 18 % of the MACmed values for the 1 and 24 h data, respectively (Table 3). Therefore, conversion of 1 and 24 h averaged babs (PSAP; λ = 550 nm) data to MBC by assuming a constant MACmed leads to uncertainty of about 19 % at Alert. We used the same method in estimating MACcor, MACmed, and VMAC for other instruments and other locations, as summarized in Table 3. Note that this estimated uncertainty can depend on the threshold value of MBC (COSMOS) assumed in the analysis. Figure S2 in the Supplement shows histograms of the babs (PSAP) / MBC (COSMOS) ratios for MBC (COSMOS) <10 ng m-3. While similar MACmed values were obtained for data with MBC (COSMOS) <10 ng m-3 and for all datasets, the interquartile ranges of the babs (PSAP) / MBC (COSMOS) ratios are larger for MBC (COSMOS) <10 ng m-3. The relative uncertainty becomes higher (lower) in summer (winter–spring) when the MBC values tend to be low (high) (Fig. 4a and b).

Measurements of babs at Alert were made by an Aethalometer at wavelengths of 370, 470, 520, 590, 660, 880, and 950 nm without any particle size cut. Time series of babs (Aethalometer; λ= 590 nm) and MBC (COSMOS) in 2018–2019 are shown in Fig. S3a and b in the Supplement. babs (Aethalometer; λ= 590 nm) was highly correlated (r2>0.90) with MBC (COSMOS) (Fig. 5a and b). The MACcor (Aethalometer; λ= 590 nm) values were 12.5 and 12.7 m2 g-1 for the 1 and 24 h data, respectively. The MACmed values of the babs (Aethalometer) / MBC (COSMOS) ratios were 13.5 and 13.8 m2 g-1 for the 1 and 24 h data, respectively (Fig. 5c and d), which agree with the MACcor values to within 8 %. Therefore, depending on the MAC values used, the estimated MBC values can differ by about 8 %. Because the interquartile ranges of the babs (Aethalometer) /MBC (COSMOS) ratios were 11.4–16.5 m2 g-1 (1 h data) and 12.1–15.7 m2 g-1 (24 h data), the VMAC was about 22 % (with an MBC threshold of 2 ng m-3) for babs (Aethalometer; λ= 590 nm) at Alert (Table 3). The MACmed values for low MBC data (MBC (COSMOS) <10 ng m-3) agree with those for all datasets to within 10 % (Fig. S3c and d in the Supplement).

The MACcor (Aethalometer) values for each wavelength are summarized in Table 4. Note that these wavelength-dependent MACcor values should be interpreted as the simple conversion factors to obtain average MBC from babs (Aethalometer), which might have been contributed to by BC and also other light-absorbing aerosols. In other words, these MACcor values differ from MACBC, as discussed in Sect. 1. The r2 values were generally high for all wavelengths examined. This weak dependence on wavelength indicates that the contribution of other light-absorbing aerosols such as brown carbon (BrC) to babs (Aethalometer) is small or the BrC / BC concentration ratio was rather stable at Alert during 2018–2019, because BrC should enhance light absorption in near-ultraviolet wavelengths.

The MACcor (Aethalometer) and MACcor (PSAP) are compared in Table 5. They agree within 10 % at three wavelengths, despite the different particle size cuts of the inlets for Aethalometer (total suspended particle) and PSAP (PM1). This agreement is consistent with the results by Backman et al. (2017), who showed that the correction factor Cf of 3.45 for Aethalometer harmonizes babs (Aethalometer) with babs (PSAP), babs (CLAP), and babs (MAAP) at Arctic sites.

Simultaneous measurements of MBC (COSMOS) for PM1 and babs (PSAP) for PM10 began at Ny-Ålesund in 2012 (Sinha et al., 2017; Fig. S4a and b in the Supplement). The 1 h and 24 h averaged babs values (PSAP; λ= 550 nm) were well correlated (r2= 0.76–0.82) with MBC (COSMOS), and the MACcor (PSAP) value for the whole period was 14.4–15.2 m2 g-1 (Fig. 6a and b). Year-to-year variations in MACcor (PSAP) are also shown in Fig. 7a and Table 6. The correlation between babs (PSAP) and MBC (COSMOS) during April–December 2012 was weak for unknown reasons. Excluding this period, average MACcor (PSAP) during 2013–2016 was 15.2 ± 2.2 (1σ) and 16.6 ± 1.4 m2 g-1 for the 1 and 24 h data, respectively. Although the reason for the relatively large change in MACcor (PSAP) values during 2014–2015 (Fig. 7a and Table 6) is not clear, this may be partly because babs (PSAP) data from December 2014 to April 2015 (during an “Arctic haze” period) were not available (Fig. S4a and b in the Supplement).

The MACmed values of the babs (PSAP) /MBC (COSMOS) ratios were 16.7 and 17.2 m2 g-1 for the 1 and 24 h data, respectively, when the MBC threshold of 2 ng m-3 was applied in the analysis (Fig. 6c and d). The MACmed values were higher by 16 % and 13 % than MACcor for 1 and 24 h data, respectively (Table 3). Therefore, conversion of babs (PSAP; λ= 550 nm) to MBC using a constant MACcor may result in a slightly biased MBC, especially for lower babs data. This is partly because the correlation of babs (PSAP) with MBC (COSMOS) is not very high, and scatter of the data, especially those with lower MBC values, contributes to large variations in the babs (PSAP) /MBC (COSMOS) ratios (Figs. 6 and S4c and d in the Supplement). The interquartile ranges of the ratios were 10.6–21.7 and 11.9–21.4 m2 g-1 for the 1 and 24 h data, respectively. Although these large variations might be partly attributed to actual variations in mixing states of BC, artifacts of babs measurements by PSAP at Ny-Ålesund may be a contributing factor, considering the higher correlations of babs (Aethalometer) and babs (MAAP) at Ny-Ålesund with MBC (COSMOS) (Sect. 3.2.2 and 3.2.3). Based on the interquartile ranges of the babs (PSAP) /MBC (COSMOS) ratios, VMAC was 37 % and 31 % for 1 and 24 h data, respectively (Table 3). The abovementioned bias leads to an additional uncertainty of about 15 % for the estimates of MBC, if the constant MACcor value is used.

Measurements of babs (Aethalometer; λ= 590 nm) for PM10 were compared with measurements of MBC (COSMOS) for PM1 during 2012–2019. The time series data of babs (Aethalometer) were highly correlated with those for MBC (COSMOS) (Fig. S5a and b in the Supplement) (r2= 0.90 for both the 1 and 24 h data; Fig. 8a and b). The MACcor (Aethalometer) values were 10.2 and 10.1 m2 g-1 for the 1 and 24 h data, respectively. Year-to-year variations in MACcor (Aethalometer) are also shown in Fig. 7a and Table 7. The r2 values were generally high for each year, and the average MACcor (Aethalometer) during 2012–2019 was 10.2 ± 1.6 (1σ) and 10.0 ± 1.3 m2 g-1 for the 1 and 24 h data, respectively. The MACcor (Aethalometer) value for 2012 was 8.7 m2 g-1 at 590 nm (i.e., 9.3 m2 g-1 at 550 nm assuming the λ-1 relationship) for 24 h data, which is consistent with the MACcor of 9.8 m2 g-1 at 550 nm inferred from the SP2 and Aethalometer measurements in the spring of 2012 (Zanatta et al., 2018). At Ny-Ålesund, the MACcor (Aethalometer) values (10.2 and 10.1 m2 g-1 for the 1 and 24 h data, respectively) were systematically lower than the MACcor (PSAP) values (14.4 and 15.2 m2 g-1). This discrepancy is different than at Alert (Sect. 3.1.3), and the reason is unclear, but could be partly due to uncertainty in the absolute values of babs, as discussed in Sects. 1 and 2.2.3.

The MACmed values of the babs (Aethalometer) /MBC (COSMOS) ratios were 11.2 and 12.3 m2 g-1 for the 1 and 24 h data, respectively (Fig. 8c and d). While the MACmed values for the 1 h data agree with MACcor to within 10 %, there is a 22 % discrepancy for the 24 h data under the assumed threshold setting (2 ng m-3) of MBC (COSMOS) (Table 3). Therefore, conversion of 24 h averaged babs (Aethalometer; λ= 590 nm) to MBC using a constant MACcor may be somewhat biased, especially for lower babs values (Fig. S5c and d in the Supplement). At Ny-Ålesund, the VMAC was about 25 % for babs (Aethalometer; λ= 590 nm). The abovementioned bias leads to an additional uncertainty of about 20 % for conversion of 24 h averaged low babs data to MBC, if the constant MACcor value is assumed.

Measurements of babs (MAAP; λ= 637 nm) without any particle size cut were compared with measurements of MBC (COSMOS) for PM1 during 2017–2020. The time series of babs (MAAP) and MBC (COSMOS) tracked each other (Fig. S6a and b in the Supplement) and were highly correlated (r2= 0.90 for the 1 h data and r2= 0.83 for the 24 h data; Fig. 9a and b). The MACcor (MAAP) values were 10.6 and 10.9 m2 g-1 for the 1 and 24 h data, respectively. These MACcor values are about 60 % higher than the manufacturer's default setting (= 6.6 m2 g-1) of MAC (MAAP). One possible reason is the difference of the methods of MBC measurements to determine MACcor (MAAP) values, as mentioned in Sect. 2.2.3. Another reason could be that the difference in microphysical properties of BC (mixing states and size distribution) and properties of LSPs led to the difference in the MACcor (MAAP) values.

Year-to-year variations in MACcor (MAAP) are also shown in Fig. 7a and Table 8. The r2 values were generally high for each year, and the average MACcor (MAAP) during 2017–2020 was 11.1 ± 0.7 (1σ) and 11.7 ± 1.1 m2 g-1 for the 1 and 24 h data, respectively. The MACmed values of the babs (MAAP) /MBC (COSMOS) ratios were 10.8 and 11.2 m2 g-1 for the 1 and 24 h data, respectively (Fig. 9c and d). The difference between MACcor and MACmed was limited to 3 % (Table 3). As discussed for the PSAP and Aethalometer in the previous sections, the relative uncertainty becomes higher when the MBC values tend to be low (Fig. S6c and d in the Supplement).

The MACcor (MAAP) and MACcor (PSAP) at Ny-Ålesund are compared in Table 11 in Sect. 3.6 after adjusting measurement wavelengths. MACcor (PSAP) values are 17 % and 20 % larger than MACcor (MAAP) values for 1 and 24 h data, respectively. A custom-built PSAP was used at Ny-Ålesund. The systematic difference of babs measured by the custom-built PSAP and MAAP was also observed at three European background sites (Zanatta et al., 2016), although the previously reported difference was much larger (more than 59 %) than that of our measurements at Ny-Ålesund.

Simultaneous measurements of PM1 for MBC (COSMOS) and babs (PSAP–CLAP) began at Barrow in 2012 (Sinha et al., 2017). At Barrow, both PSAP and CLAP aspired ambient air using PM1 and PM10 impactors alternately for 30 min of each hour. Here we used the data from PSAP–CLAP equipped with the PM1 impactor and data from PSAP in 2012–2015 and CLAP in 2016–2019 (Fig. S7 in the Supplement). Because the 24 h averaged babs (PSAP) and babs (CLAP) values agreed to within 2 % during 2012–2015 (Sinha et al., 2017) when the PSAP and CLAP overlapped, we consider the two instruments to be equivalent. The MBC (COSMOS) data from June 2018 to May 2019 were unavailable due to problems with the COSMOS instrument.

The babs (PSAP–CLAP; λ= 550 nm) data were strongly correlated with those for MBC (COSMOS) (r2= 0.88 and r2= 0.86; Fig. 10a and b), and the MACcor values (PSAP–CLAP) derived from 1 and 24 h averaged data for the whole period were 10.8 and 10.6 m2 g-1, respectively. Average MACcor (PSAP–CLAP) during 2012–2018 was stable at 11.0 ± 0.9 (1σ) m2 g-1 (Fig. 7b and Table 9). Yearly MBC (COSMOS) values did not exhibit large changes during this period (Fig. 7b). The babs (CLAP) data were weakly correlated with MBC (COSMOS) data during June–December 2019 (Table 9), indicating that either the CLAP or COSMOS results might not have been accurate during this period. Therefore, in Table 9 we calculated the average MACcor (PSAP–CLAP) by excluding the MAC value for 2019.

The MACmed values of the babs (PSAP–CLAP) /MBC (COSMOS) ratios were 11.2 and 11.0 m2 g-1 for 1 and 24 h data (Fig. 10c and d), which are very close to the MACcor values of 10.8 and 10.6 m2 g-1, respectively (Table 3). Therefore, when either MACcor or MACmed is used for conversion of babs (PSAP–CLAP; λ= 550 nm) to MBC, the resulting MBC values differ by only about 4 %. The VMAC was about 25 % for babs (PSAP–CLAP; λ = 550 nm) at Barrow (Table 3). Because of scatter in the data, especially at lower MBC values (Fig. 10a and b), the interquartile ranges of the babs (PSAP) /MBC (COSMOS) ratios are much larger when MBC (COSMOS) is less than 10 ng m-3 (Fig. S7c and d).

Measurements of babs (MAAP; λ= 637 nm) have been made since 2007 at the Global Atmospheric Watch (GAW) station at Pallas (Hyvärinen et al., 2011). PM10 and PM1 inlets were used for MAAP and COSMOS, respectively. MBC (COSMOS) measurements began in July 2019; we used the data collected up to July 2020 in this study. The MBC (COSMOS) data for about 3 months (February to April 2020) were unavailable due to an air sampling problem.

The babs (MAAP) 1 and 24 h values (Fig. S8 in the Supplement) were strongly correlated with those for MBC (COSMOS) with r2= 0.93 and r2= 0.95, respectively (Fig. 11a and b). MACcor (MAAP) was 13.0 m2 g-1 for both the 1 and 24 h data. This MACcor value is about twice the manufacturer's default setting (= 6.6 m2 g-1) of MAC (MAAP), possibly for the same reasons discussed in Sect. 3.2.3.

The MACmed values of the babs (MAAP) /MBC (COSMOS) ratios for the 1 and 24 h data were 12.4 and 13.1 m2 g-1, respectively (Fig. 11c and d), which are very close to that for MACcor (13.0 m2 g-1 for both 1 and 24 h data, Table 3). Therefore, the difference between the estimated MBC values is less than 5 % when these MACcor or MACmed values are used for conversion of babs (MAAP) to MBC. The VMAC was about 25 % for babs (MAAP) at Pallas (Table 3). The MACmed values for low MBC data (MBC (COSMOS) <10 ng m-3) are very close to those for all datasets (Fig. S8c and d in the Supplement).

The UT-SP2 was operated at Fukue for 3 weeks in April 2019 (Yoshida et al., 2020), as mentioned in Sect. 2.2.1. Figure 12a shows the number and mass size distributions of BC measured by the UT-SP2 averaged over the observation period. In addition to the MBC (SP2) derived by integrating the mass size distributions over the detectable diameter range (Dm= 70–850 nm), we also estimated MBC (SP2) in the Dm= 30–1000 nm range by fitting a lognormal function to the data. As the two sets of MBC (SP2) values deviated by less than 2 %, we used the former MBC (SP2) for comparison with MBC (COSMOS). The time series of hourly values of MBC (COSMOS) were strongly correlated (r2= 0.97) with MBC (SP2) (Fig. 12b), and the slope of the regression was 0.92 (Fig. 12c). This relationship agrees with those observed by Ohata et al. (2019) at Tokyo, Cape Hedo, and Ny-Ålesund and those observed at Alert (Sect. 3.1.1), thus confirming the clear and consistent relationship between MBC (COSMOS) and MBC (SP2). Miyakawa et al. (2017) also reported a strong correlation (r2= 0.92; regression slope 1.14) between MBC (COSMOS) and MBC (SP2) at Fukue in spring 2015 by using an SP2 maintained and calibrated by the Japan Agency for Marine-Earth Science and Technology.

The degree of agreement between MBC (COSMOS) and MBC (SP2) at Fukue was also examined on a logarithmic scale in Fig. S1b in the Supplement. When MBC (SP2) is lower than ∼ 70 ng m-3, MBC (COSMOS) tended to be slightly higher than MBC (SP2). A similar feature was previously reported at Cape Hedo in Japan (Ohata et al., 2019). The Cape Hedo site is located near the coast (i.e., the distance from this site to the coast is ∼ 0.2 km), and the interference of submicron sea salt particles might contribute to this feature (Ohata et al., 2019). At Fukue, when maritime air mass is transported to the site, the relative abundance of sea salt particles to BC might also be enhanced, possibly affecting the COSMOS measurements, although the distance from the site to the coast (∼ 1.5 km) is slightly farther than for Cape Hedo. This feature was not clearly observed by a previous study at Fukue (Miyakawa et al., 2017).

Kanaya et al. (2013, 2016, 2020) made simultaneous measurements of MBC (COSMOS) and babs (MAAP; λ= 639 nm) at Fukue for about 10 years (April 2009–May 2019; Fig. S9 in the Supplement). The air inlet for MAAP and COSMOS was equipped with a PM1 cyclone after November 2011. Before that a PM2.5 cyclone was used instead. babs (MAAP) was highly correlated (r2= 0.94) with MBC (COSMOS), and the MACcor (MAAP) for the entire period was found to be 10.8 and 10.9 m2 g-1 for the 1 and 24 h data (Fig. 13a and b), respectively. Because the correlation of babs (MAAP) with MBC (COSMOS) was also strong for individual years, MACcor (MAAP) for each year was also derived (Fig. 7c and Table 10). MBC (COSMOS) decreased by about 50 % during this period, owing to a large decrease in BC emissions in China (Kanaya et al., 2020). However, the yearly average MACcor (MAAP) values were stable at 11.1 ± 1.0 (1σ) m2 g-1 for both the 1 and 24 h data, despite the large change in MBC (COSMOS). This MACcor value is about 70 % higher than the manufacturer's default setting (= 6.6 m2 g-1), possibly for the same reasons discussed in Sect. 3.2.3.

Because the amount of data with MBC less than 2 ng m-3 was very small at Fukue, the MACmed values and the interquartile ranges of the babs (MAAP) /MBC (COSMOS) ratios were obtained for all data without applying any MBC threshold. The MACmed was 11.4 m2 g-1 for both 1 and 24 h data (Fig. 13c and d), which agrees well (within 6 %) with the MACcor values derived from correlation plots (10.8 and 10.9 m2 g-1 for 1 and 24 h data, respectively) (Table 3). Therefore, using either MACcor or MACmed for conversion of babs (MAAP) to MBC affects the resulting MBC values by less than 6 %. The VMAC was about 15 %, which is lower than those at Arctic sites (Table 3) partly because the higher MBC (COSMOS) values at Fukue make the calculated ratios more stable. Also, aerosol properties including mixing states of BC might be more stable at Fukue than those at the Arctic sites examined in this study.